| Method | Data Type | Classification | Accuracy |
| OBJ_BG | OBJ_ONLY | Hardest |
| PointNet (Qi et al., 2017a) | Points | 73.3 | 79.2 | 68.0 |
| SpiderCNN (Xu et al., 2018) | Points | 77.1 | 79.5 | 73.7 |
| PointNet ++ (Qi et al., 2017b) | Points | 82.3 | 84.3 | 77.9 |
| PointCNN (Li et al., 2018) | Points | 86.1 | 85.5 | 78.5 |
| DGCNN (Wang et al., 2019c) | Points | 82.8 | 86.2 | 78.1 |
| SimpleView (Goyal et al., 2021) | M-View | - | - | 79.5 |
| BGA-DGCNN (Uy et al., 2019) | Points | - | - | 79.7 |
| BGA-PN++ (Uy et al., 2019) | Points | - | - | 80.2 |
| MVTN (Hamdi et al., 2021) | M-View | 92.6 | 92.3 | 82.8 |
| VointNet (ours) | Voints | 93.7 | 94.0 | 85.4 |
",
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+ {
+ "type": "text",
+ "text": "Table 2: 3D Point Cloud Classification on ScanObjectNN. We report the accuracy of VointNet in 3D point cloud classification on three different variants of ScanObjectNN (Uy et al., 2019). Bold denotes the best result in its setup. Note that the Hardest variant includes rotated and translated objects, which highlights the benefits of Voints on challenging scenarios.",
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+ "text": "we test on ShapeNet Parts (Yi et al., 2016), a subset of ShapeNet (Chang et al., 2015) that consists of 16,872 point cloud objects from 16 categories and 50 parts. For occlusion robustness, we follow MVTN (Hamdi et al., 2021) and test on ModelNet40 (Wu et al., 2015), which is composed of 40 classes and 12,311 3D objects.",
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+ {
+ "type": "text",
+ "text": "Metrics. For 3D point cloud classification, we report the overall accuracy, while shape retrieval is evaluated using mean Average Precision (mAP) over test queries (Hamdi et al., 2021). 3D semantic segmentation is evaluated using mean Intersection over Union (mIoU) on points. For part segmentation, we report Instance-averaged mIoU (Ins. mIoU).",
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+ {
+ "type": "text",
+ "text": "Baselines. We include PointNet (Qi et al., 2017a), PointNet++ (Qi et al., 2017b), DGCNN (Wang et al., 2019c), as baselines that use point clouds. We also compare against multi-view classification approaches like MVCNN (Su et al., 2015), SimpleView (Goyal et al., 2021), and MVTN (Hamdi et al., 2021) as baselines for classification and retrieval and adopt some of the multi-view segmentation baselines (e.g. Label Fusion (Wang et al., 2019a) and Mean Fusion (Kundu et al., 2020)) for part segmentation.",
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+ "text": "4.2 VOINTNET VARIANTS",
+ "text_level": 1,
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+ "text": "VointNet in Eq (3) relies on the VointConv operation $h_{\\mathrm{V}}$ as the basic building block. Here, we briefly describe three examples of $h_{\\mathrm{V}}$ operations VointNet uses.",
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+ "text": "Shared Multi-Layer Perceptron (MLP). It is the most basic VointConv formulation. For a layer $l$ , the features of Voint $i$ at view $j$ are updated to layer $l + 1$ as: $\\mathbf{h}_{i,j}^{l + 1} = \\rho (\\mathbf{h}_{i,j}^{l}\\mathcal{W}_{\\rho})$ , where $\\rho$ is the shared MLP with weights $\\mathcal{W}_{\\rho}$ followed by normalization and a nonlinear function (e.g. ReLU). This operation is applied on all Voints independently and only involves the visible views-features for each Voint. This formulation extends the shared MLP formulation for PointNet (Qi et al., 2017a) to work on Voints' view-features.",
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+ "text": "Graph Convolution (GCN). We define a fully connected graph for each Voint by creating a virtual center node connected to all the view-features to aggregate their information (similar to \"cls\" token in ViT (Dosovitskiy et al., 2021)). Then, the graph convolution can be defined as the shared MLP (as described above) but on the edge features between all view features, followed by a max pool on the graph neighbors. An additional shared MLP is used before the final output.",
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+ {
+ "type": "text",
+ "text": "Graph Attention (GAT). A graph attention operation can be defined just like the GCN operation above but with learned attention weights on the graph neighbor's features before averaging them. A shared MLP computes these weights.",
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+ {
+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
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+ "type": "page_number",
+ "text": "6",
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+ "type": "table",
+ "img_path": "images/43cae6bd71c73b896b64451d5fa0cf6f9e718ca55b6a5a098f3c506b4d7bab28.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Method | Data Type | Classification \nModelNet40 | Shape Retrieval \nShapeNet | Core |
| PointNet (Qi et al., 2017a) | Points | 89.2 | - | |
| PointNet++ (Qi et al., 2017b) | Points | 91.9 | - | |
| DGCNN (Wang et al., 2019c) | Points | 92.2 | - | |
| KPConv(Thomas et al., 2019) | Points | 92.9 | - | |
| PCT(Guo et al., 2021) | Points | 93.3 | - | |
| CurveNet(Xiang et al., 2021) | Points | 93.8 | - | |
| ReVGG (Sfikas et al., 2017) | M-View | - | 74.9 | |
| MVCNN (Su et al., 2015) | M-View | 90.1 | 73.5 | |
| ViewGCN (Wei et al., 2020) | M-View | 93.3 | 78.4 | |
| MVTN (Hamdi et al., 2021) | M-View | 93.8 | 82.9 | |
| VointNet (ours) | Voints | 92.8 | 83.3 | |
",
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+ "img_path": "images/41246f32cbd2857f30db87a511231e2d1edb924ba5054097da9bb72efc2a5bd0.jpg",
+ "table_caption": [
+ "Table 7: 3D Shape Classification and Retrieval. We report VointNet's classification accuracy on ModelNet40 (Wu et al., 2015) and its 3D shape retrieval mAP on ShapeNet Core55 (Chang et al., 2015; Sfikas et al., 2017). Baseline results are reported from (Hamdi et al., 2021; Zhao et al., 2020; Xiang et al., 2021)."
+ ],
+ "table_footnote": [],
+ "table_body": "| Network | GFLOPs | Time (ms) | Parameters # (M) |
| MVCNN (Su et al., 2015) | 43.72 | 39.89 | 11.20 |
| ViewGCN (Wei et al., 2020) | 44.19 | 26.06 | 23.56 |
| ResNet 18 (He et al., 2015) | 3.64 | 3.70 | 11.20 |
| ResNet 50 (He et al., 2015) | 8.24 | 9.42 | 23.59 |
| ViT-B (Dosovitskiy et al., 2021) | 33.70 | 12.46 | 86.57 |
| ViT-L (Dosovitskiy et al., 2021) | 119.30 | 29.28 | 304.33 |
| FCN (Long et al., 2015) | 53.13 | 10.34 | 32.97 |
| DeeplabV3 (Chen et al., 2018) | 92.61 | 20.62 | 58.64 |
| PointNet (Qi et al., 2017a) | 1.78 | 4.24 | 3.50 |
| DGCNN (Wang et al., 2019c) | 10.42 | 0.95 | 16.350 |
| MVTN (Hamdi et al., 2021) | 1.78 | 4.24 | 3.5 |
| VointNet (MLP) | 1.90 | 2.90 | 0.04 |
| VointNet (GCN) | 16.18 | 32.10 | 0.05 |
| VointNet (GAT) | 32.05 | 68.71 | 0.07 |
| Full Voint pipeline | 94.51 | 23.50 | 58.68 |
",
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+ },
+ {
+ "type": "text",
+ "text": "Table 12: Time and Memory Requirements. We assess the contribution of the Voint module to the time and memory requirements in the multi-view and point cloud pipeline. Note that VointNet (shared MLP) is almost 100 times smaller than PointNet (Qi et al., 2017a).",
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+ "img_path": "images/3413317cf245b6b22fd5a908edc91f26e73ed14cffeb764360672238e7bce506.jpg",
+ "image_caption": [
+ "Figure 12: The Effect of Feature Size $d$ . We plot Ins. mIoU of 3D segmentation vs. the feature size $d$ used in training on ShapeNet Parts (Yi et al., 2016). We note that the performance peaks at $d = 128$ , but it is close to what we use in the main results ( $d = 64$ )."
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+ {
+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
+ "bbox": [
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+ "type": "page_number",
+ "text": "27",
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+ "img_path": "images/01e61314143ad25c176cabb5dc11f6aaf12fcedd834931452f72552917cdb345.jpg",
+ "image_caption": [
+ "Figure 13: The Effect of Model Depth $l_{v}$ . We plot Ins. mIoU of 3D segmentation vs. the model depth $l_{v}$ used in training on ShapeNet Parts (Yi et al., 2016). We note that model depth of VointNet does not enhance the performance significantly. Our choice of $l_{v} = 4$ balances the performance and the memory/computations requirements of VointNet (MLP)."
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+ "img_path": "images/1b0ad412327d57e53c249108a0b45a1fb42553e42323dd97babc2396302b514e.jpg",
+ "image_caption": [
+ "Figure 14: The Effect of Distance to the Object. We plot Ins. mIoU of 3D segmentation vs. the distance to the object used in inference on ShapeNet Parts (Yi et al., 2016). We note that our default choice of 1.0 is actually reasonable. This choice of distance shows the object entirely (as illustrated in Figure 17), but also cover the details needed for small parts segmentation (see Figure 11)."
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+ "img_path": "images/e3aa40f0be56a237c5c00ea85726607b465624d13e968d151ab38d5a45b193ed.jpg",
+ "image_caption": [
+ "Figure 15: The Effect of Image Size $H, W$ . We plot Ins. mIoU of 3D segmentation vs. the image size used in inference on ShapeNet Parts (Yi et al., 2016)."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ {
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+ "text": "Published as a conference paper at ICLR 2023",
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+ "img_path": "images/177dcc285a4a120e89a761450d372408dc02ebe73f3aab8f9b2f0e8c97be5aba.jpg",
+ "image_caption": [
+ "Figure 16: Multi-view Projected Segmentation 1. We show how, after rendering points, we can segment in the image space. For each example, we show (INPUT): the projections of the points (colored with normals) used in training with random view-points. (PRED 2D): the segmentation prediction of the 2D backbone (DeepLabV3) (Chen et al., 2018). (PRED 3D): the unprojected 3D segmentation prediction. $(GT)$ : the 3D segmentation ground truth."
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+ {
+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
+ "bbox": [
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+ "page_idx": 28
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+ "img_path": "images/5399f426231ab43347b5b869edd7def9af0be33cbd699d4076f8bc3b337f0b29.jpg",
+ "image_caption": [
+ "Figure 17: Multi-view Projected Segmentation 2. We show how, after rendering points, we can segment in the image space. For each example, we show (INPUT): the projections of the points (colored with normals) used in training with random view-points. (PRED 2D): the segmentation prediction of the 2D backbone (DeepLabV3) (Chen et al., 2018). (PRED 3D): the unprojected 3D segmentation prediction. $(GT)$ : the 3D segmentation ground truth."
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+ "page_idx": 29
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+ {
+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
+ "bbox": [
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+ "page_idx": 29
+ },
+ {
+ "type": "page_number",
+ "text": "30",
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+ {
+ "type": "table",
+ "img_path": "images/7fe5f73dd0d8516e3571c811e3776eddb0ec78c3b93a42b81b5126691366d2e7.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Method | Data Type | Classification | Accuracy |
| OBJ_BG | OBJ_ONLY | Hardest |
| PointNet (Qi et al., 2017a) | Points | 73.3 | 79.2 | 68.0 |
| SpiderCNN (Xu et al., 2018) | Points | 77.1 | 79.5 | 73.7 |
| PointNet ++ (Qi et al., 2017b) | Points | 82.3 | 84.3 | 77.9 |
| PointCNN (Li et al., 2018) | Points | 86.1 | 85.5 | 78.5 |
| DGCNN (Wang et al., 2019c) | Points | 82.8 | 86.2 | 78.1 |
| SimpleView (Goyal et al., 2021) | M-View | - | - | 79.5 |
| BGA-DGCNN (Uy et al., 2019) | Points | - | - | 79.7 |
| BGA-PN++ (Uy et al., 2019) | Points | - | - | 80.2 |
| MVTN (Hamdi et al., 2021) | M-View | 92.6 | 92.3 | 82.8 |
| VointNet (ours) | Voints | 93.7 | 94.0 | 85.4 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2: 3D Point Cloud Classification on ScanObjectNN. We report the accuracy of VointNet in 3D point cloud classification on three different variants of ScanObjectNN (Uy et al., 2019). Bold denotes the best result in its setup. Note that the Hardest variant includes rotated and translated objects, which highlights the benefits of Voints on challenging scenarios."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "we test on ShapeNet Parts (Yi et al., 2016), a subset of ShapeNet (Chang et al., 2015) that consists of 16,872 point cloud objects from 16 categories and 50 parts. For occlusion robustness, we follow MVTN (Hamdi et al., 2021) and test on ModelNet40 (Wu et al., 2015), which is composed of 40 classes and 12,311 3D objects."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Metrics. For 3D point cloud classification, we report the overall accuracy, while shape retrieval is evaluated using mean Average Precision (mAP) over test queries (Hamdi et al., 2021). 3D semantic segmentation is evaluated using mean Intersection over Union (mIoU) on points. For part segmentation, we report Instance-averaged mIoU (Ins. mIoU)."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Baselines. We include PointNet (Qi et al., 2017a), PointNet++ (Qi et al., 2017b), DGCNN (Wang et al., 2019c), as baselines that use point clouds. We also compare against multi-view classification approaches like MVCNN (Su et al., 2015), SimpleView (Goyal et al., 2021), and MVTN (Hamdi et al., 2021) as baselines for classification and retrieval and adopt some of the multi-view segmentation baselines (e.g. Label Fusion (Wang et al., 2019a) and Mean Fusion (Kundu et al., 2020)) for part segmentation."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "4.2 VOINTNET VARIANTS"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "VointNet in Eq (3) relies on the VointConv operation \\( h_{\\mathrm{V}} \\) as the basic building block. Here, we briefly describe three examples of \\( h_{\\mathrm{V}} \\) operations VointNet uses."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Shared Multi-Layer Perceptron (MLP). It is the most basic VointConv formulation. For a layer \\(l\\), the features of Voint \\(i\\) at view \\(j\\) are updated to layer \\(l + 1\\) as: \\(\\mathbf{h}_{i,j}^{l + 1} = \\rho (\\mathbf{h}_{i,j}^{l}\\mathcal{W}_{\\rho})\\), where \\(\\rho\\) is the shared MLP with weights \\(\\mathcal{W}_{\\rho}\\) followed by normalization and a nonlinear function (e.g. ReLU). This operation is applied on all Voints independently and only involves the visible views-features for each Voint. This formulation extends the shared MLP formulation for PointNet (Qi et al., 2017a) to work on Voints' view-features."
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Graph Convolution (GCN). We define a fully connected graph for each Voint by creating a virtual center node connected to all the view-features to aggregate their information (similar to \"cls\" token in ViT (Dosovitskiy et al., 2021)). Then, the graph convolution can be defined as the shared MLP (as described above) but on the edge features between all view features, followed by a max pool on the graph neighbors. An additional shared MLP is used before the final output."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Graph Attention (GAT). A graph attention operation can be defined just like the GCN operation above but with learned attention weights on the graph neighbor's features before averaging them. A shared MLP computes these weights."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ [
+ {
+ "type": "header",
+ "bbox": [
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+ 0.509,
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+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "table",
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+ "angle": 0,
+ "content": "| Method | Data Type | Classification \nModelNet40 | Shape Retrieval \nShapeNet | Core |
| PointNet (Qi et al., 2017a) | Points | 89.2 | - | |
| PointNet++ (Qi et al., 2017b) | Points | 91.9 | - | |
| DGCNN (Wang et al., 2019c) | Points | 92.2 | - | |
| KPConv(Thomas et al., 2019) | Points | 92.9 | - | |
| PCT(Guo et al., 2021) | Points | 93.3 | - | |
| CurveNet(Xiang et al., 2021) | Points | 93.8 | - | |
| ReVGG (Sfikas et al., 2017) | M-View | - | 74.9 | |
| MVCNN (Su et al., 2015) | M-View | 90.1 | 73.5 | |
| ViewGCN (Wei et al., 2020) | M-View | 93.3 | 78.4 | |
| MVTN (Hamdi et al., 2021) | M-View | 93.8 | 82.9 | |
| VointNet (ours) | Voints | 92.8 | 83.3 | |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.17,
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+ "angle": 0,
+ "content": "Table 7: 3D Shape Classification and Retrieval. We report VointNet's classification accuracy on ModelNet40 (Wu et al., 2015) and its 3D shape retrieval mAP on ShapeNet Core55 (Chang et al., 2015; Sfikas et al., 2017). Baseline results are reported from (Hamdi et al., 2021; Zhao et al., 2020; Xiang et al., 2021)."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Network | GFLOPs | Time (ms) | Parameters # (M) |
| MVCNN (Su et al., 2015) | 43.72 | 39.89 | 11.20 |
| ViewGCN (Wei et al., 2020) | 44.19 | 26.06 | 23.56 |
| ResNet 18 (He et al., 2015) | 3.64 | 3.70 | 11.20 |
| ResNet 50 (He et al., 2015) | 8.24 | 9.42 | 23.59 |
| ViT-B (Dosovitskiy et al., 2021) | 33.70 | 12.46 | 86.57 |
| ViT-L (Dosovitskiy et al., 2021) | 119.30 | 29.28 | 304.33 |
| FCN (Long et al., 2015) | 53.13 | 10.34 | 32.97 |
| DeeplabV3 (Chen et al., 2018) | 92.61 | 20.62 | 58.64 |
| PointNet (Qi et al., 2017a) | 1.78 | 4.24 | 3.50 |
| DGCNN (Wang et al., 2019c) | 10.42 | 0.95 | 16.350 |
| MVTN (Hamdi et al., 2021) | 1.78 | 4.24 | 3.5 |
| VointNet (MLP) | 1.90 | 2.90 | 0.04 |
| VointNet (GCN) | 16.18 | 32.10 | 0.05 |
| VointNet (GAT) | 32.05 | 68.71 | 0.07 |
| Full Voint pipeline | 94.51 | 23.50 | 58.68 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.17,
+ 0.415,
+ 0.825,
+ 0.456
+ ],
+ "angle": 0,
+ "content": "Table 12: Time and Memory Requirements. We assess the contribution of the Voint module to the time and memory requirements in the multi-view and point cloud pipeline. Note that VointNet (shared MLP) is almost 100 times smaller than PointNet (Qi et al., 2017a)."
+ },
+ {
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+ "content": "| Method | Data Type | Classification | Accuracy |
| OBJ_BG | OBJ_ONLY | Hardest |
| PointNet (Qi et al., 2017a) | Points | 73.3 | 79.2 | 68.0 |
| SpiderCNN (Xu et al., 2018) | Points | 77.1 | 79.5 | 73.7 |
| PointNet ++ (Qi et al., 2017b) | Points | 82.3 | 84.3 | 77.9 |
| PointCNN (Li et al., 2018) | Points | 86.1 | 85.5 | 78.5 |
| DGCNN (Wang et al., 2019c) | Points | 82.8 | 86.2 | 78.1 |
| SimpleView (Goyal et al., 2021) | M-View | - | - | 79.5 |
| BGA-DGCNN (Uy et al., 2019) | Points | - | - | 79.7 |
| BGA-PN++ (Uy et al., 2019) | Points | - | - | 80.2 |
| MVTN (Hamdi et al., 2021) | M-View | 92.6 | 92.3 | 82.8 |
| VointNet (ours) | Voints | 93.7 | 94.0 | 85.4 |
+
+Table 2: 3D Point Cloud Classification on ScanObjectNN. We report the accuracy of VointNet in 3D point cloud classification on three different variants of ScanObjectNN (Uy et al., 2019). Bold denotes the best result in its setup. Note that the Hardest variant includes rotated and translated objects, which highlights the benefits of Voints on challenging scenarios.
+
+we test on ShapeNet Parts (Yi et al., 2016), a subset of ShapeNet (Chang et al., 2015) that consists of 16,872 point cloud objects from 16 categories and 50 parts. For occlusion robustness, we follow MVTN (Hamdi et al., 2021) and test on ModelNet40 (Wu et al., 2015), which is composed of 40 classes and 12,311 3D objects.
+
+Metrics. For 3D point cloud classification, we report the overall accuracy, while shape retrieval is evaluated using mean Average Precision (mAP) over test queries (Hamdi et al., 2021). 3D semantic segmentation is evaluated using mean Intersection over Union (mIoU) on points. For part segmentation, we report Instance-averaged mIoU (Ins. mIoU).
+
+Baselines. We include PointNet (Qi et al., 2017a), PointNet++ (Qi et al., 2017b), DGCNN (Wang et al., 2019c), as baselines that use point clouds. We also compare against multi-view classification approaches like MVCNN (Su et al., 2015), SimpleView (Goyal et al., 2021), and MVTN (Hamdi et al., 2021) as baselines for classification and retrieval and adopt some of the multi-view segmentation baselines (e.g. Label Fusion (Wang et al., 2019a) and Mean Fusion (Kundu et al., 2020)) for part segmentation.
+
+# 4.2 VOINTNET VARIANTS
+
+VointNet in Eq (3) relies on the VointConv operation $h_{\mathrm{V}}$ as the basic building block. Here, we briefly describe three examples of $h_{\mathrm{V}}$ operations VointNet uses.
+
+Shared Multi-Layer Perceptron (MLP). It is the most basic VointConv formulation. For a layer $l$ , the features of Voint $i$ at view $j$ are updated to layer $l + 1$ as: $\mathbf{h}_{i,j}^{l + 1} = \rho (\mathbf{h}_{i,j}^{l}\mathcal{W}_{\rho})$ , where $\rho$ is the shared MLP with weights $\mathcal{W}_{\rho}$ followed by normalization and a nonlinear function (e.g. ReLU). This operation is applied on all Voints independently and only involves the visible views-features for each Voint. This formulation extends the shared MLP formulation for PointNet (Qi et al., 2017a) to work on Voints' view-features.
+
+Graph Convolution (GCN). We define a fully connected graph for each Voint by creating a virtual center node connected to all the view-features to aggregate their information (similar to "cls" token in ViT (Dosovitskiy et al., 2021)). Then, the graph convolution can be defined as the shared MLP (as described above) but on the edge features between all view features, followed by a max pool on the graph neighbors. An additional shared MLP is used before the final output.
+
+Graph Attention (GAT). A graph attention operation can be defined just like the GCN operation above but with learned attention weights on the graph neighbor's features before averaging them. A shared MLP computes these weights.
+
+| Method | Data Type | Classification
+ModelNet40 | Shape Retrieval
+ShapeNet | Core |
| PointNet (Qi et al., 2017a) | Points | 89.2 | - | |
| PointNet++ (Qi et al., 2017b) | Points | 91.9 | - | |
| DGCNN (Wang et al., 2019c) | Points | 92.2 | - | |
| KPConv(Thomas et al., 2019) | Points | 92.9 | - | |
| PCT(Guo et al., 2021) | Points | 93.3 | - | |
| CurveNet(Xiang et al., 2021) | Points | 93.8 | - | |
| ReVGG (Sfikas et al., 2017) | M-View | - | 74.9 | |
| MVCNN (Su et al., 2015) | M-View | 90.1 | 73.5 | |
| ViewGCN (Wei et al., 2020) | M-View | 93.3 | 78.4 | |
| MVTN (Hamdi et al., 2021) | M-View | 93.8 | 82.9 | |
| VointNet (ours) | Voints | 92.8 | 83.3 | |
+
+Table 7: 3D Shape Classification and Retrieval. We report VointNet's classification accuracy on ModelNet40 (Wu et al., 2015) and its 3D shape retrieval mAP on ShapeNet Core55 (Chang et al., 2015; Sfikas et al., 2017). Baseline results are reported from (Hamdi et al., 2021; Zhao et al., 2020; Xiang et al., 2021).
+
+| Network | GFLOPs | Time (ms) | Parameters # (M) |
| MVCNN (Su et al., 2015) | 43.72 | 39.89 | 11.20 |
| ViewGCN (Wei et al., 2020) | 44.19 | 26.06 | 23.56 |
| ResNet 18 (He et al., 2015) | 3.64 | 3.70 | 11.20 |
| ResNet 50 (He et al., 2015) | 8.24 | 9.42 | 23.59 |
| ViT-B (Dosovitskiy et al., 2021) | 33.70 | 12.46 | 86.57 |
| ViT-L (Dosovitskiy et al., 2021) | 119.30 | 29.28 | 304.33 |
| FCN (Long et al., 2015) | 53.13 | 10.34 | 32.97 |
| DeeplabV3 (Chen et al., 2018) | 92.61 | 20.62 | 58.64 |
| PointNet (Qi et al., 2017a) | 1.78 | 4.24 | 3.50 |
| DGCNN (Wang et al., 2019c) | 10.42 | 0.95 | 16.350 |
| MVTN (Hamdi et al., 2021) | 1.78 | 4.24 | 3.5 |
| VointNet (MLP) | 1.90 | 2.90 | 0.04 |
| VointNet (GCN) | 16.18 | 32.10 | 0.05 |
| VointNet (GAT) | 32.05 | 68.71 | 0.07 |
| Full Voint pipeline | 94.51 | 23.50 | 58.68 |
+
+Table 12: Time and Memory Requirements. We assess the contribution of the Voint module to the time and memory requirements in the multi-view and point cloud pipeline. Note that VointNet (shared MLP) is almost 100 times smaller than PointNet (Qi et al., 2017a).
+
+
+Figure 12: The Effect of Feature Size $d$ . We plot Ins. mIoU of 3D segmentation vs. the feature size $d$ used in training on ShapeNet Parts (Yi et al., 2016). We note that the performance peaks at $d = 128$ , but it is close to what we use in the main results ( $d = 64$ ).
+
+
+Figure 13: The Effect of Model Depth $l_{v}$ . We plot Ins. mIoU of 3D segmentation vs. the model depth $l_{v}$ used in training on ShapeNet Parts (Yi et al., 2016). We note that model depth of VointNet does not enhance the performance significantly. Our choice of $l_{v} = 4$ balances the performance and the memory/computations requirements of VointNet (MLP).
+
+
+Figure 14: The Effect of Distance to the Object. We plot Ins. mIoU of 3D segmentation vs. the distance to the object used in inference on ShapeNet Parts (Yi et al., 2016). We note that our default choice of 1.0 is actually reasonable. This choice of distance shows the object entirely (as illustrated in Figure 17), but also cover the details needed for small parts segmentation (see Figure 11).
+
+
+Figure 15: The Effect of Image Size $H, W$ . We plot Ins. mIoU of 3D segmentation vs. the image size used in inference on ShapeNet Parts (Yi et al., 2016).
+
+
+Figure 16: Multi-view Projected Segmentation 1. We show how, after rendering points, we can segment in the image space. For each example, we show (INPUT): the projections of the points (colored with normals) used in training with random view-points. (PRED 2D): the segmentation prediction of the 2D backbone (DeepLabV3) (Chen et al., 2018). (PRED 3D): the unprojected 3D segmentation prediction. $(GT)$ : the 3D segmentation ground truth.
+
+
+Figure 17: Multi-view Projected Segmentation 2. We show how, after rendering points, we can segment in the image space. For each example, we show (INPUT): the projections of the points (colored with normals) used in training with random view-points. (PRED 2D): the segmentation prediction of the 2D backbone (DeepLabV3) (Chen et al., 2018). (PRED 3D): the unprojected 3D segmentation prediction. $(GT)$ : the 3D segmentation ground truth.
+
+| Method | Data Type | Classification | Accuracy |
| OBJ_BG | OBJ_ONLY | Hardest |
| PointNet (Qi et al., 2017a) | Points | 73.3 | 79.2 | 68.0 |
| SpiderCNN (Xu et al., 2018) | Points | 77.1 | 79.5 | 73.7 |
| PointNet ++ (Qi et al., 2017b) | Points | 82.3 | 84.3 | 77.9 |
| PointCNN (Li et al., 2018) | Points | 86.1 | 85.5 | 78.5 |
| DGCNN (Wang et al., 2019c) | Points | 82.8 | 86.2 | 78.1 |
| SimpleView (Goyal et al., 2021) | M-View | - | - | 79.5 |
| BGA-DGCNN (Uy et al., 2019) | Points | - | - | 79.7 |
| BGA-PN++ (Uy et al., 2019) | Points | - | - | 80.2 |
| MVTN (Hamdi et al., 2021) | M-View | 92.6 | 92.3 | 82.8 |
| VointNet (ours) | Voints | 93.7 | 94.0 | 85.4 |
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+ "html": "| Method | Data Type | Classification \nModelNet40 | Shape Retrieval \nShapeNet | Core |
| PointNet (Qi et al., 2017a) | Points | 89.2 | - | |
| PointNet++ (Qi et al., 2017b) | Points | 91.9 | - | |
| DGCNN (Wang et al., 2019c) | Points | 92.2 | - | |
| KPConv(Thomas et al., 2019) | Points | 92.9 | - | |
| PCT(Guo et al., 2021) | Points | 93.3 | - | |
| CurveNet(Xiang et al., 2021) | Points | 93.8 | - | |
| ReVGG (Sfikas et al., 2017) | M-View | - | 74.9 | |
| MVCNN (Su et al., 2015) | M-View | 90.1 | 73.5 | |
| ViewGCN (Wei et al., 2020) | M-View | 93.3 | 78.4 | |
| MVTN (Hamdi et al., 2021) | M-View | 93.8 | 82.9 | |
| VointNet (ours) | Voints | 92.8 | 83.3 | |
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+ "html": "| Network | GFLOPs | Time (ms) | Parameters # (M) |
| MVCNN (Su et al., 2015) | 43.72 | 39.89 | 11.20 |
| ViewGCN (Wei et al., 2020) | 44.19 | 26.06 | 23.56 |
| ResNet 18 (He et al., 2015) | 3.64 | 3.70 | 11.20 |
| ResNet 50 (He et al., 2015) | 8.24 | 9.42 | 23.59 |
| ViT-B (Dosovitskiy et al., 2021) | 33.70 | 12.46 | 86.57 |
| ViT-L (Dosovitskiy et al., 2021) | 119.30 | 29.28 | 304.33 |
| FCN (Long et al., 2015) | 53.13 | 10.34 | 32.97 |
| DeeplabV3 (Chen et al., 2018) | 92.61 | 20.62 | 58.64 |
| PointNet (Qi et al., 2017a) | 1.78 | 4.24 | 3.50 |
| DGCNN (Wang et al., 2019c) | 10.42 | 0.95 | 16.350 |
| MVTN (Hamdi et al., 2021) | 1.78 | 4.24 | 3.5 |
| VointNet (MLP) | 1.90 | 2.90 | 0.04 |
| VointNet (GCN) | 16.18 | 32.10 | 0.05 |
| VointNet (GAT) | 32.05 | 68.71 | 0.07 |
| Full Voint pipeline | 94.51 | 23.50 | 58.68 |
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+ "content": "Figure 17: Multi-view Projected Segmentation 2. We show how, after rendering points, we can segment in the image space. For each example, we show (INPUT): the projections of the points (colored with normals) used in training with random view-points. (PRED 2D): the segmentation prediction of the 2D backbone (DeepLabV3) (Chen et al., 2018). (PRED 3D): the unprojected 3D segmentation prediction. "
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+ "html": "| Parameter | Range |
| ADAMα (minimizer) | {0.0001,0.0002,0.0003,0.001} |
| ADAMα (maximizer) | {0.0001,0.0002,0.0003,0.001} |
| ADAMβ1 | {0,0.5,0.9} |
| ADAMβ2 | {0.9,0.999} |
| neurons per layer | {64,128,256,512} |
| number of hidden layers | {1,2,3} |
| activation | {ReLU,LeakyReLU,tanh,softplus(2x+2)/2-1(smooth ELU)} |
| βwξπ | {10,25,50,75,100} |
| βLξπ | {10,25,50,75,100} |
| m | {5,10,15,20} |
| δ | {10,20} |
| use ε-mimic (cf. Delgrange et al. 2022) | {True,False} (if True, a decay rate of 10-5is used) |
| λPθ | {0.1,1/3,1/2,2/3,3/5,0.99} |
| λφl | {0.1,1/3,1/2,2/3,3/5,0.99} |
| λπθ | {1/|A|-1,1/(|A|-1).15} |
| λφlA | {1/|A|-1,1/(|A|-1).15} |
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+ "Table 3: Final hyperparameters used to evaluate ${\\mathrm{W}}^{2}\\mathrm{{AE}}$ -MDPs in Sect. 4"
+ ],
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+ "table_body": "| Environment | S⊆ | Description, for s ∈ S | ℓ(s) = <p1, ..., pn, preset> |
| CartPole | R4 | • s1: cart position\n• s2: cart velocity\n• s3: pole angle (rad)\n• s4: pole velocity at tip | • p1 = 1s1≥1.5: unsafe cart position\n• p2 = 1s3≥0.15: unsafe pole angle |
| MountainCar | R2 | • s1: position\n• s2: velocity | • p1 = 1s1>1.5: target position\n• p2 = 1s1≥-1/2: right-hand side of the mountain\n• p3 = 1s2≥0: car going forward |
| Acrobot | R6 | Let θ1, θ2 ∈ [0, 2π] be the angles of the two rotational joints,\n• s1 = cos(θ1)\n• s2 = sin(θ1)\n• s3 = cos(θ2)\n• s4 = sin(θ2)\n• s5: angular velocity 1\n• s6: angular velocity 2 | • p1 = 1-s1-s3·s1+s4·s2>1: RL agent target\n• p2 = 1s1≥0: θ1 ∈ [0, π/2] ∪ [3π/2, 2π]\n• p3 = 1s2≥0: θ1 ∈ [0, π]\n• p4 = 1s3≥0: θ2 ∈ [0, π/2] ∪ [3π/2, 2π]\n• p5 = 1s4≥0: θ2 ∈ [0, π]\n• p6 = 1s5≥0: positive angular velocity (1)\n• p7 = 1s6≥0: positive angular velocity (2) |
| Pendulum | R3 | Let θ ∈ [0, 2π] be the joint angle\n• s1 = cos(θ)\n• s2 = sin(θ)\n• s3: angular velocity | • p1 = 1s1≥cos(π/3): safe joint angle\n• p2 = 1s1≥0: θ ∈ [0, π/2] ∪ [3π/2, 2π]\n• p3 = 1s2≥0: θ ∈ [0, π]\n• p4 = 1s3≥0: positive angular velocity |
| LunarLander | R8 | • s1: horizontal coordinates\n• s2: vertical coordinates\n• s3: horizontal speed\n• s4: vertical speed\n• s5: ship angle\n• s6: angular speed\n• s7: left leg contact\n• s8: right leg contact | • p1: unsafe angle\n• p2: leg ground contact\n• p3: lands rapidly\n• p4: left inclination\n• p5: right inclination\n• p6: motors shut down |
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+ "text": "Table 4: Labeling functions for the OpenAI environments considered in our experiments (Delgrange et al., 2022). We provide a short description of the state space and the meaning of each atomic proposition. Recall that labels are binary encoded, for $n = |\\mathbf{AP}| - 1$ (one bit is reserved for reset) and $p_{\\mathrm{reset}} = 1$ iff $s$ is a reset state (cf. Appendix B.2).",
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+ "text": "Time to failure properties. Based on the labeling described in Table 4, we formally detail the time to failure properties checked in Sect. 4 whose results are listed in Table 1 for each environment. Let $\\text{Reset} = \\{\\text{reset}\\} = \\langle 0, \\dots, 1 \\rangle$ (we assume here that the last bit indicates whether the current state is a reset state or not) and define $s \\models \\mathsf{L}_1 \\land \\mathsf{L}_2$ iff $s \\models \\mathsf{L}_1$ and $s \\models \\mathsf{L}_2$ for any $s \\in S$ , then",
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+ "- CartPole: $\\varphi = \\neg$ Reset $\\mathcal{U}$ Unsafe, where Unsafe $= \\langle 1,1,0\\rangle$",
+ "- MountainCar: $\\varphi = \\neg$ GoalU Reset, where Goal $= \\langle 1,0,0,0\\rangle$",
+ "- Acrobot: $\\varphi = \\neg$ GoalU Reset, where Goal $= \\langle 1,0,\\dots ,0\\rangle$",
+ "- LunarLander: $\\varphi = \\neg$ SafeLanding $\\mathcal{U}$ Reset, where SafeLanding $=$ GroundContact $\\land$ MotorsOff, GroundContact $=\\langle 0,1,0,0,0,0,0\\rangle$ , and MotorsOff $=\\langle 0,0,0,0,0,1,0\\rangle$",
+ "- Pendulum: $\\varphi = \\diamondsuit (\\neg \\text{Safe} \\land \\bigcirc \\text{Reset})$ , where Safe = $\\langle 1,0,0,0,0\\rangle$ , $\\diamondsuit \\mathsf{T} = \\neg \\emptyset \\mathcal{U} \\mathsf{T}$ , and $s_i \\models \\bigcirc \\mathsf{T}$ iff $s_{i+1} \\models \\mathsf{T}$ , for any $\\mathsf{T} \\subseteq \\mathbf{AP}$ , $s_{i:\\infty}, a_{i:\\infty} \\in \\text{Traj}$ . Intuitively, $\\varphi$ denotes the event of ending an episode in an unsafe state, just before resetting the environment, which means that either the agent never reached the safe region or it reached and left it at some point. Formally, $\\varphi = \\{s_{0:\\infty}, a_{0:\\infty} \\mid \\exists i \\in \\mathbb{N}, s_i \\models \\text{Safe} \\land s_{i+1} \\models \\text{Reset}\\} \\subseteq \\text{Traj}$ ."
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+ "text": "C ON THE CURSE OF VARIATIONAL MODELING",
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+ "text": "Posterior collapse is a well known issue occurring in variational models (see, e.g., Alemi et al. 2018; Tolstikhin et al. 2018; He et al. 2019; Dong et al. 2020) which intuitively results in a degenerate local optimum where the model learns to ignore the latent space and use only the reconstruction functions (i.e., the decoding distribution) to optimize the objective. VAE-MDPs are no exception, as pointed out in the original paper (Delgrange et al., 2022, Section 4.3 and Appendix C.2).",
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+ "(a) Latent space distribution along training steps. The intensity of the blue hue corresponds to the frequency of latent states produced from $\\phi_{\\iota}$ during training. The vanilla model collapses to a single state."
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+ "(b) Rate of the variational model."
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+ "(c) Distortion of the variational model."
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+ "(d) Average point-wise entropy of $\\phi_{\\iota}(\\cdot \\mid s)$ , for $s \\in S$ drawn from the interaction with the original environment."
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+ "(e) Performance of the resulting distilled policy $\\bar{\\pi}_{\\theta}$ when deployed in the original environment (averaged over 30 episodes).",
+ "Figure 7: Comparison of the VAE-MDP in the CartPole environment (i) when the distortion and the rate are minimized as is (vanilla model) and (ii) when it makes use of annealing schemes, entropy regularization, and prioritized experience replay to avoid posterior collapse (cf. Delgrange et al. 2022). While the former clearly fails to learn a useful latent representation, the later does so meticulously and smoothly in two distinguishable phases: first, $\\phi_{\\iota}$ focuses on fairly distributing the latent space, setting up the stage to the concrete optimization occurring from step $4\\cdot 10^{5}$ , where the entropy of $\\phi_{\\iota}$ is lowered, which allows to get the rate of the variational model away from zero. Five instances of the models are trained with different random seeds, with the same hyperparameters than in Sect. 4."
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+ "text": "Formally, VAE- and WAE-MDPs optimize their objective by minimizing two losses: a reconstruction cost plus a regularizer term which penalizes a discrepancy between the encoding distribution and the dynamics of the latent space model. In VAE-MDPs, the former corresponds to the distortion, and the later to the rate of the variational model (further details are given in Alemi et al. 2018; Delgrange et al. 2022), while in our WAE-MDPs, the former corresponds to the raw transition distance and the later to both the steady-state and transition regularizers. Notably, the rate minimization of VAE-MDPs involves regularizing a stochastic embedding function $\\phi_{\\iota}(\\cdot | s)$ point-wise, i.e., for all different input states $s \\in S$ drawn from the interaction with the original environment. In contrast, the latent space regularization of the WAE-MDP involves the marginal embedding distribution $Q_{\\iota}$ where the embedding function $\\phi_{\\iota}$ is not required to be stochastic. Alemi et al. (2018) showed that posterior collapse occurs in VAEs when the rate of the variational model is close to zero, leading to low-quality representation.",
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+ "text": "Posterior collapse in VAE-MDPs. We illustrate the sensitivity of VAE-MDPs to the posterior collapse problem in Fig. 7, through the CartPole environment| Parameter | Range |
| ADAMα (minimizer) | {0.0001,0.0002,0.0003,0.001} |
| ADAMα (maximizer) | {0.0001,0.0002,0.0003,0.001} |
| ADAMβ1 | {0,0.5,0.9} |
| ADAMβ2 | {0.9,0.999} |
| neurons per layer | {64,128,256,512} |
| number of hidden layers | {1,2,3} |
| activation | {ReLU,LeakyReLU,tanh,softplus(2x+2)/2-1(smooth ELU)} |
| βwξπ | {10,25,50,75,100} |
| βLξπ | {10,25,50,75,100} |
| m | {5,10,15,20} |
| δ | {10,20} |
| use ε-mimic (cf. Delgrange et al. 2022) | {True,False} (if True, a decay rate of 10-5is used) |
| λPθ | {0.1,1/3,1/2,2/3,3/5,0.99} |
| λφl | {0.1,1/3,1/2,2/3,3/5,0.99} |
| λπθ | {1/|A|-1,1/(|A|-1).15} |
| λφlA | {1/|A|-1,1/(|A|-1).15} |
"
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+ "content": "Table 3: Final hyperparameters used to evaluate \\( {\\mathrm{W}}^{2}\\mathrm{{AE}} \\) -MDPs in Sect. 4"
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+ "content": "| Environment | S⊆ | Description, for s ∈ S | ℓ(s) = <p1, ..., pn, preset> |
| CartPole | R4 | • s1: cart position\n• s2: cart velocity\n• s3: pole angle (rad)\n• s4: pole velocity at tip | • p1 = 1s1≥1.5: unsafe cart position\n• p2 = 1s3≥0.15: unsafe pole angle |
| MountainCar | R2 | • s1: position\n• s2: velocity | • p1 = 1s1>1.5: target position\n• p2 = 1s1≥-1/2: right-hand side of the mountain\n• p3 = 1s2≥0: car going forward |
| Acrobot | R6 | Let θ1, θ2 ∈ [0, 2π] be the angles of the two rotational joints,\n• s1 = cos(θ1)\n• s2 = sin(θ1)\n• s3 = cos(θ2)\n• s4 = sin(θ2)\n• s5: angular velocity 1\n• s6: angular velocity 2 | • p1 = 1-s1-s3·s1+s4·s2>1: RL agent target\n• p2 = 1s1≥0: θ1 ∈ [0, π/2] ∪ [3π/2, 2π]\n• p3 = 1s2≥0: θ1 ∈ [0, π]\n• p4 = 1s3≥0: θ2 ∈ [0, π/2] ∪ [3π/2, 2π]\n• p5 = 1s4≥0: θ2 ∈ [0, π]\n• p6 = 1s5≥0: positive angular velocity (1)\n• p7 = 1s6≥0: positive angular velocity (2) |
| Pendulum | R3 | Let θ ∈ [0, 2π] be the joint angle\n• s1 = cos(θ)\n• s2 = sin(θ)\n• s3: angular velocity | • p1 = 1s1≥cos(π/3): safe joint angle\n• p2 = 1s1≥0: θ ∈ [0, π/2] ∪ [3π/2, 2π]\n• p3 = 1s2≥0: θ ∈ [0, π]\n• p4 = 1s3≥0: positive angular velocity |
| LunarLander | R8 | • s1: horizontal coordinates\n• s2: vertical coordinates\n• s3: horizontal speed\n• s4: vertical speed\n• s5: ship angle\n• s6: angular speed\n• s7: left leg contact\n• s8: right leg contact | • p1: unsafe angle\n• p2: leg ground contact\n• p3: lands rapidly\n• p4: left inclination\n• p5: right inclination\n• p6: motors shut down |
"
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+ "content": "Table 4: Labeling functions for the OpenAI environments considered in our experiments (Delgrange et al., 2022). We provide a short description of the state space and the meaning of each atomic proposition. Recall that labels are binary encoded, for \\( n = |\\mathbf{AP}| - 1 \\) (one bit is reserved for reset) and \\( p_{\\mathrm{reset}} = 1 \\) iff \\( s \\) is a reset state (cf. Appendix B.2)."
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+ "angle": 0,
+ "content": "Time to failure properties. Based on the labeling described in Table 4, we formally detail the time to failure properties checked in Sect. 4 whose results are listed in Table 1 for each environment. Let \\(\\text{Reset} = \\{\\text{reset}\\} = \\langle 0, \\dots, 1 \\rangle\\) (we assume here that the last bit indicates whether the current state is a reset state or not) and define \\(s \\models \\mathsf{L}_1 \\land \\mathsf{L}_2\\) iff \\(s \\models \\mathsf{L}_1\\) and \\(s \\models \\mathsf{L}_2\\) for any \\(s \\in S\\), then"
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+ "content": "- CartPole: \\(\\varphi = \\neg\\) Reset \\(\\mathcal{U}\\) Unsafe, where Unsafe \\(= \\langle 1,1,0\\rangle\\)"
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+ "angle": 0,
+ "content": "- MountainCar: \\(\\varphi = \\neg\\) GoalU Reset, where Goal \\(= \\langle 1,0,0,0\\rangle\\)"
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+ "content": "- Acrobot: \\(\\varphi = \\neg\\) GoalU Reset, where Goal \\(= \\langle 1,0,\\dots ,0\\rangle\\)"
+ },
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+ "type": "text",
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+ "content": "- LunarLander: \\(\\varphi = \\neg\\) SafeLanding \\(\\mathcal{U}\\) Reset, where SafeLanding \\(=\\) GroundContact \\(\\land\\) MotorsOff, GroundContact \\(=\\langle 0,1,0,0,0,0,0\\rangle\\), and MotorsOff \\(=\\langle 0,0,0,0,0,1,0\\rangle\\)"
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+ "content": "- Pendulum: \\(\\varphi = \\diamondsuit (\\neg \\text{Safe} \\land \\bigcirc \\text{Reset})\\), where Safe = \\(\\langle 1,0,0,0,0\\rangle\\), \\(\\diamondsuit \\mathsf{T} = \\neg \\emptyset \\mathcal{U} \\mathsf{T}\\), and \\(s_i \\models \\bigcirc \\mathsf{T}\\) iff \\(s_{i+1} \\models \\mathsf{T}\\), for any \\(\\mathsf{T} \\subseteq \\mathbf{AP}\\), \\(s_{i:\\infty}, a_{i:\\infty} \\in \\text{Traj}\\). Intuitively, \\(\\varphi\\) denotes the event of ending an episode in an unsafe state, just before resetting the environment, which means that either the agent never reached the safe region or it reached and left it at some point. Formally, \\(\\varphi = \\{s_{0:\\infty}, a_{0:\\infty} \\mid \\exists i \\in \\mathbb{N}, s_i \\models \\text{Safe} \\land s_{i+1} \\models \\text{Reset}\\} \\subseteq \\text{Traj}\\)."
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+ "content": "C ON THE CURSE OF VARIATIONAL MODELING"
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+ "content": "Posterior collapse is a well known issue occurring in variational models (see, e.g., Alemi et al. 2018; Tolstikhin et al. 2018; He et al. 2019; Dong et al. 2020) which intuitively results in a degenerate local optimum where the model learns to ignore the latent space and use only the reconstruction functions (i.e., the decoding distribution) to optimize the objective. VAE-MDPs are no exception, as pointed out in the original paper (Delgrange et al., 2022, Section 4.3 and Appendix C.2)."
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+ "content": "Posterior collapse in VAE-MDPs. We illustrate the sensitivity of VAE-MDPs to the posterior collapse problem in Fig. 7, through the CartPole environment| Parameter | Range |
| ADAMα (minimizer) | {0.0001,0.0002,0.0003,0.001} |
| ADAMα (maximizer) | {0.0001,0.0002,0.0003,0.001} |
| ADAMβ1 | {0,0.5,0.9} |
| ADAMβ2 | {0.9,0.999} |
| neurons per layer | {64,128,256,512} |
| number of hidden layers | {1,2,3} |
| activation | {ReLU,LeakyReLU,tanh,softplus(2x+2)/2-1(smooth ELU)} |
| βwξπ | {10,25,50,75,100} |
| βLξπ | {10,25,50,75,100} |
| m | {5,10,15,20} |
| δ | {10,20} |
| use ε-mimic (cf. Delgrange et al. 2022) | {True,False} (if True, a decay rate of 10-5is used) |
| λPθ | {0.1,1/3,1/2,2/3,3/5,0.99} |
| λφl | {0.1,1/3,1/2,2/3,3/5,0.99} |
| λπθ | {1/|A|-1,1/(|A|-1).15} |
| λφlA | {1/|A|-1,1/(|A|-1).15} |
+
+Table 3: Final hyperparameters used to evaluate ${\mathrm{W}}^{2}\mathrm{{AE}}$ -MDPs in Sect. 4
+
+| Environment | S⊆ | Description, for s ∈ S | ℓ(s) = <p1, ..., pn, preset> |
| CartPole | R4 | • s1: cart position
+• s2: cart velocity
+• s3: pole angle (rad)
+• s4: pole velocity at tip | • p1 = 1s1≥1.5: unsafe cart position
+• p2 = 1s3≥0.15: unsafe pole angle |
| MountainCar | R2 | • s1: position
+• s2: velocity | • p1 = 1s1>1.5: target position
+• p2 = 1s1≥-1/2: right-hand side of the mountain
+• p3 = 1s2≥0: car going forward |
| Acrobot | R6 | Let θ1, θ2 ∈ [0, 2π] be the angles of the two rotational joints,
+• s1 = cos(θ1)
+• s2 = sin(θ1)
+• s3 = cos(θ2)
+• s4 = sin(θ2)
+• s5: angular velocity 1
+• s6: angular velocity 2 | • p1 = 1-s1-s3·s1+s4·s2>1: RL agent target
+• p2 = 1s1≥0: θ1 ∈ [0, π/2] ∪ [3π/2, 2π]
+• p3 = 1s2≥0: θ1 ∈ [0, π]
+• p4 = 1s3≥0: θ2 ∈ [0, π/2] ∪ [3π/2, 2π]
+• p5 = 1s4≥0: θ2 ∈ [0, π]
+• p6 = 1s5≥0: positive angular velocity (1)
+• p7 = 1s6≥0: positive angular velocity (2) |
| Pendulum | R3 | Let θ ∈ [0, 2π] be the joint angle
+• s1 = cos(θ)
+• s2 = sin(θ)
+• s3: angular velocity | • p1 = 1s1≥cos(π/3): safe joint angle
+• p2 = 1s1≥0: θ ∈ [0, π/2] ∪ [3π/2, 2π]
+• p3 = 1s2≥0: θ ∈ [0, π]
+• p4 = 1s3≥0: positive angular velocity |
| LunarLander | R8 | • s1: horizontal coordinates
+• s2: vertical coordinates
+• s3: horizontal speed
+• s4: vertical speed
+• s5: ship angle
+• s6: angular speed
+• s7: left leg contact
+• s8: right leg contact | • p1: unsafe angle
+• p2: leg ground contact
+• p3: lands rapidly
+• p4: left inclination
+• p5: right inclination
+• p6: motors shut down |
+
+Table 4: Labeling functions for the OpenAI environments considered in our experiments (Delgrange et al., 2022). We provide a short description of the state space and the meaning of each atomic proposition. Recall that labels are binary encoded, for $n = |\mathbf{AP}| - 1$ (one bit is reserved for reset) and $p_{\mathrm{reset}} = 1$ iff $s$ is a reset state (cf. Appendix B.2).
+
+Time to failure properties. Based on the labeling described in Table 4, we formally detail the time to failure properties checked in Sect. 4 whose results are listed in Table 1 for each environment. Let $\text{Reset} = \{\text{reset}\} = \langle 0, \dots, 1 \rangle$ (we assume here that the last bit indicates whether the current state is a reset state or not) and define $s \models \mathsf{L}_1 \land \mathsf{L}_2$ iff $s \models \mathsf{L}_1$ and $s \models \mathsf{L}_2$ for any $s \in S$ , then
+
+- CartPole: $\varphi = \neg$ Reset $\mathcal{U}$ Unsafe, where Unsafe $= \langle 1,1,0\rangle$
+- MountainCar: $\varphi = \neg$ GoalU Reset, where Goal $= \langle 1,0,0,0\rangle$
+- Acrobot: $\varphi = \neg$ GoalU Reset, where Goal $= \langle 1,0,\dots ,0\rangle$
+- LunarLander: $\varphi = \neg$ SafeLanding $\mathcal{U}$ Reset, where SafeLanding $=$ GroundContact $\land$ MotorsOff, GroundContact $=\langle 0,1,0,0,0,0,0\rangle$ , and MotorsOff $=\langle 0,0,0,0,0,1,0\rangle$
+- Pendulum: $\varphi = \diamondsuit (\neg \text{Safe} \land \bigcirc \text{Reset})$ , where Safe = $\langle 1,0,0,0,0\rangle$ , $\diamondsuit \mathsf{T} = \neg \emptyset \mathcal{U} \mathsf{T}$ , and $s_i \models \bigcirc \mathsf{T}$ iff $s_{i+1} \models \mathsf{T}$ , for any $\mathsf{T} \subseteq \mathbf{AP}$ , $s_{i:\infty}, a_{i:\infty} \in \text{Traj}$ . Intuitively, $\varphi$ denotes the event of ending an episode in an unsafe state, just before resetting the environment, which means that either the agent never reached the safe region or it reached and left it at some point. Formally, $\varphi = \{s_{0:\infty}, a_{0:\infty} \mid \exists i \in \mathbb{N}, s_i \models \text{Safe} \land s_{i+1} \models \text{Reset}\} \subseteq \text{Traj}$ .
+
+# C ON THE CURSE OF VARIATIONAL MODELING
+
+Posterior collapse is a well known issue occurring in variational models (see, e.g., Alemi et al. 2018; Tolstikhin et al. 2018; He et al. 2019; Dong et al. 2020) which intuitively results in a degenerate local optimum where the model learns to ignore the latent space and use only the reconstruction functions (i.e., the decoding distribution) to optimize the objective. VAE-MDPs are no exception, as pointed out in the original paper (Delgrange et al., 2022, Section 4.3 and Appendix C.2).
+
+
+(a) Latent space distribution along training steps. The intensity of the blue hue corresponds to the frequency of latent states produced from $\phi_{\iota}$ during training. The vanilla model collapses to a single state.
+
+
+
+
+(b) Rate of the variational model.
+
+
+(c) Distortion of the variational model.
+
+
+(d) Average point-wise entropy of $\phi_{\iota}(\cdot \mid s)$ , for $s \in S$ drawn from the interaction with the original environment.
+
+
+(e) Performance of the resulting distilled policy $\bar{\pi}_{\theta}$ when deployed in the original environment (averaged over 30 episodes).
+Figure 7: Comparison of the VAE-MDP in the CartPole environment (i) when the distortion and the rate are minimized as is (vanilla model) and (ii) when it makes use of annealing schemes, entropy regularization, and prioritized experience replay to avoid posterior collapse (cf. Delgrange et al. 2022). While the former clearly fails to learn a useful latent representation, the later does so meticulously and smoothly in two distinguishable phases: first, $\phi_{\iota}$ focuses on fairly distributing the latent space, setting up the stage to the concrete optimization occurring from step $4\cdot 10^{5}$ , where the entropy of $\phi_{\iota}$ is lowered, which allows to get the rate of the variational model away from zero. Five instances of the models are trained with different random seeds, with the same hyperparameters than in Sect. 4.
+
+Formally, VAE- and WAE-MDPs optimize their objective by minimizing two losses: a reconstruction cost plus a regularizer term which penalizes a discrepancy between the encoding distribution and the dynamics of the latent space model. In VAE-MDPs, the former corresponds to the distortion, and the later to the rate of the variational model (further details are given in Alemi et al. 2018; Delgrange et al. 2022), while in our WAE-MDPs, the former corresponds to the raw transition distance and the later to both the steady-state and transition regularizers. Notably, the rate minimization of VAE-MDPs involves regularizing a stochastic embedding function $\phi_{\iota}(\cdot | s)$ point-wise, i.e., for all different input states $s \in S$ drawn from the interaction with the original environment. In contrast, the latent space regularization of the WAE-MDP involves the marginal embedding distribution $Q_{\iota}$ where the embedding function $\phi_{\iota}$ is not required to be stochastic. Alemi et al. (2018) showed that posterior collapse occurs in VAEs when the rate of the variational model is close to zero, leading to low-quality representation.
+
+Posterior collapse in VAE-MDPs. We illustrate the sensitivity of VAE-MDPs to the posterior collapse problem in Fig. 7, through the CartPole environment| Parameter | Range |
| ADAMα (minimizer) | {0.0001,0.0002,0.0003,0.001} |
| ADAMα (maximizer) | {0.0001,0.0002,0.0003,0.001} |
| ADAMβ1 | {0,0.5,0.9} |
| ADAMβ2 | {0.9,0.999} |
| neurons per layer | {64,128,256,512} |
| number of hidden layers | {1,2,3} |
| activation | {ReLU,LeakyReLU,tanh,softplus(2x+2)/2-1(smooth ELU)} |
| βwξπ | {10,25,50,75,100} |
| βLξπ | {10,25,50,75,100} |
| m | {5,10,15,20} |
| δ | {10,20} |
| use ε-mimic (cf. Delgrange et al. 2022) | {True,False} (if True, a decay rate of 10-5is used) |
| λPθ | {0.1,1/3,1/2,2/3,3/5,0.99} |
| λφl | {0.1,1/3,1/2,2/3,3/5,0.99} |
| λπθ | {1/|A|-1,1/(|A|-1).15} |
| λφlA | {1/|A|-1,1/(|A|-1).15} |
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| CartPole | R4 | • s1: cart position\n• s2: cart velocity\n• s3: pole angle (rad)\n• s4: pole velocity at tip | • p1 = 1s1≥1.5: unsafe cart position\n• p2 = 1s3≥0.15: unsafe pole angle |
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| LunarLander | R8 | • s1: horizontal coordinates\n• s2: vertical coordinates\n• s3: horizontal speed\n• s4: vertical speed\n• s5: ship angle\n• s6: angular speed\n• s7: left leg contact\n• s8: right leg contact | • p1: unsafe angle\n• p2: leg ground contact\n• p3: lands rapidly\n• p4: left inclination\n• p5: right inclination\n• p6: motors shut down |
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+ "content": "Posterior collapse in VAE-MDPs. We illustrate the sensitivity of VAE-MDPs to the posterior collapse problem in Fig. 7, through the CartPole environment| Model | Sent Acc | Reasoning Performance |
| FE | FC | FN | FUP | FUH | GM | AM |
| Human | - | 84.71 | 71.01 | 55.12 | 82.46 | 61.80 | 70.07 | 71.02 |
| Non-reasoning |
| Mahabadi et al. (2020)† | 85.1 | - | - | - | - | - | - | - |
| LSTM (Wang & Jiang, 2016)† | 86.1 | - | - | - | - | - | - | - |
| Transformer (Radford et al., 2018) | 89.9 | - | - | - | - | - | - | - |
| SBERT (Reimers & Gurevych, 2019) | 91.4 | - | - | - | - | - | - | - |
| Baselines |
| NNL (Feng et al., 2020)‡ | 79.91 | 62.72 | 17.49 | 1.50 | 66.22 | 0.00 | 0.00 | 29.59 |
| STP | 85.76 | 62.40 | 34.76 | 37.04 | 76.61 | 51.80 | 50.20 | 52.52 |
| GPT-3-Davinci (Brown et al., 2020) | - | 53.75 | 58.00 | 16.12 | 52.24 | 31.08 | 38.23 | 42.24 |
| Ours |
| EPR (Local, LM unfinetuned) | 76.33±0.48 | 83.11±0.29 | 38.73±0.85 | 44.63±0.88 | 76.61 | 51.80 | 56.39±0.43 | 58.98±0.34 |
| EPR (Local, LM finetuned) | 79.36±0.13 | 82.44±0.26 | 44.10±1.32 | 44.69±3.22 | 76.61 | 51.80 | 57.77±0.85 | 59.93±0.67 |
| EPR (Concat, LM unfinetuned) | 84.53±0.19 | 73.29±0.68 | 37.95±1.16 | 40.56±1.10 | 76.61 | 51.80 | 53.73±0.39 | 56.04±0.33 |
| EPR (Concat, LM finetuned) | 87.56±0.15 | 69.91±1.21 | 39.97±2.12 | 43.31±2.78 | 76.61 | 51.80 | 54.46±1.35 | 56.32±1.13 |
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| FE | FC | FN | FUP | FUH | GM | AM |
| Human | - | 84.71 | 71.01 | 55.12 | 82.46 | 61.80 | 70.07 | 71.02 |
| Non-reasoning |
| Mahabadi et al. (2020)† | 85.1 | - | - | - | - | - | - | - |
| LSTM (Wang & Jiang, 2016)† | 86.1 | - | - | - | - | - | - | - |
| Transformer (Radford et al., 2018) | 89.9 | - | - | - | - | - | - | - |
| SBERT (Reimers & Gurevych, 2019) | 91.4 | - | - | - | - | - | - | - |
| Baselines |
| NNL (Feng et al., 2020)‡ | 79.91 | 62.72 | 17.49 | 1.50 | 66.22 | 0.00 | 0.00 | 29.59 |
| STP | 85.76 | 62.40 | 34.76 | 37.04 | 76.61 | 51.80 | 50.20 | 52.52 |
| GPT-3-Davinci (Brown et al., 2020) | - | 53.75 | 58.00 | 16.12 | 52.24 | 31.08 | 38.23 | 42.24 |
| Ours |
| EPR (Local, LM unfinetuned) | 76.33±0.48 | 83.11±0.29 | 38.73±0.85 | 44.63±0.88 | 76.61 | 51.80 | 56.39±0.43 | 58.98±0.34 |
| EPR (Local, LM finetuned) | 79.36±0.13 | 82.44±0.26 | 44.10±1.32 | 44.69±3.22 | 76.61 | 51.80 | 57.77±0.85 | 59.93±0.67 |
| EPR (Concat, LM unfinetuned) | 84.53±0.19 | 73.29±0.68 | 37.95±1.16 | 40.56±1.10 | 76.61 | 51.80 | 53.73±0.39 | 56.04±0.33 |
| EPR (Concat, LM finetuned) | 87.56±0.15 | 69.91±1.21 | 39.97±2.12 | 43.31±2.78 | 76.61 | 51.80 | 54.46±1.35 | 56.32±1.13 |
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| FE | FC | FN | FUP | FUH | GM | AM |
| Human | - | 84.71 | 71.01 | 55.12 | 82.46 | 61.80 | 70.07 | 71.02 |
| Non-reasoning |
| Mahabadi et al. (2020)† | 85.1 | - | - | - | - | - | - | - |
| LSTM (Wang & Jiang, 2016)† | 86.1 | - | - | - | - | - | - | - |
| Transformer (Radford et al., 2018) | 89.9 | - | - | - | - | - | - | - |
| SBERT (Reimers & Gurevych, 2019) | 91.4 | - | - | - | - | - | - | - |
| Baselines |
| NNL (Feng et al., 2020)‡ | 79.91 | 62.72 | 17.49 | 1.50 | 66.22 | 0.00 | 0.00 | 29.59 |
| STP | 85.76 | 62.40 | 34.76 | 37.04 | 76.61 | 51.80 | 50.20 | 52.52 |
| GPT-3-Davinci (Brown et al., 2020) | - | 53.75 | 58.00 | 16.12 | 52.24 | 31.08 | 38.23 | 42.24 |
| Ours |
| EPR (Local, LM unfinetuned) | 76.33±0.48 | 83.11±0.29 | 38.73±0.85 | 44.63±0.88 | 76.61 | 51.80 | 56.39±0.43 | 58.98±0.34 |
| EPR (Local, LM finetuned) | 79.36±0.13 | 82.44±0.26 | 44.10±1.32 | 44.69±3.22 | 76.61 | 51.80 | 57.77±0.85 | 59.93±0.67 |
| EPR (Concat, LM unfinetuned) | 84.53±0.19 | 73.29±0.68 | 37.95±1.16 | 40.56±1.10 | 76.61 | 51.80 | 53.73±0.39 | 56.04±0.33 |
| EPR (Concat, LM finetuned) | 87.56±0.15 | 69.91±1.21 | 39.97±2.12 | 43.31±2.78 | 76.61 | 51.80 | 54.46±1.35 | 56.32±1.13 |
+
+We further propose a set of $F$ -scores, which are a balanced measure of precision and recall between human annotation and model output for Entailment, Contradiction, Neutral, and Unaligned in terms of word indexes. Details of human annotation and evaluation metrics are shown in Appendix B.
+
+The inter-annotator agreement is presented in Table 2 in comparison with model performance (detailed in the next part). Here, we compute the agreement by treating one annotator as the ground truth and another as the system output; the score is averaged among all annotator pairs. As seen, humans generally achieve high agreement with each other, whereas model performance is relatively low. This shows that our task and metrics are well-defined, yet phrasal logical reasoning is a challenging task for machine learning models.
+
+Textual explanation generation was evaluated on the e-SNLI dataset (Camburu et al., 2018), which extends the SNLI dataset with one reference explanation for each training sample, and three reference explanations for each validation or test sample. Each reference explanation comes with highlighted rationales, a set of annotated words in the premise or hypothesis considered as the reason for the explanation annotation. We do not use these highlighted rationales, but enhance the neural model with EPR output for textual explanation generation. We follow previous work (Camburu et al., 2018; Narang et al., 2020), adopting BLEU (Papineni et al., 2002) and SacreBLEU (Post, 2018) scores as the evaluation metrics; they mainly differ in the tokenizer. Camburu et al. (2018) also report low consistency of the third annotated reference, and thus use only two references for evaluation. In our study, we consider both two-reference and three-reference BLEU/SacreBLEU. Appendix A.2 provides additional implementation details of textual explanation generation.
+
+# 4.2 RESULTS
+
+Phrasal Reasoning Performance. To the best of our knowledge, phrasal reasoning for NLI was not explicitly evaluated in previous literature. Therefore, we propose plausible extensions to previous studies as our baselines. We consider the study of Neural Natural Logic (NNL, Feng et al., 2020) as the first baseline. It applies an attention mechanism (Parikh et al., 2016), so that each word in the hypothesis is softly aligned with the words in the premise. Then, each word in the hypothesis is predicted with one of the seven natural logic relations proposed by MacCartney & Manning (2009). We consider the maximum attention score as the alignment, and map their seven natural logic relations to our three-category NLI labels: Equivalence, ForwardEntailment $\mapsto$ Entailment; Negation, Alternation $\mapsto$ Contradiction; and ReverseEntailment, Cover, Independence $\mapsto$ Neutral.
+
+Table 2 shows that the word-level NNL approach cannot perform meaningful phrasal reasoning, although our metrics have already excluded explicit evaluation of phrases. The low performance is because their soft attention leads to many misalignments, whereas their seven-category logical relations are too fine-grained and cause complications in weakly supervised reasoning. In addition, NNL does not allow unaligned words in the hypothesis, showing that such a model is inadequate for NLI reasoning. By contrast, our EPR model extracts phrases of meaningful semantic units, being an appropriate granularity of logical reasoning. Moreover, we work with three-category NLI labels following the sentence-level NLI task formulation. This actually restricts the model's capacity, forcing the model to perform serious phrasal reasoning.
+
+Table 3: Results of ablation studies on SNLI.
+
+| Model | Sent Acc | Reasoning Performance |
| FE | FC | FN | FUP | FUH | GM | AM |
| Human | - | 84.71 | 71.01 | 55.12 | 82.46 | 61.80 | 70.07 | 71.02 |
| Non-reasoning |
| Mahabadi et al. (2020)† | 85.1 | - | - | - | - | - | - | - |
| LSTM (Wang & Jiang, 2016)† | 86.1 | - | - | - | - | - | - | - |
| Transformer (Radford et al., 2018) | 89.9 | - | - | - | - | - | - | - |
| SBERT (Reimers & Gurevych, 2019) | 91.4 | - | - | - | - | - | - | - |
| Baselines |
| NNL (Feng et al., 2020)‡ | 79.91 | 62.72 | 17.49 | 1.50 | 66.22 | 0.00 | 0.00 | 29.59 |
| STP | 85.76 | 62.40 | 34.76 | 37.04 | 76.61 | 51.80 | 50.20 | 52.52 |
| GPT-3-Davinci (Brown et al., 2020) | - | 53.75 | 58.00 | 16.12 | 52.24 | 31.08 | 38.23 | 42.24 |
| Ours |
| EPR (Local, LM unfinetuned) | 76.33±0.48 | 83.11±0.29 | 38.73±0.85 | 44.63±0.88 | 76.61 | 51.80 | 56.39±0.43 | 58.98±0.34 |
| EPR (Local, LM finetuned) | 79.36±0.13 | 82.44±0.26 | 44.10±1.32 | 44.69±3.22 | 76.61 | 51.80 | 57.77±0.85 | 59.93±0.67 |
| EPR (Concat, LM unfinetuned) | 84.53±0.19 | 73.29±0.68 | 37.95±1.16 | 40.56±1.10 | 76.61 | 51.80 | 53.73±0.39 | 56.04±0.33 |
| EPR (Concat, LM finetuned) | 87.56±0.15 | 69.91±1.21 | 39.97±2.12 | 43.31±2.78 | 76.61 | 51.80 | 54.46±1.35 | 56.32±1.13 |
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+ "content": "Phrasal Reasoning Performance. To the best of our knowledge, phrasal reasoning for NLI was not explicitly evaluated in previous literature. Therefore, we propose plausible extensions to previous studies as our baselines. We consider the study of Neural Natural Logic (NNL, Feng et al., 2020) as the first baseline. It applies an attention mechanism (Parikh et al., 2016), so that each word in the hypothesis is softly aligned with the words in the premise. Then, each word in the hypothesis is predicted with one of the seven natural logic relations proposed by MacCartney & Manning (2009). We consider the maximum attention score as the alignment, and map their seven natural logic relations to our three-category NLI labels: Equivalence, ForwardEntailment "
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+ "html": "| Model | Data Domain | CLEVR count acc. | CLEVR mAP (mAP@IoU=0.5) | Mol. count. acc | Mol. mAP (mAP@IoU=0.5) |
| Resnet50-CAM | target domain | 0.97 ± 0.005 | 0.036 ± 0.014 (0.200 ± 0.071) | 0.978 ± 0.004 | 0.0 ± 0.0 (0 ± 0) |
| Resnet50-CAM | OOD | 0.831 ± 0.016 | 0.029 ± 0.010 (0.153 ± 0.044) | 0.0 ± 0.0 | n/a* |
| Resnet50-CAM | source domain | 0.993 ± 0.003 | 0.035 ± 0.019 (0.178 ± 0.084) | 0.828 ± 0.021 | 0.0 ± 0.0 (0 ± 0) |
| WSOD-transfer | target domain | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) | 0.001 ± 0.0 | 0.018 ± 0.004 (0.061 ± 0.011) |
| WSOD-transfer | OOD | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) | 0.003 ± 0.002 | n/a* |
| WSOD-transfer | source domain | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) | 0.0 ± 0.0 | 0.021 ± 0.003 (0.069 ± 0.009) |
| DETR-joint | target domain | 0.159 ± 0.133 | 0.579 ± 0.012 (0.684 ± 0.019) | 0.357 ± 0.196 | 0.197 ± 0.055 (0.481 ± 0.071) |
| DETR-joint | OOD | 0.084 ± 0.039 | 0.534 ± 0.012 (0.66 ± 0.012) | 0.024 ± 0.021 | n/a* |
| DETR-joint | source dom. | 0.923 ± 0.049 | 0.908 ± 0.017 (0.992 ± 0.001) | 0.232 ± 0.127 | 0.23 ± 0.063 (0.565 ± 0.08) |
| RCNN (pre-trained) | target domain | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) | 0.592 ± 0.007 | 0.568 ± 0.005 (0.785 ± 0.004) |
| RCNN (pre-trained) | OOD | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) | 0.348 ± 0.036 | n/a* |
| RCNN (pre-trained) | source domain | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) | 0.948 ± 0.004 | 0.737 ± 0.005 (0.979 ± 0.0) |
| DETR (pre-trained) | target domain | 0.0 ± 0.0 | 0.498 ± 0.019 (0.533 ± 0.024) | 0.464 ± 0.033 | 0.314 ± 0.006 (0.542 ± 0.006) |
| DETR (pre-trained) | OOD | 0.0 ± 0.0 | 0.477 ± 0.013 (0.531 ± 0.021) | 0.002 ± 0.001 | n/a* |
| DETR (pre-trained) | source domain | 0.97 ± 0.009 | 0.945 ± 0.009 (0.992 ± 0.001) | 0.581 ± 0.022 | 0.409 ± 0.005 (0.722 ± 0.004) |
| ProbKT (DETR) | target domain | 0.946 ± 0.014 | 0.803 ± 0.011 (0.989 ± 0.006) | 0.508 ± 0.027 | 0.204 ± 0.02 (0.507 ± 0.014) |
| ProbKT (DETR) | OOD | 0.726 ± 0.035 | 0.715 ± 0.006 (0.974 ± 0.006) | 0.004 ± 0.003 | n/a* |
| ProbKT (DETR) | source domain | 0.987 ± 0.003 | 0.948 ± 0.005 (0.995 ± 0.001) | 0.549 ± 0.026 | 0.38 ± 0.013 (0.713 ± 0.006) |
| ProbKT (RCNN) | target domain | 0.975 ± 0.003 | 0.856 ± 0.039 (0.993 ± 0.001) | 0.942 ± 0.009 | 0.289 ± 0.041 (0.829 ± 0.054) |
| ProbKT (RCNN) | OOD | 0.89 ± 0.022 | 0.833 ± 0.042 (0.991 ± 0.001) | 0.603 ± 0.037 | n/a* |
| ProbKT (RCNN) | source domain | 0.995 ± 0.002 | 0.941 ± 0.041 (0.998 ± 0.001) | 0.96 ± 0.002 | 0.666 ± 0.005 (0.978 ± 0.002) |
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+ "text": "Table 2: Results of the experiments for the datasets: CLEVR-mini and Molecules. Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution. *: OOD test set of Molecules dataset has no bounding box labels.",
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+ "text": "We evaluate the performance of the models on the different datasets based on two criteria: the count accuracy and the objects localization performance. The count accuracy measures the ratio of correct images where all individual counts of (all detected) objects are correct. To evaluate how well the",
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+ "text": "model is performing in localizing the different objects in the image we report the mean average precision (mAP) performance, a widely used metric for evaluating object detection models.",
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+ "text": "We first investigate the performance of ProbKT when the weakly supervision consists of class counts only. The query $q$ for each image then consists of the number of objects from each class in the image. We evaluate the models on the CLEVR-mini and Molecules datasets. For the Molecules dataset, the query for an image containing 6 carbon atoms (C), 6 oxygen atoms (O) and 12 hydrogen atoms (H) would result in the following query: $q = ([C,O,H],[6,6,12])$ . These weak labels in the case of the Molecules dataset are widely and easily available in the form of the chemical formula of the molecule on the image (e.g $C_6H_{12}O_6$ ). The recognition of atomic level entities on images of molecules is a challenge in the field of Optical Chemical Structure Recognition (OCSR) [9; 33; 29; 19]. For the CLEVR-mini dataset, the query for an example image containing 2 spheres, 1 cylinder and 3 cubes would be $q = ([\\mathrm{Cube},\\mathrm{Cylinder},\\mathrm{Sphere}],[3,1,2])$ . Formal descriptions of the queries for each task are presented in Appendix E.",
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+ "text": "Results of the experiments are summarized in Table 2. We observe on both datasets that ProbKT is able to transfer knowledge from the source domain to the target domain and improve count accuracy on the target domain and in most cases also on the source domain. The count accuracy increases on both the target domain and on OOD, suggesting better generalization performance. This is in contrast with Resnet50-CAM which performs well on the target domain of the Molecules dataset but fails on OOD. We also note a significant improvement in object localization (mAP) for ProbKT on the CLEVR-mini dataset. However, fine-tuning seems detrimental for mAP on the Molecules dataset. This can be explained by the very small bounding boxes in the Molecules dataset. We therefore also report the mAP@IoU=0.5 where we observe some increase in performance after fine-tuning. Lastly, we observe that our approach outperforms WSOD-transfer on all metrics for both datasets. WSOD-transfer performs well on CLEVR-mini but fails for the Molecules dataset. This can be explained by the fact that this method only supports class indicators (whether a class is present in the image), which is particularly detrimental in molecules images containing a lot of objects.",
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+ "text": "The annotation of images is a tedious task, which limits the availability of fully annotated datasets. When the number of objects on an image is large, counting the exact number of objects of a particular class becomes too time-consuming. A typical annotation in this case consists oof class ranges where, instead of exact class counts, an interval is given for the count. For example an image from the CLEVR-mini dataset with more than 4 cubes, exactly 4 cylinders and less than 4 spheres would result in the following query: $q = ([\\text{cube}, \\text{cylinder}, \\text{sphere}], [[4, \\infty[, [4, 5[, [0, 4[}})$ . We evaluate this experimental setup and report results in Table 3. We observe that ProbKT performs significantly better than WSOD-transfer on count accuracy, which still uses only presence/absence labels. We note that Resnet50-CAM is unable to use this type of supervision and is thus reported as $n / a$ .",
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+ "table_body": "| Model | Data Domain | MNIST count acc. | MNIST sum acc. | MNIST mAP (mAP@IoU=0.5) | CLEVR* count acc. | CLEVR* mAP (mAP@IoU=0.5) |
| Resnet50-CAM | target domain | 0.044 ± 0.041 | 0.506 ± 0.063 | 0.003 ± 0.003(0.014 ± 0.011) | n/a | n/a |
| Resnet50-CAM | OOD | 0.01 ± 0.009 | 0.015 ± 0.004 | 0.003 ± 0.002(0.011 ± 0.007) | n/a | n/a |
| Resnet50-CAM | source domain | 0.127 ± 0.132 | 0.649 ± 0.108 | 0.005 ± 0.004(0.028 ± 0.018) | n/a | n/a |
| WSOD-transfer | target domain | n/a | n/a | n/a | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) |
| WSOD-transfer | OOD | n/a | n/a | n/a | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) |
| WSOD-transfer | source domain | n/a | n/a | n/a | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) |
| RCNN (pre-trained) | target domain | 0.292 ± 0.005 | 0.298 ± 0.005 | 0.632 ± 0.014 (0.685 ± 0.002) | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) |
| RCNN (pre-trained) | OOD | 0.205 ± 0.004 | 0.212 ± 0.004 | 0.631 ± 0.013 (0.683 ± 0.002) | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) |
| RCNN (pre-trained) | source domain | 0.961 ± 0.008 | 0.961 ± 0.008 | 0.917 ± 0.021 (0.988 ± 0.002) | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) |
| ProbKT (RCNN) | target domain | 0.902 ± 0.005 | 0.903 ± 0.005 | 0.786 ± 0.021 (0.974 ± 0.001) | 0.971 ± 0.006 | 0.838 ± 0.034 (0.993 ± 0.001) |
| ProbKT (RCNN) | OOD | 0.863 ± 0.008 | 0.865 ± 0.008 | 0.778 ± 0.021 (0.97 ± 0.001) | 0.884 ± 0.01 | 0.812 ± 0.036 (0.991 ± 0.001) |
| ProbKT (RCNN) | source domain | 0.967 ± 0.004 | 0.967 ± 0.004 | 0.873 ± 0.016 (0.989 ± 0.001) | 0.994 ± 0.001 | 0.922 ± 0.035 (0.998 ± 0.001) |
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+ "text": "Table 3: Results of the experiments on the MNIST object detection dataset and on CLEVR* dataset (*CLEVR uses ranges of class counts as labels instead of exact class counts). Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution.",
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+ "text": "4.5.2 COMPLEX QUERIES",
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+ "text": "More complex types of weak supervision than the ones considered above are also possible. To illustrate the capabilities of our approach, we build an MNIST object detection dataset where images show multiple digits as objects. Examples images are available in Appendix B. The weak supervision is here the sum of all digits in the image: $q = \\mathrm{SUM}(\\mathrm{digits})$ . Our ProbKT can seamlessly integrate this type of supervision as shown in Table 3. As all other baselines are unable process this type of supervision, we compare against a pre-trained RCNN and a variation of Resnet50-CAM where we add an extra neural network layer that sums the individual counts to give the resulting sum. We report count accuracy, mAP and sum accuracy. The sum accuracy measures the ratio of correct images where the predicted sum (instead of the label of the digits) is correct. Details about the results on extra experiments with DETR as backbone using complex types of weak supervision can be found in Appendix D.",
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+ "text": "4.6 ABLATION STUDIES",
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+ "(a) CLEVR iterative relabeling"
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+ "img_path": "images/d17235340db1e49a74095c49b3c4b80909d704f18f417672a46e1577bd8f7bad.jpg",
+ "image_caption": [
+ "Figure 4: Iterative relabeling performance for the different datasets. Iteration 0: pretrained on source domain. Iteration 1: fine-tuned. Iteration 2: re-labeled and re-trained. Iteration 3: relabeled and re-trained. Iteration 4: relabeled and re-trained."
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+ "image_caption": [
+ "(b) Molecules iterative relabeling",
+ "(c) MNIST iterative relabeling"
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+ "text": "Iterative relabeling. In Figure 4, we plot the evolution of the performance on the test sets after multiple rounds of fine-tuning and re-labeling, as detailed in Section 3.3.1. The final performance reported in the results tables is selected based on best relabeling iteration on the validation dataset. We observe that iterative relabeling after fine-tuning can improve performance significantly. Nevertheless, the benefit of iterative relabeling is less pronounced for DETR on the Molecules dataset. We impute it to the fact that the fine-tuned DETR model is less accurate on this dataset.",
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+ "text": "Object detection backbone",
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+ "text": "Our method can seamlessly accommodate different object detection backbones. In Table 2, we present the results for our method with a DETR[7] and a FasterRCNN[34] backbone. We observe that FasterRCNN is typically performing better. In particular, the DETR backbone performs poorly on the Molecules dataset. This could be due to the small objects in the Molecules dataset. Indeed, Carion et al. [7] recommend to use DETR-DC5 or DETR-DC5-R101 for small objects instead.",
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+ "text": "5 CONCLUSIONS AND DISCUSSION",
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+ "text": "Objects detection models are a key component of machine learning deployment in the real world. However, training such models usually requires large amounts of richly annotated images that are often prohibitive for many applications. In this work, we proposed a novel approach to train object detection models by leveraging richly annotated datasets from other domains and allowing arbitrary types of weak supervision on the target domain. Our architecture relies on a probabilistic logical programming engine that efficiently blends the power of symbolic reasoning and deep learning architecture. As such, our model also inherits the current limitations from the probabilistic reasoning implementations, such as higher computational complexity. We proposed several approaches to speed-up the inference process significantly and our work will directly benefit from further advances in this field. Lastly, the versatility of probabilistic programming could help support other related tasks in the future, such as image to graph translation.",
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+ "text": "Published as a conference paper at ICLR 2023",
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+ "text": "Reproducibility Statement Details for reproducing all experiments shown in this work are available in Appendix E. More details on the datasets used in the experiments can be found in Appendix B.",
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+ "text": "ACKNOWLEDGMENTS",
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+ "text": "AA, MO and YM are funded by (1) Research Council KU Leuven: Symbiosis 4 (C14/22/125), Symbiosis3 (C14/18/092); (2) Federated cloud-based Artificial Intelligence-driven platform for liquid biopsy analyses (C3/20/100); (3) CELSA - Active Learning (CELSA/21/019); (4) European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 956832; (5) Flemish Government (FWO: SBO (S003422N), Elixir Belgium (I002819N), SB and Postdoctoral grants: S003422N, 1SB2721N, 1S98819N, 12Y5623N) and (6) VLAIO PM: Augmenting Therapeutic Effectiveness through Novel Analytics (HBC.2019.2528); (7) YM, AA, EDB, and MO are affiliated to Leuven.AI and received funding from the Flemish Government (AI Research Program). EDB is funded by a FWO-SB grant (S98819N). Computational resources and services used in this work were partly provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government - department EWI.",
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+ "text": "REFERENCES",
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+ "text": "A TRAINING DETAILS",
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+ "text": "For the hyper-parameters the idea was to stay as close as possible to the defaults of the pre-trained standard models although some lightweight tuning was done. In Table 4 a summary is given for the hyper-parameters used for the different models.",
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+ "table_body": "| Model | Type | mnist count acc. | mnist sum acc. | mnist mAP (mAP@IoU=0.5) |
| Resnet50-CAM (baseline) | In-distribution | 0.044 ± 0.041 | 0.506 ± 0.063 | 0.003 ± 0.003(0.014 ± 0.011) |
| Resnet50-CAM (baseline) | OOD | 0.01 ± 0.009 | 0.015 ± 0.004 | 0.003 ± 0.002(0.011 ± 0.007) |
| Resnet50-CAM (baseline) | Source Domain | 0.127 ± 0.132 | 0.649 ± 0.108 | 0.005 ± 0.004(0.028 ± 0.018) |
| DETR (Pre-trained) | In-distribution | 0.26 ± 0.012 | 0.262 ± 0.01 | 0.518 ± 0.014 (0.637 ± 0.017) |
| DETR (Pre-trained) | OOD | 0.173 ± 0.01 | 0.177 ± 0.009 | 0.51 ± 0.012 (0.632 ± 0.015) |
| DETR (Pre-trained) | Source Domain | 0.859 ± 0.031 | 0.86 ± 0.031 | 0.781 ± 0.009 (0.957 ± 0.008) |
| DETR (ProbKT) | In-distribution | 0.662 ± 0.064 | 0.664 ± 0.065 | 0.615 ± 0.025 (0.856 ± 0.037) |
| DETR (ProbKT) | OOD | 0.532 ± 0.083 | 0.533 ± 0.082 | 0.591 ± 0.03 (0.845 ± 0.038) |
| DETR (ProbKT) | source domain | 0.878 ± 0.023 | 0.879 ± 0.023 | 0.737 ± 0.014 (0.952 ± 0.009) |
| RCNN (Pre-trained) | In-distribution | 0.292 ± 0.005 | 0.298 ± 0.005 | 0.632 ± 0.014 (0.685 ± 0.002) |
| RCNN (Pre-trained) | OOD | 0.205 ± 0.004 | 0.212 ± 0.004 | 0.631 ± 0.013 (0.683 ± 0.002) |
| RCNN (Pre-trained) | source domain | 0.961 ± 0.008 | 0.961 ± 0.008 | 0.917 ± 0.021 (0.988 ± 0.002) |
| RCNN (ProbKT) | In-distribution | 0.902 ± 0.005 | 0.903 ± 0.005 | 0.786 ± 0.021 (0.974 ± 0.001) |
| RCNN (ProbKT) | OOD | 0.863 ± 0.008 | 0.865 ± 0.008 | 0.778 ± 0.021 (0.97 ± 0.001) |
| RCNN (ProbKT) | source domain | 0.967 ± 0.004 | 0.967 ± 0.004 | 0.873 ± 0.016 (0.989 ± 0.001) |
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+ "text": "the digits in the image) and the mean average precision (mAP) (i.e. a common object detection metric that reflects the ability to predict the positions and labels of the objects). We observe that the Resnet baseline performs poorly, lacking the necessary logic to process this dataset. We used both DETR and RCNN as object detection backbones in our experiments, showing high test accuracies when fine-tuned with our approach. As the results suggest, RCNN backbones lead to better performance than the DETR backbone.",
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+ "Table 6: Results of the SUM experiments on the MNIST object detection dataset. Reported test accuracies over the 5 folds."
+ ],
+ "table_footnote": [],
+ "table_body": "| Model | Data Domain | CLEVR count acc. | CLEVR mAP (mAP@IoU=0.5) | Mol. count. acc | Mol. mAP (mAP@IoU=0.5) |
| Resnet50-CAM | target domain | 0.97 ± 0.005 | 0.036 ± 0.014 (0.200 ± 0.071) | 0.978 ± 0.004 | 0.0 ± 0.0 (0 ± 0) |
| Resnet50-CAM | OOD | 0.831 ± 0.016 | 0.029 ± 0.010 (0.153 ± 0.044) | 0.0 ± 0.0 | n/a1 |
| Resnet50-CAM | source domain | 0.993 ± 0.003 | 0.035 ± 0.019 (0.178 ± 0.084) | 0.828 ± 0.021 | 0.0 ± 0.0 (0 ± 0) |
| WSOD-transfer | target domain | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) | 0.001 ± 0.0 | 0.018 ± 0.004 (0.061 ± 0.011) |
| WSOD-transfer | OOD | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) | 0.003 ± 0.002 | n/a1 |
| WSOD-transfer | source domain | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) | 0.0 ± 0.0 | 0.021 ± 0.003 (0.069 ± 0.009) |
| DETR-joint | target domain | 0.159 ± 0.133 | 0.579 ± 0.012 (0.684 ± 0.019) | 0.357 ± 0.196 | 0.197 ± 0.055 (0.481 ± 0.071) |
| DETR-joint | OOD | 0.084 ± 0.039 | 0.534 ± 0.012 (0.66 ± 0.012) | 0.024 ± 0.021 | n/a1 |
| DETR-joint | source dom. | 0.923 ± 0.049 | 0.908 ± 0.017 (0.992 ± 0.001) | 0.232 ± 0.127 | 0.23 ± 0.063 (0.565 ± 0.08) |
| DETR (Pre-trained) | target domain | 0.0 ± 0.0 | 0.498 ± 0.019 (0.533 ± 0.024) | 0.464 ± 0.033 | 0.314 ± 0.006 (0.542 ± 0.006) |
| DETR (Pre-trained) | OOD | 0.0 ± 0.0 | 0.477 ± 0.013 (0.531 ± 0.021) | 0.002 ± 0.001 | n/a1 |
| DETR (Pre-trained) | source domain | 0.97 ± 0.009 | 0.945 ± 0.009 (0.992 ± 0.001) | 0.581 ± 0.022 | 0.409 ± 0.005 (0.722 ± 0.004) |
| ProbKT*(DETR) | target domain | 0.949 ± 0.005 | 0.728 ± 0.014 (0.99 ± 0.003) | 0.589 ± 0.042 | 0.373 ± 0.02 (0.669 ± 0.045) |
| ProbKT*(DETR) | OOD | 0.741 ± 0.038 | 0.606 ± 0.017 (0.977 ± 0.004) | 0.008 ± 0.008 | n/a1 |
| ProbKT*(DETR) | source domain | 0.985 ± 0.004 | 0.937 ± 0.006 (0.995 ± 0.001) | 0.275 ± 0.066 | 0.371 ± 0.021 (0.649 ± 0.041) |
| ProbKT(DETR) | target domain | 0.946 ± 0.014 | 0.803 ± 0.011 (0.989 ± 0.006) | 0.508 ± 0.027 | 0.204 ± 0.02 (0.507 ± 0.014) |
| ProbKT(DETR) | OOD | 0.726 ± 0.035 | 0.715 ± 0.006 (0.974 ± 0.006) | 0.004 ± 0.003 | n/a1 |
| ProbKT(DETR) | source domain | 0.987 ± 0.003 | 0.948 ± 0.005 (0.995 ± 0.001) | 0.549 ± 0.026 | 0.38 ± 0.013 (0.713 ± 0.006) |
| RCNN (pre-trained) | target domain | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) | 0.592 ± 0.007 | 0.568 ± 0.005 (0.785 ± 0.004) |
| RCNN (pre-trained) | OOD | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) | 0.348 ± 0.036 | n/a1 |
| RCNN (pre-trained) | source domain | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) | 0.948 ± 0.004 | 0.737 ± 0.005 (0.979 ± 0.0) |
| ProbKT*(RCNN) | target domain | 0.974 ± 0.004 | 0.855 ± 0.025 (0.994 ± 0.001) | 0.945 ± 0.006 | 0.24 ± 0.042 (0.788 ± 0.073) |
| ProbKT*(RCNN) | OOD | 0.901 ± 0.017 | 0.827 ± 0.022 (0.991 ± 0.001) | 0.592 ± 0.032 | n/a1 |
| ProbKT*(RCNN) | source domain | 0.993 ± 0.002 | 0.95 ± 0.021 (0.998 ± 0.0) | 0.96 ± 0.003 | 0.655 ± 0.01 (0.974 ± 0.004) |
| ProbKT(RCNN) | target domain | 0.975 ± 0.003 | 0.856 ± 0.039 (0.993 ± 0.001) | 0.942 ± 0.009 | 0.289 ± 0.041 (0.829 ± 0.054) |
| ProbKT(RCNN) | OOD | 0.89 ± 0.022 | 0.833 ± 0.042 (0.991 ± 0.001) | 0.603 ± 0.037 | n/a1 |
| ProbKT(RCNN) | source domain | 0.995 ± 0.002 | 0.941 ± 0.041 (0.998 ± 0.001) | 0.96 ± 0.002 | 0.666 ± 0.005 (0.978 ± 0.002) |
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+ "text": "Table 7: Results of the experiments for the datasets: CLEVR-mini and Molecules. Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution.",
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+ "text": "$^{1}$ OOD test set of Molecules dataset has no bounding box labels.",
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+ "text": "18",
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+ {
+ "type": "text",
+ "text": "E SOURCE CODE AND DATASETS",
+ "text_level": 1,
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+ "page_idx": 18
+ },
+ {
+ "type": "text",
+ "text": "The source code and basic instructions are available on https://github.com/molden/ProbKT. The source code integrates features from the Weights & Biases (WandB) platform [5]. Basic features are supported without the need for an account on WandB but to make full use of all features we recommend to create an account.",
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+ {
+ "type": "text",
+ "text": "Datasets can be downloaded here:",
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+ "type": "list",
+ "sub_type": "text",
+ "list_items": [
+ "- CLEVR-mini dataset https://figshare.com/s/db012765e5a38e14ef9c",
+ "- Molecules dataset https://figshare.com/s/3dc3508d39bf4cff8c7f",
+ "- MNIST object detection dataset https://figshare.com/s/c760de026f000524db5a"
+ ],
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+ "page_idx": 18
+ },
+ {
+ "type": "text",
+ "text": "ProbLog script used in the ProbKT Probabilistic logical reasoning framework for counting of objects on an image (as on CLEVR-mini dataset):",
+ "bbox": [
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+ ],
+ "page_idx": 18
+ },
+ {
+ "type": "code",
+ "sub_type": "code",
+ "code_caption": [],
+ "code_body": ":- use_module library(lists)). \nnn(mnist_net,[X],Y,[0,1,2,3,4,5,6,7,8,9,10,11]) :: digit(X,Y). \ncount([],X,0). \ncount([X|T],X,Y):- count(T,X,Z), Y is 1+Z. \ncount([X1|T],X,Z):- X1\\=X,count(T,X,Z). \ncountall(List,X,C) :- sort(List,List1), member(X,List1), count(List,X,C). \nroll([],L,L). \nroll([H|T],A,L):- roll(T,[Y|A],L), digit(H,Y). \ncountpart(List,[],[]) \ncountpart(List,[H|T],[F|L]):- countall(List,H,F), countpart(List,T,L). \ncount.objects(X,L,C):- roll(X,[],Result), countpart(Result,L,C).",
+ "guess_lang": "prolog",
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+ "page_idx": 18
+ },
+ {
+ "type": "text",
+ "text": "The query $q$ in the case of class counts would be count.objects(X, L, C). For example an image $X$ with 1 small metal cube and 3 large rubber cylinders would result in the following query: count.objects(X, [small métal Cube, large rubber_cylinder], [1, 3]).",
+ "bbox": [
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+ "page_idx": 18
+ },
+ {
+ "type": "text",
+ "text": "ProbLog script used in the ProbKT Probabilistic logical reasoning framework for aggregating the digits on an image:",
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+ "page_idx": 18
+ },
+ {
+ "type": "code",
+ "sub_type": "code",
+ "code_caption": [],
+ "code_body": ": - use_module library(lists)). \nnn (mnist_net, [X], Y, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) :: digit(X,Y). \nsum([[], 0). \nsum([X|T], Y) : - sum(T,Z), Y is X+Z. \nroll([[], L, L). \nroll([H|T], A, L) : - roll(T, [Y|A], L), digit(H,Y). \nsum_digits(X,Y) : - roll(X, [], Result), sum(Result,Y).",
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+ "page_idx": 18
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+ {
+ "type": "text",
+ "text": "The query $q$ in the case of sum of digits would be sum_digits(X, Y). For example an image $X$ with as sum of digits 12 would result in the following query: sum_digits(X, 12).",
+ "bbox": [
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+ "page_idx": 18
+ },
+ {
+ "type": "text",
+ "text": "ProbLog script used in the ProbKT Probabilistic logical reasoning framework for taking into account non-exact counts on images",
+ "bbox": [
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+ ],
+ "page_idx": 18
+ },
+ {
+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
+ "bbox": [
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+ },
+ {
+ "type": "page_number",
+ "text": "19",
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+ "page_idx": 18
+ },
+ {
+ "type": "code",
+ "sub_type": "code",
+ "code_caption": [],
+ "code_body": "-- useModule library(lists)) ;\ninn (mnist_net, [X], Y, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) :: digit(X,Y) . . . ..\ncount([ ], X, 0 ) ;\ncount([X|T], X,Y): - count(T,X,Z), Y is 1+Z;\ncount([X|T], X,Z): - X1 $\\equiv$ X, count(T,X,Z);\ncount(, X, 0 ) ;\ncount([X|T], X,Y): - count(T,X,Z), Y is 1+Z;\ncount(, X|T], X,Z): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X |7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(，X|7)，x,C,A):- count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), $x\\text{、} C\\text{、} B\\text{、}$ ): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount (, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z)\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7),\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- Call\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- called\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- called\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- called\n\t\t\t-- call T\n\t\t\t-- called\n\t\t\t-- called\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[-X] -- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[y,-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y变压] [- roll(x,[Y变压] [- roll(x,[Y变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [-",
+ "guess_lang": "txt",
+ "bbox": [
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+ "page_idx": 19
+ },
+ {
+ "type": "text",
+ "text": "The query $q$ in the case of non exact counts of objects would be range_countobjects(X,L,C,S). For example an image $X$ with exactly one metal small cube and multiple rubber large spheres would result in the following query: range_countobjects(X,[s_metal Cube,l_rubber Sphere],[1,1],[0,1]).",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "E.1 INFERENCE EXAMPLE FOR MNIST DATASET",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "To illustrate the inference process let us follow the evaluation of the clause sum([x1, x2], 8), what can result from query sum>digits(X, 8) in case of two visible digit in the image X.",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "This clause is true if and only if $X_{1} + X_{2} = 8$ .",
+ "bbox": [
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+ ],
+ "page_idx": 19
+ },
+ {
+ "type": "text",
+ "text": "In case of MNIST digits $\\{(0,1,\\dots ,9)\\}$ enumerating the possible worlds would give the following set:",
+ "bbox": [
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+ ],
+ "page_idx": 19
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\{(0, 8), (1, 7), (2, 6), \\dots , (8, 0) \\} \\tag {3}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "After summing the probability of all possible worlds we get:",
+ "bbox": [
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+ ],
+ "page_idx": 19
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\np _ {1} (0) p _ {2} (8) + p _ {1} (1) p _ {2} (7) + \\dots + p _ {1} (0) p _ {2} (8), \\tag {4}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "where $p_1$ and $p_2$ are the distribution of random variable $X_1$ and $X_2$ respectively.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Or in a general form:",
+ "bbox": [
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+ ],
+ "page_idx": 19
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\np _ {Y} (Y) = \\sum_ {X _ {1}} p _ {1} \\left(X _ {1}\\right) p _ {2} \\left(Y - X _ {1}\\right). \\tag {5}\n$$\n",
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+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
+ "bbox": [
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+ "type": "page_number",
+ "text": "20",
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+ },
+ {
+ "type": "text",
+ "text": "As expected the distribution of the sum is the convolution of the distributions of the two terms. This observation trivially generalizes to more than two terms. The cost function corresponding to the maximum likelihood estimation is the negative log-likelihood $-\\log (p_{Y}(Y))$ .",
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+ "page_idx": 20
+ }
+]
\ No newline at end of file
diff --git a/2023/Weakly Supervised Knowledge Transfer with Probabilistic Logical Reasoning for Object Detection/95efb798-c3e3-43db-b4b3-c866d3d1db85_model.json b/2023/Weakly Supervised Knowledge Transfer with Probabilistic Logical Reasoning for Object Detection/95efb798-c3e3-43db-b4b3-c866d3d1db85_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..81e2a43f5ff16c4f5e90060c0affde19f78633c4
--- /dev/null
+++ b/2023/Weakly Supervised Knowledge Transfer with Probabilistic Logical Reasoning for Object Detection/95efb798-c3e3-43db-b4b3-c866d3d1db85_model.json
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+ "content": "WEAKLY SUPERVISED KNOWLEDGE TRANSFER WITH PROBABILISTIC LOGICAL REASONING FOR OBJECT DETECTION"
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+ "type": "title",
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+ "content": "ABSTRACT"
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+ "content": "Training object detection models usually requires instance-level annotations, such as the positions and labels of all objects present in each image. Such supervision is unfortunately not always available and, more often, only image-level information is provided, also known as weak supervision. Recent works have addressed this limitation by leveraging knowledge from a richly annotated domain. However, the scope of weak supervision supported by these approaches has been very restrictive, preventing them to use all available information. In this work, we propose ProbKT, a framework based on probabilistic logical reasoning that allows to train object detection models with arbitrary types of weak supervision. We empirically show on different datasets that using all available information is beneficial as our ProbKT leads to significant improvement on target domain and better generalization compared to existing baselines. We also showcase the ability of our approach to handle complex logic statements as supervision signal. Our code is available at https://github.com/molden/ProbKT"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "1 INTRODUCTION"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Object detection is a fundamental ability of numerous high-level machine learning pipelines such as autonomous driving [4; 16], augmented reality [42] or image retrieval [17]. However, training state-of-the-art object detection models generally requires detailed image annotations such as the box-coordinates location and the labels of each object present in each image. If several large benchmark datasets with detailed annotations are available [26; 15], providing such detailed annotation on new specific datasets comes with a significant cost that is often not affordable for many applications."
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+ "type": "text",
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+ "angle": 0,
+ "content": "More frequently, datasets come with only limited annotation, also referred to as weak supervision. This has sparked research in weakly-supervised object detection approaches [25; 6; 40], using techniques such as multiple instance learning [40] or variations of class activation maps [3]. However, these approaches have been shown to significantly underperform their fully-supervised counterparts in terms of robustness and accurate localization of the objects [39]."
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+ "type": "text",
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+ "content": "An appealing and intuitive approach to improve the performance of weakly supervised object detection is to perform transfer learning from an existing object detection model pre-trained on a fully annotated dataset [14; 46; 43]. This approach, also referred to as transfer learning or domain adaptation, consists in leveraging transferable knowledge from the pre-trained model (such as bounding boxes prediction capabilities) to the new weakly supervised domain. This transfer has been embodied in different ways in the literature. Examples include a simple fine-tuning of the classifier of bounding box proposals of the pre-trained model [43], or an iterative relabeling of the weakly supervised dataset for retraining a new full objects detection model on the re-labeled data [46]."
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+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "image",
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+ },
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+ "type": "image_caption",
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+ "angle": 0,
+ "content": "Figure 1: ProbKT: Weakly supervised knowledge transfer with probabilistic logical reasoning. (Left) A model can be trained on the source domain using full supervision (labels, positions) but only on a limited set of shapes (cylinders and spheres). (Middle) The pre-trained model does not recognize the cubes from the target domain correctly. (Right) The model can adapt to the target domain after applying ProbKT and can recognize the cubes."
+ },
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+ "type": "text",
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+ "content": "However, existing approaches are very restrictive in the type of weak supervision they are able to harness. Indeed, some do not support new object classes in the new domain [20], others can only use a label indicating the presence of an object class [46]. However, in practice, the supervision on the new domain can come in very different forms. For instance, the count of each object class can be given, such as in atom detection from molecule images where only chemical formula might be given. Or, when many objects are present on an image, a range can be provided instead of an exact class counts (e.g. \"there are at least 4 cats on this image\"). Crucially, this variety of potential supervisory signals on the target domain cannot be fully utilized by existing domain adaption approaches."
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+ "angle": 0,
+ "content": "To address this limitation, we introduce ProbKT, a novel framework that allows to generalize knowledge transfer in object detection to arbitrary types of weak supervision using neural probabilistic logical reasoning [27]. This paradigm allows to connect probabilistic outputs of neural networks with logical rules and to infer the resulting probability of particular queries. One can then evaluate the probability of a query such as \"the image contains at least two animals\" and differentiate through the probabilistic engine to train the underlying neural network. Our approach allows for arbitrarily complex logical statements and therefore supports weak supervision like class counts or ranges, among other. To our knowledge, this is the first approach to allow for such versatility in utilizing the available information on the new domain."
+ },
+ {
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+ "content": "To assess the capabilities of this framework, we provide extensive empirical analysis of multiple object detection datasets. Our approach also supports any type of objects detection backbone architecture. We thus use two popular backbone architectures, DETR [7] and RCNN [34] and evaluate their performance in terms of accuracy, convergence as well of generalization on out-of-distribution data. Our experiments show that, due to its ability to use the complete supervisory signal, our approach outperforms previous works in a wide range of setups."
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+ "content": "Key contributions: (1) We propose a novel knowledge transfer framework for object detection relying on probabilistic programming that uniquely allows using arbitrary types of weak supervision on the target domain. (2) We make our approach amenable to different levels of computational capabilities by proposing different approximations of ProbKT. (3) We provide an extensive experimental setup to study the capabilities of our framework for knowledge transfer and out-of-distribution generalization."
+ },
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+ "content": "2 RELATED WORKS"
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+ "content": "A comparative summary of related works is given in Table 1. We distinguish three main categories: (1) pure weakly supervised object detection methods (WSOD) that do not leverage a richly annotated source domain, (2) unsupervised object detection methods with knowledge transfer (DA or domain adaptation methods) that do not use supervision on the target domain and (3) weakly supervised"
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+ [
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+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "object detection methods with knowledge transfer (WSOD w/transfer) that are restrictive in the type of supported weak supervision. To our knowledge, our work is the first to allow for arbitrary supervision on the target domain (and supporting new classes in the target domain) while also leveraging knowledge from richly annotated domains. ProbKT supports arbitrary weak supervision thanks to the inherited expressiveness of Prolog [41] which is based on a subset of first-order predicate logic, Horn clauses and is Turing-complete."
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+ "content": "Weakly supervised object detection (WSOD) This class of method allows training object detection models with only weak supervision. One can thus train these approaches directly on the target domain. However, they do not allow to leverage potentially available richly annotated datasets, which has been shown to lead to worse performance [39]. Different flavors of WSOD architectures have been proposed relying on a variety of implementations such as multiple instance learning (MIL)-based [25; 40] or class activation (CAM) based [47; 3]. In contrast to WSOD methods, our approach is designed to exploit existing richly annotated datasets and thus provides increased performance on the target domain. For a comprehensive review of WSOD methods we refer the reader to Shao et al. [39]."
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+ "angle": 0,
+ "content": "Domain adaptation methods (DA) In contrast to WSOD methods, domain adaptation methods do rely on fully supervised source domain dataset. However, they do not assume any supervision on the target domain and are therefore not equipped to exploit such signal when available [37; 8; 22; 48]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "WSOD with knowledge transfer Our approach belongs to the class of weakly supervised object detection models with knowledge transfer. These methods aim to transfer knowledge from a source domain, where full supervision is available, to a target domain where only weak labels are available. Existing work in this class of models only allows for limited type of supervision of the target domain. Most architectures only support a label indicating the presence or absence of a class of object in the image[14; 46; 43]. Inoue et al. [20] allows for class counts as weak supervision but unfortunately does not allow for new classes in the target domain. In contrast, ProbKT natively allows for class counts and new classes as well as other types of weak supervision."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Neural probabilistic logical reasoning Probabilistic logical reasoning combines logic and probability theory. Favored for its high-level reasoning abilities, it was introduced as an alternative way to deep learning in the quest for artificial intelligence [10]. Statistical artificial intelligence [32; 23] and probabilistic logic programming [11] are examples of areas relying on these premises. In a unification effort, researchers have proposed hybrid architectures, embedding both deep learning and logical reasoning components [38; 35]. Our work builds upon the recent advances in the field, where combinations of deep learning, logical, and probabilistic approaches were introduced [27], allowing high-level reasoning with uncertainty using differentiable neural network architectures."
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+ "content": "| Model | Data Domain | CLEVR count acc. | CLEVR mAP (mAP@IoU=0.5) | Mol. count. acc | Mol. mAP (mAP@IoU=0.5) |
| Resnet50-CAM | target domain | 0.97 ± 0.005 | 0.036 ± 0.014 (0.200 ± 0.071) | 0.978 ± 0.004 | 0.0 ± 0.0 (0 ± 0) |
| Resnet50-CAM | OOD | 0.831 ± 0.016 | 0.029 ± 0.010 (0.153 ± 0.044) | 0.0 ± 0.0 | n/a* |
| Resnet50-CAM | source domain | 0.993 ± 0.003 | 0.035 ± 0.019 (0.178 ± 0.084) | 0.828 ± 0.021 | 0.0 ± 0.0 (0 ± 0) |
| WSOD-transfer | target domain | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) | 0.001 ± 0.0 | 0.018 ± 0.004 (0.061 ± 0.011) |
| WSOD-transfer | OOD | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) | 0.003 ± 0.002 | n/a* |
| WSOD-transfer | source domain | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) | 0.0 ± 0.0 | 0.021 ± 0.003 (0.069 ± 0.009) |
| DETR-joint | target domain | 0.159 ± 0.133 | 0.579 ± 0.012 (0.684 ± 0.019) | 0.357 ± 0.196 | 0.197 ± 0.055 (0.481 ± 0.071) |
| DETR-joint | OOD | 0.084 ± 0.039 | 0.534 ± 0.012 (0.66 ± 0.012) | 0.024 ± 0.021 | n/a* |
| DETR-joint | source dom. | 0.923 ± 0.049 | 0.908 ± 0.017 (0.992 ± 0.001) | 0.232 ± 0.127 | 0.23 ± 0.063 (0.565 ± 0.08) |
| RCNN (pre-trained) | target domain | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) | 0.592 ± 0.007 | 0.568 ± 0.005 (0.785 ± 0.004) |
| RCNN (pre-trained) | OOD | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) | 0.348 ± 0.036 | n/a* |
| RCNN (pre-trained) | source domain | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) | 0.948 ± 0.004 | 0.737 ± 0.005 (0.979 ± 0.0) |
| DETR (pre-trained) | target domain | 0.0 ± 0.0 | 0.498 ± 0.019 (0.533 ± 0.024) | 0.464 ± 0.033 | 0.314 ± 0.006 (0.542 ± 0.006) |
| DETR (pre-trained) | OOD | 0.0 ± 0.0 | 0.477 ± 0.013 (0.531 ± 0.021) | 0.002 ± 0.001 | n/a* |
| DETR (pre-trained) | source domain | 0.97 ± 0.009 | 0.945 ± 0.009 (0.992 ± 0.001) | 0.581 ± 0.022 | 0.409 ± 0.005 (0.722 ± 0.004) |
| ProbKT (DETR) | target domain | 0.946 ± 0.014 | 0.803 ± 0.011 (0.989 ± 0.006) | 0.508 ± 0.027 | 0.204 ± 0.02 (0.507 ± 0.014) |
| ProbKT (DETR) | OOD | 0.726 ± 0.035 | 0.715 ± 0.006 (0.974 ± 0.006) | 0.004 ± 0.003 | n/a* |
| ProbKT (DETR) | source domain | 0.987 ± 0.003 | 0.948 ± 0.005 (0.995 ± 0.001) | 0.549 ± 0.026 | 0.38 ± 0.013 (0.713 ± 0.006) |
| ProbKT (RCNN) | target domain | 0.975 ± 0.003 | 0.856 ± 0.039 (0.993 ± 0.001) | 0.942 ± 0.009 | 0.289 ± 0.041 (0.829 ± 0.054) |
| ProbKT (RCNN) | OOD | 0.89 ± 0.022 | 0.833 ± 0.042 (0.991 ± 0.001) | 0.603 ± 0.037 | n/a* |
| ProbKT (RCNN) | source domain | 0.995 ± 0.002 | 0.941 ± 0.041 (0.998 ± 0.001) | 0.96 ± 0.002 | 0.666 ± 0.005 (0.978 ± 0.002) |
"
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+ "content": "Table 2: Results of the experiments for the datasets: CLEVR-mini and Molecules. Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution. *: OOD test set of Molecules dataset has no bounding box labels."
+ },
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+ "content": "4.3 EVALUATION METRICS"
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+ "angle": 0,
+ "content": "We evaluate the performance of the models on the different datasets based on two criteria: the count accuracy and the objects localization performance. The count accuracy measures the ratio of correct images where all individual counts of (all detected) objects are correct. To evaluate how well the"
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+ "content": "7"
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+ ],
+ [
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+ "type": "header",
+ "bbox": [
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+ 0.48,
+ 0.049
+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "model is performing in localizing the different objects in the image we report the mean average precision (mAP) performance, a widely used metric for evaluating object detection models."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4 WEAKLY SUPERVISED KNOWLEDGE TRANSFER WITH CLASS COUNTS"
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+ "type": "text",
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+ "angle": 0,
+ "content": "We first investigate the performance of ProbKT when the weakly supervision consists of class counts only. The query \\( q \\) for each image then consists of the number of objects from each class in the image. We evaluate the models on the CLEVR-mini and Molecules datasets. For the Molecules dataset, the query for an image containing 6 carbon atoms (C), 6 oxygen atoms (O) and 12 hydrogen atoms (H) would result in the following query: \\( q = ([C,O,H],[6,6,12]) \\). These weak labels in the case of the Molecules dataset are widely and easily available in the form of the chemical formula of the molecule on the image (e.g \\( C_6H_{12}O_6 \\)). The recognition of atomic level entities on images of molecules is a challenge in the field of Optical Chemical Structure Recognition (OCSR) [9; 33; 29; 19]. For the CLEVR-mini dataset, the query for an example image containing 2 spheres, 1 cylinder and 3 cubes would be \\( q = ([\\mathrm{Cube},\\mathrm{Cylinder},\\mathrm{Sphere}],[3,1,2]) \\). Formal descriptions of the queries for each task are presented in Appendix E."
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+ "angle": 0,
+ "content": "Results of the experiments are summarized in Table 2. We observe on both datasets that ProbKT is able to transfer knowledge from the source domain to the target domain and improve count accuracy on the target domain and in most cases also on the source domain. The count accuracy increases on both the target domain and on OOD, suggesting better generalization performance. This is in contrast with Resnet50-CAM which performs well on the target domain of the Molecules dataset but fails on OOD. We also note a significant improvement in object localization (mAP) for ProbKT on the CLEVR-mini dataset. However, fine-tuning seems detrimental for mAP on the Molecules dataset. This can be explained by the very small bounding boxes in the Molecules dataset. We therefore also report the mAP@IoU=0.5 where we observe some increase in performance after fine-tuning. Lastly, we observe that our approach outperforms WSOD-transfer on all metrics for both datasets. WSOD-transfer performs well on CLEVR-mini but fails for the Molecules dataset. This can be explained by the fact that this method only supports class indicators (whether a class is present in the image), which is particularly detrimental in molecules images containing a lot of objects."
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+ "angle": 0,
+ "content": "4.5 OTHER TYPES OF WEAK SUPERVISION"
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.5.1 CLASS RANGES"
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+ "angle": 0,
+ "content": "The annotation of images is a tedious task, which limits the availability of fully annotated datasets. When the number of objects on an image is large, counting the exact number of objects of a particular class becomes too time-consuming. A typical annotation in this case consists oof class ranges where, instead of exact class counts, an interval is given for the count. For example an image from the CLEVR-mini dataset with more than 4 cubes, exactly 4 cylinders and less than 4 spheres would result in the following query: \\( q = ([\\text{cube}, \\text{cylinder}, \\text{sphere}], [[4, \\infty[, [4, 5[, [0, 4[}}) \\). We evaluate this experimental setup and report results in Table 3. We observe that ProbKT performs significantly better than WSOD-transfer on count accuracy, which still uses only presence/absence labels. We note that Resnet50-CAM is unable to use this type of supervision and is thus reported as \\( n / a \\)."
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+ "content": "| Model | Data Domain | MNIST count acc. | MNIST sum acc. | MNIST mAP (mAP@IoU=0.5) | CLEVR* count acc. | CLEVR* mAP (mAP@IoU=0.5) |
| Resnet50-CAM | target domain | 0.044 ± 0.041 | 0.506 ± 0.063 | 0.003 ± 0.003(0.014 ± 0.011) | n/a | n/a |
| Resnet50-CAM | OOD | 0.01 ± 0.009 | 0.015 ± 0.004 | 0.003 ± 0.002(0.011 ± 0.007) | n/a | n/a |
| Resnet50-CAM | source domain | 0.127 ± 0.132 | 0.649 ± 0.108 | 0.005 ± 0.004(0.028 ± 0.018) | n/a | n/a |
| WSOD-transfer | target domain | n/a | n/a | n/a | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) |
| WSOD-transfer | OOD | n/a | n/a | n/a | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) |
| WSOD-transfer | source domain | n/a | n/a | n/a | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) |
| RCNN (pre-trained) | target domain | 0.292 ± 0.005 | 0.298 ± 0.005 | 0.632 ± 0.014 (0.685 ± 0.002) | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) |
| RCNN (pre-trained) | OOD | 0.205 ± 0.004 | 0.212 ± 0.004 | 0.631 ± 0.013 (0.683 ± 0.002) | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) |
| RCNN (pre-trained) | source domain | 0.961 ± 0.008 | 0.961 ± 0.008 | 0.917 ± 0.021 (0.988 ± 0.002) | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) |
| ProbKT (RCNN) | target domain | 0.902 ± 0.005 | 0.903 ± 0.005 | 0.786 ± 0.021 (0.974 ± 0.001) | 0.971 ± 0.006 | 0.838 ± 0.034 (0.993 ± 0.001) |
| ProbKT (RCNN) | OOD | 0.863 ± 0.008 | 0.865 ± 0.008 | 0.778 ± 0.021 (0.97 ± 0.001) | 0.884 ± 0.01 | 0.812 ± 0.036 (0.991 ± 0.001) |
| ProbKT (RCNN) | source domain | 0.967 ± 0.004 | 0.967 ± 0.004 | 0.873 ± 0.016 (0.989 ± 0.001) | 0.994 ± 0.001 | 0.922 ± 0.035 (0.998 ± 0.001) |
"
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+ "content": "Table 3: Results of the experiments on the MNIST object detection dataset and on CLEVR* dataset (*CLEVR uses ranges of class counts as labels instead of exact class counts). Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution."
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+ "content": "4.5.2 COMPLEX QUERIES"
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+ "content": "More complex types of weak supervision than the ones considered above are also possible. To illustrate the capabilities of our approach, we build an MNIST object detection dataset where images show multiple digits as objects. Examples images are available in Appendix B. The weak supervision is here the sum of all digits in the image: \\( q = \\mathrm{SUM}(\\mathrm{digits}) \\). Our ProbKT can seamlessly integrate this type of supervision as shown in Table 3. As all other baselines are unable process this type of supervision, we compare against a pre-trained RCNN and a variation of Resnet50-CAM where we add an extra neural network layer that sums the individual counts to give the resulting sum. We report count accuracy, mAP and sum accuracy. The sum accuracy measures the ratio of correct images where the predicted sum (instead of the label of the digits) is correct. Details about the results on extra experiments with DETR as backbone using complex types of weak supervision can be found in Appendix D."
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+ "content": "4.6 ABLATION STUDIES"
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+ "content": "(a) CLEVR iterative relabeling"
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+ "content": "(b) Molecules iterative relabeling"
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+ "content": "(c) MNIST iterative relabeling"
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+ "content": "Figure 4: Iterative relabeling performance for the different datasets. Iteration 0: pretrained on source domain. Iteration 1: fine-tuned. Iteration 2: re-labeled and re-trained. Iteration 3: relabeled and re-trained. Iteration 4: relabeled and re-trained."
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+ "type": "text",
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+ "angle": 0,
+ "content": "Iterative relabeling. In Figure 4, we plot the evolution of the performance on the test sets after multiple rounds of fine-tuning and re-labeling, as detailed in Section 3.3.1. The final performance reported in the results tables is selected based on best relabeling iteration on the validation dataset. We observe that iterative relabeling after fine-tuning can improve performance significantly. Nevertheless, the benefit of iterative relabeling is less pronounced for DETR on the Molecules dataset. We impute it to the fact that the fine-tuned DETR model is less accurate on this dataset."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "Object detection backbone"
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "Our method can seamlessly accommodate different object detection backbones. In Table 2, we present the results for our method with a DETR[7] and a FasterRCNN[34] backbone. We observe that FasterRCNN is typically performing better. In particular, the DETR backbone performs poorly on the Molecules dataset. This could be due to the small objects in the Molecules dataset. Indeed, Carion et al. [7] recommend to use DETR-DC5 or DETR-DC5-R101 for small objects instead."
+ },
+ {
+ "type": "title",
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+ "content": "5 CONCLUSIONS AND DISCUSSION"
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+ "type": "text",
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+ "angle": 0,
+ "content": "Objects detection models are a key component of machine learning deployment in the real world. However, training such models usually requires large amounts of richly annotated images that are often prohibitive for many applications. In this work, we proposed a novel approach to train object detection models by leveraging richly annotated datasets from other domains and allowing arbitrary types of weak supervision on the target domain. Our architecture relies on a probabilistic logical programming engine that efficiently blends the power of symbolic reasoning and deep learning architecture. As such, our model also inherits the current limitations from the probabilistic reasoning implementations, such as higher computational complexity. We proposed several approaches to speed-up the inference process significantly and our work will directly benefit from further advances in this field. Lastly, the versatility of probabilistic programming could help support other related tasks in the future, such as image to graph translation."
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+ "type": "page_number",
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+ "bbox": [
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+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Reproducibility Statement Details for reproducing all experiments shown in this work are available in Appendix E. More details on the datasets used in the experiments can be found in Appendix B."
+ },
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "ACKNOWLEDGMENTS"
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+ "type": "text",
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+ "content": "AA, MO and YM are funded by (1) Research Council KU Leuven: Symbiosis 4 (C14/22/125), Symbiosis3 (C14/18/092); (2) Federated cloud-based Artificial Intelligence-driven platform for liquid biopsy analyses (C3/20/100); (3) CELSA - Active Learning (CELSA/21/019); (4) European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 956832; (5) Flemish Government (FWO: SBO (S003422N), Elixir Belgium (I002819N), SB and Postdoctoral grants: S003422N, 1SB2721N, 1S98819N, 12Y5623N) and (6) VLAIO PM: Augmenting Therapeutic Effectiveness through Novel Analytics (HBC.2019.2528); (7) YM, AA, EDB, and MO are affiliated to Leuven.AI and received funding from the Flemish Government (AI Research Program). EDB is funded by a FWO-SB grant (S98819N). Computational resources and services used in this work were partly provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government - department EWI."
+ },
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+ "angle": 0,
+ "content": "REFERENCES"
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+ [
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+ "content": "Published as a conference paper at ICLR 2023"
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+ "content": "[48] Xinge Zhu, Jiangmiao Pang, Ceyuan Yang, Jianping Shi, and Dahua Lin. Adapting object detectors via selective cross-domain alignment. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 687-696, 2019."
+ },
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+ [
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+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "A TRAINING DETAILS"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "For the hyper-parameters the idea was to stay as close as possible to the defaults of the pre-trained standard models although some lightweight tuning was done. In Table 4 a summary is given for the hyper-parameters used for the different models."
+ },
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Model | Type | mnist count acc. | mnist sum acc. | mnist mAP (mAP@IoU=0.5) |
| Resnet50-CAM (baseline) | In-distribution | 0.044 ± 0.041 | 0.506 ± 0.063 | 0.003 ± 0.003(0.014 ± 0.011) |
| Resnet50-CAM (baseline) | OOD | 0.01 ± 0.009 | 0.015 ± 0.004 | 0.003 ± 0.002(0.011 ± 0.007) |
| Resnet50-CAM (baseline) | Source Domain | 0.127 ± 0.132 | 0.649 ± 0.108 | 0.005 ± 0.004(0.028 ± 0.018) |
| DETR (Pre-trained) | In-distribution | 0.26 ± 0.012 | 0.262 ± 0.01 | 0.518 ± 0.014 (0.637 ± 0.017) |
| DETR (Pre-trained) | OOD | 0.173 ± 0.01 | 0.177 ± 0.009 | 0.51 ± 0.012 (0.632 ± 0.015) |
| DETR (Pre-trained) | Source Domain | 0.859 ± 0.031 | 0.86 ± 0.031 | 0.781 ± 0.009 (0.957 ± 0.008) |
| DETR (ProbKT) | In-distribution | 0.662 ± 0.064 | 0.664 ± 0.065 | 0.615 ± 0.025 (0.856 ± 0.037) |
| DETR (ProbKT) | OOD | 0.532 ± 0.083 | 0.533 ± 0.082 | 0.591 ± 0.03 (0.845 ± 0.038) |
| DETR (ProbKT) | source domain | 0.878 ± 0.023 | 0.879 ± 0.023 | 0.737 ± 0.014 (0.952 ± 0.009) |
| RCNN (Pre-trained) | In-distribution | 0.292 ± 0.005 | 0.298 ± 0.005 | 0.632 ± 0.014 (0.685 ± 0.002) |
| RCNN (Pre-trained) | OOD | 0.205 ± 0.004 | 0.212 ± 0.004 | 0.631 ± 0.013 (0.683 ± 0.002) |
| RCNN (Pre-trained) | source domain | 0.961 ± 0.008 | 0.961 ± 0.008 | 0.917 ± 0.021 (0.988 ± 0.002) |
| RCNN (ProbKT) | In-distribution | 0.902 ± 0.005 | 0.903 ± 0.005 | 0.786 ± 0.021 (0.974 ± 0.001) |
| RCNN (ProbKT) | OOD | 0.863 ± 0.008 | 0.865 ± 0.008 | 0.778 ± 0.021 (0.97 ± 0.001) |
| RCNN (ProbKT) | source domain | 0.967 ± 0.004 | 0.967 ± 0.004 | 0.873 ± 0.016 (0.989 ± 0.001) |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 6: Results of the SUM experiments on the MNIST object detection dataset. Reported test accuracies over the 5 folds."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "the digits in the image) and the mean average precision (mAP) (i.e. a common object detection metric that reflects the ability to predict the positions and labels of the objects). We observe that the Resnet baseline performs poorly, lacking the necessary logic to process this dataset. We used both DETR and RCNN as object detection backbones in our experiments, showing high test accuracies when fine-tuned with our approach. As the results suggest, RCNN backbones lead to better performance than the DETR backbone."
+ },
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+ "type": "table",
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+ "angle": 0,
+ "content": "| Model | Data Domain | CLEVR count acc. | CLEVR mAP (mAP@IoU=0.5) | Mol. count. acc | Mol. mAP (mAP@IoU=0.5) |
| Resnet50-CAM | target domain | 0.97 ± 0.005 | 0.036 ± 0.014 (0.200 ± 0.071) | 0.978 ± 0.004 | 0.0 ± 0.0 (0 ± 0) |
| Resnet50-CAM | OOD | 0.831 ± 0.016 | 0.029 ± 0.010 (0.153 ± 0.044) | 0.0 ± 0.0 | n/a1 |
| Resnet50-CAM | source domain | 0.993 ± 0.003 | 0.035 ± 0.019 (0.178 ± 0.084) | 0.828 ± 0.021 | 0.0 ± 0.0 (0 ± 0) |
| WSOD-transfer | target domain | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) | 0.001 ± 0.0 | 0.018 ± 0.004 (0.061 ± 0.011) |
| WSOD-transfer | OOD | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) | 0.003 ± 0.002 | n/a1 |
| WSOD-transfer | source domain | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) | 0.0 ± 0.0 | 0.021 ± 0.003 (0.069 ± 0.009) |
| DETR-joint | target domain | 0.159 ± 0.133 | 0.579 ± 0.012 (0.684 ± 0.019) | 0.357 ± 0.196 | 0.197 ± 0.055 (0.481 ± 0.071) |
| DETR-joint | OOD | 0.084 ± 0.039 | 0.534 ± 0.012 (0.66 ± 0.012) | 0.024 ± 0.021 | n/a1 |
| DETR-joint | source dom. | 0.923 ± 0.049 | 0.908 ± 0.017 (0.992 ± 0.001) | 0.232 ± 0.127 | 0.23 ± 0.063 (0.565 ± 0.08) |
| DETR (Pre-trained) | target domain | 0.0 ± 0.0 | 0.498 ± 0.019 (0.533 ± 0.024) | 0.464 ± 0.033 | 0.314 ± 0.006 (0.542 ± 0.006) |
| DETR (Pre-trained) | OOD | 0.0 ± 0.0 | 0.477 ± 0.013 (0.531 ± 0.021) | 0.002 ± 0.001 | n/a1 |
| DETR (Pre-trained) | source domain | 0.97 ± 0.009 | 0.945 ± 0.009 (0.992 ± 0.001) | 0.581 ± 0.022 | 0.409 ± 0.005 (0.722 ± 0.004) |
| ProbKT*(DETR) | target domain | 0.949 ± 0.005 | 0.728 ± 0.014 (0.99 ± 0.003) | 0.589 ± 0.042 | 0.373 ± 0.02 (0.669 ± 0.045) |
| ProbKT*(DETR) | OOD | 0.741 ± 0.038 | 0.606 ± 0.017 (0.977 ± 0.004) | 0.008 ± 0.008 | n/a1 |
| ProbKT*(DETR) | source domain | 0.985 ± 0.004 | 0.937 ± 0.006 (0.995 ± 0.001) | 0.275 ± 0.066 | 0.371 ± 0.021 (0.649 ± 0.041) |
| ProbKT(DETR) | target domain | 0.946 ± 0.014 | 0.803 ± 0.011 (0.989 ± 0.006) | 0.508 ± 0.027 | 0.204 ± 0.02 (0.507 ± 0.014) |
| ProbKT(DETR) | OOD | 0.726 ± 0.035 | 0.715 ± 0.006 (0.974 ± 0.006) | 0.004 ± 0.003 | n/a1 |
| ProbKT(DETR) | source domain | 0.987 ± 0.003 | 0.948 ± 0.005 (0.995 ± 0.001) | 0.549 ± 0.026 | 0.38 ± 0.013 (0.713 ± 0.006) |
| RCNN (pre-trained) | target domain | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) | 0.592 ± 0.007 | 0.568 ± 0.005 (0.785 ± 0.004) |
| RCNN (pre-trained) | OOD | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) | 0.348 ± 0.036 | n/a1 |
| RCNN (pre-trained) | source domain | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) | 0.948 ± 0.004 | 0.737 ± 0.005 (0.979 ± 0.0) |
| ProbKT*(RCNN) | target domain | 0.974 ± 0.004 | 0.855 ± 0.025 (0.994 ± 0.001) | 0.945 ± 0.006 | 0.24 ± 0.042 (0.788 ± 0.073) |
| ProbKT*(RCNN) | OOD | 0.901 ± 0.017 | 0.827 ± 0.022 (0.991 ± 0.001) | 0.592 ± 0.032 | n/a1 |
| ProbKT*(RCNN) | source domain | 0.993 ± 0.002 | 0.95 ± 0.021 (0.998 ± 0.0) | 0.96 ± 0.003 | 0.655 ± 0.01 (0.974 ± 0.004) |
| ProbKT(RCNN) | target domain | 0.975 ± 0.003 | 0.856 ± 0.039 (0.993 ± 0.001) | 0.942 ± 0.009 | 0.289 ± 0.041 (0.829 ± 0.054) |
| ProbKT(RCNN) | OOD | 0.89 ± 0.022 | 0.833 ± 0.042 (0.991 ± 0.001) | 0.603 ± 0.037 | n/a1 |
| ProbKT(RCNN) | source domain | 0.995 ± 0.002 | 0.941 ± 0.041 (0.998 ± 0.001) | 0.96 ± 0.002 | 0.666 ± 0.005 (0.978 ± 0.002) |
"
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+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 7: Results of the experiments for the datasets: CLEVR-mini and Molecules. Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution."
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.2,
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+ "angle": 0,
+ "content": "\\(^{1}\\)OOD test set of Molecules dataset has no bounding box labels."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "18"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.173,
+ 0.033,
+ 0.48,
+ 0.049
+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.172,
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+ ],
+ "angle": 0,
+ "content": "E SOURCE CODE AND DATASETS"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.134,
+ 0.828,
+ 0.19
+ ],
+ "angle": 0,
+ "content": "The source code and basic instructions are available on https://github.com/molden/ProbKT. The source code integrates features from the Weights & Biases (WandB) platform [5]. Basic features are supported without the need for an account on WandB but to make full use of all features we recommend to create an account."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.172,
+ 0.197,
+ 0.4,
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+ ],
+ "angle": 0,
+ "content": "Datasets can be downloaded here:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.217,
+ 0.223,
+ 0.797,
+ 0.238
+ ],
+ "angle": 0,
+ "content": "- CLEVR-mini dataset https://figshare.com/s/db012765e5a38e14ef9c"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.217,
+ 0.242,
+ 0.777,
+ 0.256
+ ],
+ "angle": 0,
+ "content": "- Molecules dataset https://figshare.com/s/3dc3508d39bf4cff8c7f"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.217,
+ 0.261,
+ 0.825,
+ 0.288
+ ],
+ "angle": 0,
+ "content": "- MNIST object detection dataset https://figshare.com/s/c760de026f000524db5a"
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ 0.223,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "ProbLog script used in the ProbKT Probabilistic logical reasoning framework for counting of objects on an image (as on CLEVR-mini dataset):"
+ },
+ {
+ "type": "code",
+ "bbox": [
+ 0.172,
+ 0.342,
+ 0.861,
+ 0.609
+ ],
+ "angle": 0,
+ "content": ":- use_module library(lists)). \nnn(mnist_net,[X],Y,[0,1,2,3,4,5,6,7,8,9,10,11]) :: digit(X,Y). \ncount([],X,0). \ncount([X|T],X,Y):- count(T,X,Z), Y is 1+Z. \ncount([X1|T],X,Z):- X1\\=X,count(T,X,Z). \ncountall(List,X,C) :- sort(List,List1), member(X,List1), count(List,X,C). \nroll([],L,L). \nroll([H|T],A,L):- roll(T,[Y|A],L), digit(H,Y). \ncountpart(List,[],[]) \ncountpart(List,[H|T],[F|L]):- countall(List,H,F), countpart(List,T,L). \ncount.objects(X,L,C):- roll(X,[],Result), countpart(Result,L,C)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "The query \\( q \\) in the case of class counts would be count.objects(X, L, C). For example an image \\( X \\) with 1 small metal cube and 3 large rubber cylinders would result in the following query: count.objects(X, [small métal Cube, large rubber_cylinder], [1, 3])."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.668,
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+ ],
+ "angle": 0,
+ "content": "ProbLog script used in the ProbKT Probabilistic logical reasoning framework for aggregating the digits on an image:"
+ },
+ {
+ "type": "code",
+ "bbox": [
+ 0.172,
+ 0.709,
+ 0.725,
+ 0.851
+ ],
+ "angle": 0,
+ "content": ": - use_module library(lists)). \nnn (mnist_net, [X], Y, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) :: digit(X,Y). \nsum([[], 0). \nsum([X|T], Y) : - sum(T,Z), Y is X+Z. \nroll([[], L, L). \nroll([H|T], A, L) : - roll(T, [Y|A], L), digit(H,Y). \nsum_digits(X,Y) : - roll(X, [], Result), sum(Result,Y)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "The query \\( q \\) in the case of sum of digits would be sum_digits(X, Y). For example an image \\( X \\) with as sum of digits 12 would result in the following query: sum_digits(X, 12)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "ProbLog script used in the ProbKT Probabilistic logical reasoning framework for taking into account non-exact counts on images"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ [
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+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
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+ ],
+ "angle": 0,
+ "content": "-- useModule library(lists)) ;\ninn (mnist_net, [X], Y, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) :: digit(X,Y) . . . ..\ncount([ ], X, 0 ) ;\ncount([X|T], X,Y): - count(T,X,Z), Y is 1+Z;\ncount([X|T], X,Z): - X1 \\(\\equiv\\) X, count(T,X,Z);\ncount(, X, 0 ) ;\ncount([X|T], X,Y): - count(T,X,Z), Y is 1+Z;\ncount(, X|T], X,Z): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X |7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(，X|7)，x,C,A):- count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), \\(x\\text{、} C\\text{、} B\\text{、}\\) ): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount (, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z)\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7),\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- Call\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- called\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- called\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- called\n\t\t\t-- call T\n\t\t\t-- called\n\t\t\t-- called\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[-X] -- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[y,-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y变压] [- roll(x,[Y变压] [- roll(x,[Y变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [-"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.588,
+ 0.825,
+ 0.646
+ ],
+ "angle": 0,
+ "content": "The query \\( q \\) in the case of non exact counts of objects would be range_countobjects(X,L,C,S). For example an image \\( X \\) with exactly one metal small cube and multiple rubber large spheres would result in the following query: range_countobjects(X,[s_metal Cube,l_rubber Sphere],[1,1],[0,1])."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.172,
+ 0.66,
+ 0.528,
+ 0.675
+ ],
+ "angle": 0,
+ "content": "E.1 INFERENCE EXAMPLE FOR MNIST DATASET"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.686,
+ 0.827,
+ 0.716
+ ],
+ "angle": 0,
+ "content": "To illustrate the inference process let us follow the evaluation of the clause sum([x1, x2], 8), what can result from query sum>digits(X, 8) in case of two visible digit in the image X."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.172,
+ 0.721,
+ 0.485,
+ 0.737
+ ],
+ "angle": 0,
+ "content": "This clause is true if and only if \\( X_{1} + X_{2} = 8 \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.743,
+ 0.825,
+ 0.771
+ ],
+ "angle": 0,
+ "content": "In case of MNIST digits \\(\\{(0,1,\\dots ,9)\\}\\) enumerating the possible worlds would give the following set:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.391,
+ 0.776,
+ 0.825,
+ 0.794
+ ],
+ "angle": 0,
+ "content": "\\[\n\\{(0, 8), (1, 7), (2, 6), \\dots , (8, 0) \\} \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.172,
+ 0.806,
+ 0.573,
+ 0.821
+ ],
+ "angle": 0,
+ "content": "After summing the probability of all possible worlds we get:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.344,
+ 0.826,
+ 0.825,
+ 0.843
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {1} (0) p _ {2} (8) + p _ {1} (1) p _ {2} (7) + \\dots + p _ {1} (0) p _ {2} (8), \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.847,
+ 0.701,
+ 0.864
+ ],
+ "angle": 0,
+ "content": "where \\( p_1 \\) and \\( p_2 \\) are the distribution of random variable \\( X_1 \\) and \\( X_2 \\) respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.172,
+ 0.869,
+ 0.316,
+ 0.884
+ ],
+ "angle": 0,
+ "content": "Or in a general form:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.38,
+ 0.888,
+ 0.825,
+ 0.922
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {Y} (Y) = \\sum_ {X _ {1}} p _ {1} \\left(X _ {1}\\right) p _ {2} \\left(Y - X _ {1}\\right). \\tag {5}\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.49,
+ 0.948,
+ 0.51,
+ 0.961
+ ],
+ "angle": 0,
+ "content": "20"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.173,
+ 0.033,
+ 0.479,
+ 0.048
+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.175,
+ 0.104,
+ 0.825,
+ 0.147
+ ],
+ "angle": 0,
+ "content": "As expected the distribution of the sum is the convolution of the distributions of the two terms. This observation trivially generalizes to more than two terms. The cost function corresponding to the maximum likelihood estimation is the negative log-likelihood \\( -\\log (p_{Y}(Y)) \\)."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.49,
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+ 0.507,
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+ ],
+ "angle": 0,
+ "content": "21"
+ }
+ ]
+]
\ No newline at end of file
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+# WEAKLY SUPERVISED KNOWLEDGE TRANSFER WITH PROBABILISTIC LOGICAL REASONING FOR OBJECT DETECTION
+
+Martijn Oldenhof
+
+ESAT-STADIUS
+
+KU Leuven, Belgium
+
+martijn. oldenhof@kuleuven.be
+
+Adam Arany
+
+ESAT-STADIUS
+
+KU Leuven, Belgium
+
+adam.arany@esat.kuleuven.be
+
+Yves Moreau
+
+ESAT-STADIUS
+
+KU Leuven, Belgium
+
+yves.moreau@esat.kuleuven.be
+
+Edward De Brouwer
+
+ESAT-STADIUS
+
+KU Leuven, Belgium
+
+edward.debrouwer@gmail.com
+
+# ABSTRACT
+
+Training object detection models usually requires instance-level annotations, such as the positions and labels of all objects present in each image. Such supervision is unfortunately not always available and, more often, only image-level information is provided, also known as weak supervision. Recent works have addressed this limitation by leveraging knowledge from a richly annotated domain. However, the scope of weak supervision supported by these approaches has been very restrictive, preventing them to use all available information. In this work, we propose ProbKT, a framework based on probabilistic logical reasoning that allows to train object detection models with arbitrary types of weak supervision. We empirically show on different datasets that using all available information is beneficial as our ProbKT leads to significant improvement on target domain and better generalization compared to existing baselines. We also showcase the ability of our approach to handle complex logic statements as supervision signal. Our code is available at https://github.com/molden/ProbKT
+
+# 1 INTRODUCTION
+
+Object detection is a fundamental ability of numerous high-level machine learning pipelines such as autonomous driving [4; 16], augmented reality [42] or image retrieval [17]. However, training state-of-the-art object detection models generally requires detailed image annotations such as the box-coordinates location and the labels of each object present in each image. If several large benchmark datasets with detailed annotations are available [26; 15], providing such detailed annotation on new specific datasets comes with a significant cost that is often not affordable for many applications.
+
+More frequently, datasets come with only limited annotation, also referred to as weak supervision. This has sparked research in weakly-supervised object detection approaches [25; 6; 40], using techniques such as multiple instance learning [40] or variations of class activation maps [3]. However, these approaches have been shown to significantly underperform their fully-supervised counterparts in terms of robustness and accurate localization of the objects [39].
+
+An appealing and intuitive approach to improve the performance of weakly supervised object detection is to perform transfer learning from an existing object detection model pre-trained on a fully annotated dataset [14; 46; 43]. This approach, also referred to as transfer learning or domain adaptation, consists in leveraging transferable knowledge from the pre-trained model (such as bounding boxes prediction capabilities) to the new weakly supervised domain. This transfer has been embodied in different ways in the literature. Examples include a simple fine-tuning of the classifier of bounding box proposals of the pre-trained model [43], or an iterative relabeling of the weakly supervised dataset for retraining a new full objects detection model on the re-labeled data [46].
+
+
+Figure 1: ProbKT: Weakly supervised knowledge transfer with probabilistic logical reasoning. (Left) A model can be trained on the source domain using full supervision (labels, positions) but only on a limited set of shapes (cylinders and spheres). (Middle) The pre-trained model does not recognize the cubes from the target domain correctly. (Right) The model can adapt to the target domain after applying ProbKT and can recognize the cubes.
+
+However, existing approaches are very restrictive in the type of weak supervision they are able to harness. Indeed, some do not support new object classes in the new domain [20], others can only use a label indicating the presence of an object class [46]. However, in practice, the supervision on the new domain can come in very different forms. For instance, the count of each object class can be given, such as in atom detection from molecule images where only chemical formula might be given. Or, when many objects are present on an image, a range can be provided instead of an exact class counts (e.g. "there are at least 4 cats on this image"). Crucially, this variety of potential supervisory signals on the target domain cannot be fully utilized by existing domain adaption approaches.
+
+To address this limitation, we introduce ProbKT, a novel framework that allows to generalize knowledge transfer in object detection to arbitrary types of weak supervision using neural probabilistic logical reasoning [27]. This paradigm allows to connect probabilistic outputs of neural networks with logical rules and to infer the resulting probability of particular queries. One can then evaluate the probability of a query such as "the image contains at least two animals" and differentiate through the probabilistic engine to train the underlying neural network. Our approach allows for arbitrarily complex logical statements and therefore supports weak supervision like class counts or ranges, among other. To our knowledge, this is the first approach to allow for such versatility in utilizing the available information on the new domain.
+
+To assess the capabilities of this framework, we provide extensive empirical analysis of multiple object detection datasets. Our approach also supports any type of objects detection backbone architecture. We thus use two popular backbone architectures, DETR [7] and RCNN [34] and evaluate their performance in terms of accuracy, convergence as well of generalization on out-of-distribution data. Our experiments show that, due to its ability to use the complete supervisory signal, our approach outperforms previous works in a wide range of setups.
+
+Key contributions: (1) We propose a novel knowledge transfer framework for object detection relying on probabilistic programming that uniquely allows using arbitrary types of weak supervision on the target domain. (2) We make our approach amenable to different levels of computational capabilities by proposing different approximations of ProbKT. (3) We provide an extensive experimental setup to study the capabilities of our framework for knowledge transfer and out-of-distribution generalization.
+
+# 2 RELATED WORKS
+
+A comparative summary of related works is given in Table 1. We distinguish three main categories: (1) pure weakly supervised object detection methods (WSOD) that do not leverage a richly annotated source domain, (2) unsupervised object detection methods with knowledge transfer (DA or domain adaptation methods) that do not use supervision on the target domain and (3) weakly supervised
+
+object detection methods with knowledge transfer (WSOD w/transfer) that are restrictive in the type of supported weak supervision. To our knowledge, our work is the first to allow for arbitrary supervision on the target domain (and supporting new classes in the target domain) while also leveraging knowledge from richly annotated domains. ProbKT supports arbitrary weak supervision thanks to the inherited expressiveness of Prolog [41] which is based on a subset of first-order predicate logic, Horn clauses and is Turing-complete.
+
+Weakly supervised object detection (WSOD) This class of method allows training object detection models with only weak supervision. One can thus train these approaches directly on the target domain. However, they do not allow to leverage potentially available richly annotated datasets, which has been shown to lead to worse performance [39]. Different flavors of WSOD architectures have been proposed relying on a variety of implementations such as multiple instance learning (MIL)-based [25; 40] or class activation (CAM) based [47; 3]. In contrast to WSOD methods, our approach is designed to exploit existing richly annotated datasets and thus provides increased performance on the target domain. For a comprehensive review of WSOD methods we refer the reader to Shao et al. [39].
+
+Domain adaptation methods (DA) In contrast to WSOD methods, domain adaptation methods do rely on fully supervised source domain dataset. However, they do not assume any supervision on the target domain and are therefore not equipped to exploit such signal when available [37; 8; 22; 48].
+
+WSOD with knowledge transfer Our approach belongs to the class of weakly supervised object detection models with knowledge transfer. These methods aim to transfer knowledge from a source domain, where full supervision is available, to a target domain where only weak labels are available. Existing work in this class of models only allows for limited type of supervision of the target domain. Most architectures only support a label indicating the presence or absence of a class of object in the image[14; 46; 43]. Inoue et al. [20] allows for class counts as weak supervision but unfortunately does not allow for new classes in the target domain. In contrast, ProbKT natively allows for class counts and new classes as well as other types of weak supervision.
+
+Neural probabilistic logical reasoning Probabilistic logical reasoning combines logic and probability theory. Favored for its high-level reasoning abilities, it was introduced as an alternative way to deep learning in the quest for artificial intelligence [10]. Statistical artificial intelligence [32; 23] and probabilistic logic programming [11] are examples of areas relying on these premises. In a unification effort, researchers have proposed hybrid architectures, embedding both deep learning and logical reasoning components [38; 35]. Our work builds upon the recent advances in the field, where combinations of deep learning, logical, and probabilistic approaches were introduced [27], allowing high-level reasoning with uncertainty using differentiable neural network architectures.
+
+| Model | Data Domain | CLEVR count acc. | CLEVR mAP (mAP@IoU=0.5) | Mol. count. acc | Mol. mAP (mAP@IoU=0.5) |
| Resnet50-CAM | target domain | 0.97 ± 0.005 | 0.036 ± 0.014 (0.200 ± 0.071) | 0.978 ± 0.004 | 0.0 ± 0.0 (0 ± 0) |
| Resnet50-CAM | OOD | 0.831 ± 0.016 | 0.029 ± 0.010 (0.153 ± 0.044) | 0.0 ± 0.0 | n/a* |
| Resnet50-CAM | source domain | 0.993 ± 0.003 | 0.035 ± 0.019 (0.178 ± 0.084) | 0.828 ± 0.021 | 0.0 ± 0.0 (0 ± 0) |
| WSOD-transfer | target domain | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) | 0.001 ± 0.0 | 0.018 ± 0.004 (0.061 ± 0.011) |
| WSOD-transfer | OOD | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) | 0.003 ± 0.002 | n/a* |
| WSOD-transfer | source domain | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) | 0.0 ± 0.0 | 0.021 ± 0.003 (0.069 ± 0.009) |
| DETR-joint | target domain | 0.159 ± 0.133 | 0.579 ± 0.012 (0.684 ± 0.019) | 0.357 ± 0.196 | 0.197 ± 0.055 (0.481 ± 0.071) |
| DETR-joint | OOD | 0.084 ± 0.039 | 0.534 ± 0.012 (0.66 ± 0.012) | 0.024 ± 0.021 | n/a* |
| DETR-joint | source dom. | 0.923 ± 0.049 | 0.908 ± 0.017 (0.992 ± 0.001) | 0.232 ± 0.127 | 0.23 ± 0.063 (0.565 ± 0.08) |
| RCNN (pre-trained) | target domain | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) | 0.592 ± 0.007 | 0.568 ± 0.005 (0.785 ± 0.004) |
| RCNN (pre-trained) | OOD | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) | 0.348 ± 0.036 | n/a* |
| RCNN (pre-trained) | source domain | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) | 0.948 ± 0.004 | 0.737 ± 0.005 (0.979 ± 0.0) |
| DETR (pre-trained) | target domain | 0.0 ± 0.0 | 0.498 ± 0.019 (0.533 ± 0.024) | 0.464 ± 0.033 | 0.314 ± 0.006 (0.542 ± 0.006) |
| DETR (pre-trained) | OOD | 0.0 ± 0.0 | 0.477 ± 0.013 (0.531 ± 0.021) | 0.002 ± 0.001 | n/a* |
| DETR (pre-trained) | source domain | 0.97 ± 0.009 | 0.945 ± 0.009 (0.992 ± 0.001) | 0.581 ± 0.022 | 0.409 ± 0.005 (0.722 ± 0.004) |
| ProbKT (DETR) | target domain | 0.946 ± 0.014 | 0.803 ± 0.011 (0.989 ± 0.006) | 0.508 ± 0.027 | 0.204 ± 0.02 (0.507 ± 0.014) |
| ProbKT (DETR) | OOD | 0.726 ± 0.035 | 0.715 ± 0.006 (0.974 ± 0.006) | 0.004 ± 0.003 | n/a* |
| ProbKT (DETR) | source domain | 0.987 ± 0.003 | 0.948 ± 0.005 (0.995 ± 0.001) | 0.549 ± 0.026 | 0.38 ± 0.013 (0.713 ± 0.006) |
| ProbKT (RCNN) | target domain | 0.975 ± 0.003 | 0.856 ± 0.039 (0.993 ± 0.001) | 0.942 ± 0.009 | 0.289 ± 0.041 (0.829 ± 0.054) |
| ProbKT (RCNN) | OOD | 0.89 ± 0.022 | 0.833 ± 0.042 (0.991 ± 0.001) | 0.603 ± 0.037 | n/a* |
| ProbKT (RCNN) | source domain | 0.995 ± 0.002 | 0.941 ± 0.041 (0.998 ± 0.001) | 0.96 ± 0.002 | 0.666 ± 0.005 (0.978 ± 0.002) |
+
+Table 2: Results of the experiments for the datasets: CLEVR-mini and Molecules. Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution. *: OOD test set of Molecules dataset has no bounding box labels.
+
+# 4.3 EVALUATION METRICS
+
+We evaluate the performance of the models on the different datasets based on two criteria: the count accuracy and the objects localization performance. The count accuracy measures the ratio of correct images where all individual counts of (all detected) objects are correct. To evaluate how well the
+
+model is performing in localizing the different objects in the image we report the mean average precision (mAP) performance, a widely used metric for evaluating object detection models.
+
+# 4.4 WEAKLY SUPERVISED KNOWLEDGE TRANSFER WITH CLASS COUNTS
+
+We first investigate the performance of ProbKT when the weakly supervision consists of class counts only. The query $q$ for each image then consists of the number of objects from each class in the image. We evaluate the models on the CLEVR-mini and Molecules datasets. For the Molecules dataset, the query for an image containing 6 carbon atoms (C), 6 oxygen atoms (O) and 12 hydrogen atoms (H) would result in the following query: $q = ([C,O,H],[6,6,12])$ . These weak labels in the case of the Molecules dataset are widely and easily available in the form of the chemical formula of the molecule on the image (e.g $C_6H_{12}O_6$ ). The recognition of atomic level entities on images of molecules is a challenge in the field of Optical Chemical Structure Recognition (OCSR) [9; 33; 29; 19]. For the CLEVR-mini dataset, the query for an example image containing 2 spheres, 1 cylinder and 3 cubes would be $q = ([\mathrm{Cube},\mathrm{Cylinder},\mathrm{Sphere}],[3,1,2])$ . Formal descriptions of the queries for each task are presented in Appendix E.
+
+Results of the experiments are summarized in Table 2. We observe on both datasets that ProbKT is able to transfer knowledge from the source domain to the target domain and improve count accuracy on the target domain and in most cases also on the source domain. The count accuracy increases on both the target domain and on OOD, suggesting better generalization performance. This is in contrast with Resnet50-CAM which performs well on the target domain of the Molecules dataset but fails on OOD. We also note a significant improvement in object localization (mAP) for ProbKT on the CLEVR-mini dataset. However, fine-tuning seems detrimental for mAP on the Molecules dataset. This can be explained by the very small bounding boxes in the Molecules dataset. We therefore also report the mAP@IoU=0.5 where we observe some increase in performance after fine-tuning. Lastly, we observe that our approach outperforms WSOD-transfer on all metrics for both datasets. WSOD-transfer performs well on CLEVR-mini but fails for the Molecules dataset. This can be explained by the fact that this method only supports class indicators (whether a class is present in the image), which is particularly detrimental in molecules images containing a lot of objects.
+
+# 4.5 OTHER TYPES OF WEAK SUPERVISION
+
+# 4.5.1 CLASS RANGES
+
+The annotation of images is a tedious task, which limits the availability of fully annotated datasets. When the number of objects on an image is large, counting the exact number of objects of a particular class becomes too time-consuming. A typical annotation in this case consists oof class ranges where, instead of exact class counts, an interval is given for the count. For example an image from the CLEVR-mini dataset with more than 4 cubes, exactly 4 cylinders and less than 4 spheres would result in the following query: $q = ([\text{cube}, \text{cylinder}, \text{sphere}], [[4, \infty[, [4, 5[, [0, 4[}})$ . We evaluate this experimental setup and report results in Table 3. We observe that ProbKT performs significantly better than WSOD-transfer on count accuracy, which still uses only presence/absence labels. We note that Resnet50-CAM is unable to use this type of supervision and is thus reported as $n / a$ .
+
+| Model | Data Domain | MNIST count acc. | MNIST sum acc. | MNIST mAP (mAP@IoU=0.5) | CLEVR* count acc. | CLEVR* mAP (mAP@IoU=0.5) |
| Resnet50-CAM | target domain | 0.044 ± 0.041 | 0.506 ± 0.063 | 0.003 ± 0.003(0.014 ± 0.011) | n/a | n/a |
| Resnet50-CAM | OOD | 0.01 ± 0.009 | 0.015 ± 0.004 | 0.003 ± 0.002(0.011 ± 0.007) | n/a | n/a |
| Resnet50-CAM | source domain | 0.127 ± 0.132 | 0.649 ± 0.108 | 0.005 ± 0.004(0.028 ± 0.018) | n/a | n/a |
| WSOD-transfer | target domain | n/a | n/a | n/a | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) |
| WSOD-transfer | OOD | n/a | n/a | n/a | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) |
| WSOD-transfer | source domain | n/a | n/a | n/a | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) |
| RCNN (pre-trained) | target domain | 0.292 ± 0.005 | 0.298 ± 0.005 | 0.632 ± 0.014 (0.685 ± 0.002) | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) |
| RCNN (pre-trained) | OOD | 0.205 ± 0.004 | 0.212 ± 0.004 | 0.631 ± 0.013 (0.683 ± 0.002) | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) |
| RCNN (pre-trained) | source domain | 0.961 ± 0.008 | 0.961 ± 0.008 | 0.917 ± 0.021 (0.988 ± 0.002) | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) |
| ProbKT (RCNN) | target domain | 0.902 ± 0.005 | 0.903 ± 0.005 | 0.786 ± 0.021 (0.974 ± 0.001) | 0.971 ± 0.006 | 0.838 ± 0.034 (0.993 ± 0.001) |
| ProbKT (RCNN) | OOD | 0.863 ± 0.008 | 0.865 ± 0.008 | 0.778 ± 0.021 (0.97 ± 0.001) | 0.884 ± 0.01 | 0.812 ± 0.036 (0.991 ± 0.001) |
| ProbKT (RCNN) | source domain | 0.967 ± 0.004 | 0.967 ± 0.004 | 0.873 ± 0.016 (0.989 ± 0.001) | 0.994 ± 0.001 | 0.922 ± 0.035 (0.998 ± 0.001) |
+
+Table 3: Results of the experiments on the MNIST object detection dataset and on CLEVR* dataset (*CLEVR uses ranges of class counts as labels instead of exact class counts). Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution.
+
+# 4.5.2 COMPLEX QUERIES
+
+More complex types of weak supervision than the ones considered above are also possible. To illustrate the capabilities of our approach, we build an MNIST object detection dataset where images show multiple digits as objects. Examples images are available in Appendix B. The weak supervision is here the sum of all digits in the image: $q = \mathrm{SUM}(\mathrm{digits})$ . Our ProbKT can seamlessly integrate this type of supervision as shown in Table 3. As all other baselines are unable process this type of supervision, we compare against a pre-trained RCNN and a variation of Resnet50-CAM where we add an extra neural network layer that sums the individual counts to give the resulting sum. We report count accuracy, mAP and sum accuracy. The sum accuracy measures the ratio of correct images where the predicted sum (instead of the label of the digits) is correct. Details about the results on extra experiments with DETR as backbone using complex types of weak supervision can be found in Appendix D.
+
+# 4.6 ABLATION STUDIES
+
+
+(a) CLEVR iterative relabeling
+
+
+Figure 4: Iterative relabeling performance for the different datasets. Iteration 0: pretrained on source domain. Iteration 1: fine-tuned. Iteration 2: re-labeled and re-trained. Iteration 3: relabeled and re-trained. Iteration 4: relabeled and re-trained.
+
+
+(b) Molecules iterative relabeling
+(c) MNIST iterative relabeling
+
+Iterative relabeling. In Figure 4, we plot the evolution of the performance on the test sets after multiple rounds of fine-tuning and re-labeling, as detailed in Section 3.3.1. The final performance reported in the results tables is selected based on best relabeling iteration on the validation dataset. We observe that iterative relabeling after fine-tuning can improve performance significantly. Nevertheless, the benefit of iterative relabeling is less pronounced for DETR on the Molecules dataset. We impute it to the fact that the fine-tuned DETR model is less accurate on this dataset.
+
+# Object detection backbone
+
+Our method can seamlessly accommodate different object detection backbones. In Table 2, we present the results for our method with a DETR[7] and a FasterRCNN[34] backbone. We observe that FasterRCNN is typically performing better. In particular, the DETR backbone performs poorly on the Molecules dataset. This could be due to the small objects in the Molecules dataset. Indeed, Carion et al. [7] recommend to use DETR-DC5 or DETR-DC5-R101 for small objects instead.
+
+# 5 CONCLUSIONS AND DISCUSSION
+
+Objects detection models are a key component of machine learning deployment in the real world. However, training such models usually requires large amounts of richly annotated images that are often prohibitive for many applications. In this work, we proposed a novel approach to train object detection models by leveraging richly annotated datasets from other domains and allowing arbitrary types of weak supervision on the target domain. Our architecture relies on a probabilistic logical programming engine that efficiently blends the power of symbolic reasoning and deep learning architecture. As such, our model also inherits the current limitations from the probabilistic reasoning implementations, such as higher computational complexity. We proposed several approaches to speed-up the inference process significantly and our work will directly benefit from further advances in this field. Lastly, the versatility of probabilistic programming could help support other related tasks in the future, such as image to graph translation.
+
+Reproducibility Statement Details for reproducing all experiments shown in this work are available in Appendix E. More details on the datasets used in the experiments can be found in Appendix B.
+
+# ACKNOWLEDGMENTS
+
+AA, MO and YM are funded by (1) Research Council KU Leuven: Symbiosis 4 (C14/22/125), Symbiosis3 (C14/18/092); (2) Federated cloud-based Artificial Intelligence-driven platform for liquid biopsy analyses (C3/20/100); (3) CELSA - Active Learning (CELSA/21/019); (4) European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 956832; (5) Flemish Government (FWO: SBO (S003422N), Elixir Belgium (I002819N), SB and Postdoctoral grants: S003422N, 1SB2721N, 1S98819N, 12Y5623N) and (6) VLAIO PM: Augmenting Therapeutic Effectiveness through Novel Analytics (HBC.2019.2528); (7) YM, AA, EDB, and MO are affiliated to Leuven.AI and received funding from the Flemish Government (AI Research Program). EDB is funded by a FWO-SB grant (S98819N). Computational resources and services used in this work were partly provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government - department EWI.
+
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+
+# A TRAINING DETAILS
+
+For the hyper-parameters the idea was to stay as close as possible to the defaults of the pre-trained standard models although some lightweight tuning was done. In Table 4 a summary is given for the hyper-parameters used for the different models.
+
+| Model | Type | mnist count acc. | mnist sum acc. | mnist mAP (mAP@IoU=0.5) |
| Resnet50-CAM (baseline) | In-distribution | 0.044 ± 0.041 | 0.506 ± 0.063 | 0.003 ± 0.003(0.014 ± 0.011) |
| Resnet50-CAM (baseline) | OOD | 0.01 ± 0.009 | 0.015 ± 0.004 | 0.003 ± 0.002(0.011 ± 0.007) |
| Resnet50-CAM (baseline) | Source Domain | 0.127 ± 0.132 | 0.649 ± 0.108 | 0.005 ± 0.004(0.028 ± 0.018) |
| DETR (Pre-trained) | In-distribution | 0.26 ± 0.012 | 0.262 ± 0.01 | 0.518 ± 0.014 (0.637 ± 0.017) |
| DETR (Pre-trained) | OOD | 0.173 ± 0.01 | 0.177 ± 0.009 | 0.51 ± 0.012 (0.632 ± 0.015) |
| DETR (Pre-trained) | Source Domain | 0.859 ± 0.031 | 0.86 ± 0.031 | 0.781 ± 0.009 (0.957 ± 0.008) |
| DETR (ProbKT) | In-distribution | 0.662 ± 0.064 | 0.664 ± 0.065 | 0.615 ± 0.025 (0.856 ± 0.037) |
| DETR (ProbKT) | OOD | 0.532 ± 0.083 | 0.533 ± 0.082 | 0.591 ± 0.03 (0.845 ± 0.038) |
| DETR (ProbKT) | source domain | 0.878 ± 0.023 | 0.879 ± 0.023 | 0.737 ± 0.014 (0.952 ± 0.009) |
| RCNN (Pre-trained) | In-distribution | 0.292 ± 0.005 | 0.298 ± 0.005 | 0.632 ± 0.014 (0.685 ± 0.002) |
| RCNN (Pre-trained) | OOD | 0.205 ± 0.004 | 0.212 ± 0.004 | 0.631 ± 0.013 (0.683 ± 0.002) |
| RCNN (Pre-trained) | source domain | 0.961 ± 0.008 | 0.961 ± 0.008 | 0.917 ± 0.021 (0.988 ± 0.002) |
| RCNN (ProbKT) | In-distribution | 0.902 ± 0.005 | 0.903 ± 0.005 | 0.786 ± 0.021 (0.974 ± 0.001) |
| RCNN (ProbKT) | OOD | 0.863 ± 0.008 | 0.865 ± 0.008 | 0.778 ± 0.021 (0.97 ± 0.001) |
| RCNN (ProbKT) | source domain | 0.967 ± 0.004 | 0.967 ± 0.004 | 0.873 ± 0.016 (0.989 ± 0.001) |
+
+the digits in the image) and the mean average precision (mAP) (i.e. a common object detection metric that reflects the ability to predict the positions and labels of the objects). We observe that the Resnet baseline performs poorly, lacking the necessary logic to process this dataset. We used both DETR and RCNN as object detection backbones in our experiments, showing high test accuracies when fine-tuned with our approach. As the results suggest, RCNN backbones lead to better performance than the DETR backbone.
+
+Table 6: Results of the SUM experiments on the MNIST object detection dataset. Reported test accuracies over the 5 folds.
+
+| Model | Data Domain | CLEVR count acc. | CLEVR mAP (mAP@IoU=0.5) | Mol. count. acc | Mol. mAP (mAP@IoU=0.5) |
| Resnet50-CAM | target domain | 0.97 ± 0.005 | 0.036 ± 0.014 (0.200 ± 0.071) | 0.978 ± 0.004 | 0.0 ± 0.0 (0 ± 0) |
| Resnet50-CAM | OOD | 0.831 ± 0.016 | 0.029 ± 0.010 (0.153 ± 0.044) | 0.0 ± 0.0 | n/a1 |
| Resnet50-CAM | source domain | 0.993 ± 0.003 | 0.035 ± 0.019 (0.178 ± 0.084) | 0.828 ± 0.021 | 0.0 ± 0.0 (0 ± 0) |
| WSOD-transfer | target domain | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) | 0.001 ± 0.0 | 0.018 ± 0.004 (0.061 ± 0.011) |
| WSOD-transfer | OOD | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) | 0.003 ± 0.002 | n/a1 |
| WSOD-transfer | source domain | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) | 0.0 ± 0.0 | 0.021 ± 0.003 (0.069 ± 0.009) |
| DETR-joint | target domain | 0.159 ± 0.133 | 0.579 ± 0.012 (0.684 ± 0.019) | 0.357 ± 0.196 | 0.197 ± 0.055 (0.481 ± 0.071) |
| DETR-joint | OOD | 0.084 ± 0.039 | 0.534 ± 0.012 (0.66 ± 0.012) | 0.024 ± 0.021 | n/a1 |
| DETR-joint | source dom. | 0.923 ± 0.049 | 0.908 ± 0.017 (0.992 ± 0.001) | 0.232 ± 0.127 | 0.23 ± 0.063 (0.565 ± 0.08) |
| DETR (Pre-trained) | target domain | 0.0 ± 0.0 | 0.498 ± 0.019 (0.533 ± 0.024) | 0.464 ± 0.033 | 0.314 ± 0.006 (0.542 ± 0.006) |
| DETR (Pre-trained) | OOD | 0.0 ± 0.0 | 0.477 ± 0.013 (0.531 ± 0.021) | 0.002 ± 0.001 | n/a1 |
| DETR (Pre-trained) | source domain | 0.97 ± 0.009 | 0.945 ± 0.009 (0.992 ± 0.001) | 0.581 ± 0.022 | 0.409 ± 0.005 (0.722 ± 0.004) |
| ProbKT*(DETR) | target domain | 0.949 ± 0.005 | 0.728 ± 0.014 (0.99 ± 0.003) | 0.589 ± 0.042 | 0.373 ± 0.02 (0.669 ± 0.045) |
| ProbKT*(DETR) | OOD | 0.741 ± 0.038 | 0.606 ± 0.017 (0.977 ± 0.004) | 0.008 ± 0.008 | n/a1 |
| ProbKT*(DETR) | source domain | 0.985 ± 0.004 | 0.937 ± 0.006 (0.995 ± 0.001) | 0.275 ± 0.066 | 0.371 ± 0.021 (0.649 ± 0.041) |
| ProbKT(DETR) | target domain | 0.946 ± 0.014 | 0.803 ± 0.011 (0.989 ± 0.006) | 0.508 ± 0.027 | 0.204 ± 0.02 (0.507 ± 0.014) |
| ProbKT(DETR) | OOD | 0.726 ± 0.035 | 0.715 ± 0.006 (0.974 ± 0.006) | 0.004 ± 0.003 | n/a1 |
| ProbKT(DETR) | source domain | 0.987 ± 0.003 | 0.948 ± 0.005 (0.995 ± 0.001) | 0.549 ± 0.026 | 0.38 ± 0.013 (0.713 ± 0.006) |
| RCNN (pre-trained) | target domain | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) | 0.592 ± 0.007 | 0.568 ± 0.005 (0.785 ± 0.004) |
| RCNN (pre-trained) | OOD | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) | 0.348 ± 0.036 | n/a1 |
| RCNN (pre-trained) | source domain | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) | 0.948 ± 0.004 | 0.737 ± 0.005 (0.979 ± 0.0) |
| ProbKT*(RCNN) | target domain | 0.974 ± 0.004 | 0.855 ± 0.025 (0.994 ± 0.001) | 0.945 ± 0.006 | 0.24 ± 0.042 (0.788 ± 0.073) |
| ProbKT*(RCNN) | OOD | 0.901 ± 0.017 | 0.827 ± 0.022 (0.991 ± 0.001) | 0.592 ± 0.032 | n/a1 |
| ProbKT*(RCNN) | source domain | 0.993 ± 0.002 | 0.95 ± 0.021 (0.998 ± 0.0) | 0.96 ± 0.003 | 0.655 ± 0.01 (0.974 ± 0.004) |
| ProbKT(RCNN) | target domain | 0.975 ± 0.003 | 0.856 ± 0.039 (0.993 ± 0.001) | 0.942 ± 0.009 | 0.289 ± 0.041 (0.829 ± 0.054) |
| ProbKT(RCNN) | OOD | 0.89 ± 0.022 | 0.833 ± 0.042 (0.991 ± 0.001) | 0.603 ± 0.037 | n/a1 |
| ProbKT(RCNN) | source domain | 0.995 ± 0.002 | 0.941 ± 0.041 (0.998 ± 0.001) | 0.96 ± 0.002 | 0.666 ± 0.005 (0.978 ± 0.002) |
+
+Table 7: Results of the experiments for the datasets: CLEVR-mini and Molecules. Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution.
+
+# E SOURCE CODE AND DATASETS
+
+The source code and basic instructions are available on https://github.com/molden/ProbKT. The source code integrates features from the Weights & Biases (WandB) platform [5]. Basic features are supported without the need for an account on WandB but to make full use of all features we recommend to create an account.
+
+Datasets can be downloaded here:
+
+- CLEVR-mini dataset https://figshare.com/s/db012765e5a38e14ef9c
+- Molecules dataset https://figshare.com/s/3dc3508d39bf4cff8c7f
+- MNIST object detection dataset https://figshare.com/s/c760de026f000524db5a
+
+ProbLog script used in the ProbKT Probabilistic logical reasoning framework for counting of objects on an image (as on CLEVR-mini dataset):
+
+```prolog
+:- use_module library(lists)).
+nn(mnist_net,[X],Y,[0,1,2,3,4,5,6,7,8,9,10,11]) :: digit(X,Y).
+count([],X,0).
+count([X|T],X,Y):- count(T,X,Z), Y is 1+Z.
+count([X1|T],X,Z):- X1\=X,count(T,X,Z).
+countall(List,X,C) :- sort(List,List1), member(X,List1), count(List,X,C).
+roll([],L,L).
+roll([H|T],A,L):- roll(T,[Y|A],L), digit(H,Y).
+countpart(List,[],[])
+countpart(List,[H|T],[F|L]):- countall(List,H,F), countpart(List,T,L).
+count.objects(X,L,C):- roll(X,[],Result), countpart(Result,L,C).
+```
+
+The query $q$ in the case of class counts would be count.objects(X, L, C). For example an image $X$ with 1 small metal cube and 3 large rubber cylinders would result in the following query: count.objects(X, [small métal Cube, large rubber_cylinder], [1, 3]).
+
+ProbLog script used in the ProbKT Probabilistic logical reasoning framework for aggregating the digits on an image:
+
+```prolog
+: - use_module library(lists)).
+nn (mnist_net, [X], Y, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) :: digit(X,Y).
+sum([[], 0).
+sum([X|T], Y) : - sum(T,Z), Y is X+Z.
+roll([[], L, L).
+roll([H|T], A, L) : - roll(T, [Y|A], L), digit(H,Y).
+sum_digits(X,Y) : - roll(X, [], Result), sum(Result,Y).
+```
+
+The query $q$ in the case of sum of digits would be sum_digits(X, Y). For example an image $X$ with as sum of digits 12 would result in the following query: sum_digits(X, 12).
+
+ProbLog script used in the ProbKT Probabilistic logical reasoning framework for taking into account non-exact counts on images
+
+```txt
+-- useModule library(lists)) ;
+inn (mnist_net, [X], Y, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) :: digit(X,Y) . . . ..
+count([ ], X, 0 ) ;
+count([X|T], X,Y): - count(T,X,Z), Y is 1+Z;
+count([X|T], X,Z): - X1 $\equiv$ X, count(T,X,Z);
+count(, X, 0 ) ;
+count([X|T], X,Y): - count(T,X,Z), Y is 1+Z;
+count(, X|T], X,Z): - count(T,X,Z);
+count(, X|T], X,C,A): - count(T,X,Z);
+count(, X|T], X,C,A): - count(T,X,Z);
+count(, X|T], X,C,A): - count(T,X,Z);
+count(, X|T], X,C,A): - count(T,X,Z);
+count(, X|T], X,C,A): - count(T,X,Z);
+count(, X|T], X,C,A): - count(T,X,Z);
+count(, X|T], x,C,A): - count(T,X,Z);
+count(, X|T], x,C,A): - count(T,X,Z);
+count(, X|T], x,C,A): - count(T,X,Z);
+count(, X|T], x,C,A): - count(T,X,Z);
+count(, X|T], x,C,A): - count(T,X,Z);
+count(, X|T], x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X |7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(，X|7)，x,C,A):- count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,A): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, X|7), $x\text{、} C\text{、} B\text{、}$ ): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, X|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count (, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z)
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,X,Z);
+count(, x|7), x,C,B): - count(T,x,Z);
+count(, x|7), x,C,B): - count(T,x,Z);
+count(, x|7), x,C,B): - count(T,x,Z);
+count(, x|7), x,C,B): - count(T,x,Z);
+count(, x|7), x,C,B): - count(T,x,Z);
+count(, x|7), x,C,B): - count(T,x,Z);
+count(, x|7), x,C,B): - call T;
+count(, x|7), x.C,B); -- call T;
+count(, x|7), x.C,B); -- call T;
+count(, x|7), x.C,B); -- call T;
+count(, x|7), x.C,B); -- call T;
+count(, x|7), x.C,B); -- call T;
+count(, x|7), x.C,B); -- call T;
+count(, x|7), x.C,B); -- call T;
+count(, x|7),
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- Call
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- called
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- called
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T;
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- call T
+ -- called
+ -- call T
+ -- called
+ -- called
+ - roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])
+ - roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])
+ - roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])
+ - roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]
+ - roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]
+ - roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]
+ - roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]
+ - roll(x,[Y],[A],[-X] -- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[y,-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y变压] [- roll(x,[Y变压] [- roll(x,[Y变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [-
+```
+
+The query $q$ in the case of non exact counts of objects would be range_countobjects(X,L,C,S). For example an image $X$ with exactly one metal small cube and multiple rubber large spheres would result in the following query: range_countobjects(X,[s_metal Cube,l_rubber Sphere],[1,1],[0,1]).
+
+# E.1 INFERENCE EXAMPLE FOR MNIST DATASET
+
+To illustrate the inference process let us follow the evaluation of the clause sum([x1, x2], 8), what can result from query sum>digits(X, 8) in case of two visible digit in the image X.
+
+This clause is true if and only if $X_{1} + X_{2} = 8$ .
+
+In case of MNIST digits $\{(0,1,\dots ,9)\}$ enumerating the possible worlds would give the following set:
+
+$$
+\{(0, 8), (1, 7), (2, 6), \dots , (8, 0) \} \tag {3}
+$$
+
+After summing the probability of all possible worlds we get:
+
+$$
+p _ {1} (0) p _ {2} (8) + p _ {1} (1) p _ {2} (7) + \dots + p _ {1} (0) p _ {2} (8), \tag {4}
+$$
+
+where $p_1$ and $p_2$ are the distribution of random variable $X_1$ and $X_2$ respectively.
+
+Or in a general form:
+
+$$
+p _ {Y} (Y) = \sum_ {X _ {1}} p _ {1} \left(X _ {1}\right) p _ {2} \left(Y - X _ {1}\right). \tag {5}
+$$
+
+As expected the distribution of the sum is the convolution of the distributions of the two terms. This observation trivially generalizes to more than two terms. The cost function corresponding to the maximum likelihood estimation is the negative log-likelihood $-\log (p_{Y}(Y))$ .
\ No newline at end of file
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+ "content": "Training object detection models usually requires instance-level annotations, such as the positions and labels of all objects present in each image. Such supervision is unfortunately not always available and, more often, only image-level information is provided, also known as weak supervision. Recent works have addressed this limitation by leveraging knowledge from a richly annotated domain. However, the scope of weak supervision supported by these approaches has been very restrictive, preventing them to use all available information. In this work, we propose ProbKT, a framework based on probabilistic logical reasoning that allows to train object detection models with arbitrary types of weak supervision. We empirically show on different datasets that using all available information is beneficial as our ProbKT leads to significant improvement on target domain and better generalization compared to existing baselines. We also showcase the ability of our approach to handle complex logic statements as supervision signal. Our code is available at https://github.com/molden/ProbKT"
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+ "content": "Object detection is a fundamental ability of numerous high-level machine learning pipelines such as autonomous driving [4; 16], augmented reality [42] or image retrieval [17]. However, training state-of-the-art object detection models generally requires detailed image annotations such as the box-coordinates location and the labels of each object present in each image. If several large benchmark datasets with detailed annotations are available [26; 15], providing such detailed annotation on new specific datasets comes with a significant cost that is often not affordable for many applications."
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+ "content": "An appealing and intuitive approach to improve the performance of weakly supervised object detection is to perform transfer learning from an existing object detection model pre-trained on a fully annotated dataset [14; 46; 43]. This approach, also referred to as transfer learning or domain adaptation, consists in leveraging transferable knowledge from the pre-trained model (such as bounding boxes prediction capabilities) to the new weakly supervised domain. This transfer has been embodied in different ways in the literature. Examples include a simple fine-tuning of the classifier of bounding box proposals of the pre-trained model [43], or an iterative relabeling of the weakly supervised dataset for retraining a new full objects detection model on the re-labeled data [46]."
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+ "content": "Figure 1: ProbKT: Weakly supervised knowledge transfer with probabilistic logical reasoning. (Left) A model can be trained on the source domain using full supervision (labels, positions) but only on a limited set of shapes (cylinders and spheres). (Middle) The pre-trained model does not recognize the cubes from the target domain correctly. (Right) The model can adapt to the target domain after applying ProbKT and can recognize the cubes."
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+ "content": "However, existing approaches are very restrictive in the type of weak supervision they are able to harness. Indeed, some do not support new object classes in the new domain [20], others can only use a label indicating the presence of an object class [46]. However, in practice, the supervision on the new domain can come in very different forms. For instance, the count of each object class can be given, such as in atom detection from molecule images where only chemical formula might be given. Or, when many objects are present on an image, a range can be provided instead of an exact class counts (e.g. \"there are at least 4 cats on this image\"). Crucially, this variety of potential supervisory signals on the target domain cannot be fully utilized by existing domain adaption approaches."
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+ "content": "To address this limitation, we introduce ProbKT, a novel framework that allows to generalize knowledge transfer in object detection to arbitrary types of weak supervision using neural probabilistic logical reasoning [27]. This paradigm allows to connect probabilistic outputs of neural networks with logical rules and to infer the resulting probability of particular queries. One can then evaluate the probability of a query such as \"the image contains at least two animals\" and differentiate through the probabilistic engine to train the underlying neural network. Our approach allows for arbitrarily complex logical statements and therefore supports weak supervision like class counts or ranges, among other. To our knowledge, this is the first approach to allow for such versatility in utilizing the available information on the new domain."
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+ "content": "To assess the capabilities of this framework, we provide extensive empirical analysis of multiple object detection datasets. Our approach also supports any type of objects detection backbone architecture. We thus use two popular backbone architectures, DETR [7] and RCNN [34] and evaluate their performance in terms of accuracy, convergence as well of generalization on out-of-distribution data. Our experiments show that, due to its ability to use the complete supervisory signal, our approach outperforms previous works in a wide range of setups."
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+ "content": "Key contributions: (1) We propose a novel knowledge transfer framework for object detection relying on probabilistic programming that uniquely allows using arbitrary types of weak supervision on the target domain. (2) We make our approach amenable to different levels of computational capabilities by proposing different approximations of ProbKT. (3) We provide an extensive experimental setup to study the capabilities of our framework for knowledge transfer and out-of-distribution generalization."
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+ "content": "A comparative summary of related works is given in Table 1. We distinguish three main categories: (1) pure weakly supervised object detection methods (WSOD) that do not leverage a richly annotated source domain, (2) unsupervised object detection methods with knowledge transfer (DA or domain adaptation methods) that do not use supervision on the target domain and (3) weakly supervised"
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+ "content": "object detection methods with knowledge transfer (WSOD w/transfer) that are restrictive in the type of supported weak supervision. To our knowledge, our work is the first to allow for arbitrary supervision on the target domain (and supporting new classes in the target domain) while also leveraging knowledge from richly annotated domains. ProbKT supports arbitrary weak supervision thanks to the inherited expressiveness of Prolog [41] which is based on a subset of first-order predicate logic, Horn clauses and is Turing-complete."
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+ "content": "Weakly supervised object detection (WSOD) This class of method allows training object detection models with only weak supervision. One can thus train these approaches directly on the target domain. However, they do not allow to leverage potentially available richly annotated datasets, which has been shown to lead to worse performance [39]. Different flavors of WSOD architectures have been proposed relying on a variety of implementations such as multiple instance learning (MIL)-based [25; 40] or class activation (CAM) based [47; 3]. In contrast to WSOD methods, our approach is designed to exploit existing richly annotated datasets and thus provides increased performance on the target domain. For a comprehensive review of WSOD methods we refer the reader to Shao et al. [39]."
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+ "content": "Domain adaptation methods (DA) In contrast to WSOD methods, domain adaptation methods do rely on fully supervised source domain dataset. However, they do not assume any supervision on the target domain and are therefore not equipped to exploit such signal when available [37; 8; 22; 48]."
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+ "content": "WSOD with knowledge transfer Our approach belongs to the class of weakly supervised object detection models with knowledge transfer. These methods aim to transfer knowledge from a source domain, where full supervision is available, to a target domain where only weak labels are available. Existing work in this class of models only allows for limited type of supervision of the target domain. Most architectures only support a label indicating the presence or absence of a class of object in the image[14; 46; 43]. Inoue et al. [20] allows for class counts as weak supervision but unfortunately does not allow for new classes in the target domain. In contrast, ProbKT natively allows for class counts and new classes as well as other types of weak supervision."
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+ "content": "Neural probabilistic logical reasoning Probabilistic logical reasoning combines logic and probability theory. Favored for its high-level reasoning abilities, it was introduced as an alternative way to deep learning in the quest for artificial intelligence [10]. Statistical artificial intelligence [32; 23] and probabilistic logic programming [11] are examples of areas relying on these premises. In a unification effort, researchers have proposed hybrid architectures, embedding both deep learning and logical reasoning components [38; 35]. Our work builds upon the recent advances in the field, where combinations of deep learning, logical, and probabilistic approaches were introduced [27], allowing high-level reasoning with uncertainty using differentiable neural network architectures."
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| Resnet50-CAM | target domain | 0.97 ± 0.005 | 0.036 ± 0.014 (0.200 ± 0.071) | 0.978 ± 0.004 | 0.0 ± 0.0 (0 ± 0) |
| Resnet50-CAM | OOD | 0.831 ± 0.016 | 0.029 ± 0.010 (0.153 ± 0.044) | 0.0 ± 0.0 | n/a* |
| Resnet50-CAM | source domain | 0.993 ± 0.003 | 0.035 ± 0.019 (0.178 ± 0.084) | 0.828 ± 0.021 | 0.0 ± 0.0 (0 ± 0) |
| WSOD-transfer | target domain | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) | 0.001 ± 0.0 | 0.018 ± 0.004 (0.061 ± 0.011) |
| WSOD-transfer | OOD | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) | 0.003 ± 0.002 | n/a* |
| WSOD-transfer | source domain | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) | 0.0 ± 0.0 | 0.021 ± 0.003 (0.069 ± 0.009) |
| DETR-joint | target domain | 0.159 ± 0.133 | 0.579 ± 0.012 (0.684 ± 0.019) | 0.357 ± 0.196 | 0.197 ± 0.055 (0.481 ± 0.071) |
| DETR-joint | OOD | 0.084 ± 0.039 | 0.534 ± 0.012 (0.66 ± 0.012) | 0.024 ± 0.021 | n/a* |
| DETR-joint | source dom. | 0.923 ± 0.049 | 0.908 ± 0.017 (0.992 ± 0.001) | 0.232 ± 0.127 | 0.23 ± 0.063 (0.565 ± 0.08) |
| RCNN (pre-trained) | target domain | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) | 0.592 ± 0.007 | 0.568 ± 0.005 (0.785 ± 0.004) |
| RCNN (pre-trained) | OOD | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) | 0.348 ± 0.036 | n/a* |
| RCNN (pre-trained) | source domain | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) | 0.948 ± 0.004 | 0.737 ± 0.005 (0.979 ± 0.0) |
| DETR (pre-trained) | target domain | 0.0 ± 0.0 | 0.498 ± 0.019 (0.533 ± 0.024) | 0.464 ± 0.033 | 0.314 ± 0.006 (0.542 ± 0.006) |
| DETR (pre-trained) | OOD | 0.0 ± 0.0 | 0.477 ± 0.013 (0.531 ± 0.021) | 0.002 ± 0.001 | n/a* |
| DETR (pre-trained) | source domain | 0.97 ± 0.009 | 0.945 ± 0.009 (0.992 ± 0.001) | 0.581 ± 0.022 | 0.409 ± 0.005 (0.722 ± 0.004) |
| ProbKT (DETR) | target domain | 0.946 ± 0.014 | 0.803 ± 0.011 (0.989 ± 0.006) | 0.508 ± 0.027 | 0.204 ± 0.02 (0.507 ± 0.014) |
| ProbKT (DETR) | OOD | 0.726 ± 0.035 | 0.715 ± 0.006 (0.974 ± 0.006) | 0.004 ± 0.003 | n/a* |
| ProbKT (DETR) | source domain | 0.987 ± 0.003 | 0.948 ± 0.005 (0.995 ± 0.001) | 0.549 ± 0.026 | 0.38 ± 0.013 (0.713 ± 0.006) |
| ProbKT (RCNN) | target domain | 0.975 ± 0.003 | 0.856 ± 0.039 (0.993 ± 0.001) | 0.942 ± 0.009 | 0.289 ± 0.041 (0.829 ± 0.054) |
| ProbKT (RCNN) | OOD | 0.89 ± 0.022 | 0.833 ± 0.042 (0.991 ± 0.001) | 0.603 ± 0.037 | n/a* |
| ProbKT (RCNN) | source domain | 0.995 ± 0.002 | 0.941 ± 0.041 (0.998 ± 0.001) | 0.96 ± 0.002 | 0.666 ± 0.005 (0.978 ± 0.002) |
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+ "content": "). The recognition of atomic level entities on images of molecules is a challenge in the field of Optical Chemical Structure Recognition (OCSR) [9; 33; 29; 19]. For the CLEVR-mini dataset, the query for an example image containing 2 spheres, 1 cylinder and 3 cubes would be "
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| Resnet50-CAM | target domain | 0.044 ± 0.041 | 0.506 ± 0.063 | 0.003 ± 0.003(0.014 ± 0.011) | n/a | n/a |
| Resnet50-CAM | OOD | 0.01 ± 0.009 | 0.015 ± 0.004 | 0.003 ± 0.002(0.011 ± 0.007) | n/a | n/a |
| Resnet50-CAM | source domain | 0.127 ± 0.132 | 0.649 ± 0.108 | 0.005 ± 0.004(0.028 ± 0.018) | n/a | n/a |
| WSOD-transfer | target domain | n/a | n/a | n/a | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) |
| WSOD-transfer | OOD | n/a | n/a | n/a | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) |
| WSOD-transfer | source domain | n/a | n/a | n/a | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) |
| RCNN (pre-trained) | target domain | 0.292 ± 0.005 | 0.298 ± 0.005 | 0.632 ± 0.014 (0.685 ± 0.002) | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) |
| RCNN (pre-trained) | OOD | 0.205 ± 0.004 | 0.212 ± 0.004 | 0.631 ± 0.013 (0.683 ± 0.002) | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) |
| RCNN (pre-trained) | source domain | 0.961 ± 0.008 | 0.961 ± 0.008 | 0.917 ± 0.021 (0.988 ± 0.002) | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) |
| ProbKT (RCNN) | target domain | 0.902 ± 0.005 | 0.903 ± 0.005 | 0.786 ± 0.021 (0.974 ± 0.001) | 0.971 ± 0.006 | 0.838 ± 0.034 (0.993 ± 0.001) |
| ProbKT (RCNN) | OOD | 0.863 ± 0.008 | 0.865 ± 0.008 | 0.778 ± 0.021 (0.97 ± 0.001) | 0.884 ± 0.01 | 0.812 ± 0.036 (0.991 ± 0.001) |
| ProbKT (RCNN) | source domain | 0.967 ± 0.004 | 0.967 ± 0.004 | 0.873 ± 0.016 (0.989 ± 0.001) | 0.994 ± 0.001 | 0.922 ± 0.035 (0.998 ± 0.001) |
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+ "content": "Iterative relabeling. In Figure 4, we plot the evolution of the performance on the test sets after multiple rounds of fine-tuning and re-labeling, as detailed in Section 3.3.1. The final performance reported in the results tables is selected based on best relabeling iteration on the validation dataset. We observe that iterative relabeling after fine-tuning can improve performance significantly. Nevertheless, the benefit of iterative relabeling is less pronounced for DETR on the Molecules dataset. We impute it to the fact that the fine-tuned DETR model is less accurate on this dataset."
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+ "content": "Our method can seamlessly accommodate different object detection backbones. In Table 2, we present the results for our method with a DETR[7] and a FasterRCNN[34] backbone. We observe that FasterRCNN is typically performing better. In particular, the DETR backbone performs poorly on the Molecules dataset. This could be due to the small objects in the Molecules dataset. Indeed, Carion et al. [7] recommend to use DETR-DC5 or DETR-DC5-R101 for small objects instead."
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+ "content": "Objects detection models are a key component of machine learning deployment in the real world. However, training such models usually requires large amounts of richly annotated images that are often prohibitive for many applications. In this work, we proposed a novel approach to train object detection models by leveraging richly annotated datasets from other domains and allowing arbitrary types of weak supervision on the target domain. Our architecture relies on a probabilistic logical programming engine that efficiently blends the power of symbolic reasoning and deep learning architecture. As such, our model also inherits the current limitations from the probabilistic reasoning implementations, such as higher computational complexity. We proposed several approaches to speed-up the inference process significantly and our work will directly benefit from further advances in this field. Lastly, the versatility of probabilistic programming could help support other related tasks in the future, such as image to graph translation."
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+ "content": "Reproducibility Statement Details for reproducing all experiments shown in this work are available in Appendix E. More details on the datasets used in the experiments can be found in Appendix B."
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+ "content": "AA, MO and YM are funded by (1) Research Council KU Leuven: Symbiosis 4 (C14/22/125), Symbiosis3 (C14/18/092); (2) Federated cloud-based Artificial Intelligence-driven platform for liquid biopsy analyses (C3/20/100); (3) CELSA - Active Learning (CELSA/21/019); (4) European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 956832; (5) Flemish Government (FWO: SBO (S003422N), Elixir Belgium (I002819N), SB and Postdoctoral grants: S003422N, 1SB2721N, 1S98819N, 12Y5623N) and (6) VLAIO PM: Augmenting Therapeutic Effectiveness through Novel Analytics (HBC.2019.2528); (7) YM, AA, EDB, and MO are affiliated to Leuven.AI and received funding from the Flemish Government (AI Research Program). EDB is funded by a FWO-SB grant (S98819N). Computational resources and services used in this work were partly provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government - department EWI."
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+ "content": "[46] Yuanyi Zhong, Jianfeng Wang, Jian Peng, and Lei Zhang. Boosting weakly supervised object detection with progressive knowledge transfer. In European conference on computer vision, pages 615-631. Springer, 2020."
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+ "content": "For the hyper-parameters the idea was to stay as close as possible to the defaults of the pre-trained standard models although some lightweight tuning was done. In Table 4 a summary is given for the hyper-parameters used for the different models."
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| Resnet50-CAM (baseline) | In-distribution | 0.044 ± 0.041 | 0.506 ± 0.063 | 0.003 ± 0.003(0.014 ± 0.011) |
| Resnet50-CAM (baseline) | OOD | 0.01 ± 0.009 | 0.015 ± 0.004 | 0.003 ± 0.002(0.011 ± 0.007) |
| Resnet50-CAM (baseline) | Source Domain | 0.127 ± 0.132 | 0.649 ± 0.108 | 0.005 ± 0.004(0.028 ± 0.018) |
| DETR (Pre-trained) | In-distribution | 0.26 ± 0.012 | 0.262 ± 0.01 | 0.518 ± 0.014 (0.637 ± 0.017) |
| DETR (Pre-trained) | OOD | 0.173 ± 0.01 | 0.177 ± 0.009 | 0.51 ± 0.012 (0.632 ± 0.015) |
| DETR (Pre-trained) | Source Domain | 0.859 ± 0.031 | 0.86 ± 0.031 | 0.781 ± 0.009 (0.957 ± 0.008) |
| DETR (ProbKT) | In-distribution | 0.662 ± 0.064 | 0.664 ± 0.065 | 0.615 ± 0.025 (0.856 ± 0.037) |
| DETR (ProbKT) | OOD | 0.532 ± 0.083 | 0.533 ± 0.082 | 0.591 ± 0.03 (0.845 ± 0.038) |
| DETR (ProbKT) | source domain | 0.878 ± 0.023 | 0.879 ± 0.023 | 0.737 ± 0.014 (0.952 ± 0.009) |
| RCNN (Pre-trained) | In-distribution | 0.292 ± 0.005 | 0.298 ± 0.005 | 0.632 ± 0.014 (0.685 ± 0.002) |
| RCNN (Pre-trained) | OOD | 0.205 ± 0.004 | 0.212 ± 0.004 | 0.631 ± 0.013 (0.683 ± 0.002) |
| RCNN (Pre-trained) | source domain | 0.961 ± 0.008 | 0.961 ± 0.008 | 0.917 ± 0.021 (0.988 ± 0.002) |
| RCNN (ProbKT) | In-distribution | 0.902 ± 0.005 | 0.903 ± 0.005 | 0.786 ± 0.021 (0.974 ± 0.001) |
| RCNN (ProbKT) | OOD | 0.863 ± 0.008 | 0.865 ± 0.008 | 0.778 ± 0.021 (0.97 ± 0.001) |
| RCNN (ProbKT) | source domain | 0.967 ± 0.004 | 0.967 ± 0.004 | 0.873 ± 0.016 (0.989 ± 0.001) |
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| Resnet50-CAM | target domain | 0.97 ± 0.005 | 0.036 ± 0.014 (0.200 ± 0.071) | 0.978 ± 0.004 | 0.0 ± 0.0 (0 ± 0) |
| Resnet50-CAM | OOD | 0.831 ± 0.016 | 0.029 ± 0.010 (0.153 ± 0.044) | 0.0 ± 0.0 | n/a1 |
| Resnet50-CAM | source domain | 0.993 ± 0.003 | 0.035 ± 0.019 (0.178 ± 0.084) | 0.828 ± 0.021 | 0.0 ± 0.0 (0 ± 0) |
| WSOD-transfer | target domain | 0.944 ± 0.004 | 0.844 ± 0.005 (0.988 ± 0.001) | 0.001 ± 0.0 | 0.018 ± 0.004 (0.061 ± 0.011) |
| WSOD-transfer | OOD | 0.73 ± 0.011 | 0.79 ± 0.005 (0.969 ± 0.001) | 0.003 ± 0.002 | n/a1 |
| WSOD-transfer | source domain | 0.989 ± 0.001 | 0.926 ± 0.001 (0.995 ± 0.0) | 0.0 ± 0.0 | 0.021 ± 0.003 (0.069 ± 0.009) |
| DETR-joint | target domain | 0.159 ± 0.133 | 0.579 ± 0.012 (0.684 ± 0.019) | 0.357 ± 0.196 | 0.197 ± 0.055 (0.481 ± 0.071) |
| DETR-joint | OOD | 0.084 ± 0.039 | 0.534 ± 0.012 (0.66 ± 0.012) | 0.024 ± 0.021 | n/a1 |
| DETR-joint | source dom. | 0.923 ± 0.049 | 0.908 ± 0.017 (0.992 ± 0.001) | 0.232 ± 0.127 | 0.23 ± 0.063 (0.565 ± 0.08) |
| DETR (Pre-trained) | target domain | 0.0 ± 0.0 | 0.498 ± 0.019 (0.533 ± 0.024) | 0.464 ± 0.033 | 0.314 ± 0.006 (0.542 ± 0.006) |
| DETR (Pre-trained) | OOD | 0.0 ± 0.0 | 0.477 ± 0.013 (0.531 ± 0.021) | 0.002 ± 0.001 | n/a1 |
| DETR (Pre-trained) | source domain | 0.97 ± 0.009 | 0.945 ± 0.009 (0.992 ± 0.001) | 0.581 ± 0.022 | 0.409 ± 0.005 (0.722 ± 0.004) |
| ProbKT*(DETR) | target domain | 0.949 ± 0.005 | 0.728 ± 0.014 (0.99 ± 0.003) | 0.589 ± 0.042 | 0.373 ± 0.02 (0.669 ± 0.045) |
| ProbKT*(DETR) | OOD | 0.741 ± 0.038 | 0.606 ± 0.017 (0.977 ± 0.004) | 0.008 ± 0.008 | n/a1 |
| ProbKT*(DETR) | source domain | 0.985 ± 0.004 | 0.937 ± 0.006 (0.995 ± 0.001) | 0.275 ± 0.066 | 0.371 ± 0.021 (0.649 ± 0.041) |
| ProbKT(DETR) | target domain | 0.946 ± 0.014 | 0.803 ± 0.011 (0.989 ± 0.006) | 0.508 ± 0.027 | 0.204 ± 0.02 (0.507 ± 0.014) |
| ProbKT(DETR) | OOD | 0.726 ± 0.035 | 0.715 ± 0.006 (0.974 ± 0.006) | 0.004 ± 0.003 | n/a1 |
| ProbKT(DETR) | source domain | 0.987 ± 0.003 | 0.948 ± 0.005 (0.995 ± 0.001) | 0.549 ± 0.026 | 0.38 ± 0.013 (0.713 ± 0.006) |
| RCNN (pre-trained) | target domain | 0.0 ± 0.0 | 0.586 ± 0.014 (0.598 ± 0.013) | 0.592 ± 0.007 | 0.568 ± 0.005 (0.785 ± 0.004) |
| RCNN (pre-trained) | OOD | 0.0 ± 0.0 | 0.582 ± 0.012 (0.603 ± 0.011) | 0.348 ± 0.036 | n/a1 |
| RCNN (pre-trained) | source domain | 0.988 ± 0.002 | 0.984 ± 0.01 (0.996 ± 0.0) | 0.948 ± 0.004 | 0.737 ± 0.005 (0.979 ± 0.0) |
| ProbKT*(RCNN) | target domain | 0.974 ± 0.004 | 0.855 ± 0.025 (0.994 ± 0.001) | 0.945 ± 0.006 | 0.24 ± 0.042 (0.788 ± 0.073) |
| ProbKT*(RCNN) | OOD | 0.901 ± 0.017 | 0.827 ± 0.022 (0.991 ± 0.001) | 0.592 ± 0.032 | n/a1 |
| ProbKT*(RCNN) | source domain | 0.993 ± 0.002 | 0.95 ± 0.021 (0.998 ± 0.0) | 0.96 ± 0.003 | 0.655 ± 0.01 (0.974 ± 0.004) |
| ProbKT(RCNN) | target domain | 0.975 ± 0.003 | 0.856 ± 0.039 (0.993 ± 0.001) | 0.942 ± 0.009 | 0.289 ± 0.041 (0.829 ± 0.054) |
| ProbKT(RCNN) | OOD | 0.89 ± 0.022 | 0.833 ± 0.042 (0.991 ± 0.001) | 0.603 ± 0.037 | n/a1 |
| ProbKT(RCNN) | source domain | 0.995 ± 0.002 | 0.941 ± 0.041 (0.998 ± 0.001) | 0.96 ± 0.002 | 0.666 ± 0.005 (0.978 ± 0.002) |
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+ "content": "Table 7: Results of the experiments for the datasets: CLEVR-mini and Molecules. Reported test accuracies over the 5 folds. Best method is in bold for each metric and data distribution."
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+ "content": "E SOURCE CODE AND DATASETS"
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+ "content": "The source code and basic instructions are available on https://github.com/molden/ProbKT. The source code integrates features from the Weights & Biases (WandB) platform [5]. Basic features are supported without the need for an account on WandB but to make full use of all features we recommend to create an account."
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+ "content": "Datasets can be downloaded here:"
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+ "content": "- CLEVR-mini dataset https://figshare.com/s/db012765e5a38e14ef9c"
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+ "content": "- Molecules dataset https://figshare.com/s/3dc3508d39bf4cff8c7f"
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+ "content": "- MNIST object detection dataset https://figshare.com/s/c760de026f000524db5a"
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+ "content": "ProbLog script used in the ProbKT Probabilistic logical reasoning framework for counting of objects on an image (as on CLEVR-mini dataset):"
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+ "content": " in the case of class counts would be count.objects(X, L, C). For example an image "
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+ "content": " with 1 small metal cube and 3 large rubber cylinders would result in the following query: count.objects(X, [small métal Cube, large rubber_cylinder], [1, 3])."
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+ "content": "ProbLog script used in the ProbKT Probabilistic logical reasoning framework for aggregating the digits on an image:"
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+ "content": ": - use_module library(lists)). \nnn (mnist_net, [X], Y, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) :: digit(X,Y). \nsum([[], 0). \nsum([X|T], Y) : - sum(T,Z), Y is X+Z. \nroll([[], L, L). \nroll([H|T], A, L) : - roll(T, [Y|A], L), digit(H,Y). \nsum_digits(X,Y) : - roll(X, [], Result), sum(Result,Y)."
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+ "content": " in the case of sum of digits would be sum_digits(X, Y). For example an image "
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+ "content": " with as sum of digits 12 would result in the following query: sum_digits(X, 12)."
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+ "content": "ProbLog script used in the ProbKT Probabilistic logical reasoning framework for taking into account non-exact counts on images"
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+ "content": "-- useModule library(lists)) ;\ninn (mnist_net, [X], Y, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) :: digit(X,Y) . . . ..\ncount([ ], X, 0 ) ;\ncount([X|T], X,Y): - count(T,X,Z), Y is 1+Z;\ncount([X|T], X,Z): - X1 "
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+ "content": " X, count(T,X,Z);\ncount(, X, 0 ) ;\ncount([X|T], X,Y): - count(T,X,Z), Y is 1+Z;\ncount(, X|T], X,Z): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], X,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|T], x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X |7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(，X|7)，x,C,A):- count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,A): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), "
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+ "content": " ): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, X|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount (, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z)\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,X,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - count(T,x,Z);\ncount(, x|7), x,C,B): - call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7), x.C,B); -- call T;\ncount(, x|7),\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- Call\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- call T;\n\t\t-- called\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- called\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T;\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- call T\n\t\t\t-- called\n\t\t\t-- call T\n\t\t\t-- called\n\t\t\t-- called\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S])\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[L],[C],[S] -- roll(x,[Y],[A],[L],[C],[S]\n\t\t\t- roll(x,[Y],[A],[-X] -- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[y,-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y],[-X] [- roll(x,[Y变压] [- roll(x,[Y变压] [- roll(x,[Y变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- roll(x变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [- rollx变压] [-"
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+ "content": " in the case of non exact counts of objects would be range_countobjects(X,L,C,S). For example an image "
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+ "content": " with exactly one metal small cube and multiple rubber large spheres would result in the following query: range_countobjects(X,[s_metal Cube,l_rubber Sphere],[1,1],[0,1])."
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+ "content": "E.1 INFERENCE EXAMPLE FOR MNIST DATASET"
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+ "content": "To illustrate the inference process let us follow the evaluation of the clause sum([x1, x2], 8), what can result from query sum>digits(X, 8) in case of two visible digit in the image X."
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+ "content": " enumerating the possible worlds would give the following set:"
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diff --git a/2023/Weakly-supervised HOI Detection via Prior-guided Bi-level Representation Learning/b2c89086-3efa-4d35-8fb8-fa570d2c2733_content_list.json b/2023/Weakly-supervised HOI Detection via Prior-guided Bi-level Representation Learning/b2c89086-3efa-4d35-8fb8-fa570d2c2733_content_list.json
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+ {
+ "type": "text",
+ "text": "WEAKLY-SUPERVISED HOI DETECTION VIA PRIOR-GUIDED BI-LEVEL REPRESENTATION LEARNING",
+ "text_level": 1,
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+ "text": "Bo Wan $^{1,*}$ , Yongfei Liu $^{2*}$ , Desen Zhou $^{2}$ , Tinne Tuytelaars $^{1}$ , Xuming He $^{2,3}$",
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+ "text": "$^{1}$ KU Leuven, Leuven, Belgium; $^{2}$ ShanghaiTech University, Shanghai, China \n $^{3}$ Shanghai Engineering Research Center of Intelligent Vision and Imaging {bwan, tinne.tuytelaars}@esat.kuleuven.be {liuyf3,zhouds,hexm}@shanghaitech.edu.cn",
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+ "text": "ABSTRACT",
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+ {
+ "type": "text",
+ "text": "Human object interaction (HOI) detection plays a crucial role in human-centric scene understanding and serves as a fundamental building-block for many vision tasks. One generalizable and scalable strategy for HOI detection is to use weak supervision, learning from image-level annotations only. This is inherently challenging due to ambiguous human-object associations, large search space of detecting HOIs and highly noisy training signal. A promising strategy to address those challenges is to exploit knowledge from large-scale pretrained models (e.g., CLIP), but a direct knowledge distillation strategy (Liao et al., 2022) does not perform well on the weakly-supervised setting. In contrast, we develop a CLIP-guided HOI representation capable of incorporating the prior knowledge at both image level and HOI instance level, and adopt a self-taught mechanism to prune incorrect human-object associations. Experimental results on HICO-DET and V-COCO show that our method outperforms the previous works by a sizable margin, showing the efficacy of our HOI representation.",
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+ "type": "text",
+ "text": "1 INTRODUCTION",
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+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Human object interaction detection aims to simultaneously localize the human-object regions in an image and to classify their interactions, which serves as a fundamental building-block in a wide range of tasks in human-centric artificial intelligence, such as human activity recognition (Heilbron et al., 2015; Tina et al., 2021), human motion tracking (Wafae et al., 2019; Nishimura et al., 2021) and anomalous behavior detection (Liu et al., 2018; Pang et al., 2020).",
+ "bbox": [
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+ "text": "Usually, HOI detection adopts a supervised learning paradigm (Gupta & Malik, 2015; Chao et al., 2018; Wan et al., 2019; Gao et al., 2020; Zhang et al., 2021c). This requires detailed annotations (i.e. human and object bounding boxes and their interaction types) in the training stage. However, such HOI annotations are expensive to collect and prone to labeling errors. In contrast, it is much easier to acquire image-level descriptions of target scenes. Consequently, a more scalable strategy for HOI detection is to learn from weak annotations at the image level, known as weakly-supervised HOI detection (Zhang et al., 2017). Learning under such weak supervision is particularly challenging mainly due to the lack of accurate visual-semantic associations, large search space of detecting HOIs and highly noisy training signal from only image level supervision.",
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+ {
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+ "text": "Most existing works (Zhang et al., 2017; Baldassarre et al., 2020; Kumaraswamy et al., 2021) attempt to tackle the weakly-supervised HOI detection in a Multiple Instance Learning (MIL) framework (Ilse et al., 2018). They first utilize an object detector to generate human-object proposals and then train an interaction classifier with image-level labels as supervision. Despite promising results, these methods suffer from several weaknesses when coping with diverse and fine-grained HOIs. Firstly, they usually rely on visual representations derived from the external object detector, which mainly focus on the semantic concepts of the objects in the scene and hence are insufficient for capturing the concept of fine-grained interactions. Secondly, as the image-level supervision tends to ignore the imbalance in HOI classes, their representation learning is more susceptible to the dataset bias and dominated by frequent interaction classes. Finally, these methods learn the HOI concepts from a candidate set generated by pairing up all the human and object proposals, which is highly noisy and often leads to erroneous human-object associations for many interaction classes.",
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+ "type": "page_footnote",
+ "text": "*Equal Contribution. Code is available at https://github.com/bobwan1995/Weakly-HOI.",
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+ "type": "text",
+ "text": "To address the aforementioned limitations, we introduce a new weakly-supervised HOI detection strategy. It aims to incorporate the prior knowledge from pretrained foundation models to facilitate the HOI learning. In particular, we propose to integrate CLIP (Radford et al., 2021b), a large-scale vision-language pretrained model. This allows us to exploit the strong generalization capability of the CLIP representation for learning a better HOI representation under weak supervision. Compared to the representations learned by the object detector, the CLIP representations are inherently less object-centric, hence more likely to incorporate also aspects about the human-object interaction, as evidenced by Appendix A. Although a few works have successfully exploited CLIP for supervised HOI detection in the past, experimentally we find they do not perform well in the more challenging weakly-supervised setting (c.f. Appendix.B). We hypothesize this is because they only transfer knowledge at image level, and fail without supervision at the level of human-object pairs.",
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+ "text": "To this end, we develop a CLIP-guided HOI representation capable of incorporating the prior knowledge of HOIs at two different levels. First, at the image level, we utilize the visual and linguistic embeddings of the CLIP model to build a global HOI knowledge bank and generate image-level HOI predictions. In addition, for each human-object pair, we enrich the region-based HOI features by the HOI representations in the knowledge bank via a novel attention mechanism. Such a bi-level framework enables us to exploit the image-level supervision more effectively through the shared HOI knowledge bank, and to enhance the interaction feature learning by introducing the visual and text representations of the CLIP model.",
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+ "type": "text",
+ "text": "We instantiate our bi-level knowledge integration strategy as a modular deep neural network with a global and local branch. Given the human-object proposals generated by an off-the-shelf object detector, the global branch starts with a backbone network to compute image feature maps, which are used by a subsequent HOI recognition network to predict the image-wise HOI scores. The local branch builds a knowledge transfer network to extract the human-object features and augment them with the CLIP-guided knowledge bank, followed by a pairwise classification network to compute their relatedness and interaction scores| Methods | Backbone | Detector | HICO-DET (%) | V-COCO (%) |
| Full | Rare | Non-Rare | AProle | AProle |
| supervised |
| iCAN (Gao et al., 2018) | RN50 (IN-1K&COCO) | FRCNN (COCO) | 14.84 | 10.45 | 16.15 | 45.30 | 52.40 |
| PMFNet (Wan et al., 2019) | RN50-FPN (IN-1K&COCO) | FRCNN (COCO) | 17.46 | 15.56 | 18.00 | 52.00 | - |
| TIN (Li et al., 2019b) | RN50-FPN (IN-1K&COCO) | FRCNN (COCO) | 17.22 | 13.51 | 18.32 | 47.80 | 54.20 |
| DJ-RN (Li et al., 2020a) | RN50 (IN-1K&COCO) | FRCNN (COCO) | 21.34 | 18.53 | 21.18 | 53.30 | 60.30 |
| IDN (Li et al., 2020b) | RN50 (IN-1K&COCO) | FRCNN (HICO-DET) | 26.29 | 22.61 | 27.39 | 53.30 | 60.30 |
| SCG (Zhang et al., 2021c) | RN50-FPN (IN-1K&HICO-DET) | FRCNN (HICO-DET) | 31.33 | 24.72 | 33.31 | 54.20 | 60.90 |
| HOTR (Kim et al., 2021) | RN50+Transformer (IN-1K&COCO) | DETR (HICO-DET) | 25.10 | 17.34 | 27.42 | 55.20 | 64.40 |
| QPIC (Tamura et al., 2021) | RN101+Transformer (IN-1K&COCO) | DETR (COCO) | 29.90 | 23.92 | 31.69 | 58.30 | 60.70 |
| CATN (Dong et al., 2022) | RN50+Transformer (IN-1K&HICO-DET&COCO) | DETR (HICO-DET) | 31.86 | 25.15 | 33.84 | 60.10 | - |
| MSTR (Kim et al., 2022) | RN50 + Transformer (IN-1K&COCO) | DETR(HICO-DET) | 31.17 | 25.31 | 33.92 | 62.00 | 65.20 |
| DisTr (Zhou et al., 2022) | RN50+Transformer (IN-1K&COCO) | DETR (HICO-DET) | 31.75 | 27.45 | 33.03 | 66.20 | 68.50 |
| SSRT (Iftekhar et al., 2022) | R101+Transformer (IN-1K&COCO) | DETR (COCO) | 31.34 | 24.31 | 33.32 | 65.00 | 67.10 |
| GEN-VLKT (Liao et al., 2022) | RN101+Transformer (IN-1K&HICO-DET) | DETR (HICO-DET) | 34.95 | 31.18 | 36.08 | 63.58 | 65.93 |
| between supervised & weakly-supervised setting, learning with image-level HOIs and box annotations |
| AlignFormer (Kilickaya & Smeulders, 2021) | RN101+Transformer (IN-1K&HICO-DET) | DETR (HICO-DET) | 20.85 | 18.23 | 21.64 | 15.82 | 16.34 |
| weakly-supervised |
| Explanation-HOI* (Baldassarre et al., 2020) | ResNeXt101 (IN-1K&COCO) | FRCNN (COCO) | 10.63 | 8.71 | 11.20 | - | - |
| MX-HOI (Kumaraswamy et al., 2021) | RN101 (IN-1K&COCO) | FRCNN (COCO) | 16.14 | 12.06 | 17.50 | - | - |
| PPR-FCN† (Zhang et al., 2017) | RN50 (CLIP dataset) | FRCNN (COCO) | 17.55 | 15.69 | 18.41 | - | - |
| ours | RN50 (CLIP dataset) | FRCNN (COCO) | 22.89 | 22.41 | 23.03 | 42.97 | 48.06 |
| ours | RN101 (CLIP dataset) | FRCNN (COCO) | 25.70 | 24.52 | 26.05 | 44.74 | 49.97 |
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+ "type": "text",
+ "text": "4 EXPERIMENTS",
+ "text_level": 1,
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+ "text": "4.1 EXPERIMENTAL SETUP",
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+ "text": "Datasets: We benchmark our model on two public datasets: HICO-DET and V-COCO. HICO-DET consists of 47776 images (38118 for training and 9658 for test). It has $N = 600$ HOI categories, which are composed of $C = 80$ common objects (the same as MSCOCO (Lin et al., 2014)) and $A = 117$ unique interaction categories. V-COCO is a subset of MSCOCO, consisting of 2533 images for training, 2867 for validation and 4946 for test. It has 16199 human instances, each annotated with binary labels for $A = 26$ interaction categories.",
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+ "text": "Evaluation Metric: Following (Chao et al., 2015), we use mean average precision (mAP) to evaluate HOI detection performance. A human-object pair is considered as positive when both predicted human and object boxes have at least 0.5 IoU with their ground-truth boxes, and the HOI class is classified correctly.",
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+ "text": "We use an off-the-shelf Faster R-CNN (Ren et al., 2015) pretrained on MSCOCO to generate at most 100 object candidates for each image. For V-COCO, it is worth noting that we train the object detector by removing the images in MSCOCO that overlap with V-COCO to prevent information leakage. The backbone network is initialized with the visual encoder from CLIP-RN101 model and the feature dimension $D = 1024$ .",
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+ "text": "For model learning, we set the detection score weight $\\gamma = 2.8$ as default by following previous works (Zhang et al., 2021c; Li et al., 2019b), then optimize the entire network with AdamW and an initial learning rate of 1e-5 for backbone parameters and 1e-4 for others. We detach the parameters of the knowledge bank on the local branch for better model learning. We train up to 60K iterations with batch-size 24 in each on 4 NVIDIA 2080TI GPUs, and decay the learning rate by 10 times in 12K and 24K iteration.",
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+ "text": "For HICO-DET (Tab.1), our approach outperforms the previous state of the arts on the weakly supervised setting by a clear margin, achieving 22.89 mAP with ResNet-50 and 25.70 mAP with ResNet-101 as backbone. For a fair comparison, we also re-implement PPR-FCN with CLIP visual encoder. The results show that we still outperform PPR-FCN by a sizeable margin, which validates the superiority of our framework. Besides, we even perform comparably with HOTR and IDN under an inferior experimental setting where HOTR adopts a more advanced transformer encoder-decoder architecture, and both methods are trained with strong supervision. Furthermore, the mAP gap between Rare (training annotations $< 10$ ) and Non-rare HOI classes in our results is much smaller than other methods, demonstrating the superior generalization capability of our HOI representation for solving the long-tailed distribution issue. In detail, we achieve a 0.62 mAP gap with ResNet-50",
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+ "Table 2: Ablation study on HICO-DET dataset. \"RN50-FPN(COCO)\" denotes the backbone initialized with Faster R-CNN parameters pretrained on MSCOCO dataset while \"CLIP RN50\" stands for the backbone initialized with CLIP visual encoder. Besides, we construct the knowledge bank $\\mathcal{W}_T$ with random initialization, or computing HOI prompts by RoBERTa or CLIP text transformer."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods | Backbone | Detector | HICO-DET (%) | V-COCO (%) |
| Full | Rare | Non-Rare | AProle | AProle |
| supervised |
| iCAN (Gao et al., 2018) | RN50 (IN-1K&COCO) | FRCNN (COCO) | 14.84 | 10.45 | 16.15 | 45.30 | 52.40 |
| PMFNet (Wan et al., 2019) | RN50-FPN (IN-1K&COCO) | FRCNN (COCO) | 17.46 | 15.56 | 18.00 | 52.00 | - |
| TIN (Li et al., 2019b) | RN50-FPN (IN-1K&COCO) | FRCNN (COCO) | 17.22 | 13.51 | 18.32 | 47.80 | 54.20 |
| DJ-RN (Li et al., 2020a) | RN50 (IN-1K&COCO) | FRCNN (COCO) | 21.34 | 18.53 | 21.18 | 53.30 | 60.30 |
| IDN (Li et al., 2020b) | RN50 (IN-1K&COCO) | FRCNN (HICO-DET) | 26.29 | 22.61 | 27.39 | 53.30 | 60.30 |
| SCG (Zhang et al., 2021c) | RN50-FPN (IN-1K&HICO-DET) | FRCNN (HICO-DET) | 31.33 | 24.72 | 33.31 | 54.20 | 60.90 |
| HOTR (Kim et al., 2021) | RN50+Transformer (IN-1K&COCO) | DETR (HICO-DET) | 25.10 | 17.34 | 27.42 | 55.20 | 64.40 |
| QPIC (Tamura et al., 2021) | RN101+Transformer (IN-1K&COCO) | DETR (COCO) | 29.90 | 23.92 | 31.69 | 58.30 | 60.70 |
| CATN (Dong et al., 2022) | RN50+Transformer (IN-1K&HICO-DET&COCO) | DETR (HICO-DET) | 31.86 | 25.15 | 33.84 | 60.10 | - |
| MSTR (Kim et al., 2022) | RN50 + Transformer (IN-1K&COCO) | DETR(HICO-DET) | 31.17 | 25.31 | 33.92 | 62.00 | 65.20 |
| DisTr (Zhou et al., 2022) | RN50+Transformer (IN-1K&COCO) | DETR (HICO-DET) | 31.75 | 27.45 | 33.03 | 66.20 | 68.50 |
| SSRT (Iftekhar et al., 2022) | R101+Transformer (IN-1K&COCO) | DETR (COCO) | 31.34 | 24.31 | 33.32 | 65.00 | 67.10 |
| GEN-VLKT (Liao et al., 2022) | RN101+Transformer (IN-1K&HICO-DET) | DETR (HICO-DET) | 34.95 | 31.18 | 36.08 | 63.58 | 65.93 |
| between supervised & weakly-supervised setting, learning with image-level HOIs and box annotations |
| AlignFormer (Kilickaya & Smeulders, 2021) | RN101+Transformer (IN-1K&HICO-DET) | DETR (HICO-DET) | 20.85 | 18.23 | 21.64 | 15.82 | 16.34 |
| weakly-supervised |
| Explanation-HOI* (Baldassarre et al., 2020) | ResNeXt101 (IN-1K&COCO) | FRCNN (COCO) | 10.63 | 8.71 | 11.20 | - | - |
| MX-HOI (Kumaraswamy et al., 2021) | RN101 (IN-1K&COCO) | FRCNN (COCO) | 16.14 | 12.06 | 17.50 | - | - |
| PPR-FCN† (Zhang et al., 2017) | RN50 (CLIP dataset) | FRCNN (COCO) | 17.55 | 15.69 | 18.41 | - | - |
| ours | RN50 (CLIP dataset) | FRCNN (COCO) | 22.89 | 22.41 | 23.03 | 42.97 | 48.06 |
| ours | RN101 (CLIP dataset) | FRCNN (COCO) | 25.70 | 24.52 | 26.05 | 44.74 | 49.97 |
"
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+ "content": "Datasets: We benchmark our model on two public datasets: HICO-DET and V-COCO. HICO-DET consists of 47776 images (38118 for training and 9658 for test). It has \\( N = 600 \\) HOI categories, which are composed of \\( C = 80 \\) common objects (the same as MSCOCO (Lin et al., 2014)) and \\( A = 117 \\) unique interaction categories. V-COCO is a subset of MSCOCO, consisting of 2533 images for training, 2867 for validation and 4946 for test. It has 16199 human instances, each annotated with binary labels for \\( A = 26 \\) interaction categories."
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+ "content": "Evaluation Metric: Following (Chao et al., 2015), we use mean average precision (mAP) to evaluate HOI detection performance. A human-object pair is considered as positive when both predicted human and object boxes have at least 0.5 IoU with their ground-truth boxes, and the HOI class is classified correctly."
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+ "content": "For model learning, we set the detection score weight \\(\\gamma = 2.8\\) as default by following previous works (Zhang et al., 2021c; Li et al., 2019b), then optimize the entire network with AdamW and an initial learning rate of 1e-5 for backbone parameters and 1e-4 for others. We detach the parameters of the knowledge bank on the local branch for better model learning. We train up to 60K iterations with batch-size 24 in each on 4 NVIDIA 2080TI GPUs, and decay the learning rate by 10 times in 12K and 24K iteration."
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+ "content": "4.3 QUANTITATIVE RESULTS"
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+ "content": "For HICO-DET (Tab.1), our approach outperforms the previous state of the arts on the weakly supervised setting by a clear margin, achieving 22.89 mAP with ResNet-50 and 25.70 mAP with ResNet-101 as backbone. For a fair comparison, we also re-implement PPR-FCN with CLIP visual encoder. The results show that we still outperform PPR-FCN by a sizeable margin, which validates the superiority of our framework. Besides, we even perform comparably with HOTR and IDN under an inferior experimental setting where HOTR adopts a more advanced transformer encoder-decoder architecture, and both methods are trained with strong supervision. Furthermore, the mAP gap between Rare (training annotations \\(< 10\\)) and Non-rare HOI classes in our results is much smaller than other methods, demonstrating the superior generalization capability of our HOI representation for solving the long-tailed distribution issue. In detail, we achieve a 0.62 mAP gap with ResNet-50"
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+ "content": "Table 2: Ablation study on HICO-DET dataset. \"RN50-FPN(COCO)\" denotes the backbone initialized with Faster R-CNN parameters pretrained on MSCOCO dataset while \"CLIP RN50\" stands for the backbone initialized with CLIP visual encoder. Besides, we construct the knowledge bank \\(\\mathcal{W}_T\\) with random initialization, or computing HOI prompts by RoBERTa or CLIP text transformer."
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+ "angle": 0,
+ "content": "| Methods | Backbone | Detector | HICO-DET (%) | V-COCO (%) |
| Full | Rare | Non-Rare | AProle | AProle |
| supervised |
| iCAN (Gao et al., 2018) | RN50 (IN-1K&COCO) | FRCNN (COCO) | 14.84 | 10.45 | 16.15 | 45.30 | 52.40 |
| PMFNet (Wan et al., 2019) | RN50-FPN (IN-1K&COCO) | FRCNN (COCO) | 17.46 | 15.56 | 18.00 | 52.00 | - |
| TIN (Li et al., 2019b) | RN50-FPN (IN-1K&COCO) | FRCNN (COCO) | 17.22 | 13.51 | 18.32 | 47.80 | 54.20 |
| DJ-RN (Li et al., 2020a) | RN50 (IN-1K&COCO) | FRCNN (COCO) | 21.34 | 18.53 | 21.18 | 53.30 | 60.30 |
| IDN (Li et al., 2020b) | RN50 (IN-1K&COCO) | FRCNN (HICO-DET) | 26.29 | 22.61 | 27.39 | 53.30 | 60.30 |
| SCG (Zhang et al., 2021c) | RN50-FPN (IN-1K&HICO-DET) | FRCNN (HICO-DET) | 31.33 | 24.72 | 33.31 | 54.20 | 60.90 |
| HOTR (Kim et al., 2021) | RN50+Transformer (IN-1K&COCO) | DETR (HICO-DET) | 25.10 | 17.34 | 27.42 | 55.20 | 64.40 |
| QPIC (Tamura et al., 2021) | RN101+Transformer (IN-1K&COCO) | DETR (COCO) | 29.90 | 23.92 | 31.69 | 58.30 | 60.70 |
| CATN (Dong et al., 2022) | RN50+Transformer (IN-1K&HICO-DET&COCO) | DETR (HICO-DET) | 31.86 | 25.15 | 33.84 | 60.10 | - |
| MSTR (Kim et al., 2022) | RN50 + Transformer (IN-1K&COCO) | DETR(HICO-DET) | 31.17 | 25.31 | 33.92 | 62.00 | 65.20 |
| DisTr (Zhou et al., 2022) | RN50+Transformer (IN-1K&COCO) | DETR (HICO-DET) | 31.75 | 27.45 | 33.03 | 66.20 | 68.50 |
| SSRT (Iftekhar et al., 2022) | R101+Transformer (IN-1K&COCO) | DETR (COCO) | 31.34 | 24.31 | 33.32 | 65.00 | 67.10 |
| GEN-VLKT (Liao et al., 2022) | RN101+Transformer (IN-1K&HICO-DET) | DETR (HICO-DET) | 34.95 | 31.18 | 36.08 | 63.58 | 65.93 |
| between supervised & weakly-supervised setting, learning with image-level HOIs and box annotations |
| AlignFormer (Kilickaya & Smeulders, 2021) | RN101+Transformer (IN-1K&HICO-DET) | DETR (HICO-DET) | 20.85 | 18.23 | 21.64 | 15.82 | 16.34 |
| weakly-supervised |
| Explanation-HOI* (Baldassarre et al., 2020) | ResNeXt101 (IN-1K&COCO) | FRCNN (COCO) | 10.63 | 8.71 | 11.20 | - | - |
| MX-HOI (Kumaraswamy et al., 2021) | RN101 (IN-1K&COCO) | FRCNN (COCO) | 16.14 | 12.06 | 17.50 | - | - |
| PPR-FCN† (Zhang et al., 2017) | RN50 (CLIP dataset) | FRCNN (COCO) | 17.55 | 15.69 | 18.41 | - | - |
| ours | RN50 (CLIP dataset) | FRCNN (COCO) | 22.89 | 22.41 | 23.03 | 42.97 | 48.06 |
| ours | RN101 (CLIP dataset) | FRCNN (COCO) | 25.70 | 24.52 | 26.05 | 44.74 | 49.97 |
+
+# 4 EXPERIMENTS
+
+# 4.1 EXPERIMENTAL SETUP
+
+Datasets: We benchmark our model on two public datasets: HICO-DET and V-COCO. HICO-DET consists of 47776 images (38118 for training and 9658 for test). It has $N = 600$ HOI categories, which are composed of $C = 80$ common objects (the same as MSCOCO (Lin et al., 2014)) and $A = 117$ unique interaction categories. V-COCO is a subset of MSCOCO, consisting of 2533 images for training, 2867 for validation and 4946 for test. It has 16199 human instances, each annotated with binary labels for $A = 26$ interaction categories.
+
+Evaluation Metric: Following (Chao et al., 2015), we use mean average precision (mAP) to evaluate HOI detection performance. A human-object pair is considered as positive when both predicted human and object boxes have at least 0.5 IoU with their ground-truth boxes, and the HOI class is classified correctly.
+
+# 4.2 IMPLEMENTATION DETAILS
+
+We use an off-the-shelf Faster R-CNN (Ren et al., 2015) pretrained on MSCOCO to generate at most 100 object candidates for each image. For V-COCO, it is worth noting that we train the object detector by removing the images in MSCOCO that overlap with V-COCO to prevent information leakage. The backbone network is initialized with the visual encoder from CLIP-RN101 model and the feature dimension $D = 1024$ .
+
+For model learning, we set the detection score weight $\gamma = 2.8$ as default by following previous works (Zhang et al., 2021c; Li et al., 2019b), then optimize the entire network with AdamW and an initial learning rate of 1e-5 for backbone parameters and 1e-4 for others. We detach the parameters of the knowledge bank on the local branch for better model learning. We train up to 60K iterations with batch-size 24 in each on 4 NVIDIA 2080TI GPUs, and decay the learning rate by 10 times in 12K and 24K iteration.
+
+# 4.3 QUANTITATIVE RESULTS
+
+For HICO-DET (Tab.1), our approach outperforms the previous state of the arts on the weakly supervised setting by a clear margin, achieving 22.89 mAP with ResNet-50 and 25.70 mAP with ResNet-101 as backbone. For a fair comparison, we also re-implement PPR-FCN with CLIP visual encoder. The results show that we still outperform PPR-FCN by a sizeable margin, which validates the superiority of our framework. Besides, we even perform comparably with HOTR and IDN under an inferior experimental setting where HOTR adopts a more advanced transformer encoder-decoder architecture, and both methods are trained with strong supervision. Furthermore, the mAP gap between Rare (training annotations $< 10$ ) and Non-rare HOI classes in our results is much smaller than other methods, demonstrating the superior generalization capability of our HOI representation for solving the long-tailed distribution issue. In detail, we achieve a 0.62 mAP gap with ResNet-50
+
+Table 2: Ablation study on HICO-DET dataset. "RN50-FPN(COCO)" denotes the backbone initialized with Faster R-CNN parameters pretrained on MSCOCO dataset while "CLIP RN50" stands for the backbone initialized with CLIP visual encoder. Besides, we construct the knowledge bank $\mathcal{W}_T$ with random initialization, or computing HOI prompts by RoBERTa or CLIP text transformer.
+
+| Methods | Backbone | Detector | HICO-DET (%) | V-COCO (%) |
| Full | Rare | Non-Rare | AProle | AProle |
| supervised |
| iCAN (Gao et al., 2018) | RN50 (IN-1K&COCO) | FRCNN (COCO) | 14.84 | 10.45 | 16.15 | 45.30 | 52.40 |
| PMFNet (Wan et al., 2019) | RN50-FPN (IN-1K&COCO) | FRCNN (COCO) | 17.46 | 15.56 | 18.00 | 52.00 | - |
| TIN (Li et al., 2019b) | RN50-FPN (IN-1K&COCO) | FRCNN (COCO) | 17.22 | 13.51 | 18.32 | 47.80 | 54.20 |
| DJ-RN (Li et al., 2020a) | RN50 (IN-1K&COCO) | FRCNN (COCO) | 21.34 | 18.53 | 21.18 | 53.30 | 60.30 |
| IDN (Li et al., 2020b) | RN50 (IN-1K&COCO) | FRCNN (HICO-DET) | 26.29 | 22.61 | 27.39 | 53.30 | 60.30 |
| SCG (Zhang et al., 2021c) | RN50-FPN (IN-1K&HICO-DET) | FRCNN (HICO-DET) | 31.33 | 24.72 | 33.31 | 54.20 | 60.90 |
| HOTR (Kim et al., 2021) | RN50+Transformer (IN-1K&COCO) | DETR (HICO-DET) | 25.10 | 17.34 | 27.42 | 55.20 | 64.40 |
| QPIC (Tamura et al., 2021) | RN101+Transformer (IN-1K&COCO) | DETR (COCO) | 29.90 | 23.92 | 31.69 | 58.30 | 60.70 |
| CATN (Dong et al., 2022) | RN50+Transformer (IN-1K&HICO-DET&COCO) | DETR (HICO-DET) | 31.86 | 25.15 | 33.84 | 60.10 | - |
| MSTR (Kim et al., 2022) | RN50 + Transformer (IN-1K&COCO) | DETR(HICO-DET) | 31.17 | 25.31 | 33.92 | 62.00 | 65.20 |
| DisTr (Zhou et al., 2022) | RN50+Transformer (IN-1K&COCO) | DETR (HICO-DET) | 31.75 | 27.45 | 33.03 | 66.20 | 68.50 |
| SSRT (Iftekhar et al., 2022) | R101+Transformer (IN-1K&COCO) | DETR (COCO) | 31.34 | 24.31 | 33.32 | 65.00 | 67.10 |
| GEN-VLKT (Liao et al., 2022) | RN101+Transformer (IN-1K&HICO-DET) | DETR (HICO-DET) | 34.95 | 31.18 | 36.08 | 63.58 | 65.93 |
| between supervised & weakly-supervised setting, learning with image-level HOIs and box annotations |
| AlignFormer (Kilickaya & Smeulders, 2021) | RN101+Transformer (IN-1K&HICO-DET) | DETR (HICO-DET) | 20.85 | 18.23 | 21.64 | 15.82 | 16.34 |
| weakly-supervised |
| Explanation-HOI* (Baldassarre et al., 2020) | ResNeXt101 (IN-1K&COCO) | FRCNN (COCO) | 10.63 | 8.71 | 11.20 | - | - |
| MX-HOI (Kumaraswamy et al., 2021) | RN101 (IN-1K&COCO) | FRCNN (COCO) | 16.14 | 12.06 | 17.50 | - | - |
| PPR-FCN† (Zhang et al., 2017) | RN50 (CLIP dataset) | FRCNN (COCO) | 17.55 | 15.69 | 18.41 | - | - |
| ours | RN50 (CLIP dataset) | FRCNN (COCO) | 22.89 | 22.41 | 23.03 | 42.97 | 48.06 |
| ours | RN101 (CLIP dataset) | FRCNN (COCO) | 25.70 | 24.52 | 26.05 | 44.74 | 49.97 |
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+ "content": "Evaluation Metric: Following (Chao et al., 2015), we use mean average precision (mAP) to evaluate HOI detection performance. A human-object pair is considered as positive when both predicted human and object boxes have at least 0.5 IoU with their ground-truth boxes, and the HOI class is classified correctly."
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+ "content": " as default by following previous works (Zhang et al., 2021c; Li et al., 2019b), then optimize the entire network with AdamW and an initial learning rate of 1e-5 for backbone parameters and 1e-4 for others. We detach the parameters of the knowledge bank on the local branch for better model learning. We train up to 60K iterations with batch-size 24 in each on 4 NVIDIA 2080TI GPUs, and decay the learning rate by 10 times in 12K and 24K iteration."
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+ "content": "For HICO-DET (Tab.1), our approach outperforms the previous state of the arts on the weakly supervised setting by a clear margin, achieving 22.89 mAP with ResNet-50 and 25.70 mAP with ResNet-101 as backbone. For a fair comparison, we also re-implement PPR-FCN with CLIP visual encoder. The results show that we still outperform PPR-FCN by a sizeable margin, which validates the superiority of our framework. Besides, we even perform comparably with HOTR and IDN under an inferior experimental setting where HOTR adopts a more advanced transformer encoder-decoder architecture, and both methods are trained with strong supervision. Furthermore, the mAP gap between Rare (training annotations "
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+ "content": ") and Non-rare HOI classes in our results is much smaller than other methods, demonstrating the superior generalization capability of our HOI representation for solving the long-tailed distribution issue. In detail, we achieve a 0.62 mAP gap with ResNet-50"
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+ "html": "| Dataset | Syn-1 |
| N (# events) | N = 4, L = {A, B, C, D} |
| Ground truth | φ1 = (cA - cB > 1)1 ∧ (cA - cC > 3)1 |
| CLNN's rule | (cA - cB > 1.21)1.52 ∧ (cA - cC > 3.00)1.41 ∧ (cA - cD > 0.82)0.33 ∧ (cB - cC > 4.33)0 ∧ (cB - cD > 10.69)0 ∧ (cD - cC > -6.57)0.16 |
| TELLER's rule | A before D, B before D, C before D, A before D and C before D |
| OGEM-tab's rule | Excitation: [B], [C], [C, B], [B, C], [A, C, B], [A, B, C]Inhibitory: [A], [B, A], [B, A, C], [C, B, A], [A, B], [A, C], [B, C, A], [C, A, B], [C, A] |
",
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+ "text": "weight is presented. It can be clearly observed that by truncating the predicates with small weights, we could obtain the formula as",
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+ "text": "\n$$\n\\phi_ {1} = \\left(c _ {A} - c _ {B} > 1. 2 1\\right) ^ {1. 5 2} \\wedge \\left(c _ {A} - c _ {C} > 3. 0 0\\right) ^ {1. 4 1}, \\tag {45}\n$$\n",
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+ "text": "which matches well with the ground-truth rule. However, TELLER cannot capture the paired order representation between $A$ and $B$ or $A$ and $C$ . OGEM-tab captures the order representation $[A, B]$ and $[A, C]$ as inhibitory causes, which contradicts the ground-truth rule.",
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+ "text": "Generation Process. The second synthetic dataset contains 5 event labels: $A, B, C, D$ and $E$ , where $E$ is the event for prediction, and $A, B, C, D$ are causal events. The wCL formula used to generate the occurrence of event $E$ in the second synthetic dataset is set as",
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+ "text": "\n$$\n\\hat {\\phi} _ {2} = \\left(c _ {A} - c _ {B} > 0. 5\\right) ^ {1} \\wedge \\left(c _ {A} - c _ {C} > 1. 5\\right) ^ {1} \\wedge \\left(c _ {C} - c _ {D} > 2\\right) ^ {1}, \\tag {46}\n$$\n",
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+ "text": "whose unweighted version reads as \"If $A$ happens before $B$ for at least 0.5 time units, $A$ happens before $C$ for at least 1.5 time units, and $C$ happens before $D$ for at least 2 time units, then $E$ will happen.\"",
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+ "img_path": "images/5c9eb772a4b858637daaf47666b26dd2ef522b35246e1a44e155613c66b870c4.jpg",
+ "image_caption": [
+ "Figure 6: Model structure of $\\hat{\\phi}_2$ for generating the second synthetic dataset."
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+ "text": "The occurrence of events $A, B, C$ and $D$ are generated using Algorithm 1, in which $\\lambda_A = \\lambda_B = \\lambda_C = \\lambda_D = 0.2$ . After obtaining the occurrence of $A, B, C$ and $D$ , we simulate the generation of event label $E$ using Algorithm 2, in which the intensity rate $\\lambda_{E|\\hat{\\phi}_2}(t)$ is computed using the model shown in Figure 6.",
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+ "text": "Results. The rules learned by CLNN, TELLER and OGEM-tab on the second synthetic dataset are presented in Table 6, where the paired order predicate with the highest weight is presented. It can be clearly observed that by truncating the predicates with small weights, CLNN learns a wCL formula as:",
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+ "text": "\n$$\n\\phi_ {2} = \\left(c _ {A} - c _ {B} > 0. 7 7\\right) ^ {1. 2 7} \\wedge \\left(c _ {A} - c _ {C} > 2. 0 9\\right) ^ {1. 1 5} \\wedge \\left(c _ {C} - c _ {D} > 2. 6 0\\right) ^ {1. 0 6}, \\tag {47}\n$$\n",
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+ "text": "whose order representation match well with the ground-truth rule. Nevertheless, TELLER's rule only captures the ordering between $A$ , $B$ and $E$ , whereas the ordering between $A$ and $B$ or $B$ and $C$ or $C$ and $D$ are not learned. OGEM-tab's rules can only capture the relation between event label $D$ and event label $E$ can excite the occurrence of event label $E$ , whereas not able to capture the dependence of event label $E$ 's occurrence on the order relation between $A$ and $B$ or $B$ and $C$ or $C$ and $D$ .",
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+ "table_body": "| Dataset | Syn-2 |
| N (# events) | N=5, L={A,B,C,D,E} |
| Ground truth | φ2=(cA-cB>0.5)1∧(cB-cC>1.5)1∧(cC-cD>2)1 |
| CLNN's rule | (cA-cB>0.77)1.27∧(cA-cC>2.09)1.15∧((cA-cD)>−5.00)0.25∧((cA-cE)>−2.74)0.09∧(cB-cC>−9.31)0.02∧(cB-cD>−8.54)0.08∧(cB-cE>2.07)0∧((cC-cD)>2.60)1.06∧((cC-cE)>−4.27)0.03∧((cD-cE)>1.17)0.07 |
| TELLER's rule | A before E, B before E, A and B before E, A and C before E |
| OGEM-tab's rule | Excitation: [D], [D,E], [E], [E,D]Inhibitory: [D,A], [A], [A,D], [A,D,E], [E,D,A], [D,A,E], [A,E], [E,A], [D,E,A], [A,E,D], [E,A,D] |
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+ "text": "Table 6: Comparison of rule discovery for CLNN and TELLER on the Syn-2 dataset.",
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+ "text": "C.3 SYNTHETIC DATASET 3 (SYN-3).",
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+ "text": "The third synthetic dataset is generated using a more interesting scheme by combining the generation schemes of the first synthetic dataset and the second synthetic dataset. The third synthetic dataset",
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+ "image_caption": [
+ "Figure 7: Model structure of $\\hat{\\phi}_{3,1}$ for generating the occurrence of $D$ in the Syn-3 dataset."
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+ "image_footnote": [],
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+ "img_path": "images/b081e37e363fe8a10159d63a78d5d0118d701b9c610e183152ab23a0ad8a4a74.jpg",
+ "image_caption": [
+ "Figure 8: Model structure of $\\hat{\\phi}_{3,2}$ for generating the occurrence of $E$ in the Syn-3 dataset."
+ ],
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+ "type": "text",
+ "text": "includes five event labels: $A, B, C, D$ and $E$ . Here we consider $A, B$ , and $C$ as the causal events for the occurrence of $D$ , and $A, B, C$ , and $D$ as the causal events for the occurrence of $E$ . The occurrence of events $A, B, C$ are generated using Algorithm 1, in which $\\lambda_{A} = 0.2$ , $\\lambda_{b} = 0.2$ , and $\\lambda_{c} = 0.2$ . The wCL formula used to generate the occurrence of event $D$ is set as",
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+ "type": "equation",
+ "text": "\n$$\n\\hat {\\phi} _ {3, 1} = \\left(c _ {B} - c _ {A} > - 2\\right) ^ {1} \\wedge \\left(c _ {C} - c _ {A} > - 5\\right) ^ {1}, \\tag {48}\n$$\n",
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+ "type": "text",
+ "text": "whose unweighted version reads as \"If $A$ happens before $B$ for less than 2 time units, and $A$ happens before $C$ for less than 1 time unit, then $D$ will happen.\" The generation of $D$ 's occurrence follows Algorithm 2, where $\\lambda_{D|\\hat{\\phi}_{3,1}}(t)$ is computed using the model shown in Figure 7. We call the third synthetic dataset at this step as Syn-3.1.",
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+ "text": "After obtaining the occurrences of events $A, B, C$ , and $D$ , we could simulate the occurrence of $E$ using the following formula:",
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+ "type": "equation",
+ "text": "\n$$\n\\hat {\\phi} _ {3, 2} = \\left(c _ {B} - c _ {A} > - 5\\right) ^ {1} \\wedge \\left(c _ {C} - c _ {B} > - 4\\right) ^ {1} \\wedge \\left(c _ {D} - c _ {C} > - 3\\right) ^ {1}. \\tag {49}\n$$\n",
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+ "type": "text",
+ "text": "Similarly, the generation of $E$ 's occurrence follows Algorithm 2, where the intensity rate $\\lambda_{E|\\hat{\\phi}_{3,2}}(t)$ is computed using the model shown in Figure 8. We call the third synthetic dataset at this step as Syn-3.2.",
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+ "type": "text",
+ "text": "Results.",
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+ "type": "text",
+ "text": "The rules learned by CLNN, TELLER, and OGEM-tab on the cause of event $D$ in the third synthetic dataset are presented in Table 7, where the paired order predicate with the highest weight among the two candidates is reported. It can be clearly observed that by truncating the predicates with small",
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+ "text": "weights, CLNN learns a wCL formula as",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\phi_ {3, 1} = \\left(c _ {B} - c _ {A} > - 1. 8 5\\right) ^ {1. 7 2} \\wedge \\left(c _ {C} - c _ {A} > - 3. 9 0\\right) ^ {1. 5 9}, \\tag {50}\n$$\n",
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+ "type": "text",
+ "text": "whose order representation match well with the ground-truth rule. On the other hand, TELLER's rule only reveals the temporal relation between event labels $A$ , $B$ , $C$ and $D$ , but it does not capture the temporal relation between event labels $A$ and $B$ or $A$ and $C$ . In addition, we could observe that OGEM-tab does not capture that $C$ is a parent event of $D$ .",
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+ "type": "table",
+ "img_path": "images/0ade2cd181c78f6e20129e109757d9589040feebc8fc3b63f08edf29c05fc84b.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Dataset | Syn-3.1 |
| N (# events) | N = 5, L = {A, B, C, D, E} |
| Ground truth | \\(\\hat{\\phi}_{3,1} = (c_B - c_A > -2)^1 \\wedge (c_C - c_A > -5)^1\\) |
| CLNN's rule | \\((c_B - c_A > -1.85)^{1.72} \\wedge (c_C - c_A > -3.90)^{1.59} \\wedge ((c_D - c_A) > -16.25)^{0.33} \\wedge ((c_C - c_B) > -3.01)^0 \\wedge (c_D - c_B > -7.37)^{0.02} \\wedge (c_D - c_C > -7.55)^0\\) |
| TELLER's rule | A before D, B before D, C before D |
| OGEM-tab's rule | Excitation: [A], [A, B, D], [B, D, A], [D, A], [D, A, B], [B, A], [A, D], [D], [B, A, D], [D, B, A]Inhibitory: [A, B], [B, D], [B], [A, D, B], [D, B] |
",
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+ {
+ "type": "text",
+ "text": "The rules learned by CLNN, TELLER, and GEM on the cause of event $E$ in the third synthetic dataset are presented in Table 8, in which the discrete wCL formula learned by CLNN is",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\phi_ {3, 2} = \\left(c _ {B} - c _ {A} > - 3. 9 4\\right) ^ {1. 4 9} \\wedge \\left(c _ {C} - c _ {B} > - 3. 0 2\\right) ^ {2. 0 3} \\wedge \\left(\\left(c _ {D} - c _ {C}\\right) > - 2. 0 0\\right) ^ {1. 9 2}. \\tag {51}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 19
+ },
+ {
+ "type": "text",
+ "text": "It is obvious that $\\phi_{3,2}$ is able to learn the temporal relation between $A$ and $B$ , $B$ and $C$ , and $C$ and $D$ . However, TELLER's rules only reflect the temporal relation between $A$ , $B$ , $C$ and $E$ , which cannot give the information about the temporal relation between $A$ and $B$ , or $B$ and $C$ , or $C$ and $D$ . OGEM-tab's rule indicates that it considers event labels $A$ , $D$ , $E$ as the parent events of $D$ , which does not match with the ground-truth parent set.",
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+ {
+ "type": "table",
+ "img_path": "images/b73a935eff88ee2e71108810437f7f70abd97257512e582c4d2e9df8953f8845.jpg",
+ "table_caption": [
+ "Table 7: Comparison of rule discovery of ${\\phi }_{3,1}$ for CLNN and TELLER on the Syn-3.1 dataset."
+ ],
+ "table_footnote": [],
+ "table_body": "| Dataset | Syn-3.2 |
| N (# events) | N=5, L={A,B,C,D,E} |
| Ground truth | \\(\\hat{\\phi}_{3,2}=(c_{B}-c_{A}> -5)^{1}\\wedge(c_{C}-c_{B}> -4)^{1}\\wedge(c_{D}-c_{C}> -3)^{1}\\) |
| CLNN's rule | \\((c_{B}-c_{A}> -3.94)^{1.49}\\wedge(c_{C}-c_{A}> -9.12)^{0.25}\\wedge((c_{D}-c_{A})> -1.42)^{0.13}\\wedge((c_{E}-c_{A})> -3.88)^{0.15}\\wedge(c_{C}-c_{B}> -3.02)^{2.03}\\wedge(c_{D}-c_{B}> -6.27)^{0.02}\\wedge(c_{E}-c_{B}> -7.30)^{0.04}\\wedge((c_{D}- c_{C})> -2.00)^{1.92}\\wedge((c_{E}-c_{C})> -5.30)^{0.09}\\wedge((c_{E}-c_{D})> -1.57)^{0.01}\\) |
| TELLER's rule | A before E, B before E, C before E |
| OGEM-tab's rule | Excitation: [A,D], [D,A], [D,E], [E], [A,D, E], [D,E,A], [E,A], [A,E], [E,A,D], [A,E, D], [D,A,E], [E,D,A]Inhibitory: [A], [D], [E,D] |
",
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+ "type": "text",
+ "text": "Table 8: Comparison of rule discovery of ${\\phi }_{3,2}$ for CLNN and TELLER on the Syn-3.2 dataset.",
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+ },
+ {
+ "type": "text",
+ "text": "C.4 QUANTITATIVE COMPARISON OF CLNN'S RULES WITH GROUND TRUTH",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "To quantitatively evaluate the difference between the ground-truth rules and the rules learned by CLNN, we adopt the Jaccard similarity score to assess the learned formulas against the ground truth. Let $\\mathcal{G}$ denote the set of paired ordering representations from the ground-truth rule, and $\\mathcal{C}$ denote the set of paired ordering representations from the learned rules, the Jaccard similarity score is calculated as $J = \\frac{|\\mathcal{C} \\cap \\mathcal{G}|}{|\\mathcal{C} \\cup \\mathcal{G}|}$ . For TELLER and OGEM-tab, the ordering representations are extracted",
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+ },
+ {
+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
+ "bbox": [
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+ "page_idx": 19
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+ {
+ "type": "page_number",
+ "text": "20",
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+ },
+ {
+ "type": "image",
+ "img_path": "images/e778c73031d538bd262a2304c138c0361986948ec160d092a3b6c088d78183f6.jpg",
+ "image_caption": [
+ "(a)"
+ ],
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+ "page_idx": 20
+ },
+ {
+ "type": "image",
+ "img_path": "images/96858fce8cd5a11bbd1adfbb7d71a973c286ee8decdbab1100967a9142becc93.jpg",
+ "image_caption": [
+ "(b)"
+ ],
+ "image_footnote": [],
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+ "page_idx": 20
+ },
+ {
+ "type": "image",
+ "img_path": "images/a6c6bd22c64fc1f1fc65224884fde0d5cd2e30493bdc294bb501e98d1361ff80.jpg",
+ "image_caption": [
+ "(c)"
+ ],
+ "image_footnote": [],
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+ "page_idx": 20
+ },
+ {
+ "type": "image",
+ "img_path": "images/1511e755f98306b72c0769194b5a539ac0f64fffcc66182d9520ef4267f0858f.jpg",
+ "image_caption": [
+ "(d)",
+ "Figure 9: Comparison of ground-truth rules with CLNN's rules in terms of Jaccard similarity score for a) Syn-1, b) Syn-2, c) Syn-3.1, d) Syn-3.2."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 20
+ },
+ {
+ "type": "text",
+ "text": "from the excitation rules. The comparison of Jaccard similarity score for the synthetic datasets is shown in Figure 9, where the Jaccard similarity score of 0 is manually set to the minimum threshold 0.05 for clarity purposes. It is clearly observed that the Jaccard similarity scores for CLNN is higher than the ones for TELLER or OGEM, implying the rules discovered by CLNN are more consistent with the ground truth.",
+ "bbox": [
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+ "page_idx": 20
+ },
+ {
+ "type": "text",
+ "text": "C.5 STABILITY ANALYSIS OF CLNN'S RULES WITH RESPECT TO INITIALIZATION",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "To further validate the model's stability in learning wCL rules, different parameter initialization methods are carried out, including:",
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+ },
+ {
+ "type": "list",
+ "sub_type": "text",
+ "list_items": [
+ "1. rand - parameter initialization as random numbers from a uniform distribution on the interval [0, 1);",
+ "2. randn - random numbers from a normal distribution with mean 0 and variance 1;",
+ "3. ones - constant values of 1;",
+ "4. xavier - random numbers from a uniform distribution on the interval $[-1/\\sqrt{n}, 1/\\sqrt{n}]$ , where $n$ is the dimension of the parameter."
+ ],
+ "bbox": [
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+ "page_idx": 20
+ },
+ {
+ "type": "text",
+ "text": "The rules learned by CLNN for the above parameter initializations are summarized in Table 9. By inspecting the rules for different initialization methods, it is clear that CLNN can still recover the correct paired order representations even if initializing the learning process from a different position. In the meantime, the logic formulas learned by CLNN are stable as the variance of learned parameters is relatively small.",
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+ "page_idx": 20
+ },
+ {
+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
+ "bbox": [
+ 171,
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+ "page_idx": 20
+ },
+ {
+ "type": "page_number",
+ "text": "21",
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+ },
+ {
+ "type": "table",
+ "img_path": "images/720e0b182ecd75a826d23884634877955fe58becb261d25acc4e0e57933c455c.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Dataset | Initialization | Rules |
| Syn - 1 | Ground truth | \\(\\hat{\\phi}=(c_{A}-c_{B}>1)^{1}\\wedge(c_{A}-c_{C}>3)^{1}\\) |
| rand | \\(\\phi=(c_{A}-c_{B}>1.21)^{1.52}\\wedge(c_{A}-c_{C}>3.00)^{1.41}\\) |
| randn | \\(\\phi=(c_{A}-c_{B}>1.21)^{1.58}\\wedge(c_{A}-c_{C}>3.32)^{1.56}\\) |
| ones | \\(\\phi=(c_{A}-c_{B}>1.17)^{1.59}\\wedge(c_{A}-c_{C}>3.14)^{1.32}\\) |
| xavier | \\(\\phi=(c_{A}-c_{B}>1.12)^{1.45}\\wedge(c_{A}-c_{C}>3.20)^{1.33}\\) |
| Syn - 2 | Ground truth | \\(\\hat{\\phi}=(c_{A}-c_{B}>0.5)^{1}\\wedge(c_{A}-c_{C}>1.5)^{1}\\wedge(c_{C}-c_{D}>2)^{1}\\) |
| rand | \\(\\phi=(c_{A}-c_{B}>0.77)^{1.27}\\wedge(c_{A}-c_{C}>2.09)^{1.15}\\wedge((c_{C}-c_{D})>2.60)^{1.06}\\) |
| randn | \\(\\phi=(c_{A}-c_{B}>0.80)^{1.97}\\wedge(c_{A}-c_{C}>1.92)^{1.62}\\wedge((c_{C}-c_{D})>1.74)^{1.45}\\) |
| ones | \\(\\phi=(c_{A}-c_{B}>1.03)^{1.63}\\wedge(c_{A}-c_{C}>1.92)^{1.50}\\wedge((c_{C}-c_{D})>2.03)^{1.44}\\) |
| xavier | \\(\\phi=(c_{A}-c_{B}>0.97)^{1.92}\\wedge(c_{A}-c_{C}>2.07)^{1.63}\\wedge((c_{C}-c_{D})>1.97)^{1.62}\\) |
| Syn - 3.1 | Ground truth | \\(\\hat{\\phi}=(c_{B}-c_{A}>-2)^{1}\\wedge(c_{C}-c_{A}>-5)^{1}\\) |
| rand | \\(\\phi=(c_{B}-c_{A}>-1.85)^{1.72}\\wedge(c_{C}-c_{A}>-3.90)^{1.59}\\) |
| randn | \\(\\phi=(c_{B}-c_{A}>-1.98)^{1.51}\\wedge(c_{C}-c_{A}>-3.89)^{1.68}\\) |
| ones | \\(\\phi_{3,1}=(c_{B}-c_{A}>-1.94)^{1.84}\\wedge(c_{C}-c_{A}>-3.68)^{2.33}\\) |
| xavier | \\(\\phi_{3,1}=(c_{B}-c_{A}>-1.89)^{1.54}\\wedge(c_{C}-c_{A}>-3.92)^{1.62}\\) |
| Syn - 3.2 | Ground truth | \\(\\hat{\\phi}=(c_{B}-c_{A}>-5)^{1}\\wedge(c_{C}-c_{B}>-4)^{1}\\wedge(c_{D}-c_{C}>-3)^{1}\\) |
| rand | \\(\\phi=(c_{B}-c_{A}>-3.94)^{1.49}\\wedge(c_{C}-c_{B}>-3.02)^{2.03}\\wedge((c_{D}-c_{C})> -2.00)^{1.92}\\) |
| randn | \\(\\phi=(c_{B}-c_{A}>-3.79)^{1.71}\\wedge(c_{C}-c_{B}>-3.04)^{1.89}\\wedge((c_{D}-c_{C})> -1.68)^{1.65}\\) |
| ones | \\(\\phi=(c_{B}-c_{A}>-3.53)^{1.66}\\wedge(c_{C}-c_{B}>-3.09)^{1.88}\\wedge((c_{D}-c_{C})> -1.25)^{1.81}\\) |
| xavier | \\(\\phi=(c_{B}-c_{A}>-3.71)^{1.53}\\wedge(c_{C}-c_{B}>-3.09)^{2.04}\\wedge((c_{D}-c_{C})> -1.86)^{1.73}\\) |
",
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+ "page_idx": 21
+ },
+ {
+ "type": "text",
+ "text": "C.6 ANALYSIS OF LOGICAL CONSTRAINTS ON THE LL",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 21
+ },
+ {
+ "type": "text",
+ "text": "In this part, we investigate the effect of the interpretability using an experiment of the impact of logical constraints on the model's performance. The log-likelihood on the synthetic datasets for CLNN with and without logical constraints is summarized in Table 10. Table 10 demonstrates that the log-likelihood for CLNN with logical constraints is higher than the log-likelihood for CLNN without constraints, implying that interpretability (logical constraints) is helpful to improve the performance.",
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+ {
+ "type": "table",
+ "img_path": "images/2658b04aa74bc189fbdd0573cbd758c6395726b3651feecc9a6fb422e3c6d043.jpg",
+ "table_caption": [
+ "Table 9: Comparison of rules learned by CLNN for different parameter initialization methods."
+ ],
+ "table_footnote": [],
+ "table_body": "| Dataset | Syn-1 |
| N (# events) | N = 4, L = {A, B, C, D} |
| Ground truth | φ1 = (cA - cB > 1)1 ∧ (cA - cC > 3)1 |
| CLNN's rule | (cA - cB > 1.21)1.52 ∧ (cA - cC > 3.00)1.41 ∧ (cA - cD > 0.82)0.33 ∧ (cB - cC > 4.33)0 ∧ (cB - cD > 10.69)0 ∧ (cD - cC > -6.57)0.16 |
| TELLER's rule | A before D, B before D, C before D, A before D and C before D |
| OGEM-tab's rule | Excitation: [B], [C], [C, B], [B, C], [A, C, B], [A, B, C]Inhibitory: [A], [B, A], [B, A, C], [C, B, A], [A, B], [A, C], [B, C, A], [C, A, B], [C, A] |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.218,
+ 0.617,
+ 0.779,
+ 0.632
+ ],
+ "angle": 0,
+ "content": "Table 5: Comparison of rule discovery for CLNN and TELLER on the Syn-1 dataset."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.659,
+ 0.825,
+ 0.686
+ ],
+ "angle": 0,
+ "content": "weight is presented. It can be clearly observed that by truncating the predicates with small weights, we could obtain the formula as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.321,
+ 0.694,
+ 0.825,
+ 0.712
+ ],
+ "angle": 0,
+ "content": "\\[\n\\phi_ {1} = \\left(c _ {A} - c _ {B} > 1. 2 1\\right) ^ {1. 5 2} \\wedge \\left(c _ {A} - c _ {C} > 3. 0 0\\right) ^ {1. 4 1}, \\tag {45}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "which matches well with the ground-truth rule. However, TELLER cannot capture the paired order representation between \\( A \\) and \\( B \\) or \\( A \\) and \\( C \\). OGEM-tab captures the order representation \\( [A, B] \\) and \\( [A, C] \\) as inhibitory causes, which contradicts the ground-truth rule."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.172,
+ 0.779,
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+ 0.794
+ ],
+ "angle": 0,
+ "content": "C.2 SYNTHETIC DATASET-2 (SYN-2)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.806,
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+ ],
+ "angle": 0,
+ "content": "Generation Process. The second synthetic dataset contains 5 event labels: \\( A, B, C, D \\) and \\( E \\), where \\( E \\) is the event for prediction, and \\( A, B, C, D \\) are causal events. The wCL formula used to generate the occurrence of event \\( E \\) in the second synthetic dataset is set as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.283,
+ 0.856,
+ 0.825,
+ 0.875
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\phi} _ {2} = \\left(c _ {A} - c _ {B} > 0. 5\\right) ^ {1} \\wedge \\left(c _ {A} - c _ {C} > 1. 5\\right) ^ {1} \\wedge \\left(c _ {C} - c _ {D} > 2\\right) ^ {1}, \\tag {46}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.882,
+ 0.826,
+ 0.926
+ ],
+ "angle": 0,
+ "content": "whose unweighted version reads as \"If \\( A \\) happens before \\( B \\) for at least 0.5 time units, \\( A \\) happens before \\( C \\) for at least 1.5 time units, and \\( C \\) happens before \\( D \\) for at least 2 time units, then \\( E \\) will happen.\""
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.491,
+ 0.948,
+ 0.509,
+ 0.96
+ ],
+ "angle": 0,
+ "content": "17"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.173,
+ 0.033,
+ 0.48,
+ 0.049
+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.262,
+ 0.107,
+ 0.734,
+ 0.319
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.249,
+ 0.332,
+ 0.747,
+ 0.35
+ ],
+ "angle": 0,
+ "content": "Figure 6: Model structure of \\(\\hat{\\phi}_2\\) for generating the second synthetic dataset."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.374,
+ 0.825,
+ 0.435
+ ],
+ "angle": 0,
+ "content": "The occurrence of events \\( A, B, C \\) and \\( D \\) are generated using Algorithm 1, in which \\( \\lambda_A = \\lambda_B = \\lambda_C = \\lambda_D = 0.2 \\). After obtaining the occurrence of \\( A, B, C \\) and \\( D \\), we simulate the generation of event label \\( E \\) using Algorithm 2, in which the intensity rate \\( \\lambda_{E|\\hat{\\phi}_2}(t) \\) is computed using the model shown in Figure 6."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.44,
+ 0.825,
+ 0.495
+ ],
+ "angle": 0,
+ "content": "Results. The rules learned by CLNN, TELLER and OGEM-tab on the second synthetic dataset are presented in Table 6, where the paired order predicate with the highest weight is presented. It can be clearly observed that by truncating the predicates with small weights, CLNN learns a wCL formula as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.24,
+ 0.495,
+ 0.825,
+ 0.513
+ ],
+ "angle": 0,
+ "content": "\\[\n\\phi_ {2} = \\left(c _ {A} - c _ {B} > 0. 7 7\\right) ^ {1. 2 7} \\wedge \\left(c _ {A} - c _ {C} > 2. 0 9\\right) ^ {1. 1 5} \\wedge \\left(c _ {C} - c _ {D} > 2. 6 0\\right) ^ {1. 0 6}, \\tag {47}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.517,
+ 0.827,
+ 0.6
+ ],
+ "angle": 0,
+ "content": "whose order representation match well with the ground-truth rule. Nevertheless, TELLER's rule only captures the ordering between \\( A \\), \\( B \\) and \\( E \\), whereas the ordering between \\( A \\) and \\( B \\) or \\( B \\) and \\( C \\) or \\( C \\) and \\( D \\) are not learned. OGEM-tab's rules can only capture the relation between event label \\( D \\) and event label \\( E \\) can excite the occurrence of event label \\( E \\), whereas not able to capture the dependence of event label \\( E \\)'s occurrence on the order relation between \\( A \\) and \\( B \\) or \\( B \\) and \\( C \\) or \\( C \\) and \\( D \\)."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "| Dataset | Syn-2 |
| N (# events) | N=5, L={A,B,C,D,E} |
| Ground truth | φ2=(cA-cB>0.5)1∧(cB-cC>1.5)1∧(cC-cD>2)1 |
| CLNN's rule | (cA-cB>0.77)1.27∧(cA-cC>2.09)1.15∧((cA-cD)>−5.00)0.25∧((cA-cE)>−2.74)0.09∧(cB-cC>−9.31)0.02∧(cB-cD>−8.54)0.08∧(cB-cE>2.07)0∧((cC-cD)>2.60)1.06∧((cC-cE)>−4.27)0.03∧((cD-cE)>1.17)0.07 |
| TELLER's rule | A before E, B before E, A and B before E, A and C before E |
| OGEM-tab's rule | Excitation: [D], [D,E], [E], [E,D]Inhibitory: [D,A], [A], [A,D], [A,D,E], [E,D,A], [D,A,E], [A,E], [E,A], [D,E,A], [A,E,D], [E,A,D] |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.218,
+ 0.826,
+ 0.779,
+ 0.842
+ ],
+ "angle": 0,
+ "content": "Table 6: Comparison of rule discovery for CLNN and TELLER on the Syn-2 dataset."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.172,
+ 0.87,
+ 0.449,
+ 0.884
+ ],
+ "angle": 0,
+ "content": "C.3 SYNTHETIC DATASET 3 (SYN-3)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.896,
+ 0.825,
+ 0.926
+ ],
+ "angle": 0,
+ "content": "The third synthetic dataset is generated using a more interesting scheme by combining the generation schemes of the first synthetic dataset and the second synthetic dataset. The third synthetic dataset"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.491,
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+ 0.96
+ ],
+ "angle": 0,
+ "content": "18"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.173,
+ 0.033,
+ 0.48,
+ 0.049
+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.319,
+ 0.104,
+ 0.675,
+ 0.31
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.203,
+ 0.325,
+ 0.794,
+ 0.341
+ ],
+ "angle": 0,
+ "content": "Figure 7: Model structure of \\(\\hat{\\phi}_{3,1}\\) for generating the occurrence of \\(D\\) in the Syn-3 dataset."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.292,
+ 0.354,
+ 0.706,
+ 0.54
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.203,
+ 0.555,
+ 0.794,
+ 0.571
+ ],
+ "angle": 0,
+ "content": "Figure 8: Model structure of \\(\\hat{\\phi}_{3,2}\\) for generating the occurrence of \\(E\\) in the Syn-3 dataset."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.596,
+ 0.825,
+ 0.653
+ ],
+ "angle": 0,
+ "content": "includes five event labels: \\( A, B, C, D \\) and \\( E \\). Here we consider \\( A, B \\), and \\( C \\) as the causal events for the occurrence of \\( D \\), and \\( A, B, C \\), and \\( D \\) as the causal events for the occurrence of \\( E \\). The occurrence of events \\( A, B, C \\) are generated using Algorithm 1, in which \\( \\lambda_{A} = 0.2 \\), \\( \\lambda_{b} = 0.2 \\), and \\( \\lambda_{c} = 0.2 \\). The wCL formula used to generate the occurrence of event \\( D \\) is set as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.341,
+ 0.659,
+ 0.825,
+ 0.679
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\phi} _ {3, 1} = \\left(c _ {B} - c _ {A} > - 2\\right) ^ {1} \\wedge \\left(c _ {C} - c _ {A} > - 5\\right) ^ {1}, \\tag {48}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.684,
+ 0.825,
+ 0.744
+ ],
+ "angle": 0,
+ "content": "whose unweighted version reads as \"If \\( A \\) happens before \\( B \\) for less than 2 time units, and \\( A \\) happens before \\( C \\) for less than 1 time unit, then \\( D \\) will happen.\" The generation of \\( D \\)'s occurrence follows Algorithm 2, where \\( \\lambda_{D|\\hat{\\phi}_{3,1}}(t) \\) is computed using the model shown in Figure 7. We call the third synthetic dataset at this step as Syn-3.1."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.749,
+ 0.827,
+ 0.779
+ ],
+ "angle": 0,
+ "content": "After obtaining the occurrences of events \\( A, B, C \\), and \\( D \\), we could simulate the occurrence of \\( E \\) using the following formula:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.272,
+ 0.785,
+ 0.825,
+ 0.804
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\phi} _ {3, 2} = \\left(c _ {B} - c _ {A} > - 5\\right) ^ {1} \\wedge \\left(c _ {C} - c _ {B} > - 4\\right) ^ {1} \\wedge \\left(c _ {D} - c _ {C} > - 3\\right) ^ {1}. \\tag {49}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.809,
+ 0.826,
+ 0.854
+ ],
+ "angle": 0,
+ "content": "Similarly, the generation of \\( E \\)'s occurrence follows Algorithm 2, where the intensity rate \\( \\lambda_{E|\\hat{\\phi}_{3,2}}(t) \\) is computed using the model shown in Figure 8. We call the third synthetic dataset at this step as Syn-3.2."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.173,
+ 0.861,
+ 0.233,
+ 0.874
+ ],
+ "angle": 0,
+ "content": "Results."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.882,
+ 0.826,
+ 0.926
+ ],
+ "angle": 0,
+ "content": "The rules learned by CLNN, TELLER, and OGEM-tab on the cause of event \\( D \\) in the third synthetic dataset are presented in Table 7, where the paired order predicate with the highest weight among the two candidates is reported. It can be clearly observed that by truncating the predicates with small"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.491,
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+ ],
+ "angle": 0,
+ "content": "19"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.173,
+ 0.033,
+ 0.48,
+ 0.049
+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.172,
+ 0.104,
+ 0.445,
+ 0.119
+ ],
+ "angle": 0,
+ "content": "weights, CLNN learns a wCL formula as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.303,
+ 0.126,
+ 0.825,
+ 0.143
+ ],
+ "angle": 0,
+ "content": "\\[\n\\phi_ {3, 1} = \\left(c _ {B} - c _ {A} > - 1. 8 5\\right) ^ {1. 7 2} \\wedge \\left(c _ {C} - c _ {A} > - 3. 9 0\\right) ^ {1. 5 9}, \\tag {50}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.151,
+ 0.827,
+ 0.207
+ ],
+ "angle": 0,
+ "content": "whose order representation match well with the ground-truth rule. On the other hand, TELLER's rule only reveals the temporal relation between event labels \\( A \\), \\( B \\), \\( C \\) and \\( D \\), but it does not capture the temporal relation between event labels \\( A \\) and \\( B \\) or \\( A \\) and \\( C \\). In addition, we could observe that OGEM-tab does not capture that \\( C \\) is a parent event of \\( D \\)."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.188,
+ 0.22,
+ 0.808,
+ 0.37
+ ],
+ "angle": 0,
+ "content": "| Dataset | Syn-3.1 |
| N (# events) | N = 5, L = {A, B, C, D, E} |
| Ground truth | \\(\\hat{\\phi}_{3,1} = (c_B - c_A > -2)^1 \\wedge (c_C - c_A > -5)^1\\) |
| CLNN's rule | \\((c_B - c_A > -1.85)^{1.72} \\wedge (c_C - c_A > -3.90)^{1.59} \\wedge ((c_D - c_A) > -16.25)^{0.33} \\wedge ((c_C - c_B) > -3.01)^0 \\wedge (c_D - c_B > -7.37)^{0.02} \\wedge (c_D - c_C > -7.55)^0\\) |
| TELLER's rule | A before D, B before D, C before D |
| OGEM-tab's rule | Excitation: [A], [A, B, D], [B, D, A], [D, A], [D, A, B], [B, A], [A, D], [D], [B, A, D], [D, B, A]Inhibitory: [A, B], [B, D], [B], [A, D, B], [D, B] |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.187,
+ 0.38,
+ 0.809,
+ 0.396
+ ],
+ "angle": 0,
+ "content": "Table 7: Comparison of rule discovery of \\( {\\phi }_{3,1} \\) for CLNN and TELLER on the Syn-3.1 dataset."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.41,
+ 0.825,
+ 0.44
+ ],
+ "angle": 0,
+ "content": "The rules learned by CLNN, TELLER, and GEM on the cause of event \\( E \\) in the third synthetic dataset are presented in Table 8, in which the discrete wCL formula learned by CLNN is"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.195,
+ 0.445,
+ 0.825,
+ 0.466
+ ],
+ "angle": 0,
+ "content": "\\[\n\\phi_ {3, 2} = \\left(c _ {B} - c _ {A} > - 3. 9 4\\right) ^ {1. 4 9} \\wedge \\left(c _ {C} - c _ {B} > - 3. 0 2\\right) ^ {2. 0 3} \\wedge \\left(\\left(c _ {D} - c _ {C}\\right) > - 2. 0 0\\right) ^ {1. 9 2}. \\tag {51}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.47,
+ 0.827,
+ 0.542
+ ],
+ "angle": 0,
+ "content": "It is obvious that \\(\\phi_{3,2}\\) is able to learn the temporal relation between \\(A\\) and \\(B\\), \\(B\\) and \\(C\\), and \\(C\\) and \\(D\\). However, TELLER's rules only reflect the temporal relation between \\(A\\), \\(B\\), \\(C\\) and \\(E\\), which cannot give the information about the temporal relation between \\(A\\) and \\(B\\), or \\(B\\) and \\(C\\), or \\(C\\) and \\(D\\). OGEM-tab's rule indicates that it considers event labels \\(A\\), \\(D\\), \\(E\\) as the parent events of \\(D\\), which does not match with the ground-truth parent set."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.256,
+ 0.553,
+ 0.74,
+ 0.774
+ ],
+ "angle": 0,
+ "content": "| Dataset | Syn-3.2 |
| N (# events) | N=5, L={A,B,C,D,E} |
| Ground truth | \\(\\hat{\\phi}_{3,2}=(c_{B}-c_{A}> -5)^{1}\\wedge(c_{C}-c_{B}> -4)^{1}\\wedge(c_{D}-c_{C}> -3)^{1}\\) |
| CLNN's rule | \\((c_{B}-c_{A}> -3.94)^{1.49}\\wedge(c_{C}-c_{A}> -9.12)^{0.25}\\wedge((c_{D}-c_{A})> -1.42)^{0.13}\\wedge((c_{E}-c_{A})> -3.88)^{0.15}\\wedge(c_{C}-c_{B}> -3.02)^{2.03}\\wedge(c_{D}-c_{B}> -6.27)^{0.02}\\wedge(c_{E}-c_{B}> -7.30)^{0.04}\\wedge((c_{D}- c_{C})> -2.00)^{1.92}\\wedge((c_{E}-c_{C})> -5.30)^{0.09}\\wedge((c_{E}-c_{D})> -1.57)^{0.01}\\) |
| TELLER's rule | A before E, B before E, C before E |
| OGEM-tab's rule | Excitation: [A,D], [D,A], [D,E], [E], [A,D, E], [D,E,A], [E,A], [A,E], [E,A,D], [A,E, D], [D,A,E], [E,D,A]Inhibitory: [A], [D], [E,D] |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.187,
+ 0.784,
+ 0.809,
+ 0.8
+ ],
+ "angle": 0,
+ "content": "Table 8: Comparison of rule discovery of \\( {\\phi }_{3,2} \\) for CLNN and TELLER on the Syn-3.2 dataset."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.171,
+ 0.825,
+ 0.724,
+ 0.84
+ ],
+ "angle": 0,
+ "content": "C.4 QUANTITATIVE COMPARISON OF CLNN'S RULES WITH GROUND TRUTH"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.851,
+ 0.827,
+ 0.929
+ ],
+ "angle": 0,
+ "content": "To quantitatively evaluate the difference between the ground-truth rules and the rules learned by CLNN, we adopt the Jaccard similarity score to assess the learned formulas against the ground truth. Let \\(\\mathcal{G}\\) denote the set of paired ordering representations from the ground-truth rule, and \\(\\mathcal{C}\\) denote the set of paired ordering representations from the learned rules, the Jaccard similarity score is calculated as \\(J = \\frac{|\\mathcal{C} \\cap \\mathcal{G}|}{|\\mathcal{C} \\cup \\mathcal{G}|}\\). For TELLER and OGEM-tab, the ordering representations are extracted"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.49,
+ 0.948,
+ 0.51,
+ 0.961
+ ],
+ "angle": 0,
+ "content": "20"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.173,
+ 0.033,
+ 0.48,
+ 0.049
+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.197,
+ 0.109,
+ 0.495,
+ 0.277
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.334,
+ 0.279,
+ 0.353,
+ 0.292
+ ],
+ "angle": 0,
+ "content": "(a)"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.504,
+ 0.108,
+ 0.804,
+ 0.274
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.64,
+ 0.279,
+ 0.66,
+ 0.291
+ ],
+ "angle": 0,
+ "content": "(b)"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.197,
+ 0.302,
+ 0.49,
+ 0.467
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.333,
+ 0.473,
+ 0.351,
+ 0.485
+ ],
+ "angle": 0,
+ "content": "(c)"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.504,
+ 0.304,
+ 0.795,
+ 0.468
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.638,
+ 0.472,
+ 0.657,
+ 0.484
+ ],
+ "angle": 0,
+ "content": "(d)"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.171,
+ 0.501,
+ 0.825,
+ 0.531
+ ],
+ "angle": 0,
+ "content": "Figure 9: Comparison of ground-truth rules with CLNN's rules in terms of Jaccard similarity score for a) Syn-1, b) Syn-2, c) Syn-3.1, d) Syn-3.2."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.561,
+ 0.825,
+ 0.631
+ ],
+ "angle": 0,
+ "content": "from the excitation rules. The comparison of Jaccard similarity score for the synthetic datasets is shown in Figure 9, where the Jaccard similarity score of 0 is manually set to the minimum threshold 0.05 for clarity purposes. It is clearly observed that the Jaccard similarity scores for CLNN is higher than the ones for TELLER or OGEM, implying the rules discovered by CLNN are more consistent with the ground truth."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.171,
+ 0.654,
+ 0.749,
+ 0.669
+ ],
+ "angle": 0,
+ "content": "C.5 STABILITY ANALYSIS OF CLNN'S RULES WITH RESPECT TO INITIALIZATION"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.682,
+ 0.825,
+ 0.711
+ ],
+ "angle": 0,
+ "content": "To further validate the model's stability in learning wCL rules, different parameter initialization methods are carried out, including:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.211,
+ 0.725,
+ 0.825,
+ 0.754
+ ],
+ "angle": 0,
+ "content": "1. rand - parameter initialization as random numbers from a uniform distribution on the interval [0, 1);"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.209,
+ 0.763,
+ 0.765,
+ 0.777
+ ],
+ "angle": 0,
+ "content": "2. randn - random numbers from a normal distribution with mean 0 and variance 1;"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.211,
+ 0.788,
+ 0.416,
+ 0.802
+ ],
+ "angle": 0,
+ "content": "3. ones - constant values of 1;"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.209,
+ 0.811,
+ 0.825,
+ 0.841
+ ],
+ "angle": 0,
+ "content": "4. xavier - random numbers from a uniform distribution on the interval \\([-1/\\sqrt{n}, 1/\\sqrt{n}]\\), where \\(n\\) is the dimension of the parameter."
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.209,
+ 0.725,
+ 0.825,
+ 0.841
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.171,
+ 0.855,
+ 0.826,
+ 0.926
+ ],
+ "angle": 0,
+ "content": "The rules learned by CLNN for the above parameter initializations are summarized in Table 9. By inspecting the rules for different initialization methods, it is clear that CLNN can still recover the correct paired order representations even if initializing the learning process from a different position. In the meantime, the logic formulas learned by CLNN are stable as the variance of learned parameters is relatively small."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.49,
+ 0.948,
+ 0.508,
+ 0.96
+ ],
+ "angle": 0,
+ "content": "21"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.173,
+ 0.033,
+ 0.48,
+ 0.049
+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.197,
+ 0.102,
+ 0.803,
+ 0.359
+ ],
+ "angle": 0,
+ "content": "| Dataset | Initialization | Rules |
| Syn - 1 | Ground truth | \\(\\hat{\\phi}=(c_{A}-c_{B}>1)^{1}\\wedge(c_{A}-c_{C}>3)^{1}\\) |
| rand | \\(\\phi=(c_{A}-c_{B}>1.21)^{1.52}\\wedge(c_{A}-c_{C}>3.00)^{1.41}\\) |
| randn | \\(\\phi=(c_{A}-c_{B}>1.21)^{1.58}\\wedge(c_{A}-c_{C}>3.32)^{1.56}\\) |
| ones | \\(\\phi=(c_{A}-c_{B}>1.17)^{1.59}\\wedge(c_{A}-c_{C}>3.14)^{1.32}\\) |
| xavier | \\(\\phi=(c_{A}-c_{B}>1.12)^{1.45}\\wedge(c_{A}-c_{C}>3.20)^{1.33}\\) |
| Syn - 2 | Ground truth | \\(\\hat{\\phi}=(c_{A}-c_{B}>0.5)^{1}\\wedge(c_{A}-c_{C}>1.5)^{1}\\wedge(c_{C}-c_{D}>2)^{1}\\) |
| rand | \\(\\phi=(c_{A}-c_{B}>0.77)^{1.27}\\wedge(c_{A}-c_{C}>2.09)^{1.15}\\wedge((c_{C}-c_{D})>2.60)^{1.06}\\) |
| randn | \\(\\phi=(c_{A}-c_{B}>0.80)^{1.97}\\wedge(c_{A}-c_{C}>1.92)^{1.62}\\wedge((c_{C}-c_{D})>1.74)^{1.45}\\) |
| ones | \\(\\phi=(c_{A}-c_{B}>1.03)^{1.63}\\wedge(c_{A}-c_{C}>1.92)^{1.50}\\wedge((c_{C}-c_{D})>2.03)^{1.44}\\) |
| xavier | \\(\\phi=(c_{A}-c_{B}>0.97)^{1.92}\\wedge(c_{A}-c_{C}>2.07)^{1.63}\\wedge((c_{C}-c_{D})>1.97)^{1.62}\\) |
| Syn - 3.1 | Ground truth | \\(\\hat{\\phi}=(c_{B}-c_{A}>-2)^{1}\\wedge(c_{C}-c_{A}>-5)^{1}\\) |
| rand | \\(\\phi=(c_{B}-c_{A}>-1.85)^{1.72}\\wedge(c_{C}-c_{A}>-3.90)^{1.59}\\) |
| randn | \\(\\phi=(c_{B}-c_{A}>-1.98)^{1.51}\\wedge(c_{C}-c_{A}>-3.89)^{1.68}\\) |
| ones | \\(\\phi_{3,1}=(c_{B}-c_{A}>-1.94)^{1.84}\\wedge(c_{C}-c_{A}>-3.68)^{2.33}\\) |
| xavier | \\(\\phi_{3,1}=(c_{B}-c_{A}>-1.89)^{1.54}\\wedge(c_{C}-c_{A}>-3.92)^{1.62}\\) |
| Syn - 3.2 | Ground truth | \\(\\hat{\\phi}=(c_{B}-c_{A}>-5)^{1}\\wedge(c_{C}-c_{B}>-4)^{1}\\wedge(c_{D}-c_{C}>-3)^{1}\\) |
| rand | \\(\\phi=(c_{B}-c_{A}>-3.94)^{1.49}\\wedge(c_{C}-c_{B}>-3.02)^{2.03}\\wedge((c_{D}-c_{C})> -2.00)^{1.92}\\) |
| randn | \\(\\phi=(c_{B}-c_{A}>-3.79)^{1.71}\\wedge(c_{C}-c_{B}>-3.04)^{1.89}\\wedge((c_{D}-c_{C})> -1.68)^{1.65}\\) |
| ones | \\(\\phi=(c_{B}-c_{A}>-3.53)^{1.66}\\wedge(c_{C}-c_{B}>-3.09)^{1.88}\\wedge((c_{D}-c_{C})> -1.25)^{1.81}\\) |
| xavier | \\(\\phi=(c_{B}-c_{A}>-3.71)^{1.53}\\wedge(c_{C}-c_{B}>-3.09)^{2.04}\\wedge((c_{D}-c_{C})> -1.86)^{1.73}\\) |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "content": "Table 9: Comparison of rules learned by CLNN for different parameter initialization methods."
+ },
+ {
+ "type": "title",
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+ "content": "C.6 ANALYSIS OF LOGICAL CONSTRAINTS ON THE LL"
+ },
+ {
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+ "content": "In this part, we investigate the effect of the interpretability using an experiment of the impact of logical constraints on the model's performance. The log-likelihood on the synthetic datasets for CLNN with and without logical constraints is summarized in Table 10. Table 10 demonstrates that the log-likelihood for CLNN with logical constraints is higher than the log-likelihood for CLNN without constraints, implying that interpretability (logical constraints) is helpful to improve the performance."
+ },
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+ "type": "table",
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+ "content": "| Dataset | Syn-1 |
| N (# events) | N = 4, L = {A, B, C, D} |
| Ground truth | φ1 = (cA - cB > 1)1 ∧ (cA - cC > 3)1 |
| CLNN's rule | (cA - cB > 1.21)1.52 ∧ (cA - cC > 3.00)1.41 ∧ (cA - cD > 0.82)0.33 ∧ (cB - cC > 4.33)0 ∧ (cB - cD > 10.69)0 ∧ (cD - cC > -6.57)0.16 |
| TELLER's rule | A before D, B before D, C before D, A before D and C before D |
| OGEM-tab's rule | Excitation: [B], [C], [C, B], [B, C], [A, C, B], [A, B, C]Inhibitory: [A], [B, A], [B, A, C], [C, B, A], [A, B], [A, C], [B, C, A], [C, A, B], [C, A] |
+
+Table 5: Comparison of rule discovery for CLNN and TELLER on the Syn-1 dataset.
+
+weight is presented. It can be clearly observed that by truncating the predicates with small weights, we could obtain the formula as
+
+$$
+\phi_ {1} = \left(c _ {A} - c _ {B} > 1. 2 1\right) ^ {1. 5 2} \wedge \left(c _ {A} - c _ {C} > 3. 0 0\right) ^ {1. 4 1}, \tag {45}
+$$
+
+which matches well with the ground-truth rule. However, TELLER cannot capture the paired order representation between $A$ and $B$ or $A$ and $C$ . OGEM-tab captures the order representation $[A, B]$ and $[A, C]$ as inhibitory causes, which contradicts the ground-truth rule.
+
+# C.2 SYNTHETIC DATASET-2 (SYN-2).
+
+Generation Process. The second synthetic dataset contains 5 event labels: $A, B, C, D$ and $E$ , where $E$ is the event for prediction, and $A, B, C, D$ are causal events. The wCL formula used to generate the occurrence of event $E$ in the second synthetic dataset is set as
+
+$$
+\hat {\phi} _ {2} = \left(c _ {A} - c _ {B} > 0. 5\right) ^ {1} \wedge \left(c _ {A} - c _ {C} > 1. 5\right) ^ {1} \wedge \left(c _ {C} - c _ {D} > 2\right) ^ {1}, \tag {46}
+$$
+
+whose unweighted version reads as "If $A$ happens before $B$ for at least 0.5 time units, $A$ happens before $C$ for at least 1.5 time units, and $C$ happens before $D$ for at least 2 time units, then $E$ will happen."
+
+
+Figure 6: Model structure of $\hat{\phi}_2$ for generating the second synthetic dataset.
+
+The occurrence of events $A, B, C$ and $D$ are generated using Algorithm 1, in which $\lambda_A = \lambda_B = \lambda_C = \lambda_D = 0.2$ . After obtaining the occurrence of $A, B, C$ and $D$ , we simulate the generation of event label $E$ using Algorithm 2, in which the intensity rate $\lambda_{E|\hat{\phi}_2}(t)$ is computed using the model shown in Figure 6.
+
+Results. The rules learned by CLNN, TELLER and OGEM-tab on the second synthetic dataset are presented in Table 6, where the paired order predicate with the highest weight is presented. It can be clearly observed that by truncating the predicates with small weights, CLNN learns a wCL formula as:
+
+$$
+\phi_ {2} = \left(c _ {A} - c _ {B} > 0. 7 7\right) ^ {1. 2 7} \wedge \left(c _ {A} - c _ {C} > 2. 0 9\right) ^ {1. 1 5} \wedge \left(c _ {C} - c _ {D} > 2. 6 0\right) ^ {1. 0 6}, \tag {47}
+$$
+
+whose order representation match well with the ground-truth rule. Nevertheless, TELLER's rule only captures the ordering between $A$ , $B$ and $E$ , whereas the ordering between $A$ and $B$ or $B$ and $C$ or $C$ and $D$ are not learned. OGEM-tab's rules can only capture the relation between event label $D$ and event label $E$ can excite the occurrence of event label $E$ , whereas not able to capture the dependence of event label $E$ 's occurrence on the order relation between $A$ and $B$ or $B$ and $C$ or $C$ and $D$ .
+
+| Dataset | Syn-2 |
| N (# events) | N=5, L={A,B,C,D,E} |
| Ground truth | φ2=(cA-cB>0.5)1∧(cB-cC>1.5)1∧(cC-cD>2)1 |
| CLNN's rule | (cA-cB>0.77)1.27∧(cA-cC>2.09)1.15∧((cA-cD)>−5.00)0.25∧((cA-cE)>−2.74)0.09∧(cB-cC>−9.31)0.02∧(cB-cD>−8.54)0.08∧(cB-cE>2.07)0∧((cC-cD)>2.60)1.06∧((cC-cE)>−4.27)0.03∧((cD-cE)>1.17)0.07 |
| TELLER's rule | A before E, B before E, A and B before E, A and C before E |
| OGEM-tab's rule | Excitation: [D], [D,E], [E], [E,D]Inhibitory: [D,A], [A], [A,D], [A,D,E], [E,D,A], [D,A,E], [A,E], [E,A], [D,E,A], [A,E,D], [E,A,D] |
+
+Table 6: Comparison of rule discovery for CLNN and TELLER on the Syn-2 dataset.
+
+# C.3 SYNTHETIC DATASET 3 (SYN-3).
+
+The third synthetic dataset is generated using a more interesting scheme by combining the generation schemes of the first synthetic dataset and the second synthetic dataset. The third synthetic dataset
+
+
+Figure 7: Model structure of $\hat{\phi}_{3,1}$ for generating the occurrence of $D$ in the Syn-3 dataset.
+
+
+Figure 8: Model structure of $\hat{\phi}_{3,2}$ for generating the occurrence of $E$ in the Syn-3 dataset.
+
+includes five event labels: $A, B, C, D$ and $E$ . Here we consider $A, B$ , and $C$ as the causal events for the occurrence of $D$ , and $A, B, C$ , and $D$ as the causal events for the occurrence of $E$ . The occurrence of events $A, B, C$ are generated using Algorithm 1, in which $\lambda_{A} = 0.2$ , $\lambda_{b} = 0.2$ , and $\lambda_{c} = 0.2$ . The wCL formula used to generate the occurrence of event $D$ is set as
+
+$$
+\hat {\phi} _ {3, 1} = \left(c _ {B} - c _ {A} > - 2\right) ^ {1} \wedge \left(c _ {C} - c _ {A} > - 5\right) ^ {1}, \tag {48}
+$$
+
+whose unweighted version reads as "If $A$ happens before $B$ for less than 2 time units, and $A$ happens before $C$ for less than 1 time unit, then $D$ will happen." The generation of $D$ 's occurrence follows Algorithm 2, where $\lambda_{D|\hat{\phi}_{3,1}}(t)$ is computed using the model shown in Figure 7. We call the third synthetic dataset at this step as Syn-3.1.
+
+After obtaining the occurrences of events $A, B, C$ , and $D$ , we could simulate the occurrence of $E$ using the following formula:
+
+$$
+\hat {\phi} _ {3, 2} = \left(c _ {B} - c _ {A} > - 5\right) ^ {1} \wedge \left(c _ {C} - c _ {B} > - 4\right) ^ {1} \wedge \left(c _ {D} - c _ {C} > - 3\right) ^ {1}. \tag {49}
+$$
+
+Similarly, the generation of $E$ 's occurrence follows Algorithm 2, where the intensity rate $\lambda_{E|\hat{\phi}_{3,2}}(t)$ is computed using the model shown in Figure 8. We call the third synthetic dataset at this step as Syn-3.2.
+
+# Results.
+
+The rules learned by CLNN, TELLER, and OGEM-tab on the cause of event $D$ in the third synthetic dataset are presented in Table 7, where the paired order predicate with the highest weight among the two candidates is reported. It can be clearly observed that by truncating the predicates with small
+
+weights, CLNN learns a wCL formula as
+
+$$
+\phi_ {3, 1} = \left(c _ {B} - c _ {A} > - 1. 8 5\right) ^ {1. 7 2} \wedge \left(c _ {C} - c _ {A} > - 3. 9 0\right) ^ {1. 5 9}, \tag {50}
+$$
+
+whose order representation match well with the ground-truth rule. On the other hand, TELLER's rule only reveals the temporal relation between event labels $A$ , $B$ , $C$ and $D$ , but it does not capture the temporal relation between event labels $A$ and $B$ or $A$ and $C$ . In addition, we could observe that OGEM-tab does not capture that $C$ is a parent event of $D$ .
+
+| Dataset | Syn-3.1 |
| N (# events) | N = 5, L = {A, B, C, D, E} |
| Ground truth | \(\hat{\phi}_{3,1} = (c_B - c_A > -2)^1 \wedge (c_C - c_A > -5)^1\) |
| CLNN's rule | \((c_B - c_A > -1.85)^{1.72} \wedge (c_C - c_A > -3.90)^{1.59} \wedge ((c_D - c_A) > -16.25)^{0.33} \wedge ((c_C - c_B) > -3.01)^0 \wedge (c_D - c_B > -7.37)^{0.02} \wedge (c_D - c_C > -7.55)^0\) |
| TELLER's rule | A before D, B before D, C before D |
| OGEM-tab's rule | Excitation: [A], [A, B, D], [B, D, A], [D, A], [D, A, B], [B, A], [A, D], [D], [B, A, D], [D, B, A]Inhibitory: [A, B], [B, D], [B], [A, D, B], [D, B] |
+
+The rules learned by CLNN, TELLER, and GEM on the cause of event $E$ in the third synthetic dataset are presented in Table 8, in which the discrete wCL formula learned by CLNN is
+
+$$
+\phi_ {3, 2} = \left(c _ {B} - c _ {A} > - 3. 9 4\right) ^ {1. 4 9} \wedge \left(c _ {C} - c _ {B} > - 3. 0 2\right) ^ {2. 0 3} \wedge \left(\left(c _ {D} - c _ {C}\right) > - 2. 0 0\right) ^ {1. 9 2}. \tag {51}
+$$
+
+It is obvious that $\phi_{3,2}$ is able to learn the temporal relation between $A$ and $B$ , $B$ and $C$ , and $C$ and $D$ . However, TELLER's rules only reflect the temporal relation between $A$ , $B$ , $C$ and $E$ , which cannot give the information about the temporal relation between $A$ and $B$ , or $B$ and $C$ , or $C$ and $D$ . OGEM-tab's rule indicates that it considers event labels $A$ , $D$ , $E$ as the parent events of $D$ , which does not match with the ground-truth parent set.
+
+Table 7: Comparison of rule discovery of ${\phi }_{3,1}$ for CLNN and TELLER on the Syn-3.1 dataset.
+
+| Dataset | Syn-3.2 |
| N (# events) | N=5, L={A,B,C,D,E} |
| Ground truth | \(\hat{\phi}_{3,2}=(c_{B}-c_{A}> -5)^{1}\wedge(c_{C}-c_{B}> -4)^{1}\wedge(c_{D}-c_{C}> -3)^{1}\) |
| CLNN's rule | \((c_{B}-c_{A}> -3.94)^{1.49}\wedge(c_{C}-c_{A}> -9.12)^{0.25}\wedge((c_{D}-c_{A})> -1.42)^{0.13}\wedge((c_{E}-c_{A})> -3.88)^{0.15}\wedge(c_{C}-c_{B}> -3.02)^{2.03}\wedge(c_{D}-c_{B}> -6.27)^{0.02}\wedge(c_{E}-c_{B}> -7.30)^{0.04}\wedge((c_{D}- c_{C})> -2.00)^{1.92}\wedge((c_{E}-c_{C})> -5.30)^{0.09}\wedge((c_{E}-c_{D})> -1.57)^{0.01}\) |
| TELLER's rule | A before E, B before E, C before E |
| OGEM-tab's rule | Excitation: [A,D], [D,A], [D,E], [E], [A,D, E], [D,E,A], [E,A], [A,E], [E,A,D], [A,E, D], [D,A,E], [E,D,A]Inhibitory: [A], [D], [E,D] |
+
+Table 8: Comparison of rule discovery of ${\phi }_{3,2}$ for CLNN and TELLER on the Syn-3.2 dataset.
+
+# C.4 QUANTITATIVE COMPARISON OF CLNN'S RULES WITH GROUND TRUTH
+
+To quantitatively evaluate the difference between the ground-truth rules and the rules learned by CLNN, we adopt the Jaccard similarity score to assess the learned formulas against the ground truth. Let $\mathcal{G}$ denote the set of paired ordering representations from the ground-truth rule, and $\mathcal{C}$ denote the set of paired ordering representations from the learned rules, the Jaccard similarity score is calculated as $J = \frac{|\mathcal{C} \cap \mathcal{G}|}{|\mathcal{C} \cup \mathcal{G}|}$ . For TELLER and OGEM-tab, the ordering representations are extracted
+
+
+(a)
+
+
+(b)
+
+
+(c)
+
+
+(d)
+Figure 9: Comparison of ground-truth rules with CLNN's rules in terms of Jaccard similarity score for a) Syn-1, b) Syn-2, c) Syn-3.1, d) Syn-3.2.
+
+from the excitation rules. The comparison of Jaccard similarity score for the synthetic datasets is shown in Figure 9, where the Jaccard similarity score of 0 is manually set to the minimum threshold 0.05 for clarity purposes. It is clearly observed that the Jaccard similarity scores for CLNN is higher than the ones for TELLER or OGEM, implying the rules discovered by CLNN are more consistent with the ground truth.
+
+# C.5 STABILITY ANALYSIS OF CLNN'S RULES WITH RESPECT TO INITIALIZATION
+
+To further validate the model's stability in learning wCL rules, different parameter initialization methods are carried out, including:
+
+1. rand - parameter initialization as random numbers from a uniform distribution on the interval [0, 1);
+2. randn - random numbers from a normal distribution with mean 0 and variance 1;
+3. ones - constant values of 1;
+4. xavier - random numbers from a uniform distribution on the interval $[-1/\sqrt{n}, 1/\sqrt{n}]$ , where $n$ is the dimension of the parameter.
+
+The rules learned by CLNN for the above parameter initializations are summarized in Table 9. By inspecting the rules for different initialization methods, it is clear that CLNN can still recover the correct paired order representations even if initializing the learning process from a different position. In the meantime, the logic formulas learned by CLNN are stable as the variance of learned parameters is relatively small.
+
+| Dataset | Initialization | Rules |
| Syn - 1 | Ground truth | \(\hat{\phi}=(c_{A}-c_{B}>1)^{1}\wedge(c_{A}-c_{C}>3)^{1}\) |
| rand | \(\phi=(c_{A}-c_{B}>1.21)^{1.52}\wedge(c_{A}-c_{C}>3.00)^{1.41}\) |
| randn | \(\phi=(c_{A}-c_{B}>1.21)^{1.58}\wedge(c_{A}-c_{C}>3.32)^{1.56}\) |
| ones | \(\phi=(c_{A}-c_{B}>1.17)^{1.59}\wedge(c_{A}-c_{C}>3.14)^{1.32}\) |
| xavier | \(\phi=(c_{A}-c_{B}>1.12)^{1.45}\wedge(c_{A}-c_{C}>3.20)^{1.33}\) |
| Syn - 2 | Ground truth | \(\hat{\phi}=(c_{A}-c_{B}>0.5)^{1}\wedge(c_{A}-c_{C}>1.5)^{1}\wedge(c_{C}-c_{D}>2)^{1}\) |
| rand | \(\phi=(c_{A}-c_{B}>0.77)^{1.27}\wedge(c_{A}-c_{C}>2.09)^{1.15}\wedge((c_{C}-c_{D})>2.60)^{1.06}\) |
| randn | \(\phi=(c_{A}-c_{B}>0.80)^{1.97}\wedge(c_{A}-c_{C}>1.92)^{1.62}\wedge((c_{C}-c_{D})>1.74)^{1.45}\) |
| ones | \(\phi=(c_{A}-c_{B}>1.03)^{1.63}\wedge(c_{A}-c_{C}>1.92)^{1.50}\wedge((c_{C}-c_{D})>2.03)^{1.44}\) |
| xavier | \(\phi=(c_{A}-c_{B}>0.97)^{1.92}\wedge(c_{A}-c_{C}>2.07)^{1.63}\wedge((c_{C}-c_{D})>1.97)^{1.62}\) |
| Syn - 3.1 | Ground truth | \(\hat{\phi}=(c_{B}-c_{A}>-2)^{1}\wedge(c_{C}-c_{A}>-5)^{1}\) |
| rand | \(\phi=(c_{B}-c_{A}>-1.85)^{1.72}\wedge(c_{C}-c_{A}>-3.90)^{1.59}\) |
| randn | \(\phi=(c_{B}-c_{A}>-1.98)^{1.51}\wedge(c_{C}-c_{A}>-3.89)^{1.68}\) |
| ones | \(\phi_{3,1}=(c_{B}-c_{A}>-1.94)^{1.84}\wedge(c_{C}-c_{A}>-3.68)^{2.33}\) |
| xavier | \(\phi_{3,1}=(c_{B}-c_{A}>-1.89)^{1.54}\wedge(c_{C}-c_{A}>-3.92)^{1.62}\) |
| Syn - 3.2 | Ground truth | \(\hat{\phi}=(c_{B}-c_{A}>-5)^{1}\wedge(c_{C}-c_{B}>-4)^{1}\wedge(c_{D}-c_{C}>-3)^{1}\) |
| rand | \(\phi=(c_{B}-c_{A}>-3.94)^{1.49}\wedge(c_{C}-c_{B}>-3.02)^{2.03}\wedge((c_{D}-c_{C})> -2.00)^{1.92}\) |
| randn | \(\phi=(c_{B}-c_{A}>-3.79)^{1.71}\wedge(c_{C}-c_{B}>-3.04)^{1.89}\wedge((c_{D}-c_{C})> -1.68)^{1.65}\) |
| ones | \(\phi=(c_{B}-c_{A}>-3.53)^{1.66}\wedge(c_{C}-c_{B}>-3.09)^{1.88}\wedge((c_{D}-c_{C})> -1.25)^{1.81}\) |
| xavier | \(\phi=(c_{B}-c_{A}>-3.71)^{1.53}\wedge(c_{C}-c_{B}>-3.09)^{2.04}\wedge((c_{D}-c_{C})> -1.86)^{1.73}\) |
+
+# C.6 ANALYSIS OF LOGICAL CONSTRAINTS ON THE LL
+
+In this part, we investigate the effect of the interpretability using an experiment of the impact of logical constraints on the model's performance. The log-likelihood on the synthetic datasets for CLNN with and without logical constraints is summarized in Table 10. Table 10 demonstrates that the log-likelihood for CLNN with logical constraints is higher than the log-likelihood for CLNN without constraints, implying that interpretability (logical constraints) is helpful to improve the performance.
+
+Table 9: Comparison of rules learned by CLNN for different parameter initialization methods.
+
+| Dataset | Syn-1 |
| N (# events) | N = 4, L = {A, B, C, D} |
| Ground truth | φ1 = (cA - cB > 1)1 ∧ (cA - cC > 3)1 |
| CLNN's rule | (cA - cB > 1.21)1.52 ∧ (cA - cC > 3.00)1.41 ∧ (cA - cD > 0.82)0.33 ∧ (cB - cC > 4.33)0 ∧ (cB - cD > 10.69)0 ∧ (cD - cC > -6.57)0.16 |
| TELLER's rule | A before D, B before D, C before D, A before D and C before D |
| OGEM-tab's rule | Excitation: [B], [C], [C, B], [B, C], [A, C, B], [A, B, C]Inhibitory: [A], [B, A], [B, A, C], [C, B, A], [A, B], [A, C], [B, C, A], [C, A, B], [C, A] |
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+ "html": "| Dataset | Syn-2 |
| N (# events) | N=5, L={A,B,C,D,E} |
| Ground truth | φ2=(cA-cB>0.5)1∧(cB-cC>1.5)1∧(cC-cD>2)1 |
| CLNN's rule | (cA-cB>0.77)1.27∧(cA-cC>2.09)1.15∧((cA-cD)>−5.00)0.25∧((cA-cE)>−2.74)0.09∧(cB-cC>−9.31)0.02∧(cB-cD>−8.54)0.08∧(cB-cE>2.07)0∧((cC-cD)>2.60)1.06∧((cC-cE)>−4.27)0.03∧((cD-cE)>1.17)0.07 |
| TELLER's rule | A before E, B before E, A and B before E, A and C before E |
| OGEM-tab's rule | Excitation: [D], [D,E], [E], [E,D]Inhibitory: [D,A], [A], [A,D], [A,D,E], [E,D,A], [D,A,E], [A,E], [E,A], [D,E,A], [A,E,D], [E,A,D] |
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| N (# events) | N = 5, L = {A, B, C, D, E} |
| Ground truth | \\(\\hat{\\phi}_{3,1} = (c_B - c_A > -2)^1 \\wedge (c_C - c_A > -5)^1\\) |
| CLNN's rule | \\((c_B - c_A > -1.85)^{1.72} \\wedge (c_C - c_A > -3.90)^{1.59} \\wedge ((c_D - c_A) > -16.25)^{0.33} \\wedge ((c_C - c_B) > -3.01)^0 \\wedge (c_D - c_B > -7.37)^{0.02} \\wedge (c_D - c_C > -7.55)^0\\) |
| TELLER's rule | A before D, B before D, C before D |
| OGEM-tab's rule | Excitation: [A], [A, B, D], [B, D, A], [D, A], [D, A, B], [B, A], [A, D], [D], [B, A, D], [D, B, A]Inhibitory: [A, B], [B, D], [B], [A, D, B], [D, B] |
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+ "content": "Table 7: Comparison of rule discovery of "
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+ ],
+ "type": "inline_equation",
+ "content": "{\\phi }_{3,1}"
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+ "type": "text",
+ "content": " for CLNN and TELLER on the Syn-3.1 dataset."
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+ "html": "| Dataset | Syn-3.2 |
| N (# events) | N=5, L={A,B,C,D,E} |
| Ground truth | \\(\\hat{\\phi}_{3,2}=(c_{B}-c_{A}> -5)^{1}\\wedge(c_{C}-c_{B}> -4)^{1}\\wedge(c_{D}-c_{C}> -3)^{1}\\) |
| CLNN's rule | \\((c_{B}-c_{A}> -3.94)^{1.49}\\wedge(c_{C}-c_{A}> -9.12)^{0.25}\\wedge((c_{D}-c_{A})> -1.42)^{0.13}\\wedge((c_{E}-c_{A})> -3.88)^{0.15}\\wedge(c_{C}-c_{B}> -3.02)^{2.03}\\wedge(c_{D}-c_{B}> -6.27)^{0.02}\\wedge(c_{E}-c_{B}> -7.30)^{0.04}\\wedge((c_{D}- c_{C})> -2.00)^{1.92}\\wedge((c_{E}-c_{C})> -5.30)^{0.09}\\wedge((c_{E}-c_{D})> -1.57)^{0.01}\\) |
| TELLER's rule | A before E, B before E, C before E |
| OGEM-tab's rule | Excitation: [A,D], [D,A], [D,E], [E], [A,D, E], [D,E,A], [E,A], [A,E], [E,A,D], [A,E, D], [D,A,E], [E,D,A]Inhibitory: [A], [D], [E,D] |
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+ "type": "text",
+ "content": " for CLNN and TELLER on the Syn-3.2 dataset."
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+ "content": "C.4 QUANTITATIVE COMPARISON OF CLNN'S RULES WITH GROUND TRUTH"
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+ "type": "text",
+ "content": " denote the set of paired ordering representations from the learned rules, the Jaccard similarity score is calculated as "
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+ "type": "inline_equation",
+ "content": "J = \\frac{|\\mathcal{C} \\cap \\mathcal{G}|}{|\\mathcal{C} \\cup \\mathcal{G}|}"
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+ "content": "from the excitation rules. The comparison of Jaccard similarity score for the synthetic datasets is shown in Figure 9, where the Jaccard similarity score of 0 is manually set to the minimum threshold 0.05 for clarity purposes. It is clearly observed that the Jaccard similarity scores for CLNN is higher than the ones for TELLER or OGEM, implying the rules discovered by CLNN are more consistent with the ground truth."
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| Syn - 1 | Ground truth | \\(\\hat{\\phi}=(c_{A}-c_{B}>1)^{1}\\wedge(c_{A}-c_{C}>3)^{1}\\) |
| rand | \\(\\phi=(c_{A}-c_{B}>1.21)^{1.52}\\wedge(c_{A}-c_{C}>3.00)^{1.41}\\) |
| randn | \\(\\phi=(c_{A}-c_{B}>1.21)^{1.58}\\wedge(c_{A}-c_{C}>3.32)^{1.56}\\) |
| ones | \\(\\phi=(c_{A}-c_{B}>1.17)^{1.59}\\wedge(c_{A}-c_{C}>3.14)^{1.32}\\) |
| xavier | \\(\\phi=(c_{A}-c_{B}>1.12)^{1.45}\\wedge(c_{A}-c_{C}>3.20)^{1.33}\\) |
| Syn - 2 | Ground truth | \\(\\hat{\\phi}=(c_{A}-c_{B}>0.5)^{1}\\wedge(c_{A}-c_{C}>1.5)^{1}\\wedge(c_{C}-c_{D}>2)^{1}\\) |
| rand | \\(\\phi=(c_{A}-c_{B}>0.77)^{1.27}\\wedge(c_{A}-c_{C}>2.09)^{1.15}\\wedge((c_{C}-c_{D})>2.60)^{1.06}\\) |
| randn | \\(\\phi=(c_{A}-c_{B}>0.80)^{1.97}\\wedge(c_{A}-c_{C}>1.92)^{1.62}\\wedge((c_{C}-c_{D})>1.74)^{1.45}\\) |
| ones | \\(\\phi=(c_{A}-c_{B}>1.03)^{1.63}\\wedge(c_{A}-c_{C}>1.92)^{1.50}\\wedge((c_{C}-c_{D})>2.03)^{1.44}\\) |
| xavier | \\(\\phi=(c_{A}-c_{B}>0.97)^{1.92}\\wedge(c_{A}-c_{C}>2.07)^{1.63}\\wedge((c_{C}-c_{D})>1.97)^{1.62}\\) |
| Syn - 3.1 | Ground truth | \\(\\hat{\\phi}=(c_{B}-c_{A}>-2)^{1}\\wedge(c_{C}-c_{A}>-5)^{1}\\) |
| rand | \\(\\phi=(c_{B}-c_{A}>-1.85)^{1.72}\\wedge(c_{C}-c_{A}>-3.90)^{1.59}\\) |
| randn | \\(\\phi=(c_{B}-c_{A}>-1.98)^{1.51}\\wedge(c_{C}-c_{A}>-3.89)^{1.68}\\) |
| ones | \\(\\phi_{3,1}=(c_{B}-c_{A}>-1.94)^{1.84}\\wedge(c_{C}-c_{A}>-3.68)^{2.33}\\) |
| xavier | \\(\\phi_{3,1}=(c_{B}-c_{A}>-1.89)^{1.54}\\wedge(c_{C}-c_{A}>-3.92)^{1.62}\\) |
| Syn - 3.2 | Ground truth | \\(\\hat{\\phi}=(c_{B}-c_{A}>-5)^{1}\\wedge(c_{C}-c_{B}>-4)^{1}\\wedge(c_{D}-c_{C}>-3)^{1}\\) |
| rand | \\(\\phi=(c_{B}-c_{A}>-3.94)^{1.49}\\wedge(c_{C}-c_{B}>-3.02)^{2.03}\\wedge((c_{D}-c_{C})> -2.00)^{1.92}\\) |
| randn | \\(\\phi=(c_{B}-c_{A}>-3.79)^{1.71}\\wedge(c_{C}-c_{B}>-3.04)^{1.89}\\wedge((c_{D}-c_{C})> -1.68)^{1.65}\\) |
| ones | \\(\\phi=(c_{B}-c_{A}>-3.53)^{1.66}\\wedge(c_{C}-c_{B}>-3.09)^{1.88}\\wedge((c_{D}-c_{C})> -1.25)^{1.81}\\) |
| xavier | \\(\\phi=(c_{B}-c_{A}>-3.71)^{1.53}\\wedge(c_{C}-c_{B}>-3.09)^{2.04}\\wedge((c_{D}-c_{C})> -1.86)^{1.73}\\) |
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| Avg Acc | Acc Gap | Avg Acc | Acc Gap |
| OPTIMUM | 75.00 | 0.00 | 75.00 | 0.00 |
| GRAYSCALE | 73.82±0.11 | 0.37±0.05 | 73.97±0.14 | 0.29±0.08 |
| ERM | 49.21±0.79 | 91.88±3.31 | 49.03±0.93 | 92.17±3.04 |
| IRMv1 | 67.36±0.31 | 2.77±0.15 | 67.11±0.34 | \\( {2.42} \\pm {0.12} \\) |
| IRMv0 | 67.01±0.42 | \\( {2.85} \\pm {0.18} \\) | 66.71±0.42 | \\( {2.36} \\pm {0.19} \\) |
| IRM-GAME | 66.39±0.72 | 4.47±0.61 | 65.93±0.53 | \\( {4.25} \\pm {0.84} \\) |
| REX | 66.82±0.44 | \\( {2.59} \\pm {0.11} \\) | 67.14±0.38 | \\( {2.16} \\pm {0.13} \\) |
| BIRM | 67.35±0.39 | \\( {2.65} \\pm {0.10} \\) | 68.05±0.43 | \\( {1.99} \\pm {0.07} \\) |
| SPARSEIRM | 67.12±0.53 | \\( {2.33} \\pm {0.18} \\) | 67.72±0.41 | \\( {2.11} \\pm {0.19} \\) |
| FISHR | 67.22±0.43 | \\( {2.44} \\pm {0.15} \\) | 67.32±0.39 | \\( {2.59} \\pm {0.15} \\) |
| BLO-IRM | 68.72±0.41 | \\( {2.19} \\pm {0.15} \\) | 68.89±0.31 | \\( {2.39} \\pm {0.09} \\) |
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+ "text": "BLOC-IRM with different regularizations. Based on the penalty terms used in the existing IRM variants, we explore the performance of our proposed BLOC-IRM with various regularization, including the ones used in IRMv1 (BLOC-IRM-v1), REX (BLOC-IRM-REX), and FISHR (BLOC-IRM-FISHR). We conduct experiments on three different datasets and the results are shown in Table A3. It is obvious that the best performance is always achieved when the per-environment stationarity is penalized in the upper-level. This is not surprising since without an explicit promotion of stationarity, other forms of penalties do not guarantee the BLO algorithm to achieve an optimal solution.",
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+ "table_body": "| Environment Metrics (%) | \\( {p}_{\\text{tr }} \\in \\{ {0.1},{0.15}\\} \\) | \\( {p}_{\\text{tr }} \\in \\{ {0.1},{0.15},{0.2}\\} \\) |
| Avg Acc | Acc Gap | Avg Acc | Acc Gap |
| OPTIMUM | 75.00 | 0.00 | 75.00 | 0.00 |
| GRAYSCALE | 73.82±0.11 | 0.37±0.05 | 73.97±0.14 | 0.29±0.08 |
| ERM | 49.21±0.79 | 91.88±3.31 | 49.03±0.93 | 92.17±3.04 |
| IRMv1 | 67.36±0.31 | 2.77±0.15 | 67.11±0.34 | \\( {2.42} \\pm {0.12} \\) |
| IRMv0 | 67.01±0.42 | \\( {2.85} \\pm {0.18} \\) | 66.71±0.42 | \\( {2.36} \\pm {0.19} \\) |
| IRM-GAME | 66.39±0.72 | 4.47±0.61 | 65.93±0.53 | \\( {4.25} \\pm {0.84} \\) |
| REX | 66.82±0.44 | \\( {2.59} \\pm {0.11} \\) | 67.14±0.38 | \\( {2.16} \\pm {0.13} \\) |
| BIRM | 67.35±0.39 | \\( {2.65} \\pm {0.10} \\) | 68.05±0.43 | \\( {1.99} \\pm {0.07} \\) |
| SPARSEIRM | 67.12±0.53 | \\( {2.33} \\pm {0.18} \\) | 67.72±0.41 | \\( {2.11} \\pm {0.19} \\) |
| FISHR | 67.22±0.43 | \\( {2.44} \\pm {0.15} \\) | 67.32±0.39 | \\( {2.59} \\pm {0.15} \\) |
| BLO-IRM | 68.72±0.41 | \\( {2.19} \\pm {0.15} \\) | 68.89±0.31 | \\( {2.39} \\pm {0.09} \\) |
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+ "content": "| Environment Metrics (%) | \\( {p}_{\\text{tr }} \\in \\{ {0.1},{0.15}\\} \\) | \\( {p}_{\\text{tr }} \\in \\{ {0.1},{0.15},{0.2}\\} \\) |
| Avg Acc | Acc Gap | Avg Acc | Acc Gap |
| OPTIMUM | 75.00 | 0.00 | 75.00 | 0.00 |
| GRAYSCALE | 73.82±0.11 | 0.37±0.05 | 73.97±0.14 | 0.29±0.08 |
| ERM | 49.21±0.79 | 91.88±3.31 | 49.03±0.93 | 92.17±3.04 |
| IRMv1 | 67.36±0.31 | 2.77±0.15 | 67.11±0.34 | \\( {2.42} \\pm {0.12} \\) |
| IRMv0 | 67.01±0.42 | \\( {2.85} \\pm {0.18} \\) | 66.71±0.42 | \\( {2.36} \\pm {0.19} \\) |
| IRM-GAME | 66.39±0.72 | 4.47±0.61 | 65.93±0.53 | \\( {4.25} \\pm {0.84} \\) |
| REX | 66.82±0.44 | \\( {2.59} \\pm {0.11} \\) | 67.14±0.38 | \\( {2.16} \\pm {0.13} \\) |
| BIRM | 67.35±0.39 | \\( {2.65} \\pm {0.10} \\) | 68.05±0.43 | \\( {1.99} \\pm {0.07} \\) |
| SPARSEIRM | 67.12±0.53 | \\( {2.33} \\pm {0.18} \\) | 67.72±0.41 | \\( {2.11} \\pm {0.19} \\) |
| FISHR | 67.22±0.43 | \\( {2.44} \\pm {0.15} \\) | 67.32±0.39 | \\( {2.59} \\pm {0.15} \\) |
| BLO-IRM | 68.72±0.41 | \\( {2.19} \\pm {0.15} \\) | 68.89±0.31 | \\( {2.39} \\pm {0.09} \\) |
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+ "html": "| Algorithm 1 Bayes-OCP |
| 1: Initialize μx and σx2 for all x ∈ X |
| 2: X ← X, t ← 0, D0 ← ∅ |
| 3: Start experiment ψ = (X,τ,ρ) |
| 4: loop: |
| 5: t ← t + 1; Dt ← Dt-1 ∪ {xt,yt} |
| 6: 1/σxt2 ← 1/σxt2 + 1 |
| 7: μxt← μxt + (yt - μxt)σxt2 |
| (i) Identify a candidate subpopulation X' to replace X: |
| 8: X' ← ∅ |
| 9: while X \\ X' ⊃ ∅: |
| 10: x* ← argmaxx∈X\\X' |
| Eθx~N(μx,σx2)[G(0)(X' ∪ {x}; {θx})] |
| 11: if Eθx~N(μx,σx2)[G(0)(X' ∪ {x*}; {θx})] > Eθx~N(μx,σx2)[G(0)(X'; {θx})]: |
| 12: X' ← X' ∪ {x*} |
| 13: else: break |
| (ii) Decide whether to actually replace X with X': |
| 14: if Pθx~N(μx,σx2)[G(0)(X'; {θx}) > G(X, Dt; {θx})] > β: |
| 15: X ← X', t ← 0, D0 ← ∅ |
| 16: Start a new experiment ψ = (X,τ,ρ) |
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+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "OCP in managing various experiments would degrade (see Appendix C for related experiments). Making use of the posteriors it maintains, Bayes-OCP performs two steps at each iteration:",
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+ "text": "(i) First, a subpopulation $X' \\subset X$ within the currently targeted population $X$ is identified as a potential candidate to target next; due to the combinatorial size of $\\Psi$ , it would not be practical to consider every subpopulation individually as a candidate for large $|\\mathcal{X}|$ . The ideal candidate would be the subpopulation with the largest expected utility: $X' = \\operatorname{argmax}_{X' \\subset X} \\mathbb{E}_{\\theta_x \\sim \\mathcal{N}(\\mu_x, \\sigma_x^2)} [\\mathcal{G}^{(0)}(X'; \\{\\theta_x\\})]$ . But again due to the combinatorial size of the search space, Bayes-OCP employs a greedy algorithm instead and forms candidate subpopulations by combining, one by one, the atomic-subpopulations that increase the expected utility the most, until the expected utility no longer improves. Note that it is common to use greedy algorithms to solve combinatorial optimization problems (Lawler, 1976; Papadimitriou and Steiglitz, 1982).",
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+ "type": "text",
+ "text": "(ii) Then, it is decided whether the current experiment targeting population $X$ should be stopped in favor of targeting candidate $X^{\\prime}$ identified earlier instead. A greedy strategy would have done so whenever $\\mathbb{E}_{\\theta_x} \\sim \\mathcal{N}(\\mu_x, \\sigma_x^2)[\\mathcal{G}^{(0)}(X'; \\{\\theta_x\\})] > \\mathbb{E}_{\\theta_x} \\sim \\mathcal{N}(\\mu_x, \\sigma_x^2)[\\mathcal{G}(X, \\mathcal{D}_t; \\{\\theta_x\\})]$ . But from our earlier analysis, we have learned that the optimal strategy is optimistic (cf. Proposition 3). As such, Bayes-OCP checks whether it is overwhelmingly likely that the alternative experiment has higher expected utility—that is whether $\\mathbb{P}_{\\theta_x} \\sim \\mathcal{N}(\\mu_x, \\sigma_x^2)\\{\\mathcal{G}^{(0)}(X'; \\{\\theta_x\\}) > \\mathcal{G}(X, \\mathcal{D}_t; \\{\\theta_x\\})\\} > \\beta$ , where $\\beta \\in (1/2, 1)$ controls the decision-making threshold. When $\\beta$ is large, we are more optimistic that the current experiment will succeed and require stronger evidence that the alternative experiment has higher expected utility. Note that, as the posteriors $\\mathcal{N}(\\mu_x, \\sigma_x^2)$ get narrower, the optimism of this rule naturally decreases, which should be the case for the optimal strategy (cf. Proposition 4). As one extreme, the two switching rules become equivalent when $\\{\\sigma_x^2 \\to 0\\}$ .",
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+ "type": "text",
+ "text": "5 RELATED WORK",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Optimal stopping Optimal commitment is essentially a new type of optimal stopping/switching problem. In typical optimal stopping problems (OSPs), the reward an agent can receive evolves based on a stochastic process and the goal of the agent is to determine the optimal time step to stop when the reward to be received is in some sense maximized (Shiryaev, 2007). Optimal commitment is unique in that a positive reward can only be received by not stopping until a pre-specified time horizon $\\tau$ . In optimal commitment, there is still a stochastic process (namely, samples $y_{t}$ ) that gradually reveals more information regarding what that positive reward will be at the end, however, the reward—or rather the cost—of stopping earlier is independent of this stochastic process (and is equal to $-tC$ ).",
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+ "text": "Sequential hypothesis testing Among other OSPs, optimal commitment is most closely related to sequential hypothesis testing (SHT), where an agent makes sequential observations regarding a given hypothesis and eventually needs to decide whether to reject the said (alternate) hypothesis or reject some null hypothesis (Wald and Wolfowitz, 1948; Yu et al., 2009; Drugowitsch et al., 2012; Shenoy and Angela, 2012; Zhang and Angela, 2013; Drugowitsch et al., 2014; Khalvati and Rao, 2015; Schonbrodt et al., 2017; Fauß et al., 2020). Rejecting the correct hypothesis provides a positive reward whereas waiting for more observations, while informative, is also costly as in OCP. It is well known that the optimal policy in the classic setting of SHT is a thresholding-type policy with fixed thresholds that do not vary over time: The null hypothesis is rejected if some test statistic gets above a threshold (and the alternate hypothesis is rejected if the same statistic gets below a different threshold).",
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+ "type": "text",
+ "text": "Optimal commitment can be thought of as a SHT problem with the crucial difference that the meta-experimenter has only the option of discarding the alternate hypothesis (i.e. breaking a commitment), and once some time horizon is reached (i.e. when a commitment is kept), either the null hypothesis or the alternate hypothesis is automatically rejected according to some external success criterion $\\rho$ , regardless of what the meta-experimenters' decision might have been otherwise. As we have shown in Proposition 2, the optimal policy still remains a thresholding-type policy, but since there is now a deadline to discard the alternate hypothesis early, the thresholds become time-varying; in particular, they become less and less optimistic as the said deadline approaches (cf. Proposition 4).",
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+ "type": "text",
+ "text": "Frazier and Angela (2007); Dayanik and Angela (2013); Alaa and van der Schaar (2016) consider SHT under stochastic deadlines, but different from optimal commitment, they still allow agents to reject both hypotheses at any time. In these works, the agent must make the rejection decision before the deadline is reached to be able to receive a positive reward, whereas in our case, the agent must wait until the deadline to see whether the null hypothesis will be rejected or not. Naghshvar and",
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+ "type": "header",
+ "text": "Published as a conference paper at ICLR 2023",
+ "bbox": [
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+ "type": "page_number",
+ "text": "6",
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+ "Table 2: Comparison of related experiment designs. Optimal commitment is the only design that aims to decide both when an alternative population should be targeted—as opposed to switching the target population only at a fixed decision point—as well as which population to target among many potential candidates—as opposed to a simple binary decision of “overall population vs. sub-population” or “go vs. no-go”."
+ ],
+ "table_footnote": [],
+ "table_body": "| Term | Notation | Description |
| Experiment | - | Conducted to confirm efficacy of an intervention, e.g. a new treatment in clinical trials, or a new recommendation policy in online advertisement |
| Subject | - | Individual participant of an experiment, e.g. patients in a clinical trial, or customers in online advertisement |
| Population | X⊆X | Collection of subjects that all share the same qualities, e.g. all female patients in a clinical trial, or all customers with the same preferences in online advertisement |
| Atomic-population | x∈X | Indivisible populations |
| Propensities | ηx | The probability that a subject being from atomic-population x |
| ηx | The probability that a subject being from population X |
| ηx|X | The probability that a subject being from atomic-population x conditioned on the fact that they from population X |
| Outcome distribution | Ωx | Distribution of outcomes that is indicative of the effect of the intervention of interest for atomic-population x |
| Mean outcomes | θx | Expected outcome, i.e. the effect of the intervention of interest, for atomic-population x |
| θX | Expected outcome for population X |
| Experiment design | ψ=(X,τ,ρ) | Target population X, sample horizon τ, and success criterion ρ that characterize an experiment |
| Viable experiment designs | Ψ | Experiment designs that can potentially be followed by a meta-experimenter |
| Meta-experimenter | - | The decision-making agent that decides when to run experiments according to which experiment design in Ψ |
| Sample/time horizon | τ | An experiment is terminated when t=τ |
| Success criterion | ρ | An experiment is declared a success if ρ(Dτ)=1 |
| Online dataset | Dt | Data collected by an ongoing experiment at time step t |
| Dt | Data collected by the i-th experiment run by the meta-experimenter at time step t |
| Aggregate dataset | DIt | Collective data collected by all experiments up to time step t of the i-th experiment |
| - | Tt | Number of time steps for which the i-th experiment is conducted until it was stopped or its time horizon was reached |
| Cost | Cψ | Cost incurred per time step by running experiment ψ |
| Reward | Rψ | Reward received if experiment ψ is successful |
| Utility | G | Sum of costs and rewards received after all experimentation is concluded |
| Policy | π | Decision-making policy of the meta-experiment |
| Optimal policy | π* | The optimal policy that maximizes utility G in expectation |
| Greedy policy | πgreedy | See Section 3 |
| Test statistic | μt | In the simplified case in Section 3, the empirical mean outcome |
| Value function | Vπ(t,μ) | The expected utility of following policy π when μt=μ |
| Q-function | Qπ(t,μ) | The expected utility of following policy π after conducting the ongoing experiment for one more time step when μt=μ |
| - | Ttπ | The first time step at or after time step t that policy π decides to stop all experimentation |
| Optimal value function | V* | The value function associated with π* |
| Optimal Q-function | Q* | The Q-function associated with π* |
| Thresholds | μt* | Decision-making thresholds associated with π* |
| μtgreedy | Decision-making thresholds associated with πgreedy |
| Conditional power function | P(X, Dt; {θx}) | The probability of a hypothesis test being successful condi- tioned on mean outcomes {θx} |
| Expected utility function | G(X, Dt; {θx}) | The expected utility of fully committing to an experiment and waiting until it terminates when the experiment targets popula-tion X, is currently at time step t, and collected dataset Dt |
| Posteriors | N(μx, σx2) | Posterior distributions over mean outcomes {θx} maintained by Bayes-OCP such that θx|D ~ N(μx, σx2) |
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+ "type": "text",
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+ "angle": 0,
+ "content": "The Alan Turing Institute"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "mv472@cam.ac.uk"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "ABSTRACT"
+ },
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+ "bbox": [
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+ "content": "In many scenarios, decision-makers must commit to long-term actions until their resolution before receiving the payoff of said actions, and usually, staying committed to such actions incurs continual costs. For instance, in healthcare, a newly-discovered treatment cannot be marketed to patients until a clinical trial is conducted, which both requires time and is also costly. Of course in such scenarios, not all commitments eventually pay off. For instance, a clinical trial might end up failing to show efficacy. Given the time pressure created by the continual cost of keeping a commitment, we aim to answer: When should a decision-maker break a commitment that is likely to fail—either to make an alternative commitment or to make no further commitments at all? First, we formulate this question as a new type of optimal stopping/switching problem called the optimal commitment problem (OCP). Then, we theoretically analyze OCP, and based on the insight we gain, propose a practical algorithm for solving it. Finally, we empirically evaluate the performance of our algorithm in running clinical trials with subpopulation selection."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "1 INTRODUCTION"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In many real-world settings, decision-makers must commit to long-term actions and wait until their resolution before receiving the payoff of said actions. Meanwhile, staying committed to such actions incurs continual costs. For instance, in portfolio management, it might take time for an asset to develop additional value after an initial investment, and keeping capital tied up in an asset comes with an opportunity cost for the investor (Markowitz, 1959; Merton, 1969; Karatzas and Wang, 2020). In an energy network, turning power stations on and off is not an immediate action, hence a sudden increase in energy demand can only be met with a delay after putting more stations into operation, and keeping stations operational obviously consumes resources (Rafique and Jianhua, 2018; Olofsson et al., 2022). In healthcare, a newly-discovered treatment can only be marketed to patients once a successful clinical trial that targets the said treatment is conducted, which both requires time and is also costly (Kaitin, 2010; Umscheid et al., 2011)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Of course, not all commitments eventually pay off: An asset might end up losing value despite investments, energy demands might shift faster than a network can react to, and a clinical trial might fail to show efficacy for the targeted treatment. Given the time pressure created by the continual cost of keeping a commitment, our goal in this paper is to answer the question: When should a decision-maker break a commitment—thereby avoiding future costs but also forfeiting any potential returns—either to make an alternative commitment instead or to make no further commitments at all? Solving this problem optimally requires a careful balance between exploration and exploitation: The earlier a commitment that is bound to fail is broken, the more resources would be saved (cf. exploitation); but the longer one is kept, the more information is revealed regarding whether the commitment is actually failing or might still succeed (cf. exploration)—and in certain cases, also regarding the prospects of similar commitments one could make instead."
+ },
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+ "content": "Related problems are mostly studied within the context of adaptive experimentation and sequential hypothesis testing (see Section 5). As such, we focus on adaptive experimentation as our main application as well. More specifically, we consider the problem of selecting the target population of an adaptive experiment. Suppose an experimenter, who is interested in proving the efficacy of a new treatment, starts running an initial experiment that targets a certain population of patients. Incidentally, the treatment being tested is effective only for a relatively narrow subpopulation of patients but not for the wider population as a whole. Hence, an experiment targeting the overall population, but not the subpopulation specifically, will most probably fail to prove efficacy and prevent the deployment of the treatment for the patients who would have actually benefited from it, not to mention waste"
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+ "type": "page_number",
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+ "angle": 0,
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+ "type": "header",
+ "bbox": [
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+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.17,
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+ ],
+ "angle": 0,
+ "content": "time and resources (Moineddin et al., 2008; Lipkovich et al., 2017; Chiu et al., 2018). Of course, the experimenter has no knowledge of this in advance but the initial experiment they have set up would slowly reveal more information regarding the effects of the treatment and the fact that the ongoing experiment is bound to fail. In that case, we want to be able to determine at what point the experimenter has enough information to justify breaking their commitment to the initial experiment that targets too wide of a population to be successful, in favor of making a new commitment to a follow-up experiment that focuses on a narrower subpopulation instead?"
+ },
+ {
+ "type": "text",
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+ "content": "Contributions Our contributions are threefold: First, we formulate the problem of making and breaking commitments in a timely manner as a new type of optimal stopping/switching problem called the optimal commitment problem (OCP) (Section 2). The defining feature of OCP is that rewards are received only when a known time point is reached but costs are incurred continually, requiring commitment to actions but with incentive to abandon those commitments. As we will show later, OCP cannot be easily solved via conventional reinforcement learning techniques due to its non-convex nature. Second, we theoretically analyze a simplified case of OCP to identify the characteristics of the optimal solution (Section 3), and based on the insights we gain, propose a practical algorithm for the more general case (Section 4). Third, we empirically evaluate the performance of our algorithm in running experiments with subpopulation selection (Section 6). Before we move on, it should be emphasized that, although we predominantly consider adaptive experimentation as our main application, our contributions remain generally applicable to portfolio management, energy systems, and any other decision-making scenarios that require commitments to long-term actions."
+ },
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+ "content": "2 OPTIMAL COMMITMENT PROBLEM"
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+ "content": "We first introduce the problem of optimal commitment from the perspective of running experiments. As far as our formulation is concerned, experiments are conducted to confirm the efficacy of an intervention by observing the outcome of the said intervention for subjects belonging to a particular population. However, this experiment-focused perspective does not limit the applicability of OCP; we stress its generality later at the end of the section. We provide a glossary of terms and notation in Appendix K."
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+ "content": "Populations Let \\(\\mathcal{X}\\) be a discrete set of atomic-populations such that every subject is only the member of exactly one atomic-population \\(x\\in \\mathcal{X}\\). Denote with \\(\\eta_{x}\\in [0,1]\\) the probability of a subject being from atomic-population \\(x\\) (such that \\(\\sum_{x\\in \\mathcal{X}}\\eta_x = 1\\)), and with \\(\\Omega_{x}\\) the distribution of outcomes for atomic-population \\(x\\) such that the mean outcome \\(\\theta_{x} = \\mathbb{E}_{y\\sim \\Omega_{x}}[y]\\) is the effect of some intervention for atomic-population \\(x\\). Now, wider populations can be constructed by combining various atomic-populations. Let any \\(X\\subseteq \\mathcal{X}\\) represent the population of subjects who belong to either one of the atomic-populations \\(\\{x\\in X\\}\\). Then, the probability of a subject being from population \\(X\\) can be written as \\(\\eta_{X} = \\sum_{x\\in X}\\eta_{x}\\), the probability of a subject being from atomic-population \\(x\\) conditioned on the fact that they are from population \\(X\\) can be written as \\(\\eta_{x|X} = \\eta_x / \\eta_X\\), and the average effect for population \\(X\\) can be written as \\(\\bar{\\theta}_X = \\sum_{x\\in X}\\eta_{x|X}\\theta_x\\)."
+ },
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+ "type": "text",
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+ "content": "Experiments An experiment is largely characterized by the population it targets, its sample horizon, and its success criterion. During an experiment that targets population \\( X \\), at each time step \\( t \\in \\{1, 2, \\ldots\\} \\) that the experiment continues, first a subject from some atomic-population \\( x_{t} \\) within the targeted population \\( X \\) arrives with probability \\( \\eta_{x_{t}|X} \\), and then the outcome \\( y_{t} \\sim \\Omega_{x_{t}} \\) for that subject is observed. This process generates an online dataset \\( \\mathcal{D}_{t} = \\{x_{t'}, y_{t'}\\}_{t' = 1}^{t} \\). The experiment terminates when a pre-specified sample/time horizon \\( \\tau \\) is reached. Once terminated, the experiment is declared a success if \\( \\rho(\\mathcal{D}_{\\tau}) = 1 \\), where \\( \\rho: (\\mathcal{X} \\times \\mathbb{R})^{\\tau} \\to \\{0, 1\\} \\) is the success criterion, and declared a failure otherwise. Formally, the tuple \\( \\psi = (X, \\tau, \\rho) \\) constitutes an experiment design."
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+ "content": "Meta-experimenter Suppose a meta-experimenter is given a set of viable experiment designs \\(\\Psi\\) and is tasked with running at least one successful experiment. Each experiment \\(\\psi \\in \\Psi\\) has an associated cost \\(C_{\\psi} \\in \\mathbb{R}_{+}\\), which the experiment incurs per time step that it continues, and an associated reward \\(R_{\\psi} \\in \\mathbb{R}_{+}\\), which the experiment provides only if it eventually succeeds. The meta-experimenter aims to maximize utility—that is the difference between any eventual reward received and the total costs incurred by running experiments. They first pick an initial experiment \\(\\psi^{1} \\in \\Psi\\) and start conducting it, which generates an online dataset \\(\\mathcal{D}_t^1\\) as described earlier. Now at each time step \\(t\\), they need to decide whether they should stay committed to their initial decision and wait until \\(\\psi^{1}\\) terminates, or stop \\(\\psi^{1}\\) early in favor of starting a new experiment \\(\\psi^{2}\\). They might decide on the latter to avoid unnecessary costs if \\(\\mathcal{D}_t^1\\) already indicates \\(\\psi^{1}\\) is unlikely to succeed. If at some point a secondary experiment \\(\\psi^{2}\\) is started, now the meta-experiment has a similar decision to make"
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+ [
+ {
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+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "regarding whether to stop \\(\\psi^2\\) early in favor of starting a new experiment \\(\\psi^3 \\in \\Psi\\). This process continues until either an experiment finally succeeds or the meta-experimenter decides not to conduct any further experiments; let the random variable \\(n \\in \\{1, 2, \\ldots\\}\\) be such that \\(\\psi^n\\) is the last experiment. We denote with \\(\\psi^i = (X^i, \\tau^i, \\rho^i)\\) the \\(i\\)-th experiment conducted by the meta-experimenter, and with \\(T^i\\) the number of time steps for which the \\(i\\)-th experiment is conducted either until it was stopped by the meta-experimenter or the time horizon \\(\\tau^i\\) was reached. Denote with \\(\\pi(t, \\psi^i, \\bar{\\mathcal{D}}_t^i)\\) the decision-making policy of the meta-experimenter, where \\(t\\) is the current time step of the latest experiment \\(\\psi^i\\) and \\(\\bar{\\mathcal{D}}_t^i = (\\cup_{j=1}^{i-1} \\mathcal{D}_{T^j}^j) \\cup \\mathcal{D}_t^i\\) is an aggregate dataset. We write (i) \\(\\pi(t, \\psi^i, \\bar{\\mathcal{D}}_t^i) = \\psi^i\\) if the meta-experiment decides to keep conducting the current experiment \\(\\psi^i\\), (ii) \\(\\pi(t, \\psi^i, \\bar{\\mathcal{D}}_t^i) = \\psi' \\neq \\psi^i\\) if the meta-experimenter decides to stop experiment \\(\\psi^i\\) and start experiment \\(\\psi'\\) instead, and (iii) \\(\\pi(t, \\psi^i, \\bar{\\mathcal{D}}_t^i) = \\emptyset\\) if the meta-experimenter decides not to conduct any further experiments."
+ },
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+ "angle": 0,
+ "content": "Objective Once all experimentation is concluded, the meta-experimenter achieves the total utility"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\nG = R _ {\\psi^ {n}} \\cdot \\mathbb {1} \\left\\{T ^ {n} = \\tau^ {n} \\right\\} \\cdot \\rho^ {n} \\left(\\mathcal {D} _ {\\tau^ {n}} ^ {n}\\right) - \\sum_ {i = 1} ^ {n} C _ {\\psi^ {i}} \\cdot T ^ {i}. \\tag {1}\n\\]"
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "Then, the optimal commitment problem is to find the optimal policy \\(\\pi^{*} = \\operatorname{argmax}_{\\pi} \\mathbb{E}_{\\pi}[G]\\) that maximizes the expected utility given \\(\\Psi\\), \\(\\{\\eta_x\\}\\). \\(\\{R_{\\psi}, C_{\\psi}\\}\\) without knowing mean outcomes \\(\\{\\theta_x\\}\\) or outcome distributions \\(\\{\\Omega_x\\}\\). It is called the optimal commitment problem because each experiment \\(\\psi = (X, \\tau, \\rho)\\) only provides a reward if the meta-experimenter commits to incurring its costs for at least \\(\\tau\\) time steps, and the meta-experimenter needs to decide which experiment in \\(\\Psi\\) is the better commitment—or if there is any experiment worth committing to at all—adaptively."
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "General applicability of OCP Although we have described OCP from the perspective of (meta-)experiment design, it can potentially be useful in modeling many other problems as we have stressed during the introduction (see Table 1). For instance, in portfolio management, atomic-populations can be regarded as various assets one can invest in, then a population would correspond to a portfolio"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "of assets. Similar to experiments, when these portfolios require a time commitment (cf. \\(\\tau\\)) before they provide their payoff (cf. \\(R_{\\psi}\\)) and incur an opportunity cost (cf. \\(C_{\\psi}\\)) in the mean time, the decision-making problem of managing when and which portfolio to invest in constitutes an instance of the optimal commitment problem. Another good examples is energy management, where power stations and the networks they form are akin to atomic-populations and populations. Since power stations cannot be turned on and off immediately, putting one in operation requires a certain amount of commitment."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1: Equivalent concepts across different domains. OCP can model scenarios other than adaptive experimentation."
+ },
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Algorithm 1 Bayes-OCP |
| 1: Initialize μx and σx2 for all x ∈ X |
| 2: X ← X, t ← 0, D0 ← ∅ |
| 3: Start experiment ψ = (X,τ,ρ) |
| 4: loop: |
| 5: t ← t + 1; Dt ← Dt-1 ∪ {xt,yt} |
| 6: 1/σxt2 ← 1/σxt2 + 1 |
| 7: μxt← μxt + (yt - μxt)σxt2 |
| (i) Identify a candidate subpopulation X' to replace X: |
| 8: X' ← ∅ |
| 9: while X \\ X' ⊃ ∅: |
| 10: x* ← argmaxx∈X\\X' |
| Eθx~N(μx,σx2)[G(0)(X' ∪ {x}; {θx})] |
| 11: if Eθx~N(μx,σx2)[G(0)(X' ∪ {x*}; {θx})] > Eθx~N(μx,σx2)[G(0)(X'; {θx})]: |
| 12: X' ← X' ∪ {x*} |
| 13: else: break |
| (ii) Decide whether to actually replace X with X': |
| 14: if Pθx~N(μx,σx2)[G(0)(X'; {θx}) > G(X, Dt; {θx})] > β: |
| 15: X ← X', t ← 0, D0 ← ∅ |
| 16: Start a new experiment ψ = (X,τ,ρ) |
"
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+ "type": "page_number",
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+ "angle": 0,
+ "content": "5"
+ }
+ ],
+ [
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+ "type": "header",
+ "bbox": [
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+ 0.033,
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+ ],
+ "angle": 0,
+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "OCP in managing various experiments would degrade (see Appendix C for related experiments). Making use of the posteriors it maintains, Bayes-OCP performs two steps at each iteration:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "(i) First, a subpopulation \\( X' \\subset X \\) within the currently targeted population \\( X \\) is identified as a potential candidate to target next; due to the combinatorial size of \\( \\Psi \\), it would not be practical to consider every subpopulation individually as a candidate for large \\( |\\mathcal{X}| \\). The ideal candidate would be the subpopulation with the largest expected utility: \\( X' = \\operatorname{argmax}_{X' \\subset X} \\mathbb{E}_{\\theta_x \\sim \\mathcal{N}(\\mu_x, \\sigma_x^2)} [\\mathcal{G}^{(0)}(X'; \\{\\theta_x\\})] \\). But again due to the combinatorial size of the search space, Bayes-OCP employs a greedy algorithm instead and forms candidate subpopulations by combining, one by one, the atomic-subpopulations that increase the expected utility the most, until the expected utility no longer improves. Note that it is common to use greedy algorithms to solve combinatorial optimization problems (Lawler, 1976; Papadimitriou and Steiglitz, 1982)."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "(ii) Then, it is decided whether the current experiment targeting population \\(X\\) should be stopped in favor of targeting candidate \\(X^{\\prime}\\) identified earlier instead. A greedy strategy would have done so whenever \\(\\mathbb{E}_{\\theta_x} \\sim \\mathcal{N}(\\mu_x, \\sigma_x^2)[\\mathcal{G}^{(0)}(X'; \\{\\theta_x\\})] > \\mathbb{E}_{\\theta_x} \\sim \\mathcal{N}(\\mu_x, \\sigma_x^2)[\\mathcal{G}(X, \\mathcal{D}_t; \\{\\theta_x\\})]\\). But from our earlier analysis, we have learned that the optimal strategy is optimistic (cf. Proposition 3). As such, Bayes-OCP checks whether it is overwhelmingly likely that the alternative experiment has higher expected utility—that is whether \\(\\mathbb{P}_{\\theta_x} \\sim \\mathcal{N}(\\mu_x, \\sigma_x^2)\\{\\mathcal{G}^{(0)}(X'; \\{\\theta_x\\}) > \\mathcal{G}(X, \\mathcal{D}_t; \\{\\theta_x\\})\\} > \\beta\\), where \\(\\beta \\in (1/2, 1)\\) controls the decision-making threshold. When \\(\\beta\\) is large, we are more optimistic that the current experiment will succeed and require stronger evidence that the alternative experiment has higher expected utility. Note that, as the posteriors \\(\\mathcal{N}(\\mu_x, \\sigma_x^2)\\) get narrower, the optimism of this rule naturally decreases, which should be the case for the optimal strategy (cf. Proposition 4). As one extreme, the two switching rules become equivalent when \\(\\{\\sigma_x^2 \\to 0\\}\\)."
+ },
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+ "type": "title",
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+ "angle": 0,
+ "content": "5 RELATED WORK"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Optimal stopping Optimal commitment is essentially a new type of optimal stopping/switching problem. In typical optimal stopping problems (OSPs), the reward an agent can receive evolves based on a stochastic process and the goal of the agent is to determine the optimal time step to stop when the reward to be received is in some sense maximized (Shiryaev, 2007). Optimal commitment is unique in that a positive reward can only be received by not stopping until a pre-specified time horizon \\(\\tau\\). In optimal commitment, there is still a stochastic process (namely, samples \\(y_{t}\\)) that gradually reveals more information regarding what that positive reward will be at the end, however, the reward—or rather the cost—of stopping earlier is independent of this stochastic process (and is equal to \\(-tC\\))."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Sequential hypothesis testing Among other OSPs, optimal commitment is most closely related to sequential hypothesis testing (SHT), where an agent makes sequential observations regarding a given hypothesis and eventually needs to decide whether to reject the said (alternate) hypothesis or reject some null hypothesis (Wald and Wolfowitz, 1948; Yu et al., 2009; Drugowitsch et al., 2012; Shenoy and Angela, 2012; Zhang and Angela, 2013; Drugowitsch et al., 2014; Khalvati and Rao, 2015; Schonbrodt et al., 2017; Fauß et al., 2020). Rejecting the correct hypothesis provides a positive reward whereas waiting for more observations, while informative, is also costly as in OCP. It is well known that the optimal policy in the classic setting of SHT is a thresholding-type policy with fixed thresholds that do not vary over time: The null hypothesis is rejected if some test statistic gets above a threshold (and the alternate hypothesis is rejected if the same statistic gets below a different threshold)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Optimal commitment can be thought of as a SHT problem with the crucial difference that the meta-experimenter has only the option of discarding the alternate hypothesis (i.e. breaking a commitment), and once some time horizon is reached (i.e. when a commitment is kept), either the null hypothesis or the alternate hypothesis is automatically rejected according to some external success criterion \\(\\rho\\), regardless of what the meta-experimenters' decision might have been otherwise. As we have shown in Proposition 2, the optimal policy still remains a thresholding-type policy, but since there is now a deadline to discard the alternate hypothesis early, the thresholds become time-varying; in particular, they become less and less optimistic as the said deadline approaches (cf. Proposition 4)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Frazier and Angela (2007); Dayanik and Angela (2013); Alaa and van der Schaar (2016) consider SHT under stochastic deadlines, but different from optimal commitment, they still allow agents to reject both hypotheses at any time. In these works, the agent must make the rejection decision before the deadline is reached to be able to receive a positive reward, whereas in our case, the agent must wait until the deadline to see whether the null hypothesis will be rejected or not. Naghshvar and"
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+ {
+ "type": "page_number",
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+ "angle": 0,
+ "content": "6"
+ }
+ ],
+ [
+ {
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+ "content": "Published as a conference paper at ICLR 2023"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2: Comparison of related experiment designs. Optimal commitment is the only design that aims to decide both when an alternative population should be targeted—as opposed to switching the target population only at a fixed decision point—as well as which population to target among many potential candidates—as opposed to a simple binary decision of “overall population vs. sub-population” or “go vs. no-go”."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Term | Notation | Description |
| Experiment | - | Conducted to confirm efficacy of an intervention, e.g. a new treatment in clinical trials, or a new recommendation policy in online advertisement |
| Subject | - | Individual participant of an experiment, e.g. patients in a clinical trial, or customers in online advertisement |
| Population | X⊆X | Collection of subjects that all share the same qualities, e.g. all female patients in a clinical trial, or all customers with the same preferences in online advertisement |
| Atomic-population | x∈X | Indivisible populations |
| Propensities | ηx | The probability that a subject being from atomic-population x |
| ηx | The probability that a subject being from population X |
| ηx|X | The probability that a subject being from atomic-population x conditioned on the fact that they from population X |
| Outcome distribution | Ωx | Distribution of outcomes that is indicative of the effect of the intervention of interest for atomic-population x |
| Mean outcomes | θx | Expected outcome, i.e. the effect of the intervention of interest, for atomic-population x |
| θX | Expected outcome for population X |
| Experiment design | ψ=(X,τ,ρ) | Target population X, sample horizon τ, and success criterion ρ that characterize an experiment |
| Viable experiment designs | Ψ | Experiment designs that can potentially be followed by a meta-experimenter |
| Meta-experimenter | - | The decision-making agent that decides when to run experiments according to which experiment design in Ψ |
| Sample/time horizon | τ | An experiment is terminated when t=τ |
| Success criterion | ρ | An experiment is declared a success if ρ(Dτ)=1 |
| Online dataset | Dt | Data collected by an ongoing experiment at time step t |
| Dt | Data collected by the i-th experiment run by the meta-experimenter at time step t |
| Aggregate dataset | DIt | Collective data collected by all experiments up to time step t of the i-th experiment |
| - | Tt | Number of time steps for which the i-th experiment is conducted until it was stopped or its time horizon was reached |
| Cost | Cψ | Cost incurred per time step by running experiment ψ |
| Reward | Rψ | Reward received if experiment ψ is successful |
| Utility | G | Sum of costs and rewards received after all experimentation is concluded |
| Policy | π | Decision-making policy of the meta-experiment |
| Optimal policy | π* | The optimal policy that maximizes utility G in expectation |
| Greedy policy | πgreedy | See Section 3 |
| Test statistic | μt | In the simplified case in Section 3, the empirical mean outcome |
| Value function | Vπ(t,μ) | The expected utility of following policy π when μt=μ |
| Q-function | Qπ(t,μ) | The expected utility of following policy π after conducting the ongoing experiment for one more time step when μt=μ |
| - | Ttπ | The first time step at or after time step t that policy π decides to stop all experimentation |
| Optimal value function | V* | The value function associated with π* |
| Optimal Q-function | Q* | The Q-function associated with π* |
| Thresholds | μt* | Decision-making thresholds associated with π* |
| μtgreedy | Decision-making thresholds associated with πgreedy |
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+ "content": "| Algorithm 1 Bayes-OCP |
| 1: Initialize μx and σx2 for all x ∈ X |
| 2: X ← X, t ← 0, D0 ← ∅ |
| 3: Start experiment ψ = (X,τ,ρ) |
| 4: loop: |
| 5: t ← t + 1; Dt ← Dt-1 ∪ {xt,yt} |
| 6: 1/σxt2 ← 1/σxt2 + 1 |
| 7: μxt← μxt + (yt - μxt)σxt2 |
| (i) Identify a candidate subpopulation X' to replace X: |
| 8: X' ← ∅ |
| 9: while X \ X' ⊃ ∅: |
| 10: x* ← argmaxx∈X\X' |
| Eθx~N(μx,σx2)[G(0)(X' ∪ {x}; {θx})] |
| 11: if Eθx~N(μx,σx2)[G(0)(X' ∪ {x*}; {θx})] > Eθx~N(μx,σx2)[G(0)(X'; {θx})]: |
| 12: X' ← X' ∪ {x*} |
| 13: else: break |
| (ii) Decide whether to actually replace X with X': |
| 14: if Pθx~N(μx,σx2)[G(0)(X'; {θx}) > G(X, Dt; {θx})] > β: |
| 15: X ← X', t ← 0, D0 ← ∅ |
| 16: Start a new experiment ψ = (X,τ,ρ) |
+
+OCP in managing various experiments would degrade (see Appendix C for related experiments). Making use of the posteriors it maintains, Bayes-OCP performs two steps at each iteration:
+
+(i) First, a subpopulation $X' \subset X$ within the currently targeted population $X$ is identified as a potential candidate to target next; due to the combinatorial size of $\Psi$ , it would not be practical to consider every subpopulation individually as a candidate for large $|\mathcal{X}|$ . The ideal candidate would be the subpopulation with the largest expected utility: $X' = \operatorname{argmax}_{X' \subset X} \mathbb{E}_{\theta_x \sim \mathcal{N}(\mu_x, \sigma_x^2)} [\mathcal{G}^{(0)}(X'; \{\theta_x\})]$ . But again due to the combinatorial size of the search space, Bayes-OCP employs a greedy algorithm instead and forms candidate subpopulations by combining, one by one, the atomic-subpopulations that increase the expected utility the most, until the expected utility no longer improves. Note that it is common to use greedy algorithms to solve combinatorial optimization problems (Lawler, 1976; Papadimitriou and Steiglitz, 1982).
+
+(ii) Then, it is decided whether the current experiment targeting population $X$ should be stopped in favor of targeting candidate $X^{\prime}$ identified earlier instead. A greedy strategy would have done so whenever $\mathbb{E}_{\theta_x} \sim \mathcal{N}(\mu_x, \sigma_x^2)[\mathcal{G}^{(0)}(X'; \{\theta_x\})] > \mathbb{E}_{\theta_x} \sim \mathcal{N}(\mu_x, \sigma_x^2)[\mathcal{G}(X, \mathcal{D}_t; \{\theta_x\})]$ . But from our earlier analysis, we have learned that the optimal strategy is optimistic (cf. Proposition 3). As such, Bayes-OCP checks whether it is overwhelmingly likely that the alternative experiment has higher expected utility—that is whether $\mathbb{P}_{\theta_x} \sim \mathcal{N}(\mu_x, \sigma_x^2)\{\mathcal{G}^{(0)}(X'; \{\theta_x\}) > \mathcal{G}(X, \mathcal{D}_t; \{\theta_x\})\} > \beta$ , where $\beta \in (1/2, 1)$ controls the decision-making threshold. When $\beta$ is large, we are more optimistic that the current experiment will succeed and require stronger evidence that the alternative experiment has higher expected utility. Note that, as the posteriors $\mathcal{N}(\mu_x, \sigma_x^2)$ get narrower, the optimism of this rule naturally decreases, which should be the case for the optimal strategy (cf. Proposition 4). As one extreme, the two switching rules become equivalent when $\{\sigma_x^2 \to 0\}$ .
+
+# 5 RELATED WORK
+
+Optimal stopping Optimal commitment is essentially a new type of optimal stopping/switching problem. In typical optimal stopping problems (OSPs), the reward an agent can receive evolves based on a stochastic process and the goal of the agent is to determine the optimal time step to stop when the reward to be received is in some sense maximized (Shiryaev, 2007). Optimal commitment is unique in that a positive reward can only be received by not stopping until a pre-specified time horizon $\tau$ . In optimal commitment, there is still a stochastic process (namely, samples $y_{t}$ ) that gradually reveals more information regarding what that positive reward will be at the end, however, the reward—or rather the cost—of stopping earlier is independent of this stochastic process (and is equal to $-tC$ ).
+
+Sequential hypothesis testing Among other OSPs, optimal commitment is most closely related to sequential hypothesis testing (SHT), where an agent makes sequential observations regarding a given hypothesis and eventually needs to decide whether to reject the said (alternate) hypothesis or reject some null hypothesis (Wald and Wolfowitz, 1948; Yu et al., 2009; Drugowitsch et al., 2012; Shenoy and Angela, 2012; Zhang and Angela, 2013; Drugowitsch et al., 2014; Khalvati and Rao, 2015; Schonbrodt et al., 2017; Fauß et al., 2020). Rejecting the correct hypothesis provides a positive reward whereas waiting for more observations, while informative, is also costly as in OCP. It is well known that the optimal policy in the classic setting of SHT is a thresholding-type policy with fixed thresholds that do not vary over time: The null hypothesis is rejected if some test statistic gets above a threshold (and the alternate hypothesis is rejected if the same statistic gets below a different threshold).
+
+Optimal commitment can be thought of as a SHT problem with the crucial difference that the meta-experimenter has only the option of discarding the alternate hypothesis (i.e. breaking a commitment), and once some time horizon is reached (i.e. when a commitment is kept), either the null hypothesis or the alternate hypothesis is automatically rejected according to some external success criterion $\rho$ , regardless of what the meta-experimenters' decision might have been otherwise. As we have shown in Proposition 2, the optimal policy still remains a thresholding-type policy, but since there is now a deadline to discard the alternate hypothesis early, the thresholds become time-varying; in particular, they become less and less optimistic as the said deadline approaches (cf. Proposition 4).
+
+Frazier and Angela (2007); Dayanik and Angela (2013); Alaa and van der Schaar (2016) consider SHT under stochastic deadlines, but different from optimal commitment, they still allow agents to reject both hypotheses at any time. In these works, the agent must make the rejection decision before the deadline is reached to be able to receive a positive reward, whereas in our case, the agent must wait until the deadline to see whether the null hypothesis will be rejected or not. Naghshvar and
+
+Table 2: Comparison of related experiment designs. Optimal commitment is the only design that aims to decide both when an alternative population should be targeted—as opposed to switching the target population only at a fixed decision point—as well as which population to target among many potential candidates—as opposed to a simple binary decision of “overall population vs. sub-population” or “go vs. no-go”.
+
+| Term | Notation | Description |
| Experiment | - | Conducted to confirm efficacy of an intervention, e.g. a new treatment in clinical trials, or a new recommendation policy in online advertisement |
| Subject | - | Individual participant of an experiment, e.g. patients in a clinical trial, or customers in online advertisement |
| Population | X⊆X | Collection of subjects that all share the same qualities, e.g. all female patients in a clinical trial, or all customers with the same preferences in online advertisement |
| Atomic-population | x∈X | Indivisible populations |
| Propensities | ηx | The probability that a subject being from atomic-population x |
| ηx | The probability that a subject being from population X |
| ηx|X | The probability that a subject being from atomic-population x conditioned on the fact that they from population X |
| Outcome distribution | Ωx | Distribution of outcomes that is indicative of the effect of the intervention of interest for atomic-population x |
| Mean outcomes | θx | Expected outcome, i.e. the effect of the intervention of interest, for atomic-population x |
| θX | Expected outcome for population X |
| Experiment design | ψ=(X,τ,ρ) | Target population X, sample horizon τ, and success criterion ρ that characterize an experiment |
| Viable experiment designs | Ψ | Experiment designs that can potentially be followed by a meta-experimenter |
| Meta-experimenter | - | The decision-making agent that decides when to run experiments according to which experiment design in Ψ |
| Sample/time horizon | τ | An experiment is terminated when t=τ |
| Success criterion | ρ | An experiment is declared a success if ρ(Dτ)=1 |
| Online dataset | Dt | Data collected by an ongoing experiment at time step t |
| Dt | Data collected by the i-th experiment run by the meta-experimenter at time step t |
| Aggregate dataset | DIt | Collective data collected by all experiments up to time step t of the i-th experiment |
| - | Tt | Number of time steps for which the i-th experiment is conducted until it was stopped or its time horizon was reached |
| Cost | Cψ | Cost incurred per time step by running experiment ψ |
| Reward | Rψ | Reward received if experiment ψ is successful |
| Utility | G | Sum of costs and rewards received after all experimentation is concluded |
| Policy | π | Decision-making policy of the meta-experiment |
| Optimal policy | π* | The optimal policy that maximizes utility G in expectation |
| Greedy policy | πgreedy | See Section 3 |
| Test statistic | μt | In the simplified case in Section 3, the empirical mean outcome |
| Value function | Vπ(t,μ) | The expected utility of following policy π when μt=μ |
| Q-function | Qπ(t,μ) | The expected utility of following policy π after conducting the ongoing experiment for one more time step when μt=μ |
| - | Ttπ | The first time step at or after time step t that policy π decides to stop all experimentation |
| Optimal value function | V* | The value function associated with π* |
| Optimal Q-function | Q* | The Q-function associated with π* |
| Thresholds | μt* | Decision-making thresholds associated with π* |
| μtgreedy | Decision-making thresholds associated with πgreedy |
| Conditional power function | P(X, Dt; {θx}) | The probability of a hypothesis test being successful condi- tioned on mean outcomes {θx} |
| Expected utility function | G(X, Dt; {θx}) | The expected utility of fully committing to an experiment and waiting until it terminates when the experiment targets popula-tion X, is currently at time step t, and collected dataset Dt |
| Posteriors | N(μx, σx2) | Posterior distributions over mean outcomes {θx} maintained by Bayes-OCP such that θx|D ~ N(μx, σx2) |
\ No newline at end of file
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+ "type": "text",
+ "content": "time and resources (Moineddin et al., 2008; Lipkovich et al., 2017; Chiu et al., 2018). Of course, the experimenter has no knowledge of this in advance but the initial experiment they have set up would slowly reveal more information regarding the effects of the treatment and the fact that the ongoing experiment is bound to fail. In that case, we want to be able to determine at what point the experimenter has enough information to justify breaking their commitment to the initial experiment that targets too wide of a population to be successful, in favor of making a new commitment to a follow-up experiment that focuses on a narrower subpopulation instead?"
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+ "content": "Contributions Our contributions are threefold: First, we formulate the problem of making and breaking commitments in a timely manner as a new type of optimal stopping/switching problem called the optimal commitment problem (OCP) (Section 2). The defining feature of OCP is that rewards are received only when a known time point is reached but costs are incurred continually, requiring commitment to actions but with incentive to abandon those commitments. As we will show later, OCP cannot be easily solved via conventional reinforcement learning techniques due to its non-convex nature. Second, we theoretically analyze a simplified case of OCP to identify the characteristics of the optimal solution (Section 3), and based on the insights we gain, propose a practical algorithm for the more general case (Section 4). Third, we empirically evaluate the performance of our algorithm in running experiments with subpopulation selection (Section 6). Before we move on, it should be emphasized that, although we predominantly consider adaptive experimentation as our main application, our contributions remain generally applicable to portfolio management, energy systems, and any other decision-making scenarios that require commitments to long-term actions."
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+ "content": "2 OPTIMAL COMMITMENT PROBLEM"
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+ "content": "We first introduce the problem of optimal commitment from the perspective of running experiments. As far as our formulation is concerned, experiments are conducted to confirm the efficacy of an intervention by observing the outcome of the said intervention for subjects belonging to a particular population. However, this experiment-focused perspective does not limit the applicability of OCP; we stress its generality later at the end of the section. We provide a glossary of terms and notation in Appendix K."
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+ "content": "General applicability of OCP Although we have described OCP from the perspective of (meta-)experiment design, it can potentially be useful in modeling many other problems as we have stressed during the introduction (see Table 1). For instance, in portfolio management, atomic-populations can be regarded as various assets one can invest in, then a population would correspond to a portfolio"
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+ "content": ") in the mean time, the decision-making problem of managing when and which portfolio to invest in constitutes an instance of the optimal commitment problem. Another good examples is energy management, where power stations and the networks they form are akin to atomic-populations and populations. Since power stations cannot be turned on and off immediately, putting one in operation requires a certain amount of commitment."
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+ "html": "| Algorithm 1 Bayes-OCP |
| 1: Initialize μx and σx2 for all x ∈ X |
| 2: X ← X, t ← 0, D0 ← ∅ |
| 3: Start experiment ψ = (X,τ,ρ) |
| 4: loop: |
| 5: t ← t + 1; Dt ← Dt-1 ∪ {xt,yt} |
| 6: 1/σxt2 ← 1/σxt2 + 1 |
| 7: μxt← μxt + (yt - μxt)σxt2 |
| (i) Identify a candidate subpopulation X' to replace X: |
| 8: X' ← ∅ |
| 9: while X \\ X' ⊃ ∅: |
| 10: x* ← argmaxx∈X\\X' |
| Eθx~N(μx,σx2)[G(0)(X' ∪ {x}; {θx})] |
| 11: if Eθx~N(μx,σx2)[G(0)(X' ∪ {x*}; {θx})] > Eθx~N(μx,σx2)[G(0)(X'; {θx})]: |
| 12: X' ← X' ∪ {x*} |
| 13: else: break |
| (ii) Decide whether to actually replace X with X': |
| 14: if Pθx~N(μx,σx2)[G(0)(X'; {θx}) > G(X, Dt; {θx})] > β: |
| 15: X ← X', t ← 0, D0 ← ∅ |
| 16: Start a new experiment ψ = (X,τ,ρ) |
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+ "content": "OCP in managing various experiments would degrade (see Appendix C for related experiments). Making use of the posteriors it maintains, Bayes-OCP performs two steps at each iteration:"
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+ "content": "X' = \\operatorname{argmax}_{X' \\subset X} \\mathbb{E}_{\\theta_x \\sim \\mathcal{N}(\\mu_x, \\sigma_x^2)} [\\mathcal{G}^{(0)}(X'; \\{\\theta_x\\})]"
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+ "content": ". But again due to the combinatorial size of the search space, Bayes-OCP employs a greedy algorithm instead and forms candidate subpopulations by combining, one by one, the atomic-subpopulations that increase the expected utility the most, until the expected utility no longer improves. Note that it is common to use greedy algorithms to solve combinatorial optimization problems (Lawler, 1976; Papadimitriou and Steiglitz, 1982)."
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+ "content": "Optimal stopping Optimal commitment is essentially a new type of optimal stopping/switching problem. In typical optimal stopping problems (OSPs), the reward an agent can receive evolves based on a stochastic process and the goal of the agent is to determine the optimal time step to stop when the reward to be received is in some sense maximized (Shiryaev, 2007). Optimal commitment is unique in that a positive reward can only be received by not stopping until a pre-specified time horizon "
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+ "content": "Sequential hypothesis testing Among other OSPs, optimal commitment is most closely related to sequential hypothesis testing (SHT), where an agent makes sequential observations regarding a given hypothesis and eventually needs to decide whether to reject the said (alternate) hypothesis or reject some null hypothesis (Wald and Wolfowitz, 1948; Yu et al., 2009; Drugowitsch et al., 2012; Shenoy and Angela, 2012; Zhang and Angela, 2013; Drugowitsch et al., 2014; Khalvati and Rao, 2015; Schonbrodt et al., 2017; Fauß et al., 2020). Rejecting the correct hypothesis provides a positive reward whereas waiting for more observations, while informative, is also costly as in OCP. It is well known that the optimal policy in the classic setting of SHT is a thresholding-type policy with fixed thresholds that do not vary over time: The null hypothesis is rejected if some test statistic gets above a threshold (and the alternate hypothesis is rejected if the same statistic gets below a different threshold)."
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+ "content": ", regardless of what the meta-experimenters' decision might have been otherwise. As we have shown in Proposition 2, the optimal policy still remains a thresholding-type policy, but since there is now a deadline to discard the alternate hypothesis early, the thresholds become time-varying; in particular, they become less and less optimistic as the said deadline approaches (cf. Proposition 4)."
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+ "html": "| Term | Notation | Description |
| Experiment | - | Conducted to confirm efficacy of an intervention, e.g. a new treatment in clinical trials, or a new recommendation policy in online advertisement |
| Subject | - | Individual participant of an experiment, e.g. patients in a clinical trial, or customers in online advertisement |
| Population | X⊆X | Collection of subjects that all share the same qualities, e.g. all female patients in a clinical trial, or all customers with the same preferences in online advertisement |
| Atomic-population | x∈X | Indivisible populations |
| Propensities | ηx | The probability that a subject being from atomic-population x |
| ηx | The probability that a subject being from population X |
| ηx|X | The probability that a subject being from atomic-population x conditioned on the fact that they from population X |
| Outcome distribution | Ωx | Distribution of outcomes that is indicative of the effect of the intervention of interest for atomic-population x |
| Mean outcomes | θx | Expected outcome, i.e. the effect of the intervention of interest, for atomic-population x |
| θX | Expected outcome for population X |
| Experiment design | ψ=(X,τ,ρ) | Target population X, sample horizon τ, and success criterion ρ that characterize an experiment |
| Viable experiment designs | Ψ | Experiment designs that can potentially be followed by a meta-experimenter |
| Meta-experimenter | - | The decision-making agent that decides when to run experiments according to which experiment design in Ψ |
| Sample/time horizon | τ | An experiment is terminated when t=τ |
| Success criterion | ρ | An experiment is declared a success if ρ(Dτ)=1 |
| Online dataset | Dt | Data collected by an ongoing experiment at time step t |
| Dt | Data collected by the i-th experiment run by the meta-experimenter at time step t |
| Aggregate dataset | DIt | Collective data collected by all experiments up to time step t of the i-th experiment |
| - | Tt | Number of time steps for which the i-th experiment is conducted until it was stopped or its time horizon was reached |
| Cost | Cψ | Cost incurred per time step by running experiment ψ |
| Reward | Rψ | Reward received if experiment ψ is successful |
| Utility | G | Sum of costs and rewards received after all experimentation is concluded |
| Policy | π | Decision-making policy of the meta-experiment |
| Optimal policy | π* | The optimal policy that maximizes utility G in expectation |
| Greedy policy | πgreedy | See Section 3 |
| Test statistic | μt | In the simplified case in Section 3, the empirical mean outcome |
| Value function | Vπ(t,μ) | The expected utility of following policy π when μt=μ |
| Q-function | Qπ(t,μ) | The expected utility of following policy π after conducting the ongoing experiment for one more time step when μt=μ |
| - | Ttπ | The first time step at or after time step t that policy π decides to stop all experimentation |
| Optimal value function | V* | The value function associated with π* |
| Optimal Q-function | Q* | The Q-function associated with π* |
| Thresholds | μt* | Decision-making thresholds associated with π* |
| μtgreedy | Decision-making thresholds associated with πgreedy |
| Conditional power function | P(X, Dt; {θx}) | The probability of a hypothesis test being successful condi- tioned on mean outcomes {θx} |
| Expected utility function | G(X, Dt; {θx}) | The expected utility of fully committing to an experiment and waiting until it terminates when the experiment targets popula-tion X, is currently at time step t, and collected dataset Dt |
| Posteriors | N(μx, σx2) | Posterior distributions over mean outcomes {θx} maintained by Bayes-OCP such that θx|D ~ N(μx, σx2) |
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diff --git a/2023/Where to Diffuse, How to Diffuse, and How to Get Back_ Automated Learning for Multivariate Diffusions/f7a9c89f-158a-46a9-8f48-9b5bcdfbc0da_content_list.json b/2023/Where to Diffuse, How to Diffuse, and How to Get Back_ Automated Learning for Multivariate Diffusions/f7a9c89f-158a-46a9-8f48-9b5bcdfbc0da_content_list.json
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+ "text": "WHERE TO DIFFUSE, HOW TO DIFFUSE, AND HOW TO GET BACK: AUTOMATED LEARNING FOR MULTIVARI-ATE DIFFUSIONS",
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+ "text": "Raghav Singhal\\*,1, Mark Goldstein\\*,1, Rajesh Ranganath\\*,2",
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+ "text": "Courant Institute of Mathematical Sciences| Dataset | Size (train/test) | Classes | Data description |
| Sine regression | 5000/5000 | n/a | Function with four sine components, domain [-2,2] |
| ImageNet | 1,281,167/50,000 | 1000 | Photos of common objects |
| CIFAR-10 | 50,000/10,000 | 10 | Photos of common objects, image sizes 32 × 32 |
| CIFAR-100 | 50,000/10,000 | 100 | Photos of common objects, image sizes 32 × 32 |
| Flowers | 1,088/272 | 17 | Find-grained photos of flowers |
| FGVC Aircraft | 6,667/3,333 | 100 | Find-grained photos of aircrafts |
| Caltech-101 | 3,060/6,084 | 102 | Photos/paintings/sketches of common objects |
| CUB-200 | 5,994/5,794 | 200 | Find-grained photos of birds |
| DomainNet painting | 50,416/21,850 | 345 | Oil Paintings, murals, drawings, tattoos |
",
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+ "Table 2: Complexities and architectures of DNNs used in this work."
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+ "table_body": "| Dataset | Size (train/test) | Classes | Data description |
| Sine regression | 5000/5000 | n/a | Function with four sine components, domain [-2,2] |
| ImageNet | 1,281,167/50,000 | 1000 | Photos of common objects |
| CIFAR-10 | 50,000/10,000 | 10 | Photos of common objects, image sizes 32 × 32 |
| CIFAR-100 | 50,000/10,000 | 100 | Photos of common objects, image sizes 32 × 32 |
| Flowers | 1,088/272 | 17 | Find-grained photos of flowers |
| FGVC Aircraft | 6,667/3,333 | 100 | Find-grained photos of aircrafts |
| Caltech-101 | 3,060/6,084 | 102 | Photos/paintings/sketches of common objects |
| CUB-200 | 5,994/5,794 | 200 | Find-grained photos of birds |
| DomainNet painting | 50,416/21,850 | 345 | Oil Paintings, murals, drawings, tattoos |
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| Sine regression | 5000/5000 | n/a | Function with four sine components, domain [-2,2] |
| ImageNet | 1,281,167/50,000 | 1000 | Photos of common objects |
| CIFAR-10 | 50,000/10,000 | 10 | Photos of common objects, image sizes 32 × 32 |
| CIFAR-100 | 50,000/10,000 | 100 | Photos of common objects, image sizes 32 × 32 |
| Flowers | 1,088/272 | 17 | Find-grained photos of flowers |
| FGVC Aircraft | 6,667/3,333 | 100 | Find-grained photos of aircrafts |
| Caltech-101 | 3,060/6,084 | 102 | Photos/paintings/sketches of common objects |
| CUB-200 | 5,994/5,794 | 200 | Find-grained photos of birds |
| DomainNet painting | 50,416/21,850 | 345 | Oil Paintings, murals, drawings, tattoos |
+
+Network Architectures. The FCNNs, CNNs, and Vision Transformers are summarized in the Tab. 2.
+
+Table 2: Complexities and architectures of DNNs used in this work.
+
+| Dataset | Size (train/test) | Classes | Data description |
| Sine regression | 5000/5000 | n/a | Function with four sine components, domain [-2,2] |
| ImageNet | 1,281,167/50,000 | 1000 | Photos of common objects |
| CIFAR-10 | 50,000/10,000 | 10 | Photos of common objects, image sizes 32 × 32 |
| CIFAR-100 | 50,000/10,000 | 100 | Photos of common objects, image sizes 32 × 32 |
| Flowers | 1,088/272 | 17 | Find-grained photos of flowers |
| FGVC Aircraft | 6,667/3,333 | 100 | Find-grained photos of aircrafts |
| Caltech-101 | 3,060/6,084 | 102 | Photos/paintings/sketches of common objects |
| CUB-200 | 5,994/5,794 | 200 | Find-grained photos of birds |
| DomainNet painting | 50,416/21,850 | 345 | Oil Paintings, murals, drawings, tattoos |
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| 1 | wav2vec 2.0 lv60k (100h) | 0.49 | 317 |
| 2 | wav2vec 2.0 lv60k (960h) | 0.49 | 317 |
| 3 | wav2vec 2.0 lv60k | 0.51 | 317 |
| 4 | wav2vec 2.0 lv60k (10m) | 0.51 | 317 |
| 5 | HuBERT xlarge ASR | 0.45 | 1000 |
| 6 | HuBERT xlarge | 0.46 | 1000 |
| 7 | HuBERT large ASR | 0.46 | 300 |
| 8 | wav2vec 2.0 large XLSR53 | 0.47 | 317 |
| 9 | HuBERT large | 0.46 | 300 |
| 10 | wav2vec 2.0 (Audeering, emotion) | 0.49 | 317 |
| 11 | HuBERT base | 0.41 | 90 |
| 12 | WavLM large | 0.46 | 316.62 |
| 13 | HuBERT base (superb, emotion) | 0.42 | 90 |
| 14 | HuBERT base (superb, speaker) | 0.42 | 90 |
| 15 | WavLM base+ | 0.41 | 94.70 |
| 16 | wav2vec 2.0 base (960h) | 0.38 | 95 |
| 17 | WavLM base | 0.39 | 94.70 |
| 18 | wav2vec 2.0 base | 0.34 | 95 |
| 19 | wav2vec 2.0 base (10m) | 0.34 | 95 |
| 20 | wav2vec 2.0 base (superb, emotion) | 0.34 | 95 |
| 21 | wav2vec 2.0 base (superb, speaker) | 0.34 | 95 |
| 22 | wav2vec 2.0 base (100h) | 0.32 | 95 |
| 23 | HuBERT large (superb, emotion) | 0.29 | 300 |
| 24 | HuBERT large (superb, speaker) | 0.29 | 300 |
| 25 | wav2vec 2.0 large (100h) | 0.32 | 317 |
| 26 | wav2vec 2.0 large (superb, emotion) | 0.31 | 317 |
| 27 | wav2vec 2.0 large (superb, speaker) | 0.31 | 317 |
| 28 | wav2vec 2.0 large (960h) | 0.31 | 317 |
| 29 | wav2vec 2.0 large (10m) | 0.31 | 317 |
| 30 | data2vec audio large (960h) | 0.31 | 313.28 |
| 31 | data2vec audio base (100h) | 0.23 | 313.28 |
| 32 | data2vec audio large (100h) | 0.23 | 313.28 |
| 33 | data2vec audio large (10m) | 0.21 | 313.28 |
| 34 | wav2vec 2.0 (SpeechBrain, emotion) | 0.11 | 95 |
| 35 | data2vec audio base (960h) | 0.16 | 93.16 |
| 36 | data2vec audio base (10m) | 0.15 | 93.16 |
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+ "table_body": "| People described pairs of images using words. |
| How similar are the two images in each pair on a scale of 0-1 where 0 is completely dissimilar and 1 is completely similar? |
| Here are the descriptions of image one: tortoise, slow, protected, shell, turtle, scaly, old, cold-blooded |
| Here are the descriptions of image two: monkey, ape, mammal, black and white, hairy, agile, primate, smart, tree-dwelling |
| Rating: 0.05 |
| Here are the descriptions of image one: rhinoceros, horn, gray, standing, heavy body, endangered, wild, africa, african |
| Here are the descriptions of image two: tiger, open mouth, stripes, feline, predator |
| Rating: 0.27 |
| Here are the descriptions of image one: goat, eye, leg |
| Here are the descriptions of image two: mammal, wide-nosed, mandrill, primate, baboon, smart |
| Rating: 0.19 |
| Here are the descriptions of image one: black, primate, mammal, hairy, chimpanzee, africa, african, great ape, smart, omnivore |
| Here are the descriptions of image two: zebra, striped, two-toned, wild, staring, mammal, equine, herd animal, africa |
| Rating: [0.14] |
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| 1 | wav2vec 2.0 lv60k (100h) | 0.49 | 317 |
| 2 | wav2vec 2.0 lv60k (960h) | 0.49 | 317 |
| 3 | wav2vec 2.0 lv60k | 0.51 | 317 |
| 4 | wav2vec 2.0 lv60k (10m) | 0.51 | 317 |
| 5 | HuBERT xlarge ASR | 0.45 | 1000 |
| 6 | HuBERT xlarge | 0.46 | 1000 |
| 7 | HuBERT large ASR | 0.46 | 300 |
| 8 | wav2vec 2.0 large XLSR53 | 0.47 | 317 |
| 9 | HuBERT large | 0.46 | 300 |
| 10 | wav2vec 2.0 (Audeering, emotion) | 0.49 | 317 |
| 11 | HuBERT base | 0.41 | 90 |
| 12 | WavLM large | 0.46 | 316.62 |
| 13 | HuBERT base (superb, emotion) | 0.42 | 90 |
| 14 | HuBERT base (superb, speaker) | 0.42 | 90 |
| 15 | WavLM base+ | 0.41 | 94.70 |
| 16 | wav2vec 2.0 base (960h) | 0.38 | 95 |
| 17 | WavLM base | 0.39 | 94.70 |
| 18 | wav2vec 2.0 base | 0.34 | 95 |
| 19 | wav2vec 2.0 base (10m) | 0.34 | 95 |
| 20 | wav2vec 2.0 base (superb, emotion) | 0.34 | 95 |
| 21 | wav2vec 2.0 base (superb, speaker) | 0.34 | 95 |
| 22 | wav2vec 2.0 base (100h) | 0.32 | 95 |
| 23 | HuBERT large (superb, emotion) | 0.29 | 300 |
| 24 | HuBERT large (superb, speaker) | 0.29 | 300 |
| 25 | wav2vec 2.0 large (100h) | 0.32 | 317 |
| 26 | wav2vec 2.0 large (superb, emotion) | 0.31 | 317 |
| 27 | wav2vec 2.0 large (superb, speaker) | 0.31 | 317 |
| 28 | wav2vec 2.0 large (960h) | 0.31 | 317 |
| 29 | wav2vec 2.0 large (10m) | 0.31 | 317 |
| 30 | data2vec audio large (960h) | 0.31 | 313.28 |
| 31 | data2vec audio base (100h) | 0.23 | 313.28 |
| 32 | data2vec audio large (100h) | 0.23 | 313.28 |
| 33 | data2vec audio large (10m) | 0.21 | 313.28 |
| 34 | wav2vec 2.0 (SpeechBrain, emotion) | 0.11 | 95 |
| 35 | data2vec audio base (960h) | 0.16 | 93.16 |
| 36 | data2vec audio base (10m) | 0.15 | 93.16 |
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| How similar are the two images in each pair on a scale of 0-1 where 0 is completely dissimilar and 1 is completely similar? |
| Here are the descriptions of image one: tortoise, slow, protected, shell, turtle, scaly, old, cold-blooded |
| Here are the descriptions of image two: monkey, ape, mammal, black and white, hairy, agile, primate, smart, tree-dwelling |
| Rating: 0.05 |
| Here are the descriptions of image one: rhinoceros, horn, gray, standing, heavy body, endangered, wild, africa, african |
| Here are the descriptions of image two: tiger, open mouth, stripes, feline, predator |
| Rating: 0.27 |
| Here are the descriptions of image one: goat, eye, leg |
| Here are the descriptions of image two: mammal, wide-nosed, mandrill, primate, baboon, smart |
| Rating: 0.19 |
| Here are the descriptions of image one: black, primate, mammal, hairy, chimpanzee, africa, african, great ape, smart, omnivore |
| Here are the descriptions of image two: zebra, striped, two-toned, wild, staring, mammal, equine, herd animal, africa |
| Rating: [0.14] |
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| 1 | wav2vec 2.0 lv60k (100h) | 0.49 | 317 |
| 2 | wav2vec 2.0 lv60k (960h) | 0.49 | 317 |
| 3 | wav2vec 2.0 lv60k | 0.51 | 317 |
| 4 | wav2vec 2.0 lv60k (10m) | 0.51 | 317 |
| 5 | HuBERT xlarge ASR | 0.45 | 1000 |
| 6 | HuBERT xlarge | 0.46 | 1000 |
| 7 | HuBERT large ASR | 0.46 | 300 |
| 8 | wav2vec 2.0 large XLSR53 | 0.47 | 317 |
| 9 | HuBERT large | 0.46 | 300 |
| 10 | wav2vec 2.0 (Audeering, emotion) | 0.49 | 317 |
| 11 | HuBERT base | 0.41 | 90 |
| 12 | WavLM large | 0.46 | 316.62 |
| 13 | HuBERT base (superb, emotion) | 0.42 | 90 |
| 14 | HuBERT base (superb, speaker) | 0.42 | 90 |
| 15 | WavLM base+ | 0.41 | 94.70 |
| 16 | wav2vec 2.0 base (960h) | 0.38 | 95 |
| 17 | WavLM base | 0.39 | 94.70 |
| 18 | wav2vec 2.0 base | 0.34 | 95 |
| 19 | wav2vec 2.0 base (10m) | 0.34 | 95 |
| 20 | wav2vec 2.0 base (superb, emotion) | 0.34 | 95 |
| 21 | wav2vec 2.0 base (superb, speaker) | 0.34 | 95 |
| 22 | wav2vec 2.0 base (100h) | 0.32 | 95 |
| 23 | HuBERT large (superb, emotion) | 0.29 | 300 |
| 24 | HuBERT large (superb, speaker) | 0.29 | 300 |
| 25 | wav2vec 2.0 large (100h) | 0.32 | 317 |
| 26 | wav2vec 2.0 large (superb, emotion) | 0.31 | 317 |
| 27 | wav2vec 2.0 large (superb, speaker) | 0.31 | 317 |
| 28 | wav2vec 2.0 large (960h) | 0.31 | 317 |
| 29 | wav2vec 2.0 large (10m) | 0.31 | 317 |
| 30 | data2vec audio large (960h) | 0.31 | 313.28 |
| 31 | data2vec audio base (100h) | 0.23 | 313.28 |
| 32 | data2vec audio large (100h) | 0.23 | 313.28 |
| 33 | data2vec audio large (10m) | 0.21 | 313.28 |
| 34 | wav2vec 2.0 (SpeechBrain, emotion) | 0.11 | 95 |
| 35 | data2vec audio base (960h) | 0.16 | 93.16 |
| 36 | data2vec audio base (10m) | 0.15 | 93.16 |
+
+2020). We expected that the layers closer to the input of the model (where the representation is more low-level) to be less predictive. In general, we found that this was the case (Figure 10). In some variants of wav2vec, however, intermediate representations performed better, possibly due to the misalignment of the training task of wav2vec with the emotion task. This analysis confirms the choice we made in the paper to mostly use the last two layers of the models. Preliminary analysis of the image and video models also explored different layers, but the results were similar to those we presented in audio, and are therefore not reported here.
+
+Video models We extracted embeddings from the 'Slow' (a 3D ResNet; see Feichtenhofer et al. (2019)), Slowfast (a 2-path model with one path capturing semantics and the other capturing fine details; see Feichtenhofer et al. (2019)), and X3d (a model that initially starts as a simple 2D image classifier but is expanded in several axes; see Feichtenhofer (2020)) architectures implemented in pytorchvideo (Fan et al., 2021). All video models were pre-trained on the Kinetics-400 dataset (Kay et al., 2017). The performance of the models is displayed in Figure 3C. Numeric correlation values are detailed in Table 6 along with model accuracy (Top1 and Top5) on Kinetics-400, and the number of parameters in each model. The accuracies and parameter counts are listed as reported in
+
+Fan et al. (2021). As with previous modalities, the number of parameters appears to be positively correlated with correlation to human similarity.
+
+Table 6: All video baseline models used in the analysis.
+
+| People described pairs of images using words. |
| How similar are the two images in each pair on a scale of 0-1 where 0 is completely dissimilar and 1 is completely similar? |
| Here are the descriptions of image one: tortoise, slow, protected, shell, turtle, scaly, old, cold-blooded |
| Here are the descriptions of image two: monkey, ape, mammal, black and white, hairy, agile, primate, smart, tree-dwelling |
| Rating: 0.05 |
| Here are the descriptions of image one: rhinoceros, horn, gray, standing, heavy body, endangered, wild, africa, african |
| Here are the descriptions of image two: tiger, open mouth, stripes, feline, predator |
| Rating: 0.27 |
| Here are the descriptions of image one: goat, eye, leg |
| Here are the descriptions of image two: mammal, wide-nosed, mandrill, primate, baboon, smart |
| Rating: 0.19 |
| Here are the descriptions of image one: black, primate, mammal, hairy, chimpanzee, africa, african, great ape, smart, omnivore |
| Here are the descriptions of image two: zebra, striped, two-toned, wild, staring, mammal, equine, herd animal, africa |
| Rating: [0.14] |
+
+We repeated this four times for each pair of images in each image dataset with a different set of context examples during each repetition and averaged together the GPT responses to get a final
+
+similarity prediction for each pair. In total, creating the context examples required having access to human similarity judgments over only 12 pairs of images. We found that this approach yielded surprisingly good predictions, with an average correlation of $r = 0.62$ across the image datasets. We believe this approach merits future investigation to determine whether prompt engineering can further increase the performance.
+
+Image captioning models We experimented with using pre-trained image captioning models to generate captions for our images and then using those captions with our best-performing LLM ('sup-simcse-roberta-large') the same way we do with user-generated captions. We used three pre-trained image captioning models from HuggingFace ('flamingo-mini', 'vilt-b32-finetuned-vqa', and 'vit-gpt2-image-captioning') to generate text descriptions for our images. However, the performance was quite poor with an average of $r = 0.29$ across the three models. As a result, $O(N)$ language-based methods cannot easily be reduced to $O(1)$ even when domain-relevant pre-trained caption models are available.
+
+# C.2 WORD FREQUENCY ANALYSIS METHODS
+
+In this work, we also conducted an additional evaluation of prediction models beyond embedding-based techniques (described in the previous section). Specifically, we compared the predictions of embedding-based models, which utilize deep learning representations, with those of traditional methods of text mining.
+
+Before the word frequency analysis, we performed the following initial pre-processing steps
+
+- For caption data, we concatenated all the captions describing the same stimulus into a single long "document."
+- For tag data, we wanted to prioritize tags that appeared earlier in the tag-mining chains and were rated higher. To that end, we gathered all tags from all iterations and duplicated tags from a given iteration based on the ratings they received. For example, if the tag "tomato" received three stars, then we would add the repeated tokens "tomato, tomato, tomato" to the aggregated list ("document"). In a given iteration, flagged tags are removed, but if they are rated later, then they are included. The total number of repetitions per token is equal to the sum of all the stars they received in all iterations. As a result, each token is repeated multiple times, which we take into consideration in consequent analysis.
+
+For the next steps, we used the Matlab text analytics toolbox $^{9}$ . Unless otherwise specified, we used default parameters for all functions. To generate similarity matrices, we applied the following methods:
+
+Co-occurrence method. In this approach, we simply counted the number of repeated pairs of words in documents $i$ and $j$ and normalized by the total number of pairs. Formally, we use $w_{i}$ to denote the word list of a document $i$ . Let $w_{i,k}$ be the $k$ -th word in the $w_{i}$ list of words, and let $|w_{i}|$ denote the length of the list. We denote by $\delta(c,d)$ the indicator function that returns 1 if and only if the word $c$ is identical to the word $d$ , and 0 otherwise. We computed the co-occurrence score $S(w_{i},w_{j})$ according to the following formula:
+
+$$
+S (w _ {i}, w _ {j}) = \frac {\sum_ {k} \sum_ {l} \delta (w _ {i , k} , w _ {j , l})}{| w _ {i} | | w _ {j} |}
+$$
+
+We suggest using this method only with tags and not with captions.
+
+Co-occurrence-rep. This method was applied only to tags. We used an identical procedure to the Co-occurrence method, except that we did not separate the words within a tag as separate tokens and instead treated the entire tag (that may include multiple words) as a single token.
+
+Rouge score. In this approach, similarity was estimated by computing the rouge score of the word lists associated with each pair of documents. The Rouge score was computed using rougeEvaluationScore (Rouge, 2004). We suggest using this method only with tags and not with captions.
+
+The following methods make use of tokenized data and a pre-processing procedure that we found effective. Pre-processing was applied to both tag and caption data and tokenization was performed as follows:
+
+- We separate all text into single words by applying the tokenizedDocument function.
+- We added part of speech information using the addPartOfSpeechDetails function.
+- We performed Lemmatization using the normalizeWords function.
+- We erased punctuation from the token using the erasePunctuation function.
+- We removed stopwords using the removeStopWords function.
+- We removed words with less than two characters or more than 15 characters.
+- We created a bag of words representation of each tokenized document using the bagOfWords function.
+- We also removed words that were not present in more than two documents using the InfrequentWords function.
+
+With the results of these pre-processing steps, we then computed similarity matrices based on the following methods:
+
+bm25S. We used bm25+ to compute similarity between documents (Barrios et al., 2016) using Matlab's bm25Similarity function. This function represents TF-IDF-like retrieval functions used in document retrieval. We used a variant that has a normalization function that properly handles documents with a long list of words.
+
+tfidf-cosine. We computed pairwise cosine similarities between document pairs using the TF-IDF matrix derived from their word counts and Matlab's cosineSimilarity function.
+
+# C.3 SUPERVISED METHODS
+
+Several previous studies investigated improving correlations by applying and fine-tuning simple linear transformations to embedding vectors $z^T \mathbf{W}z$ where $\mathbf{W} = \mathrm{diag}(w_1, \ldots, w_d)$ via a cross-validated ridge regression procedure that could be fit to ground-truth similarity judgments. The parameters of the diagonal reweighting matrix $\mathbf{W}$ are fitted to a training subset of stimuli and used to predict similarity of pairs in a held-out validation set Peterson et al. (2018); Marjieh et al. (2022). To be consistent and make results comparable, here we report the results of performing this 6-fold cross-validated linear transformation (LT-CCV) on the model embeddings and datasets considered in this work. The analysis was carried out using the RidgeCV package from the scikit-learn Python library Pedregosa et al. (2011). Results with both normalized ('LT CCV (norm') and unnormalized ('LT CCV') regressors are shown in Figure 11; see RidgeCV documentation for details on normalization $^{10}$ . We see that the linear transformation does not consistently improve performance (and can even decrease it) when applied to many of the modality-based or stacked embeddings, but it does frequently improve performance when applied to caption embeddings. Due to their instability and risk of overfitting, we do not use these methods in our main analysis.
+
+
+Figure 11: Effect of fine-tuning model embeddings using a small subset of similarity judgments.
\ No newline at end of file
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| 1 | wav2vec 2.0 lv60k (100h) | 0.49 | 317 |
| 2 | wav2vec 2.0 lv60k (960h) | 0.49 | 317 |
| 3 | wav2vec 2.0 lv60k | 0.51 | 317 |
| 4 | wav2vec 2.0 lv60k (10m) | 0.51 | 317 |
| 5 | HuBERT xlarge ASR | 0.45 | 1000 |
| 6 | HuBERT xlarge | 0.46 | 1000 |
| 7 | HuBERT large ASR | 0.46 | 300 |
| 8 | wav2vec 2.0 large XLSR53 | 0.47 | 317 |
| 9 | HuBERT large | 0.46 | 300 |
| 10 | wav2vec 2.0 (Audeering, emotion) | 0.49 | 317 |
| 11 | HuBERT base | 0.41 | 90 |
| 12 | WavLM large | 0.46 | 316.62 |
| 13 | HuBERT base (superb, emotion) | 0.42 | 90 |
| 14 | HuBERT base (superb, speaker) | 0.42 | 90 |
| 15 | WavLM base+ | 0.41 | 94.70 |
| 16 | wav2vec 2.0 base (960h) | 0.38 | 95 |
| 17 | WavLM base | 0.39 | 94.70 |
| 18 | wav2vec 2.0 base | 0.34 | 95 |
| 19 | wav2vec 2.0 base (10m) | 0.34 | 95 |
| 20 | wav2vec 2.0 base (superb, emotion) | 0.34 | 95 |
| 21 | wav2vec 2.0 base (superb, speaker) | 0.34 | 95 |
| 22 | wav2vec 2.0 base (100h) | 0.32 | 95 |
| 23 | HuBERT large (superb, emotion) | 0.29 | 300 |
| 24 | HuBERT large (superb, speaker) | 0.29 | 300 |
| 25 | wav2vec 2.0 large (100h) | 0.32 | 317 |
| 26 | wav2vec 2.0 large (superb, emotion) | 0.31 | 317 |
| 27 | wav2vec 2.0 large (superb, speaker) | 0.31 | 317 |
| 28 | wav2vec 2.0 large (960h) | 0.31 | 317 |
| 29 | wav2vec 2.0 large (10m) | 0.31 | 317 |
| 30 | data2vec audio large (960h) | 0.31 | 313.28 |
| 31 | data2vec audio base (100h) | 0.23 | 313.28 |
| 32 | data2vec audio large (100h) | 0.23 | 313.28 |
| 33 | data2vec audio large (10m) | 0.21 | 313.28 |
| 34 | wav2vec 2.0 (SpeechBrain, emotion) | 0.11 | 95 |
| 35 | data2vec audio base (960h) | 0.16 | 93.16 |
| 36 | data2vec audio base (10m) | 0.15 | 93.16 |
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+ "content": "Video models We extracted embeddings from the 'Slow' (a 3D ResNet; see Feichtenhofer et al. (2019)), Slowfast (a 2-path model with one path capturing semantics and the other capturing fine details; see Feichtenhofer et al. (2019)), and X3d (a model that initially starts as a simple 2D image classifier but is expanded in several axes; see Feichtenhofer (2020)) architectures implemented in pytorchvideo (Fan et al., 2021). All video models were pre-trained on the Kinetics-400 dataset (Kay et al., 2017). The performance of the models is displayed in Figure 3C. Numeric correlation values are detailed in Table 6 along with model accuracy (Top1 and Top5) on Kinetics-400, and the number of parameters in each model. The accuracies and parameter counts are listed as reported in"
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+ "html": "| People described pairs of images using words. |
| How similar are the two images in each pair on a scale of 0-1 where 0 is completely dissimilar and 1 is completely similar? |
| Here are the descriptions of image one: tortoise, slow, protected, shell, turtle, scaly, old, cold-blooded |
| Here are the descriptions of image two: monkey, ape, mammal, black and white, hairy, agile, primate, smart, tree-dwelling |
| Rating: 0.05 |
| Here are the descriptions of image one: rhinoceros, horn, gray, standing, heavy body, endangered, wild, africa, african |
| Here are the descriptions of image two: tiger, open mouth, stripes, feline, predator |
| Rating: 0.27 |
| Here are the descriptions of image one: goat, eye, leg |
| Here are the descriptions of image two: mammal, wide-nosed, mandrill, primate, baboon, smart |
| Rating: 0.19 |
| Here are the descriptions of image one: black, primate, mammal, hairy, chimpanzee, africa, african, great ape, smart, omnivore |
| Here are the descriptions of image two: zebra, striped, two-toned, wild, staring, mammal, equine, herd animal, africa |
| Rating: [0.14] |
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+ "content": "| Model | #Params. | Text MNLI Acc | Vision ImageNet LE / FT | Image2Text COCO B@4 / C | Text2Image COCO IS↑ / FID↓ | Multi-modal |
| VQA test-dev / test-standard | NLVR2 dev / test-P |
| Encoder-only Multi-modal Models |
| VinVL (Zhang et al., 2021b) | 157M | - | - | 38.2 / 129.3 | - | 75.95 / 76.12 | 82.05 / 83.08 |
| ViLT (Kim et al., 2021) | 88M | - | - | - | - | 70.85 / - | 74.91 / 75.57 |
| ALBEF (Li et al., 2021) | 210M | - | - | - | - | 75.84 / 76.04 | 82.55 / 83.14 |
| X-VLM (Zeng et al., 2021) | 240M | - | - | 39.6 / 132.6 | - | 78.22 / 78.37 | 84.41 / 84.76 |
| VLMO (Wang et al., 2021a) | | - | - | - | - | 76.64 / 76.89 | 82.77 / 83.34 |
| Encoder-Decoder Multi-modal Models |
| UNICORN (Yang et al., 2021) | | - | - | 35.8 / 119.1 | - | 69.20 / 69.40 | -/- |
| Uni-ENDN (Li et al., 2022b) | 110M | - | - | - | - | 72.20 / 72.50 | -/- |
| Pixel-BERT (Huang et al., 2020) | 144M | - | - | - | - | 74.45 / 74.55 | 76.50 / 77.20 |
| E2E-VLP (Xu et al., 2021a) | 94M | - | - | 36.2 / 117.3 | - | 73.25 / 73.67 | 77.25 / 77.96 |
| VL-T5 (Cho et al., 2021) | 220M | - | - | 34.5 / 116.5 | - | - / 70.30 | 74.60 / 73.60 |
| VL-BART (Cho et al., 2021) | 220M | - | - | 35.1 / 116.6 | - | - / 71.30 | 71.70 / 70.30 |
| Text2Image Models |
| DM-GAN (Zhu et al., 2019) | | - | - | - | 32.20 / 26.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (250M) | 12B | - | - | - | 17.90 / 27.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (640M)† | 82M | - | - | - | 15.79 / 29.22 | -/- | -/- |
| CogView (Ding et al., 2021) | 4B | - | - | - | 18.20 / 27.10 | -/- | -/- |
| Unified Models |
| Unifying (Huang et al., 2021) | 228M | - | - | 37.3 / 122.6 | - / 29.90 | -/- | -/- |
| FLAVA (Singh et al., 2021) | 240M | 80.33 | 75.54 / - | - | - | 72.80 / 72.49 | -/- |
| SimVLM (Wang et al., 2021b) (640M)† | 153M | 83.27 | 76.04 / - | 38.5 / 128.7 | - | 75.04 / 75.03 | 78.82 / 79.72 |
| SimVLM (Wang et al., 2021b) (1.8B) | | 83.40 | 80.60 / - | 39.0 / 134.8 | - | 77.87 / 78.14 | 81.72 / 81.77 |
| OFA (Wang et al., 2022) | 182M | 84.30 | - / 82.20 | 41.0 / 138.2 | 21.50* / 20.80* | 78.00 / 78.10 | -/- |
| Florence (Yuan et al., 2021) | 637M | - | - / 90.05 | -/- | -/- | 80.16 / 80.36 | -/- |
| DAVINCI | 154M | 83.13 | 78.81 / 83.92 | 39.2 / 130.4 | 17.44 (22.41*) / 24.21 (19.82*) | 76.32 / 76.44 | 80.03 / 80.25 |
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+ "text": "Table 3: Comparison with state-of-the-art vision-language models on vision, language, and multi-modal downstream tasks. All results are from base-size models. LE and FT denote linear evaluation and fine-tuning performance, respectively. Image2Text results are reported without CIDEr optimization. $\\dagger$ are our reproduced models. \\* are the results after fine-tuning. SimVLM (1.8B) and OFA are pre-trained with much larger corpus or human-labeled data of many downstream tasks, and thus they are not comparable and are labeled in gray. Florence (Yuan et al., 2021) is pre-trained with much larger model size (Florence-CoSwin-H, 637M) and more pre-training data (900M), so the numbers are in grey. bold denotes the best across unified models.",
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+ "text": "foundation models. We also include comparisons with some baseline models (e.g., MIM, MLM, CLIP). There are several observations. First, DAVINCI (column 8) outperforms FLAVA (column 3) and SimVLM (column 7) across almost all tasks, providing a new and stronger unified foundation model. Compared with FLAVA, DAVINCI improves an average of $2.04\\%$ , $1.68\\%$ on language and vision tasks, respectively. Compared with SimVLM, DAVINCI achieves comparable results on language tasks $(+0.13\\%)$ while performing much better on vision tasks $(+2.46\\%)$ . To make a fair comparison in terms of similar data size, we compare FLAVA (70M data, column 3) with DAVINCI (46.4M data, column 6). It is observed that DAVINCI still outperforms FLAVA even with much less data. Considering the multi-modal tasks, DAVINCI consistently outperforms FLAVA and SimVLM on VQA and VE. Note that FLAVA is incapable of generation and SimVLM cannot generate images; only DAVINCI is competent to all tasks and demonstrates a stronger capability of unifying vision and language tasks.",
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+ "text": "Zero-shot and Few-shot Transfer One of the critical benefits of generative pre-trained vision-language models is the good generalization ability on zero-shot and few-shot tasks. For zero-shot transfer, two out-of-domain distribution datasets are considered (NoCaps and VLINE), with results shown in Table 2. First, DAVinci outperforms SimVLM on both zero-shot and few-shot settings, demonstrating its better transfer capabilities. It also shows the effectiveness and robustness of the synergy of our proposed language supervision and image supervision. Second, it is observed that the performance improvement is bigger on 647.7M data (column 7 v.s. column 8) than 46.4M data (column 5 v.s. column 6). This shows DAVinci generalizes well with the increase of large-scale data. We even observe some performance drops on small data (46.4M) but excellent performance improvements on large data (647.7M). It is consistent with the recent observation that zero-shot ability could only be triggered with large pre-training data (Wei et al., 2022) and scaling to large data and keeping simple training objectives benefit generalization performance (Wang et al., 2021b).",
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+ "text": "Comparison with state-of-the-art vision-language models In addition to unified vision-language foundation models, we compare DAVinci with state-of-the-art vision-language models as well. The results are shown in Table 2. DAVinci demonstrates its superiority in vision understanding and text-to-image generation. Compared with current popular auto-regressive image generation models like DALLE and CogView, our model achieves comparable IS and better FID scores with significantly fewer model parameters than DALLE and CogView. Note that the original DALLE is implemented based on VQVAE, so here, we compare our model with reproduced VQGAN-based DALLE with",
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+ "table_body": "| Model | #Params. | Text MNLI Acc | Vision ImageNet LE / FT | Image2Text COCO B@4 / C | Text2Image COCO IS† / FID↓ | Multi-modal VQA test-dev / test-standard | NLVR2 dev / test-P |
| Encoder-only Multi-modal Models |
| VisualBERT (Li et al., 2019) | 170M | 81.60 | - | - | - | 70.80 / 71.00 | 67.40 / 67.00 |
| ViLBERT (Lu et al., 2019) | 274M | 79.90 | - | - | - | 70.55 / 70.92 | - |
| VL-BERT (Su et al., 2020) | 170M | 81.20 | - | - | - | 71.16 / - | - |
| LXMERT (Tan & Bansal, 2019a) | 240M | 80.40 | - | - | - | 72.42 / 72.54 | 74.90 / 74.50 |
| OSCAR (Li et al., 2020) | 155M | - | - | 36.5 / 123.7 | - | 73.16 / 73.44 | 78.07 / 78.36 |
| VinVL (Zhang et al., 2021b) | 157M | - | - | 38.2 / 129.3 | - | 75.95 / 76.12 | 82.05 / 83.08 |
| ViLT (Kim et al., 2021) | 88M | - | - | - | - | 70.85 / - | 74.91 / 75.57 |
| ALBEF (Li et al., 2021) | 210M | - | - | - | - | 75.84 / 76.04 | 82.55 / 83.14 |
| X-VLM (Zeng et al., 2021) | 240M | - | - | 39.6 / 132.6 | - | 78.22 / 78.37 | 84.41 / 84.76 |
| VLMO (Wang et al., 2021a) | | - | - | - | - | 76.64 / 76.89 | 82.77 / 83.34 |
| Encoder-Decoder Multi-modal Models |
| UNICORN (Yang et al., 2021) | | - | - | 35.8 / 119.1 | - | 69.20 / 69.40 | -/- |
| Uni-ENDN (Li et al., 2022b) | 110M | - | - | - | - | 72.20 / 72.50 | -/- |
| Pixel-BERT (Huang et al., 2020) | 144M | - | - | - | - | 74.45 / 74.55 | 76.50 / 77.20 |
| E2E-VLP (Xu et al., 2021a) | 94M | - | - | 36.2 / 117.3 | - | 73.25 / 73.67 | 77.25 / 77.96 |
| VL-T5 (Cho et al., 2021) | 220M | - | - | 34.5 / 116.5 | - | - / 70.30 | 74.60 / 73.60 |
| VL-BART (Cho et al., 2021) | 220M | - | - | 35.1 / 116.6 | - | - / 71.30 | 71.70 / 70.30 |
| Text2Image Models |
| AttnGAN (Xu et al., 2018) | | - | - | - | 23.30 / 35.20 | -/- | -/- |
| DM-GAN (Zhu et al., 2019) | | - | - | - | 32.20 / 26.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (250M) | 12B | - | - | - | 17.90 / 27.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (640M)† | 82M | - | - | - | 15.79 / 29.22 | -/- | -/- |
| CogView (Ding et al., 2021) | 4B | - | - | - | 18.20 / 27.10 | -/- | -/- |
| Unified Models |
| Unifying (Huang et al., 2021) | 228M | - | - | 37.3 / 122.6 | - / 29.90 | -/- | -/- |
| FLAVA (Singh et al., 2021) | 240M | 80.33 | 75.54 / - | - | - | 72.80 / 72.49 | -/- |
| SimVLM (Wang et al., 2021b) (640M)† | 153M | 83.27 | 76.04 / - | 38.5 / 128.7 | - | 75.04 / 75.03 | 78.82 / 79.72 |
| SimVLM (Wang et al., 2021b) (1.8B) | | 83.40 | 80.60 / - | 39.0 / 134.8 | - | 77.87 / 78.14 | 81.72 / 81.77 |
| OFA (Wang et al., 2022) | 182M | 84.30 | - / 82.20 | 41.0 / 138.2 | 21.50* / 20.80* | 78.00 / 78.10 | -/- |
| Florence (Yuan et al., 2021) | 637M | - | - / 90.05 | -/- | -/- | 80.16 / 80.36 | -/- |
| DAVINCI | 154M | 83.13 | 78.81 / 83.92 | 39.2 / 130.4 | 17.44 (22.41*) / 24.21 (19.82*) | 76.32 / 76.44 | 80.03 / 80.25 |
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diff --git a/2023/Write and Paint_ Generative Vision-Language Models are Unified Modal Learners/fd6fd19a-99f2-4a1c-9940-84627f28fb05_model.json b/2023/Write and Paint_ Generative Vision-Language Models are Unified Modal Learners/fd6fd19a-99f2-4a1c-9940-84627f28fb05_model.json
new file mode 100644
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+ "content": "WRITE AND PAINT: GENERATIVE VISION-LANGUAGE MODELS ARE UNIFIED MODAL LEARNERS"
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+ "content": "Shizhe Diao*"
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+ "angle": 0,
+ "content": "The Hong Kong University of Science and Technology sdiaoaa@connect.ust.hk"
+ },
+ {
+ "type": "text",
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+ "content": "Wangchunshu Zhou"
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+ "content": "Xinsong Zhang†"
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+ "content": "Jiawei Wang"
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+ "content": "Shanghai Jiao Tong University"
+ },
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+ },
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "ABSTRACT"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Recent advances in vision-language pre-training have pushed the state-of-the-art on various vision-language tasks, making machines more capable of multi-modal writing (image-to-text generation) and painting (text-to-image generation). However, few studies investigate if these two essential capabilities can be learned together and boost each other, making a versatile and powerful multi-modal foundation model. In this work, we disclose the potential of symmetric generative vision-language pre-training in learning to write and paint concurrently, and propose a new unified modal model, named DAVINCI, trained with prefix language modeling and prefix image modeling, a simple generative self-supervised objective on image-text pairs. Thanks to the proposed prefix multi-modal modeling framework, DAVINCI is simple to train, scalable to huge data, adaptable to both writing and painting tasks, and also strong on other vision, text, and multi-modal understanding tasks. DAVINCI achieves competitive performance on a wide range of 27 generation/understanding tasks and demonstrates the superiority of combining vision/language generative pre-training. Furthermore, we carefully benchmark the performance of different vision-language pre-training objectives on different scales of pre-training datasets on a heterogeneous and broad distribution coverage. Our results demonstrate the potential of exploiting self-supervision in both language and vision inputs, and establish new, stronger baselines for future comparisons at different data scales.\\(^{1}\\)"
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "1 INTRODUCTION"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Self-supervised language model pre-training (Peters et al., 2018; Radford et al., 2018; Devlin et al., 2019; Liu et al., 2019; Lewis et al., 2020; Raffel et al., 2020; Brown et al., 2020; Fu et al., 2022; Zhou et al., 2021b; Diao et al., 2020; 2021; Zhou et al., 2021a; Xu et al., 2020; Zhou et al., 2020; 2022a; Pan et al., 2022; Diao et al., 2023) has reshaped the landscape of modern natural language processing (NLP) research, pushing the state-of-the-art of a wide range of NLP tasks. Recently, this success has been transferred to the multi-modal context and resulted in a number of vision-language pretrained models (VLMs) (Lu et al., 2019; Tan & Bansal, 2019a), achieving state-of-the-art results on various vision-language tasks. Most existing VLMs are BERT-like Transformer (Vaswani et al., 2017) encoders pre-trained with a combination of different vision-language pre-training (VLP) objectives: masked multi-modal modeling (Lu et al., 2019; Tan & Bansal, 2019b; Chen et al., 2020; Li et al., 2020), multi-modal alignment prediction (Lu et al., 2019; Tan & Bansal, 2019b; Chen et al., 2020; Li et al., 2020), region of interest feature regression (Tan & Bansal, 2019b), image-text matching (Li et al., 2021; Zeng et al., 2021), to name a few. However, the roadmap towards large language models reveals a transition pattern from encoder-only models like BERT (Devlin et al., 2019) / RoBERTa (Liu et al., 2019) to sequence-to-sequence models like T5 (Raffel et al., 2020) / BART (Lewis et al., 2020) and autoregressive models like GPT-3 (Brown et al., 2020) / PaLM (Chowdhery et al., 2022) to tackle"
+ },
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+ "type": "page_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "*Work done during the internship at ByteDance AI Lab."
+ },
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+ "content": "† Corresponding author"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
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+ "content": "| Model | #Params. | Text MNLI Acc | Vision ImageNet LE / FT | Image2Text COCO B@4 / C | Text2Image COCO IS↑ / FID↓ | Multi-modal |
| VQA test-dev / test-standard | NLVR2 dev / test-P |
| Encoder-only Multi-modal Models |
| VinVL (Zhang et al., 2021b) | 157M | - | - | 38.2 / 129.3 | - | 75.95 / 76.12 | 82.05 / 83.08 |
| ViLT (Kim et al., 2021) | 88M | - | - | - | - | 70.85 / - | 74.91 / 75.57 |
| ALBEF (Li et al., 2021) | 210M | - | - | - | - | 75.84 / 76.04 | 82.55 / 83.14 |
| X-VLM (Zeng et al., 2021) | 240M | - | - | 39.6 / 132.6 | - | 78.22 / 78.37 | 84.41 / 84.76 |
| VLMO (Wang et al., 2021a) | | - | - | - | - | 76.64 / 76.89 | 82.77 / 83.34 |
| Encoder-Decoder Multi-modal Models |
| UNICORN (Yang et al., 2021) | | - | - | 35.8 / 119.1 | - | 69.20 / 69.40 | -/- |
| Uni-ENDN (Li et al., 2022b) | 110M | - | - | - | - | 72.20 / 72.50 | -/- |
| Pixel-BERT (Huang et al., 2020) | 144M | - | - | - | - | 74.45 / 74.55 | 76.50 / 77.20 |
| E2E-VLP (Xu et al., 2021a) | 94M | - | - | 36.2 / 117.3 | - | 73.25 / 73.67 | 77.25 / 77.96 |
| VL-T5 (Cho et al., 2021) | 220M | - | - | 34.5 / 116.5 | - | - / 70.30 | 74.60 / 73.60 |
| VL-BART (Cho et al., 2021) | 220M | - | - | 35.1 / 116.6 | - | - / 71.30 | 71.70 / 70.30 |
| Text2Image Models |
| DM-GAN (Zhu et al., 2019) | | - | - | - | 32.20 / 26.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (250M) | 12B | - | - | - | 17.90 / 27.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (640M)† | 82M | - | - | - | 15.79 / 29.22 | -/- | -/- |
| CogView (Ding et al., 2021) | 4B | - | - | - | 18.20 / 27.10 | -/- | -/- |
| Unified Models |
| Unifying (Huang et al., 2021) | 228M | - | - | 37.3 / 122.6 | - / 29.90 | -/- | -/- |
| FLAVA (Singh et al., 2021) | 240M | 80.33 | 75.54 / - | - | - | 72.80 / 72.49 | -/- |
| SimVLM (Wang et al., 2021b) (640M)† | 153M | 83.27 | 76.04 / - | 38.5 / 128.7 | - | 75.04 / 75.03 | 78.82 / 79.72 |
| SimVLM (Wang et al., 2021b) (1.8B) | | 83.40 | 80.60 / - | 39.0 / 134.8 | - | 77.87 / 78.14 | 81.72 / 81.77 |
| OFA (Wang et al., 2022) | 182M | 84.30 | - / 82.20 | 41.0 / 138.2 | 21.50* / 20.80* | 78.00 / 78.10 | -/- |
| Florence (Yuan et al., 2021) | 637M | - | - / 90.05 | -/- | -/- | 80.16 / 80.36 | -/- |
| DAVINCI | 154M | 83.13 | 78.81 / 83.92 | 39.2 / 130.4 | 17.44 (22.41*) / 24.21 (19.82*) | 76.32 / 76.44 | 80.03 / 80.25 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3: Comparison with state-of-the-art vision-language models on vision, language, and multi-modal downstream tasks. All results are from base-size models. LE and FT denote linear evaluation and fine-tuning performance, respectively. Image2Text results are reported without CIDEr optimization. \\(\\dagger\\) are our reproduced models. \\* are the results after fine-tuning. SimVLM (1.8B) and OFA are pre-trained with much larger corpus or human-labeled data of many downstream tasks, and thus they are not comparable and are labeled in gray. Florence (Yuan et al., 2021) is pre-trained with much larger model size (Florence-CoSwin-H, 637M) and more pre-training data (900M), so the numbers are in grey. bold denotes the best across unified models."
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+ "content": "foundation models. We also include comparisons with some baseline models (e.g., MIM, MLM, CLIP). There are several observations. First, DAVINCI (column 8) outperforms FLAVA (column 3) and SimVLM (column 7) across almost all tasks, providing a new and stronger unified foundation model. Compared with FLAVA, DAVINCI improves an average of \\(2.04\\%\\), \\(1.68\\%\\) on language and vision tasks, respectively. Compared with SimVLM, DAVINCI achieves comparable results on language tasks \\((+0.13\\%)\\) while performing much better on vision tasks \\((+2.46\\%)\\). To make a fair comparison in terms of similar data size, we compare FLAVA (70M data, column 3) with DAVINCI (46.4M data, column 6). It is observed that DAVINCI still outperforms FLAVA even with much less data. Considering the multi-modal tasks, DAVINCI consistently outperforms FLAVA and SimVLM on VQA and VE. Note that FLAVA is incapable of generation and SimVLM cannot generate images; only DAVINCI is competent to all tasks and demonstrates a stronger capability of unifying vision and language tasks."
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+ "content": "Zero-shot and Few-shot Transfer One of the critical benefits of generative pre-trained vision-language models is the good generalization ability on zero-shot and few-shot tasks. For zero-shot transfer, two out-of-domain distribution datasets are considered (NoCaps and VLINE), with results shown in Table 2. First, DAVinci outperforms SimVLM on both zero-shot and few-shot settings, demonstrating its better transfer capabilities. It also shows the effectiveness and robustness of the synergy of our proposed language supervision and image supervision. Second, it is observed that the performance improvement is bigger on 647.7M data (column 7 v.s. column 8) than 46.4M data (column 5 v.s. column 6). This shows DAVinci generalizes well with the increase of large-scale data. We even observe some performance drops on small data (46.4M) but excellent performance improvements on large data (647.7M). It is consistent with the recent observation that zero-shot ability could only be triggered with large pre-training data (Wei et al., 2022) and scaling to large data and keeping simple training objectives benefit generalization performance (Wang et al., 2021b)."
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+ "content": "Comparison with state-of-the-art vision-language models In addition to unified vision-language foundation models, we compare DAVinci with state-of-the-art vision-language models as well. The results are shown in Table 2. DAVinci demonstrates its superiority in vision understanding and text-to-image generation. Compared with current popular auto-regressive image generation models like DALLE and CogView, our model achieves comparable IS and better FID scores with significantly fewer model parameters than DALLE and CogView. Note that the original DALLE is implemented based on VQVAE, so here, we compare our model with reproduced VQGAN-based DALLE with"
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+ "content": "| Model | #Params. | Text MNLI Acc | Vision ImageNet LE / FT | Image2Text COCO B@4 / C | Text2Image COCO IS† / FID↓ | Multi-modal VQA test-dev / test-standard | NLVR2 dev / test-P |
| Encoder-only Multi-modal Models |
| VisualBERT (Li et al., 2019) | 170M | 81.60 | - | - | - | 70.80 / 71.00 | 67.40 / 67.00 |
| ViLBERT (Lu et al., 2019) | 274M | 79.90 | - | - | - | 70.55 / 70.92 | - |
| VL-BERT (Su et al., 2020) | 170M | 81.20 | - | - | - | 71.16 / - | - |
| LXMERT (Tan & Bansal, 2019a) | 240M | 80.40 | - | - | - | 72.42 / 72.54 | 74.90 / 74.50 |
| OSCAR (Li et al., 2020) | 155M | - | - | 36.5 / 123.7 | - | 73.16 / 73.44 | 78.07 / 78.36 |
| VinVL (Zhang et al., 2021b) | 157M | - | - | 38.2 / 129.3 | - | 75.95 / 76.12 | 82.05 / 83.08 |
| ViLT (Kim et al., 2021) | 88M | - | - | - | - | 70.85 / - | 74.91 / 75.57 |
| ALBEF (Li et al., 2021) | 210M | - | - | - | - | 75.84 / 76.04 | 82.55 / 83.14 |
| X-VLM (Zeng et al., 2021) | 240M | - | - | 39.6 / 132.6 | - | 78.22 / 78.37 | 84.41 / 84.76 |
| VLMO (Wang et al., 2021a) | | - | - | - | - | 76.64 / 76.89 | 82.77 / 83.34 |
| Encoder-Decoder Multi-modal Models |
| UNICORN (Yang et al., 2021) | | - | - | 35.8 / 119.1 | - | 69.20 / 69.40 | -/- |
| Uni-ENDN (Li et al., 2022b) | 110M | - | - | - | - | 72.20 / 72.50 | -/- |
| Pixel-BERT (Huang et al., 2020) | 144M | - | - | - | - | 74.45 / 74.55 | 76.50 / 77.20 |
| E2E-VLP (Xu et al., 2021a) | 94M | - | - | 36.2 / 117.3 | - | 73.25 / 73.67 | 77.25 / 77.96 |
| VL-T5 (Cho et al., 2021) | 220M | - | - | 34.5 / 116.5 | - | - / 70.30 | 74.60 / 73.60 |
| VL-BART (Cho et al., 2021) | 220M | - | - | 35.1 / 116.6 | - | - / 71.30 | 71.70 / 70.30 |
| Text2Image Models |
| AttnGAN (Xu et al., 2018) | | - | - | - | 23.30 / 35.20 | -/- | -/- |
| DM-GAN (Zhu et al., 2019) | | - | - | - | 32.20 / 26.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (250M) | 12B | - | - | - | 17.90 / 27.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (640M)† | 82M | - | - | - | 15.79 / 29.22 | -/- | -/- |
| CogView (Ding et al., 2021) | 4B | - | - | - | 18.20 / 27.10 | -/- | -/- |
| Unified Models |
| Unifying (Huang et al., 2021) | 228M | - | - | 37.3 / 122.6 | - / 29.90 | -/- | -/- |
| FLAVA (Singh et al., 2021) | 240M | 80.33 | 75.54 / - | - | - | 72.80 / 72.49 | -/- |
| SimVLM (Wang et al., 2021b) (640M)† | 153M | 83.27 | 76.04 / - | 38.5 / 128.7 | - | 75.04 / 75.03 | 78.82 / 79.72 |
| SimVLM (Wang et al., 2021b) (1.8B) | | 83.40 | 80.60 / - | 39.0 / 134.8 | - | 77.87 / 78.14 | 81.72 / 81.77 |
| OFA (Wang et al., 2022) | 182M | 84.30 | - / 82.20 | 41.0 / 138.2 | 21.50* / 20.80* | 78.00 / 78.10 | -/- |
| Florence (Yuan et al., 2021) | 637M | - | - / 90.05 | -/- | -/- | 80.16 / 80.36 | -/- |
| DAVINCI | 154M | 83.13 | 78.81 / 83.92 | 39.2 / 130.4 | 17.44 (22.41*) / 24.21 (19.82*) | 76.32 / 76.44 | 80.03 / 80.25 |
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+ "content": "Table 12: Comparison with state-of-the-art vision-language models on vision, language, and multi-modal downstream tasks. All results are from base-size models. LE and FT denote linear evaluation and fine-tuning performance, respectively. Image2Text results are reported without CIDEr optimization. \\(\\dagger\\) are our reproduced models. \\* are the results after fine-tuning. SimVLM (1.8B) and OFA are pre-trained with much larger corpus or human-labeled data of many downstream tasks, and thus they are not comparable and are labeled in gray. Florence (Yuan et al., 2021) is pre-trained with a much larger model size (Florence-CoSwin-H, 637M) and more pre-training data (900M), so the numbers are in grey. bold denotes the best across unified models."
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+# WRITE AND PAINT: GENERATIVE VISION-LANGUAGE MODELS ARE UNIFIED MODAL LEARNERS
+
+Shizhe Diao*
+
+The Hong Kong University of Science and Technology sdiaoaa@connect.ust.hk
+
+Wangchunshu Zhou
+
+ByteDance AI Lab
+
+wangchunshu.zhou@inf.ethz.ch
+
+Xinsong Zhang†
+
+ByteDance AI Lab
+
+zhangxinsong.0320@bytedance.com
+
+Jiawei Wang
+
+Shanghai Jiao Tong University
+
+wjw_sjt@sjtu.edu.cn
+
+# ABSTRACT
+
+Recent advances in vision-language pre-training have pushed the state-of-the-art on various vision-language tasks, making machines more capable of multi-modal writing (image-to-text generation) and painting (text-to-image generation). However, few studies investigate if these two essential capabilities can be learned together and boost each other, making a versatile and powerful multi-modal foundation model. In this work, we disclose the potential of symmetric generative vision-language pre-training in learning to write and paint concurrently, and propose a new unified modal model, named DAVINCI, trained with prefix language modeling and prefix image modeling, a simple generative self-supervised objective on image-text pairs. Thanks to the proposed prefix multi-modal modeling framework, DAVINCI is simple to train, scalable to huge data, adaptable to both writing and painting tasks, and also strong on other vision, text, and multi-modal understanding tasks. DAVINCI achieves competitive performance on a wide range of 27 generation/understanding tasks and demonstrates the superiority of combining vision/language generative pre-training. Furthermore, we carefully benchmark the performance of different vision-language pre-training objectives on different scales of pre-training datasets on a heterogeneous and broad distribution coverage. Our results demonstrate the potential of exploiting self-supervision in both language and vision inputs, and establish new, stronger baselines for future comparisons at different data scales. $^{1}$
+
+# 1 INTRODUCTION
+
+Self-supervised language model pre-training (Peters et al., 2018; Radford et al., 2018; Devlin et al., 2019; Liu et al., 2019; Lewis et al., 2020; Raffel et al., 2020; Brown et al., 2020; Fu et al., 2022; Zhou et al., 2021b; Diao et al., 2020; 2021; Zhou et al., 2021a; Xu et al., 2020; Zhou et al., 2020; 2022a; Pan et al., 2022; Diao et al., 2023) has reshaped the landscape of modern natural language processing (NLP) research, pushing the state-of-the-art of a wide range of NLP tasks. Recently, this success has been transferred to the multi-modal context and resulted in a number of vision-language pretrained models (VLMs) (Lu et al., 2019; Tan & Bansal, 2019a), achieving state-of-the-art results on various vision-language tasks. Most existing VLMs are BERT-like Transformer (Vaswani et al., 2017) encoders pre-trained with a combination of different vision-language pre-training (VLP) objectives: masked multi-modal modeling (Lu et al., 2019; Tan & Bansal, 2019b; Chen et al., 2020; Li et al., 2020), multi-modal alignment prediction (Lu et al., 2019; Tan & Bansal, 2019b; Chen et al., 2020; Li et al., 2020), region of interest feature regression (Tan & Bansal, 2019b), image-text matching (Li et al., 2021; Zeng et al., 2021), to name a few. However, the roadmap towards large language models reveals a transition pattern from encoder-only models like BERT (Devlin et al., 2019) / RoBERTa (Liu et al., 2019) to sequence-to-sequence models like T5 (Raffel et al., 2020) / BART (Lewis et al., 2020) and autoregressive models like GPT-3 (Brown et al., 2020) / PaLM (Chowdhery et al., 2022) to tackle
+
+more tasks in a unified way, and from complicated objectives like masked language modeling / next sentence prediction / replace token detection to a simple language modeling objective to improve the scalability of pre-training. This suggests that the generative pre-training paradigm with simple targets shows great potential for pre-training more scalable and general VLMs.
+
+To this end, several recent studies (Cho et al., 2021; Zhang et al., 2021a; Wang et al., 2021b; 2022) investigated sequence-to-sequence (seq2seq) vision-language pre-training and achieved state-of-the-art results on a range of vision-language understanding and generation tasks. For example, VL-T5 (Cho et al., 2021), OFA (Wang et al., 2022) and PaLI (Chen et al., 2022) formulate various vision-and-language problems into seq2seq tasks and pre-train a seq2seq VLM by multi-tasking on these tasks. In addition, ERNIE-ViLG (Zhang et al., 2021a) and SimVLM (Wang et al., 2021b) pre-train seq2seq VLMs with a simple language modeling or prefix language modeling objective on a large number of image-caption pairs. While achieving promising results, these objectives are not versatile enough, resulting in VLMs that are only capable of a subset of tasks in image-text modalities. On the other hand, the recent success of generative language pre-training (Brown et al., 2020) and generative vision pre-training (He et al., 2022; Bao et al., 2021) motivates us to explore generative vision-language pre-training to learn more versatile and scalable vision-language models.
+
+In this work, we introduce prefix multi-modal modeling, a unified generative pre-training framework that extends prefix language modeling to the multi-modal context and learns a multi-modal foundation model by learning to write and paint simultaneously. As illustrated in Figure 1, given an image-caption pair, we split the image and caption into two parts denoted as prefix and suffix. To make prefix image modeling compatible with the seq2seq formulation of conventional prefix language modeling, we follow DALLE (Ramesh et al., 2021) and convert images into discrete sequences of image tokens (van den Oord et al., 2017). We then train the model to generate the suffix in one modality based on the prefix in the same modality and the complete input in the other modality. In this way, prefix multi-modal modeling can fully exploit self-supervision from large-scale image-caption pairs by learning to write and paint simultaneously. We pre-train DAVinci| Model | #Params. | Text MNLI Acc | Vision ImageNet LE / FT | Image2Text COCO B@4 / C | Text2Image COCO IS↑ / FID↓ | Multi-modal |
| VQA test-dev / test-standard | NLVR2 dev / test-P |
| Encoder-only Multi-modal Models |
| VinVL (Zhang et al., 2021b) | 157M | - | - | 38.2 / 129.3 | - | 75.95 / 76.12 | 82.05 / 83.08 |
| ViLT (Kim et al., 2021) | 88M | - | - | - | - | 70.85 / - | 74.91 / 75.57 |
| ALBEF (Li et al., 2021) | 210M | - | - | - | - | 75.84 / 76.04 | 82.55 / 83.14 |
| X-VLM (Zeng et al., 2021) | 240M | - | - | 39.6 / 132.6 | - | 78.22 / 78.37 | 84.41 / 84.76 |
| VLMO (Wang et al., 2021a) | | - | - | - | - | 76.64 / 76.89 | 82.77 / 83.34 |
| Encoder-Decoder Multi-modal Models |
| UNICORN (Yang et al., 2021) | | - | - | 35.8 / 119.1 | - | 69.20 / 69.40 | -/- |
| Uni-ENDN (Li et al., 2022b) | 110M | - | - | - | - | 72.20 / 72.50 | -/- |
| Pixel-BERT (Huang et al., 2020) | 144M | - | - | - | - | 74.45 / 74.55 | 76.50 / 77.20 |
| E2E-VLP (Xu et al., 2021a) | 94M | - | - | 36.2 / 117.3 | - | 73.25 / 73.67 | 77.25 / 77.96 |
| VL-T5 (Cho et al., 2021) | 220M | - | - | 34.5 / 116.5 | - | - / 70.30 | 74.60 / 73.60 |
| VL-BART (Cho et al., 2021) | 220M | - | - | 35.1 / 116.6 | - | - / 71.30 | 71.70 / 70.30 |
| Text2Image Models |
| DM-GAN (Zhu et al., 2019) | | - | - | - | 32.20 / 26.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (250M) | 12B | - | - | - | 17.90 / 27.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (640M)† | 82M | - | - | - | 15.79 / 29.22 | -/- | -/- |
| CogView (Ding et al., 2021) | 4B | - | - | - | 18.20 / 27.10 | -/- | -/- |
| Unified Models |
| Unifying (Huang et al., 2021) | 228M | - | - | 37.3 / 122.6 | - / 29.90 | -/- | -/- |
| FLAVA (Singh et al., 2021) | 240M | 80.33 | 75.54 / - | - | - | 72.80 / 72.49 | -/- |
| SimVLM (Wang et al., 2021b) (640M)† | 153M | 83.27 | 76.04 / - | 38.5 / 128.7 | - | 75.04 / 75.03 | 78.82 / 79.72 |
| SimVLM (Wang et al., 2021b) (1.8B) | | 83.40 | 80.60 / - | 39.0 / 134.8 | - | 77.87 / 78.14 | 81.72 / 81.77 |
| OFA (Wang et al., 2022) | 182M | 84.30 | - / 82.20 | 41.0 / 138.2 | 21.50* / 20.80* | 78.00 / 78.10 | -/- |
| Florence (Yuan et al., 2021) | 637M | - | - / 90.05 | -/- | -/- | 80.16 / 80.36 | -/- |
| DAVINCI | 154M | 83.13 | 78.81 / 83.92 | 39.2 / 130.4 | 17.44 (22.41*) / 24.21 (19.82*) | 76.32 / 76.44 | 80.03 / 80.25 |
+
+Table 3: Comparison with state-of-the-art vision-language models on vision, language, and multi-modal downstream tasks. All results are from base-size models. LE and FT denote linear evaluation and fine-tuning performance, respectively. Image2Text results are reported without CIDEr optimization. $\dagger$ are our reproduced models. \* are the results after fine-tuning. SimVLM (1.8B) and OFA are pre-trained with much larger corpus or human-labeled data of many downstream tasks, and thus they are not comparable and are labeled in gray. Florence (Yuan et al., 2021) is pre-trained with much larger model size (Florence-CoSwin-H, 637M) and more pre-training data (900M), so the numbers are in grey. bold denotes the best across unified models.
+
+foundation models. We also include comparisons with some baseline models (e.g., MIM, MLM, CLIP). There are several observations. First, DAVINCI (column 8) outperforms FLAVA (column 3) and SimVLM (column 7) across almost all tasks, providing a new and stronger unified foundation model. Compared with FLAVA, DAVINCI improves an average of $2.04\%$ , $1.68\%$ on language and vision tasks, respectively. Compared with SimVLM, DAVINCI achieves comparable results on language tasks $(+0.13\%)$ while performing much better on vision tasks $(+2.46\%)$ . To make a fair comparison in terms of similar data size, we compare FLAVA (70M data, column 3) with DAVINCI (46.4M data, column 6). It is observed that DAVINCI still outperforms FLAVA even with much less data. Considering the multi-modal tasks, DAVINCI consistently outperforms FLAVA and SimVLM on VQA and VE. Note that FLAVA is incapable of generation and SimVLM cannot generate images; only DAVINCI is competent to all tasks and demonstrates a stronger capability of unifying vision and language tasks.
+
+Zero-shot and Few-shot Transfer One of the critical benefits of generative pre-trained vision-language models is the good generalization ability on zero-shot and few-shot tasks. For zero-shot transfer, two out-of-domain distribution datasets are considered (NoCaps and VLINE), with results shown in Table 2. First, DAVinci outperforms SimVLM on both zero-shot and few-shot settings, demonstrating its better transfer capabilities. It also shows the effectiveness and robustness of the synergy of our proposed language supervision and image supervision. Second, it is observed that the performance improvement is bigger on 647.7M data (column 7 v.s. column 8) than 46.4M data (column 5 v.s. column 6). This shows DAVinci generalizes well with the increase of large-scale data. We even observe some performance drops on small data (46.4M) but excellent performance improvements on large data (647.7M). It is consistent with the recent observation that zero-shot ability could only be triggered with large pre-training data (Wei et al., 2022) and scaling to large data and keeping simple training objectives benefit generalization performance (Wang et al., 2021b).
+
+Comparison with state-of-the-art vision-language models In addition to unified vision-language foundation models, we compare DAVinci with state-of-the-art vision-language models as well. The results are shown in Table 2. DAVinci demonstrates its superiority in vision understanding and text-to-image generation. Compared with current popular auto-regressive image generation models like DALLE and CogView, our model achieves comparable IS and better FID scores with significantly fewer model parameters than DALLE and CogView. Note that the original DALLE is implemented based on VQVAE, so here, we compare our model with reproduced VQGAN-based DALLE with
+
+| Model | #Params. | Text MNLI Acc | Vision ImageNet LE / FT | Image2Text COCO B@4 / C | Text2Image COCO IS† / FID↓ | Multi-modal VQA test-dev / test-standard | NLVR2 dev / test-P |
| Encoder-only Multi-modal Models |
| VisualBERT (Li et al., 2019) | 170M | 81.60 | - | - | - | 70.80 / 71.00 | 67.40 / 67.00 |
| ViLBERT (Lu et al., 2019) | 274M | 79.90 | - | - | - | 70.55 / 70.92 | - |
| VL-BERT (Su et al., 2020) | 170M | 81.20 | - | - | - | 71.16 / - | - |
| LXMERT (Tan & Bansal, 2019a) | 240M | 80.40 | - | - | - | 72.42 / 72.54 | 74.90 / 74.50 |
| OSCAR (Li et al., 2020) | 155M | - | - | 36.5 / 123.7 | - | 73.16 / 73.44 | 78.07 / 78.36 |
| VinVL (Zhang et al., 2021b) | 157M | - | - | 38.2 / 129.3 | - | 75.95 / 76.12 | 82.05 / 83.08 |
| ViLT (Kim et al., 2021) | 88M | - | - | - | - | 70.85 / - | 74.91 / 75.57 |
| ALBEF (Li et al., 2021) | 210M | - | - | - | - | 75.84 / 76.04 | 82.55 / 83.14 |
| X-VLM (Zeng et al., 2021) | 240M | - | - | 39.6 / 132.6 | - | 78.22 / 78.37 | 84.41 / 84.76 |
| VLMO (Wang et al., 2021a) | | - | - | - | - | 76.64 / 76.89 | 82.77 / 83.34 |
| Encoder-Decoder Multi-modal Models |
| UNICORN (Yang et al., 2021) | | - | - | 35.8 / 119.1 | - | 69.20 / 69.40 | -/- |
| Uni-ENDN (Li et al., 2022b) | 110M | - | - | - | - | 72.20 / 72.50 | -/- |
| Pixel-BERT (Huang et al., 2020) | 144M | - | - | - | - | 74.45 / 74.55 | 76.50 / 77.20 |
| E2E-VLP (Xu et al., 2021a) | 94M | - | - | 36.2 / 117.3 | - | 73.25 / 73.67 | 77.25 / 77.96 |
| VL-T5 (Cho et al., 2021) | 220M | - | - | 34.5 / 116.5 | - | - / 70.30 | 74.60 / 73.60 |
| VL-BART (Cho et al., 2021) | 220M | - | - | 35.1 / 116.6 | - | - / 71.30 | 71.70 / 70.30 |
| Text2Image Models |
| AttnGAN (Xu et al., 2018) | | - | - | - | 23.30 / 35.20 | -/- | -/- |
| DM-GAN (Zhu et al., 2019) | | - | - | - | 32.20 / 26.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (250M) | 12B | - | - | - | 17.90 / 27.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (640M)† | 82M | - | - | - | 15.79 / 29.22 | -/- | -/- |
| CogView (Ding et al., 2021) | 4B | - | - | - | 18.20 / 27.10 | -/- | -/- |
| Unified Models |
| Unifying (Huang et al., 2021) | 228M | - | - | 37.3 / 122.6 | - / 29.90 | -/- | -/- |
| FLAVA (Singh et al., 2021) | 240M | 80.33 | 75.54 / - | - | - | 72.80 / 72.49 | -/- |
| SimVLM (Wang et al., 2021b) (640M)† | 153M | 83.27 | 76.04 / - | 38.5 / 128.7 | - | 75.04 / 75.03 | 78.82 / 79.72 |
| SimVLM (Wang et al., 2021b) (1.8B) | | 83.40 | 80.60 / - | 39.0 / 134.8 | - | 77.87 / 78.14 | 81.72 / 81.77 |
| OFA (Wang et al., 2022) | 182M | 84.30 | - / 82.20 | 41.0 / 138.2 | 21.50* / 20.80* | 78.00 / 78.10 | -/- |
| Florence (Yuan et al., 2021) | 637M | - | - / 90.05 | -/- | -/- | 80.16 / 80.36 | -/- |
| DAVINCI | 154M | 83.13 | 78.81 / 83.92 | 39.2 / 130.4 | 17.44 (22.41*) / 24.21 (19.82*) | 76.32 / 76.44 | 80.03 / 80.25 |
+
+Table 12: Comparison with state-of-the-art vision-language models on vision, language, and multi-modal downstream tasks. All results are from base-size models. LE and FT denote linear evaluation and fine-tuning performance, respectively. Image2Text results are reported without CIDEr optimization. $\dagger$ are our reproduced models. \* are the results after fine-tuning. SimVLM (1.8B) and OFA are pre-trained with much larger corpus or human-labeled data of many downstream tasks, and thus they are not comparable and are labeled in gray. Florence (Yuan et al., 2021) is pre-trained with a much larger model size (Florence-CoSwin-H, 637M) and more pre-training data (900M), so the numbers are in grey. bold denotes the best across unified models.
+
+
+Figure 4: Comparison with DALLE and OFA on text-to-image generation.
+
+
+a decorative flower vase full of purple and yellow flowers
+
+
+a vase full of flowers on table
+
+
+a park with flowers on a sunny day
+
+
+a fire hydrant sitting in a front yard next to a sign
+
+
+a beach on a sunny day
+
+
+a one cart train coming down the railroad tracks
+
+
+a red and white boat docked on shore
+
+
+a picture of a snowy mountain
+
+
+a red stop sign on the side of the road
+
+
+a building in front of a roundabout with a tree in the center.
+
+
+bathroom with marble walls and counter surrounds a large mirror
+
+
+trees by the river in the mountains
+
+
+many fruits on the plate on the table
+
+
+a bunch of fruit in a fruit shop
+
+
+a table set with a sandwich and a drink
+
+
+noodles and broccoli on a plate
+Figure 5: Generation samples by DAVINCI.
\ No newline at end of file
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+ "content": "| Model | #Params. | Text MNLI Acc | Vision ImageNet LE / FT | Image2Text COCO B@4 / C | Text2Image COCO IS↑ / FID↓ | Multi-modal |
| VQA test-dev / test-standard | NLVR2 dev / test-P |
| Encoder-only Multi-modal Models |
| VinVL (Zhang et al., 2021b) | 157M | - | - | 38.2 / 129.3 | - | 75.95 / 76.12 | 82.05 / 83.08 |
| ViLT (Kim et al., 2021) | 88M | - | - | - | - | 70.85 / - | 74.91 / 75.57 |
| ALBEF (Li et al., 2021) | 210M | - | - | - | - | 75.84 / 76.04 | 82.55 / 83.14 |
| X-VLM (Zeng et al., 2021) | 240M | - | - | 39.6 / 132.6 | - | 78.22 / 78.37 | 84.41 / 84.76 |
| VLMO (Wang et al., 2021a) | | - | - | - | - | 76.64 / 76.89 | 82.77 / 83.34 |
| Encoder-Decoder Multi-modal Models |
| UNICORN (Yang et al., 2021) | | - | - | 35.8 / 119.1 | - | 69.20 / 69.40 | -/- |
| Uni-ENDN (Li et al., 2022b) | 110M | - | - | - | - | 72.20 / 72.50 | -/- |
| Pixel-BERT (Huang et al., 2020) | 144M | - | - | - | - | 74.45 / 74.55 | 76.50 / 77.20 |
| E2E-VLP (Xu et al., 2021a) | 94M | - | - | 36.2 / 117.3 | - | 73.25 / 73.67 | 77.25 / 77.96 |
| VL-T5 (Cho et al., 2021) | 220M | - | - | 34.5 / 116.5 | - | - / 70.30 | 74.60 / 73.60 |
| VL-BART (Cho et al., 2021) | 220M | - | - | 35.1 / 116.6 | - | - / 71.30 | 71.70 / 70.30 |
| Text2Image Models |
| DM-GAN (Zhu et al., 2019) | | - | - | - | 32.20 / 26.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (250M) | 12B | - | - | - | 17.90 / 27.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (640M)† | 82M | - | - | - | 15.79 / 29.22 | -/- | -/- |
| CogView (Ding et al., 2021) | 4B | - | - | - | 18.20 / 27.10 | -/- | -/- |
| Unified Models |
| Unifying (Huang et al., 2021) | 228M | - | - | 37.3 / 122.6 | - / 29.90 | -/- | -/- |
| FLAVA (Singh et al., 2021) | 240M | 80.33 | 75.54 / - | - | - | 72.80 / 72.49 | -/- |
| SimVLM (Wang et al., 2021b) (640M)† | 153M | 83.27 | 76.04 / - | 38.5 / 128.7 | - | 75.04 / 75.03 | 78.82 / 79.72 |
| SimVLM (Wang et al., 2021b) (1.8B) | | 83.40 | 80.60 / - | 39.0 / 134.8 | - | 77.87 / 78.14 | 81.72 / 81.77 |
| OFA (Wang et al., 2022) | 182M | 84.30 | - / 82.20 | 41.0 / 138.2 | 21.50* / 20.80* | 78.00 / 78.10 | -/- |
| Florence (Yuan et al., 2021) | 637M | - | - / 90.05 | -/- | -/- | 80.16 / 80.36 | -/- |
| DAVINCI | 154M | 83.13 | 78.81 / 83.92 | 39.2 / 130.4 | 17.44 (22.41*) / 24.21 (19.82*) | 76.32 / 76.44 | 80.03 / 80.25 |
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+ "content": " are our reproduced models. \\* are the results after fine-tuning. SimVLM (1.8B) and OFA are pre-trained with much larger corpus or human-labeled data of many downstream tasks, and thus they are not comparable and are labeled in gray. Florence (Yuan et al., 2021) is pre-trained with much larger model size (Florence-CoSwin-H, 637M) and more pre-training data (900M), so the numbers are in grey. bold denotes the best across unified models."
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+ "content": "foundation models. We also include comparisons with some baseline models (e.g., MIM, MLM, CLIP). There are several observations. First, DAVINCI (column 8) outperforms FLAVA (column 3) and SimVLM (column 7) across almost all tasks, providing a new and stronger unified foundation model. Compared with FLAVA, DAVINCI improves an average of "
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+ "content": " on language and vision tasks, respectively. Compared with SimVLM, DAVINCI achieves comparable results on language tasks "
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+ "content": ". To make a fair comparison in terms of similar data size, we compare FLAVA (70M data, column 3) with DAVINCI (46.4M data, column 6). It is observed that DAVINCI still outperforms FLAVA even with much less data. Considering the multi-modal tasks, DAVINCI consistently outperforms FLAVA and SimVLM on VQA and VE. Note that FLAVA is incapable of generation and SimVLM cannot generate images; only DAVINCI is competent to all tasks and demonstrates a stronger capability of unifying vision and language tasks."
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+ "html": "| Model | #Params. | Text MNLI Acc | Vision ImageNet LE / FT | Image2Text COCO B@4 / C | Text2Image COCO IS† / FID↓ | Multi-modal VQA test-dev / test-standard | NLVR2 dev / test-P |
| Encoder-only Multi-modal Models |
| VisualBERT (Li et al., 2019) | 170M | 81.60 | - | - | - | 70.80 / 71.00 | 67.40 / 67.00 |
| ViLBERT (Lu et al., 2019) | 274M | 79.90 | - | - | - | 70.55 / 70.92 | - |
| VL-BERT (Su et al., 2020) | 170M | 81.20 | - | - | - | 71.16 / - | - |
| LXMERT (Tan & Bansal, 2019a) | 240M | 80.40 | - | - | - | 72.42 / 72.54 | 74.90 / 74.50 |
| OSCAR (Li et al., 2020) | 155M | - | - | 36.5 / 123.7 | - | 73.16 / 73.44 | 78.07 / 78.36 |
| VinVL (Zhang et al., 2021b) | 157M | - | - | 38.2 / 129.3 | - | 75.95 / 76.12 | 82.05 / 83.08 |
| ViLT (Kim et al., 2021) | 88M | - | - | - | - | 70.85 / - | 74.91 / 75.57 |
| ALBEF (Li et al., 2021) | 210M | - | - | - | - | 75.84 / 76.04 | 82.55 / 83.14 |
| X-VLM (Zeng et al., 2021) | 240M | - | - | 39.6 / 132.6 | - | 78.22 / 78.37 | 84.41 / 84.76 |
| VLMO (Wang et al., 2021a) | | - | - | - | - | 76.64 / 76.89 | 82.77 / 83.34 |
| Encoder-Decoder Multi-modal Models |
| UNICORN (Yang et al., 2021) | | - | - | 35.8 / 119.1 | - | 69.20 / 69.40 | -/- |
| Uni-ENDN (Li et al., 2022b) | 110M | - | - | - | - | 72.20 / 72.50 | -/- |
| Pixel-BERT (Huang et al., 2020) | 144M | - | - | - | - | 74.45 / 74.55 | 76.50 / 77.20 |
| E2E-VLP (Xu et al., 2021a) | 94M | - | - | 36.2 / 117.3 | - | 73.25 / 73.67 | 77.25 / 77.96 |
| VL-T5 (Cho et al., 2021) | 220M | - | - | 34.5 / 116.5 | - | - / 70.30 | 74.60 / 73.60 |
| VL-BART (Cho et al., 2021) | 220M | - | - | 35.1 / 116.6 | - | - / 71.30 | 71.70 / 70.30 |
| Text2Image Models |
| AttnGAN (Xu et al., 2018) | | - | - | - | 23.30 / 35.20 | -/- | -/- |
| DM-GAN (Zhu et al., 2019) | | - | - | - | 32.20 / 26.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (250M) | 12B | - | - | - | 17.90 / 27.50 | -/- | -/- |
| DALLE (Ramesh et al., 2021) (640M)† | 82M | - | - | - | 15.79 / 29.22 | -/- | -/- |
| CogView (Ding et al., 2021) | 4B | - | - | - | 18.20 / 27.10 | -/- | -/- |
| Unified Models |
| Unifying (Huang et al., 2021) | 228M | - | - | 37.3 / 122.6 | - / 29.90 | -/- | -/- |
| FLAVA (Singh et al., 2021) | 240M | 80.33 | 75.54 / - | - | - | 72.80 / 72.49 | -/- |
| SimVLM (Wang et al., 2021b) (640M)† | 153M | 83.27 | 76.04 / - | 38.5 / 128.7 | - | 75.04 / 75.03 | 78.82 / 79.72 |
| SimVLM (Wang et al., 2021b) (1.8B) | | 83.40 | 80.60 / - | 39.0 / 134.8 | - | 77.87 / 78.14 | 81.72 / 81.77 |
| OFA (Wang et al., 2022) | 182M | 84.30 | - / 82.20 | 41.0 / 138.2 | 21.50* / 20.80* | 78.00 / 78.10 | -/- |
| Florence (Yuan et al., 2021) | 637M | - | - / 90.05 | -/- | -/- | 80.16 / 80.36 | -/- |
| DAVINCI | 154M | 83.13 | 78.81 / 83.92 | 39.2 / 130.4 | 17.44 (22.41*) / 24.21 (19.82*) | 76.32 / 76.44 | 80.03 / 80.25 |
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diff --git a/2023/Your Contrastive Learning Is Secretly Doing Stochastic Neighbor Embedding/97d2e52c-457b-46f6-8c21-13d5d765eb07_content_list.json b/2023/Your Contrastive Learning Is Secretly Doing Stochastic Neighbor Embedding/97d2e52c-457b-46f6-8c21-13d5d765eb07_content_list.json
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+ "text": "YOUR CONTRASTIVE LEARNING IS SECRETLY DOING STOCHASTIC NEIGHBOR EMBEDDING",
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