Visual Explanation for Deep Metric Learning
Authors: Sijie Zhu
Taojiannan Yang
Chen Chen
Venue:  (2020)
Keywords: Metric Learning
Visual Explanation

Abstract: This work explores the visual explanation for deep metric learning and its applications. As an important problem for learning representation, metric learning has attracted much attention recently, while the interpretation of such model is not as well studied as classification. To this end, we propose an intuitive idea to show where contributes the most to the overall similarity of two input images by decomposing the final activation. Instead of only providing the overall activation map of each image, we propose to generate point-to-point activation intensity between two images so that the relationship between different regions is uncovered. We show that the proposed framework can be directly deployed to a large range of metric learning applications and provides valuable information for understanding the model. Furthermore, our experiments show its effectiveness on two potential applications, i.e. cross-view pattern discovery and interactive retrieval. 

Under review as a conference paper at ICLR 2020
VISUAL EXPLANATION FOR DEEP METRIC LEARNING
Anonymous authors
Paper under double-blind review
ABSTRACT
This work explores the visual explanation for deep metric learning and its appli- cations. As an important problem for learning representation, metric learning has attracted much attention recently, while the interpretation of such model is not well studied as classification. To this end, we propose an intuitive idea to show where contributes the most to the overall similarity of two input images by decom- posing the final activation. Instead of only providing the overall activation map of each image, we propose generate point-to-poing activation intensity between two images so that the relationship between different regions is uncovered. We show that the proposed framework can be directly deployed large range of metric learning applications and provides valuable information for understanding the model. Furthermore, our experiments show its effectiveness on two potential applications, i.e. cross-view pattern discovery and interactive retrieval.
INTRODUCTION
Learning the similarity metrics between arbitrary images is fundamental problem for variety of tasks, such as image retrieval (Oh Song et al. (2016), verification (Schroff al. (2015): Luo et al.) (2019)) localization (Hu et al. (2018). video tracking (Bertinetto et al. (2016)), etc. Recently the deep Siamese network (Chopra et al. 2005)) based framework has become a standard architecture for metric learning and achieves exciting results wide range of applications (Wang et al. (019)). However, there are surprisingly few papers conducting visual analyses to explain why the learned similarity of a given image pair is high low. Specifically, which part contributes the most to the similarity is a straightforward question and the answer can reveal important hidden information about the model as well as the data.
Previous visual explanation works mainly focus on the interpretation of deep neural network for clas- sification (Springenberg et al. (2014); /hhou al. (2016] 2018); Fong & Vedaldi (2017)). Guided back propagation (Guided BP) (Springenberg et al. (2014) has been used for explanation by gen- erating the gradient from prediction input, which shows how much the output will change with a little change in each dimension of the input. Another representative visual explanation, class activa- tion map (CAM) Zhou al. (0066), generates the heatmap of discriminative regions corresponding to specific class based on the linearity of global average pooling (GAP) and fully connected (FC) layer. However, the original method only works on this specific architecture configuration and needs retraining for visualizing other applications. Based on the gradient of the last convolutional layer instead of the input, Grad-CAN (Selvaraju et al. (2017)) is proposed to generate activation maps for all convolutional neural network (CNN) architectures. Besides, other existing methods explore network ablation (Zhou et al. (2018), the taner-taak--al strategy (Zhang et al. (2018)), inversion Maheendran & Vedaldi 2015)) ) and perturbation (Fong & Vedaldi (2017)) for visual explanation.
Since the verification applications like person re-identification (re-ID) (Luo et al. (019)) )) usually
train metric learning models along with classification, recent work (Yang al. (2099) starts to
leverage the classification activation map to help improve the overall performance, but the activation map of metric learning is still not well explored. For two given images, a variant of Grad-CAM has been used for visualization of image retrieval (Gordo& & Larlus (017)) by computing the gradient from the cosine similarity of the embedding features to the last convolutional layers of both images. However, Grad-CAM only provides the overall highlighted regions of two input images, the rela- tionship between each activated region of two images is yet to be uncovered. Since the similarity is calculated from two images and possibly based on several similar patterns between them, the relationship between these patterns critical for understanding the model.

---

Under review as a conference paper at ICLR 2020
In this paper, we propose activation decom- position framework for visual explanation of deep metric learning and explore the relation- ship between each activated region by point-to- point activation response between two images. As shown in Fig. [ the overall activation map of the proposed method generated by decom- posing the similarity along each image. In this example, the query image (A) has a high acti- vation on both the eyes and mouth areas, but the overall map of the retrieved image (B) only highlights the eyes. It is actually hard to under- stand how the model works only based on the overall maps. For image B, the mouth region (green point) has a low activation which means the activation between the mouth and the whole image A is low compared to the overall activa- tion (similarity). However, by further decom- posing this activation (green point) along image A, that is to give the activation between the mouth region of image B and each position in image A, the resulting partial (or point-specific) activation map (green box) reveals that the mouth region of image B still has a high response on the mouth region of image A. This partial activation map can be generated for each pixel, which renders the point-to-poin to-nt activation intensity representing the relationship between regions in both images, e.g. eye-to-nose nose or mouth-to-mouth. The partial activation map provides much more refined information about the model which is crucial for explanation. The contributions are summarized as follows.
Overall
Partial
Similarity
0.5
An overview of activation decomposi- tion. The overall activation map on each image highlights the regions contributing the most the similarity. The partial activation map highlights the regions in one image that have large activa- tion responses a specific position in the other image, e.g. mouth or eye.
Figure 1:
We propose a novel explanation framework for deep metric learning architectures and it may serve as analysis tool for host of applications, e.g. face recognition, person re-ID.
The proposed method uncovers the point-to-point activation intensity which not explored by existing methods. Our experiments further show the importance of the partial activation map on several new applications, i.e. cross-view pattern discovery and interactive retrieval.
Our analysis suggests that two widely believed arguments (Section 2.1 about CAM and Grad- CAM are inaccurate.
2 RELATED WORK
2.1 INTERPRETATION FOR CLASSIFICATION
As a default setting, most existing interpretation methods (Zhou et al. (2016); Springenberg et al. (2014): /Zhang et al. (2018); Fong & Vedaldi (017)) are designed in classification context where the output score is generated from one input image. Among the approaches that do not require architecture change, one intuitive idea (Zhou et al. 2016): Zhang et al. (2018)) is to look into the model and see where contributes the most to the final prediction. CAM and its variant Grad-CAM are among the most widely used approaches, but recent works simply consider CAM as a heuristic linear combination of convolutional feature maps which is limited to the original architecture. It is also believed (Zhou et al. (2016) 2018); (eelvrrauu et al. (2017)) that CAM only applies to the specific architecture configuration of GAP and one FC layer (Argument 1). On the contrary, we argue that CAM is only special case of activation decomposition on the specific architecture, and the idea applies to much more architectures, even beyond the classification problem. It is also believed that Grad-CAM is generalization of CAM for arbitrary CNN architecture (Argument 2), but the original paper only provides the proof on CAM's architecture. We show that Grad-CAM is not equivalent to activation decomposition for some architectures (Section 4.3) Another direction of explanation is to check the black box model by modifying the input and observing the response in the prediction. A representative method Fong & Vedaldi (2017) aims to optimize the blurred region and see which region has the strongest response on the output signal when it is blurred. Perturbation optimization is applicable for any black box model, but the optimization can be computational expensive.
2

---

Under review as a conference paper at ICLR 2020
2.2 INTERPRETATION FOR METRIC LEARNING
Guided BP (Springenberg et al. (2014) can be easily adopted to metric learning, but recent works (Adebayo al. 2018); Fong & Vedaldi (2017)) claim that gradient can be irrelevant the model and guided-BP fails on the sanity check (Adebayo et al. (2018)). Among methods that pass the san- ity check, Grad-CAM has been used for visualization image retrieval (Gordo Larlus (2177). ). but no quantitative result is provided. Instead of adding more gradient heuristics like Grad CAM++ Chattopadhay al. 2018), ) we propose to explain the result of Grad-CAM under the decomposi- tion framework. As shown in Section by removing the heuristic step in Grad-CAM, the meaning of the generated activation map can be explained as the first two terms of the proposed framework. The perturbation optimization needs reformulation for metric learning and can be more computa- tional expensive if the point-to-point activation map is desired.
ACTIVATION DECOMPOSITION ON A SIMPLE ARCHITECTURE
Partial map for (i))
ALj
Consoiee
Query
GAP(AR)
CNN
A
S:Cosino Similarity
GAP(AT)
CNN
A"
Convolve
Retrieved
Partial map for (xy)
Figure 2: Activation decomposition on a simple architecture for deep metric learning.
To better introduce our method, we first review the formulation of CAM and illustrate our idea on simple architecture (CNN+GAP in Fig. 2 for metric learning. As shown in Eq. [ CAM is actually a spatial decomposition of the prediction score of each class, and the original method only applies for CNN with GAP and one FC layer without bias. The decomposition clearly shows how much each part of the input image contributes to the overall prediction of one class and provides valuable information about how the decision is made inside the classification model. The idea is based on the linearity of GAP:
S. -==x Σ wk.cl 1
A...k) EA. = Z
Σ 1.j
Σ &
Wk wk.cAi.j.k).
(1)
Here S. denotes the overall score (before softmax) of class e and Wi.c is the FC layer parameter for the k-th channel of class c. Ar,,, denotes the feature map of the last convolutional layer at position (i,j), and Z is the normalization term of GAP. In fact, the result Σx Ai....ii.. can be considered as decomposition
S. along (i.j). For two-stream architecture (see Fig. 2 with GAP and the cosine similarity metric (5) for metric learning application (e.g. image retrieval), we propose to do decomposition along (i,j, x) so that the relationship between different parts of two images are uncovered:
5=Σ GAP(A))APPA)) Σ
4 J.
Σ 2.9
A A
Σ K....M
Σ
4 high
A.
(2)
Here the normalization terms of the cosine similarity (1.2 norm) and GAP are included in Z. We for different streams because cross-view applications (Hu et al. (2018)) may have different image sizes for two streams. A denotes the feature map of the last convolutional layer. The superseripts and r respectively denote the query and the retrieved image
use (i,j). (x,
this paper. For each query point (i. in the query image, the corresponding activation map in the retrieved image is given by En A Ay r.y,k which is the contribution of features at (i,j, y) to the overall cosine bilinear interpolation is implemented to generate the con- tribution of each pixel pair and the full resolution map. The overall activation maps of two images
similarity. Like CAM and
3

---

Under review as a conference paper at ICLR 2020
generated by simple summation along (i, or (z, v). Although we only show the positive activation in the map, the negative value is still available for counterfactual explanation (Selvaraju et al. (2017)).
Since recent works (Liu et al. (2017): : Wang et al. (018)) have highlighted the superiority of L2 normalization,
the cosine similarity S the default metrie. With L.2 normalization, the squared Euclidean distance D equals to 2 2S so that S and D are equivalent as metrics. Although there are still number of existing works (Luo et al. (2019); Ristani & Tomasi (2018) training with the Euclidean distance without L2 normalization, Luo et al. (2019) shows that the cosine similarity still performs well the evaluation metric. We further empirically show that the cosine similarity works well for this case (Section 5.4h.
4 EXTENSION FOR COMPLEX ARCHITECTURES
Recent metric learning approaches usually leverage more complex architectures to improve perfor- mance, c.g. adding several FC layers after the flattened feature or global pooling, Although different metric learning applications have different head architectures (e.g. GAP+FC) on CNN, the basic components are highly similar. We introduce unified extension to make method applicable to most existing state-of-the-an art architectures for various applications. including image retrieval (Wang al. (2019)), face recognition (Deng al. (2019)), re-ID (Luo al. (019g) and geo-localization (Hu et al. (2018)). Note that the extension also applies to classification architectures. In Section we address linear components by considering them together as one linear transformation. Then
Section 4.2 focuses on transforming nonlinear components to linear in the validation phase.
4.1 LINEAR COMPONENT
The GAP can be considered as a special case of flattened layer (directly reshape the last convolu- tional layer A E Rmxxxx as one vector Á e map without pooling) multiplied by a transformation matrix TCAP E R'xmmn where I denotes the length of the feature embedding vector (see Appendix A.3 for details). Without loss of generality, we consider a two-stream framework with flattened layer followed by one FC layer with weights W E RRimmp and biases B E RR., Since the vi- sual explanation is generated at the test phase when typical components such FC layer and batch normalization (BN) are linear, all the linear components together are formulated as one linear trans- formation (A) WA+B = E., Ai. + B in the FC layer. Here Wa, E IR and Ai,j RR denote the weights matrix and feature vector corresponding to position (i. j). Although B is ignored in CAM, we keep it as a residual term in the decomposition. Then Eq. 2 is re-formulated as:
sZ = (A (AA"
= Σ WT, A + B9) E WT WE BB) J.y
1.3
Σ (Wi,)1,)) ( (W,y K... Here Z denotes the normalization term for cosine similarity (1.2 norm), and is the inner product. The decomposition of S has four terms, and the last three terms contain the bias B. The first term clearly shows the activation response for location pair (i,j, x. y) and is considered as the point-to- point activation in this paper. The second and third terms correspond to the activation between one image and the bias of the other image. Although they can be considered as negligible bias term, they actually contribute to the overall activation map. For the overall activation map of the query image, the second term can be included, because W9JA2, A B" varies at different (i,j) positions while the third and last terms stay unchanged. Similarly, the first and third terms are considered when caleulating the overall map for the retrieved image. We investigate both settings about the bias term (i.c. or w/o) on the overall activation map and they are referred to as "Decomposition" (W2. 1.j "A, -(E(., 2 A.,yAEE.) and "Decomposition- Bias" (W,4 (Ex,y Wr.yAr. + B") in Section []] The last term is pure bias which is the same for every input image. Therefore, we ignore this term if not mentioned.
EOW B*) + E B²) + B8.
1.
2.3
4.2 NON-LINEAR COMPONENT
4

---

Under review as a conference paper at ICLR 2020
A
GMP
Non-linear transformation increases the difficulty of ac- tivation decomposition, fortunately, the most widely used non-linear components global maximum pooling (GMP) and rectified linear unit (ReLU) can be trans- formed linear operations in the validation phase by multiplying a mask") We only focus on GMP and ReLU in this paper, and all the mentioned components together have covered all the popular architectures for deep metric learning applications. In the validation phase, the GMP can be considered as a combination of maximum mask M and GAP or flattened layer as shown in Fig. 3 The result of Hadamard product (M @ A) is considered as the new feature map which can be directly applied to Eq. 3 Similarly, by adding a mask for ReLU, the FC layer with ReLU can be included in W and B in the vali- dation phase.
Equivalent
GAP Z
3
5
2
X
5
Maximum Mask
Figure 3: Maximum mask for GMP. Z is the constant normalization term for GAP.
4.3 RELATIONSHIP WITH GRAD-CAM
Grad-CAM is another way for generating overall activation map on more complex architecture. When we calculate the activation map based Grad-CAM, what do we get? [Selvaraju et al.) (2017) has shown that Grad-CAM is equivalent to CAM on GAP based architecture. However, for clas- sification architecture with flattened feature and one FC layer, the prediction score for class c may be formulated as S. = Ex,,, W.j.k.cAA...k where W is the reshaped weights of FC layer following the shape of the last convolutional feature (A). From our activation decomposition perspective, the contribution of each position (i. j) clearly given by Σx W.J.k.A.... while the Grad-CAM map
for class c at (i,j) position is given by:
GradCAMiJ.e = ECAAAAAAP (5:))=
( ((AAAAGA(WW)) DA
(4)
In this case, the result Grad-CAM is different from activation decomposition because of the GAP in Eq. 4 For architectures using GMP, they are also different, because only the maximal value of each channel contributes to the overall prediction score, while Grad-CAM puts the same weight for features at all positions (sce Appendix A.4 for details). Although Selvaraju al. (2017) empirically shows that the heuristic GAP step can help improve the performance of localization, this step makes the meaning of the generated map unclear. By removing this step. which means combining the as.,, the modified version would generate the same result as activation decomposition for flattened and GMP based architectures. As for the metric learning architecture discussed in Section 4.1 the Grad-CAM map of query image is written as (the derivation
gradient and feature directly AA.j..AA...."
included Appendix A.
GradCAM:5
2
1
0 L ((E7)
GAP(W9)AA,)
E WT A + B")
(5)
z OE
Es denotes the embedding vector of query image before L2 normalization and Z is the normalization
term. The gradient term Ø /E which comes from the L2 normalization, would put less weights on dominant channels that the generated activation map becomes more scattering (Appendix[A.3 A.5).
#Fv
can be removed by calculating gradient from E E" without L.2 normalization. If we remove the gradient term well as the GAP term, the result is actually equivalent to the overall map of "Decomposition--iaa" given by the first two terms of Eq. 3 as (W3AA1,) (E Wr
z,y A Br).
EXPERIMENT
5.1
WEAKLY SUPERVISED LOCALIZATION
Weakly supervised localization has been adopted as evaluation metric in most existing works, we thus conduct localization experiment in the context of metrie learning to evaluate the overall ac-
The mask is computed once for each input image.
5

---

Under review as a conference paper at ICLR 2020
tivation map. We follow the state-of-the-art image retrieval method Wang et al. 20199 CUB Wellindrr et al. (0100), which contains over 10,000 images from 200 bird spices. CUB a chal- lenging dataset for metric learning and the bounding box is available for localization evaluation. We first train a model on CUB with the loss function and architecture of Wang et al. (2019), and then conduct the weakly supervised localization proposed methods. As CAM and Grad-CAM generate the mask with different threshold settings (0.2 and 0.15), we use multiple thresholds and find the result is sensitive to threshold (see Appendix A.1. We report the best result of each method in Table The "Grad -AM (no norm)" means the Grad-CAM with gradient computed from the product of two embedding vectors without normaliza- tion and the "Decomposition Bias" denotes the first two terms of Eq. 3 'hee proposed framework outperforms Grad-CAM for metric learning as well as CAM based on classification. As justified in Section 4. computing the gradients before normalization does improve the performance of Grad- CAM by a large margin. Since the architecture of Wang et al. (2019) is based on GMP, "Grad-CAM (no norm)" is not equivalent to "Decomposition Bias" as shown in Section
show the differences between the variants of
4.3
Table I: Localization accuracy for 0.5 IOU CUB val- idation set.
Method
Accuracy
Classification
CAM (Zhou et al. 2016)
41.0%
Grad-CAM
16.7%
Grad-CAM (no norm)
48.3%
Metric Learning
Decomposition+-iin (ours)
44.9%
Iepur
GradCAM
Decompositon Decompostion
Decomposition (ours)
50.6%
Figure 4: Qualitative results on CUB,
5.2 MODEL DIAGNOSIS
A large number of loss functions have been proposed for metric learning (Schroff et al. (2015); Oh Song et al. (2016); Wang al. (2019)), while only the performance and embedding distribution are evaluated. Here we show that the overall activation map can also help evaluate the generalization ability of different metrie learning methods. We follow the setting of Wang al. (019) and train
Table 2: Top-1 I recall accuracy on Table 3: Localization accuracy (0.5 IOU) CUB training CUB.
Decomposition+Bias
Decomposition
Loss
Train
Validation
MS
52.
58.999
MS Triplet
82.69% 82.98%
65.45%
Triplet
39.93%
55.60%
60.55%
Accuracy Drop
12. 17%
3.39%
Multiple Similarity Loss
Triplet Loss
Multiple Similarity Loss
Triplet Loss
Input
Decomposition
Decomposition Bias
Figure 5: Qualitative results for model diagnosis.
two metric learning models with multiple similarity (MS) loss Wang et al.) (2019) and triplet loss Schroff et al. (2015), respectively. As shown in Table although they have almost the same accuracy on training set, there is a big gap between their generalization ability the validation set. Before checking the result on the validation set, is there any clue the training set for such gap? Despite the similar training accuracies, the predictions of two models are actually based on different regions (see Fig. 5). The quantitative results in Table 3 also support the fact that "Triplet" model is more likely to focus the background region rather than the object as witness the localization accuracy drop

---

Under review as a conference paper at ICLR 2020
for Triplet loss. Although "Decompositiont-iats can be more sensitive to different loss functions, implying that the bias term does provide valuable information on overall map, both settings of the proposed method have the same trend on accuracy. Therefore, activation decomposition framework can help shed light on the generalization ability loss functions for metric learning.
5.3 APPLICATION I: CROSS-VIEW PATTERN DISCOVERY
180'
Partial
Aligned Image Pair
180
90.2'
122.1
302.1
90
270'
Ground Truth
90.2'
Overall Estimated:
Partial Estimated:
Rotation Angle
147.9*
31.9"
Figure 6: Example of cross-view pattern discovery, e.g. image orientation estimation. (Best viewed in color)
When the metric learning is applied to cross-view applications, c.g. image retrieval (Zhai et al. (2017): Hu et al.] (2018); Tian et al. (2017). the model is capable learning similar patterns in different views which may provide geometric information of the two views, e.g. the camera pose or orientation information. We conduct orientation estimation experiment to show the advantage of partial activation map compared with the overall activation map on providing geometric information based on cross-view patterns. In our experiment, we take street-to-aerial image geo-localization as an example and train Siamese network following the loss function of Hu al. (2018). The ob- jective of geo-localization is to find the best matched aerial-view image in a reference dataset for query street-view image. We conduct the experiment on CVUSA (Zhai et al. (2017), ) which is the most popular benchmark for this problem containing 35,532 training pairs and 8,884 test pairs. Each pair consists of query street image and the corresponding at the same GPS location. The orientation example is illustrated as angle degree in Fig. 6 (the yellow lines on both images correspond to 09). We train the Siamese image matching model with randomly rotated aerial images so that the activation map is approximately rotation invariant for acrial image. As shown in Fig. [6] the overall activation map may contain multiple highlighted re- gions contributing to the overall matching/simillrity score. Our method can further provide detailed point-to-point relationship which is critical for orientation estimation. Here we utilize the maximum activated region for orientation estimation show the superiority of the partial map compared with the overall map. We first generate the overall activation map as well as the partial map correspond- ing to the maximum activation position of the query street-view image. For both activation maps. the activation peaks from different views are selected for orientation estimation as shown in Fig. In this example, the overall activation maps contain multiple highlighted regions and the relationship between them are un- clear. The activation peaks in the two views (the cyan boxes) actually correspond to different objects which leads to fail- ure estimation. However, the partial activation map clearly shows the relationship between these regions and provides more accurate estimation (the red line). We also present the quantitative results in Fig. 7 As be seen from this fig- ure, the partial activation map significantly outperforms the overall map for cross-view orientation estimation. Partial ac- tivation based orientation estimation has over 16% samples with angle error less than +3.5 (the red bar at 0%), while overall map based method only has less than 12%.
identation-aligaee
aerial image
Overall
Parttal
0.00
0.00
0.00
0.04
0.00
130
-120
-40
60
120
180
Angle error
Figure Estimation error distri- bution of overall and partial map. (Better viewed with zoom in)
5.4 APPLICATION II: INTERACTIVE RETRIEVAL
Verification applications like face recognition and re-ID usually retrieve images with a complete query image. However, the complete query image may be not available in some scenarios. For example, only part of person is captured in surveillance image/video due to occlusion or view- point. Interactive retrieval, which retrieves images with interactively selected region of the query
7

---

Under review as a conference paper at ICLR 2020
Beard
Nose
Clothes
Shoes
Figure 8: Top retrieved images by interactive retrieval on face and re-ID datasets. The red box on the left column indicates the query part.
image, can provide critical information for such circumstance. Since our framework provides point- to-point activation map, it can be served as a reasonable tool for measuring partial similarity. With the partial similarity, we are able to interactively retrieve images having similar parts with the query image instead of the overall most similar image, which may contain irrelevant noisy informa- tion. As shown in Fig, 88 the partial activation generated by the proposed method works well on retrieving people with similar clothes and faces with similar beard. We follow the pipeline of re- cent approaches
face recognition (Deng et al. (2019)) and person re-identification (Luo et al. (2019). For re-ID, the model is trained and evaluated on Market- 1501 (Zheng et al. (2015)) where some validation images only contain small part of a person. Although the model is trained with Eu- clidean distance without 1.2 normalization, cosine similarity still works well as the evaluation metric. For face recognition,
take the trained model
CASIA-
Overall
Partial
WebFace eY et al. (2014)) and evaluate the model on FIW (Robin- son al. (2018) where the face identification and kinship rela- tionship are available. The interactive search is adopted by simply matching the equivalent partial feature in Eq. ( (F,A with the reference embedding features. Fig. g shows that different im- ages are retrieved when searching with different partial features on the same query image. However, we do find some failure cases shown in the last row of Fig. wwith the red box. There is no shoes the failure image, but why is this image retrieved with top rank? In the activation map of Fig. three regions of the query image have high activation on the retrieved image. And there is a high activa- tion on the purse in the retrieved image corresponding to the shoes in the query image. This might be because of their similar red color and the arm of the retrieved person may appears like leg from a specific viewpoint. This example also validates the importance of partial activation map generated by our framework for explanation.
Figure 9: Explanation for the failure case by decomposi- tion.
6 CONCLUSION
We propose simple yet effective framework for visual explanation of deep metric learning based on the idea of activation decomposition. The framework applicable to a host applications, e.g. image retrieval, face recognition, person re-ID, geo-localization, etc. Experiments show the importance of visual explanation for metric learning as well as the superiority of both the overall and partial activation map generated by the proposed method. Furthermore, introduce two po- tential applications, i.e. cross-view pattern discovery and interactive retrieval, which highlight the importance of partial activation map.
8

---

Under review as a conference paper at ICLR 2020
REFERENCES
Julius Adebayo, Justin Gilmer, Michael Muelly, lan Goodfellow, Moritz Hardt, and Been Kim. Sanity checks for saliency maps. In Advances in Neural Information Processing Systems, pp. 9505-9515, 2018.
Luca Bertinetto, Jack Valmadre. Joao F Henriques, Andrea Vedaldi, and Philip HS Tomr Fully- convolutional siamese networks for object tracking. European conference on computer vision, pp. 850-865. Springer, 2016.
Aditya Chattopadhay, Anirban Sarkar, Prantik Howlader, and Vineeth N Balasubramanian. Grad- cam++: Generalized gradient- based visual explanations for deep convolutional networks. In 2018 IEEE Winter Conference on Applications of Computer Vision (WACV), pp. 839-847. IEEE, 2018.
Sumit Chopra, Raia Hadsell, Yann LeCun, et al. Learning similarity metric discriminatively, with application to face verification. In CVPR (1), pp. 539-546, 2005.
Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos Zafeiriou. Areface: Additive angular mar- gin loss for deep face recognition. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2019.
Ruth C Fong and Andrea Vedaldi. Interpretable explanations of black boxes by meaningful perturba- tion, In Proceedings of the IEEE International Conference on Computer Vision, pp. 3429-3437, 2017.
Albert Gordo and Diane Larlus. Beyond instance-level image retrieval: Leveraging captions to learn a global visual representation for semantic retrieval. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 6589-6598, 2017.
Sixing Hu, Mengdan Feng, Rang MH Nguyen, and Gim Hee Lee. Cvm-net: Cross-view matching network for image-based ground-to-aerial geo-localization. In Proceedings of the IEEE Confer- on Computer Vision and Pattern Recognition, pp. 7258-7267, 2018.
Weiyang Liu, Yandong Wen, Zhiding Yu, Ming Li, Bhiksha Raj, and Le Song. Sphereface: Deep hypersphere embedding for face recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 212-2222222222122222222222112221 220, 2017.
Hao Luo, Youzhi Gu, Xingyu Liao, Shenqi Lai, and Wei Jiang. Bag of tricks and strong baseline for deep person re- identification. In Proceedings the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pp. 0-0, 2019.
Aravindh Mahendran and Andrea Vedaldi. Understanding deep image representations by inverting them. In Proceedings of the IEEE conference computer vision and pattern recognition, pp. 5188-5196, 2015.
Hyun Oh Song. Yu Xiang, Stefanie Jegelka, and Silvio Savarese. Deep metric learning via lifted structured feature embedding. In The IEEE Conference Computer Vision and Pattern Recog- nition (CVPR), June 2016.
Ergys Ristani and Carlo Tomasi. Features for multi-target multi-camera tracking and re- identification. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2018
J P Robinson, M Shao, Y Wu, H Liu, T Gillis, and Y Fu. Visual kinship recognition of families in the wild. In IEEE Transactions on pattern analysis and machine intelligence, 2018
Florian Schroff, Dmitry Kalenichenko, and James Philbin. Facenet: A unified embedding for face recognition and clustering. In The IEEE Conference Computer Vision and Pattern Recognition (CVPR), June 2015.
Ramprasaath R Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi Parikh, and Dhruv Batra. Grad-cam: Visual explanations from deep networks via gradient-based local- ization. In Proceedings of the IEEE International Conference on Computer Vision, pp. 618-626, 2017.

---

Under review as a conference paper at ICLR 2020
Jost Tobias Springenberg. Alexey Dosovitskiy. Thomas Brox, and Martin Riedmiller. Striving for simplicity: The all convolutional net. arXiv preprint arXiv:1412.6806, 2014.
Yicong Tian, Chen Chen, and Mubarak Shah. Cross-view image matching for geo-localization in urban environments. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3608-3616, 2017.
Hao Wang, Yitong Wang, Zheng Zhou, Xing Ji, Dihong Gong, Jingchao Zhou, Zhifeng Li, and Wei Liu. Cosface: Large margin cosine loss for deep face recognition. In Proceedings of the IEEE Conference Computer Vision and Puttern Recognition, pp. 5265-5274, 2018.
Xun Wang, Xintong Han, Weilin Huang, Dengke Dong, and Matthew R Scott. Multi-similarity loss with general pair weighting for deep metric learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5022-5030, 2019.
Welinder, Branson. Mita, C. Wah, Schroff, Belongie, and P. Perona. Caltech-UCSD California Institute of Technology, 2010.
Birds 200. Technical Report
Wenjie Yang, Houjing Huang, Zhang Zhang, Xiaotang Chen, Kaiqi Huang, and Shu Zhang. Towards rich feature discovery with class activation maps augmentation for person re-identification. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1389- 1398, 2019.
Dong Yi, Zhen Lei, Shengcai Liao, and Stan Li. Learning face representation from scratch. arXiv preprint arXiv:1411.770 11144411.9999 2014.
Menghua Zhai, Zachary Bessinger, Scott Workman, and Nathan Jacobs. Predicting ground-level scene layout from aerial imagery. In Proceedings of the IEEE Conference on Computer Vision and Puttern Recognition, pp. 867-875, 2017.
Jianming Zhang, Sarah Adel Bargal, Zhe Lin, Jonathan Brandt, Xiaohui Shen, and Stan Sclaroff. Tow-down neural attention by excitation backprop. International Journal of Computer Vision, 126 (00):1084-1100 2018.
Liang Zheng, Liyue Shen, Lu Tian, Shengjin Wang, Jingdong Wang, and Qi Tian. Scalable person re-identification: A benchmark. In Proceedings of the IEEE international conference on computer vision, pp. 1 111--1144 2015.
Bolei Zhou, Aditya Khosla, Agata Lapedriza, Aude Oliva, and Antonio Torralba. Learning deep features for discriminative localization. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2016.
Bolei Zhou, David Bau, Aude Oliva, and Antonio Torralba. Interpreting deep visual representations via network dissection. IEEE transactions on pattern analysis and machine intelligence, 2018.
10

---

Under review as a conference paper at ICLR 2020
A APPENDIX
A.1 WEAKLY SUPERVISED LOCALIZATION DETAILS
As discussed in Appendix A.4 the activation map of Grad-CAM GMP architecture is scat- tering, as larger threshold is needed for Grad-CAM to generate comparable result in our experiment.
Table Localization accuracy (IOU 0.5) with different thresholds on CUB validation set.
Threshold
Grad-CAM
Grad-CAM(no norm)
Decomposition--Baas
Decomposition
0.15
16.71%
16.83%
23.49%
17.38%
0.2
16.26%
17.06%
32.01% %
19.77%
0.3
14.48%
21.59%
44.94%
34.92%
9,43%
35.01 %
37.85%
50.64%
0.5
4.43%
47.00%
21.99%
45.78%
0.6
1.54%
48.27%
9.35%
27.98%
0.7
0.27%
20.90%
2.25%
9.11%
A.2
MODEL DIAGNOSIS DETAILS
Table 5: Localization accuracy (IOU 0.5) CUB training set with MS (multiple similarity) loss.
Threshold
Decomposition+Biaa
Decomposition
0.2
41.05%
36.16%
0.3
52.10%
44.41% 1
0,4
42.77%
58.99%
0.5
24.97%
51.17%
0.6
9.35%
27.98%
Table 6: Localization accuracy (IOU 0.5) on CUB training set with Triplet loss.
Threshold
Decomposition+-Baa
Decomposition
0.2
36.60%
24.00%
0.3
39.93%
38.57%
0.4
29.03%
55.60%
0.5
14.22%
53.49%
0.6
4.93%
32.49%
A.3 TRANSFORMATION MATRIX FOR GAP AND GMP
For the feature A E ęuxXXP, the GAP (global average pooling) is equivalent to the flattened feature E IR mnp followed by transformation matrix TGAP E Rpxm
GAP(A)
Σ Arj = TaaPÂ
(6)
mi
Here (i. denotes the spatial coordinates. By reshaping the TGAP xxxxxXXx GAP the matrix is given by:
c=k mn
Teap(c, k,j,k
(7)
c k
The matrix TeAP is simply calculated by reshaping T to mnp. As shown in Section 4.2 GMP equivalent to GAP with a maximum mask validation phase. The transformation matrix of GMP (global maximum pooling) is given by:
Tomp mn m M)
(8)
11

---

Under review as a conference paper at ICLR 2020
Here M& E R is the maximum matrix of A where only the maximum position of each channel has nonzero value as 1. ToMP is computed by reshaping TCMP to p x mnp.
A.4 GRAD-CAM ON GMP
Considering classification architecture with GMP and FC (W E Rxxl and bias), the prediction score for class is given by S. = Σn ma...)(A...)) W = E.j.A M.s.M. where M is the maximum matrix in Appendix A.3 The decomposition of position (i.j) is En A Wk.o and only the maximum position each channel has a nonzero value. However, for Grad-CAM, the activation map is given by:
as aA
GradCAMs = As. GAP(
Σ
A.s.WW..e.
(9)
mi k
where all (i.j) positions have nonzero weight resulting in a more scattering activation map.
A.5 GRAD-CAM FOR METRIC LEARNING
For metric learning architecture like Section 4.1, the similarity is formulated as S EY Til and E" R' are the embedding vector of query and retrieved image. |aa| denotes the I.2 norm and a is the inner product of a and b. The Grad-CAM map of query image is given by:
[ where
E..
GradCAMi, A GAP aS 0A
OS
(GAP( ))² A9.
(10)
0A
With the gradient chain rule, the gradient is written as:
2 FF
as
ET
O(E O
E
HEE E
W4
(11)
0A9
OA
0F
OA
OF
By expanding E" Ex.y W
+ B" (Section 4.1) and merging Eq. Grad-CAM map is reformulated
A
10 with Eq.
11 the
E 8(14/ W
GradC = (GAP((
A
FFa
a /1E")
-
E
3 )
W
Z
DE
O E (EE/\EE))
(ET)T
W )-)
0E4
(12)
0 |E9)
WT
A + B")
GAP(W99AA))
Z
8F4
2.31
O
E (E9)
GAP(WDAA)))
WT A2 + B²)
z
OE
Here the the normalization term for simplicity.
GE/EE 3E
the Jacobian matrix given by:
E i=
((E/(E)) (O(E./18))
E
E
(13)
aE
0E, ij
E,E,
i i
LET
is the normalization term. For dominant channel i, the weight more scattering activation map.
(1-
is small resulting in
[ET
12

---

Under review as a conference paper at ICLR 2020
A.6 QUALITATIVE RESULTS
We provide more qualitative results of using our activation decomposition framework for the two new applications, i.e., cross-view pattern discovery and interactive retrieval.
A.6.1
CROSS-VIEW PATTERN DISCOVERY
90"
180"
270
360
12.00
Point-specific Map
Ground Truth Angle= 72"
180
135.0
Overall Estimated: 7.0*
Partial Estimated: 91.2"
90
270
0"
90"
180"
270
360
29.5
Point-speciin Map
Ground Truth Angle= 173
180
Partial
Overall Estimated: 57.7
90"
270
229.2
Estimated: 199.7"
0"
Figure 10: Examples of cross-view pattern discovery, i.c., image orientation estimation. (Best viewed in color)
A.6.2 INTERACTIVE RETRIEVAL ON FACE
Mouth
Eyes
Cheek
Figure 11: Top retrieved images by interactive retrieval on face recognition.
13

---

Under review as a conference paper at ICLR 2020
A.6.3 INTERACTIVE RETRIEVAL ON PERSON RE-ID
Hair
Skirt
Purse
Figure 12: Top retrieved images by interactive retrieval person re-identification.
A.7 CROSS-VIEW PATTERN DISCOVERY DETAILS
A.7.1 EXPLANATION OF FIGURE 6
90
180'
270'
360
Partial
Aligned Image
90.2"
122.1
30
302.1
302.1
90.2"
Ground Truth Rotation Angle
Overall Estimated: 147.9*
Partial Estimated:
31.9
Figure 13: Example of cross-view pattern discovery, e.g. image orientation estimation. (Best viewed in color)
details. We first reiterate the application and experiment setting. The dataset (CVUSA) we used in the experiment is for image-based cross- view geo-localization (Zhai et al. (207)): Hu et al. (2018) and contains image pairs from street and aerial views. Each matched image pair corresponds to the same GPS location. The objective of geo-localization is find the best matching GPS-tagged acrial-view image for a query street-view image. In the CVUSA dataset (Zhai et al, (2017)). the image pairs are aligned in terms of orientation. For example, as shown in Fig. [3 the left two images (street- view panorama and aerial-view images) are the original image pair and the yellow line denotes the 0" which corresponds to the south direction (180" corresponds to the North direction). We use [0, 360 to denote different angles marked these two images.
Here explain Fig. 6 again (Fig. 13 with
reference dataset
For the cross-view image matching/retrieval task, if the image pairs are not aligned (e.g., randomly rotate the aerial view images), discovered that the activation map can be used for orientation estimation. Specifically, we train the Siamese image matching model with randomly rotated aerial images so that the model is cotation-invarial and so is the overall activation map for aerial image. In the example Fig. [3] the overall activation maps for the original aligned pair are first generated show the highlighted regions, and both views focus the road area in this example. The most
14

---

Under review as a conference paper at ICLR 2020
activated regions are highly relevant in both views and most of them similar patterns. When randomly rotate the aerial image (30" in this example), the aerial view activation map still focuses on the road area which is relevant to the street view. In this paper, simply use the pixel with the maximum activation value for orientation estimation, because the most activated areas (highlighted in cyan boxes in Fig. (3) are likely to he relevant from two views. For the street view image, the selected pixel lies in the angle of 90.2 (the cyan line) based on the angle marks on the left aligned image. For the rotated aerial view, the selected pixel lies in the angle of 302.1 (the cyan line). Since the overall map contains multiple activated regions, the selected pixels in both views actually do not correspond to the same object, which reveals one disadvantage by only using the overall activation map. The estimated angle is 302.1 - 90.2" = 147.9 which is not correct. However, for the selected pixel (the one with the maximum activation value) in the street view image, if we generate its corresponding point-specific (partial) activation map on the aerial view image (as shown on the very right of Fig. [3), the new selected pixel on this point-specific activation map lies in the angle of 122.1 (the red line). Then, the estimated angle is calculated 122.1 90.2 31.9", which is very close to the ground truth (30%). This demonstrates the advantage of the point-specific activation decomposition for finding more fine- ine-grained information in this application.
A.7.2 How TO COMPUTE THE ANGLE ERROR
The angle error is computed by error ground truth - seteh---smmmaleedd ongle. We then add or subtract 360 to this term to make it in the range of [-180, 180] if the absolute value of the error is greater than 180% For example, when the error is 359", we will subtract it by 360 and get -10 degree as the error. This is a reasonable setting adopted from the previous work (Zhai et al. (2017))
A.7.3 SENSITIVITY OF POINT-SPECIFIC ACTIVATION MAP
We present a demo to show how the point-specific map changes according to the query pixel: https://gi thub. wow/Jefff Zi welleece//ie aanice//nnoymouus In this example, the resolution of the query image is 224 x 1232. As shown in the demo, the point-specific activation map changes dramat- ically when the query pixel moves from the left to the right in the query image because the object changes. As in this example, when the query pixel moves by 10 pixels, the object would change and the corresponding point-specific activation map on the retrieved aerial image will be quite dif- ferent. By generating the point-specific activation map, we can obtain fine-grained information or interpretation for deep metric learning.
A.8 INTERACTIVE RETRIEVAL DETAILS
A.8.1 How TO COMPUTE THE SIMILARITY GIVEN A POINT OF INTEREST
Following Eq. we first compute W VY A4 as the feature of each position the last convolutional layer, and a bilinear interpolation is adopted to generate the feature for every pixel of the original image. For a point of interest (i, compute the cosine similarity between the calculated feature on (i and the embedding feature of the reference images as the point-specific similarity, so the embedding features of the reference dataset do not need to be recomputed. This similarity can be also considered as the summation of the values in the point-specific map corresponding to j.. In A.
the case of Eq. 2 (CNN+GAP), the similarity can be simplified as Ex,y EE A A Ar.y,)))
15


Reviews:
[{"review_id": "Syx91gcotr", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This work proposes a novel approach for visualizing the predictions of neural network models on pairwise tasks, e.g. predicting whether two images are similar. The authors show that to see similarity between two images down on the pixel/region level, it is not sufficient to apply methods like Grad-CAM which do not aim for decomposition. Instead, the authors' approach namely targets decomposition, and shows the benefit of decomposition through intuitive examples and qualitative results. The authors also quantitatively show the benefit of their method. First, they measure the performance of their method vs CAM and Grad-CAM, on the weakly supervised localization (WSL) task. They also show how their method reveals the disadvantages of standard triplet loss compared to a recent metric learning loss. \n\nMy concerns:\n1) While showing performance on WSL is appealing as it allows for a way to quantitatively evaluate the method, I wonder if there are other ways to evaluate, that explicitly measure the quality of the proposed technique for allowing interpretability and understanding of the base model's performance. \n2) The Triplet vs MS experiment is interesting, but I'm not sure this is the most convincing way to show that this proposed visualization technique is better than something else. Just because something shows one method is worse than another, doesn't mean that this better/worse assessment is accurate. Further, how would Grad-CAM do on the same task?\n3) The retrieval experiment only shows qualitative results, and again, no baseline is compared. \n4) Similarity is a relative judgement; it's hard to say if two items are similar, but easier to say if A and B are more similar than A and C. It seems the proposed method doesn't consider negatives, which is perhaps a limitation.", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly."}, "extra_text": {}}, {"review_id": "SylvE-sx5r", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "= Summary \nThis paper presents a simple method that draws visual attention of deep embedding networks for metric learning. It basically follows the class attention mapping strategy based on global pooling operation [Zhou et al., CVPR 2016], but extends the original version to point-specific attention which is novel and enable interesting applications on image retrieval. In addition, the proposed method seems also independent of the loss function used for metric learning, thus it can be applied to most of existing deep embedding networks to understand their behaviors in a qualitative manner. \n\n\n= Decision\nMy current decision is officially \"weak reject\" but \"borderline\" in my mind. The major concern of mine is its weaknesses in clarity and technical novelty. However, I still believe this submission is valuable since it addresses a relatively new and timely topic, the proposed method is simple yet effective, and the applications of point-specific attention (i.e., \"cross-view pattern discovery\" and \"interactive retrieval\") are all interesting and practically useful. If the clarity issues are all clearly addressed, I would upgrade my rating. \n\n\n= Comments\n[Pros]\n1) The motivation and implementation of the point-specific attention are convincing. \n2) The point-specific attention enables not only image-to-image retrieval, but also more elaborate understanding about a pair of images and their similarity.\n3) The proposed technique is model-agnostic and loss-agnostic, thus can be applied to most of existing deep embedding networks for image retrieval. Also, the proposed technique does not degrade the retrieval performance.\n4) The proposed technique is simple yet effective in multiple applications, most of which are practically useful and have great impact. For example, the weakly supervised localization is an essential step towards many weakly supervised approaches for higher-level recognition tasks like semantic segmentation, and the interactive retrieval will allow us to build more realistic and useful image retrieval systems.\n\n[Cons]\n1) The proposed technique itself is not new but a straightforward extension of an existing work [Zhou et al., CVPR 2016].\n2) The manuscript is not crystal clear.\n- The name of the proposed point-specific attention (i.e., \"Partial attention\") is misleading.\n- The way to compute the point-specific attention map is not clearly described in Section 3.\n- It is hard to understand the contents in Figure 6 as they are not clearly illustrated. \n- The experimental and implementation details of the last two applications are not given. For example: (cross-view pattern discovery) how to compute the angle error, and how much the proposed technique is sensitive to the position selected on the query image, (interactive retrieval) how to compute the similarity between images given a specific region of interest on query.\n3) More qualitative results on the last two applications should be presented, even in an appendix, to convince future readers. Especially, in the case of \"interactive retrieval\", more results are demanded as quantitative performance analysis seems not straightforward.\n\n\n= Post-rebuttal review\nThe rebuttal resolves my major concerns and the manuscript has been carefully revised accordingly. So as I promised in my original review, I upgrade the score to weak accept. ", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I made a quick assessment of this paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "B1gxS8ARFS", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper proposes a visualization method for deep metric learning, which derived by analyzing the inner product of two globally averaged activations. The proposed method can generate an overall activation map which highlights the regions contributing most to the similarity. Also, it can generate a partial activation map that lights the regions in one image that have significant activation responses on a specific potion in the other image. The authors also analyzed the linearly of the fully connected layers and global max pooling. These contributions make the applicability of CAM to many CNN architectures. Further, the metric learning architecture is extended to Grad-CAM map, and the problem of Grad-CAM map is pointed out. To the best of my knowledge, these contributions are novel, and derivations seem to be correct. \n\nExperiments on weakly-supervised localization, model diagnosis, and the applications of the proposed decomposition model in cross-view pattern discovery and interactive retrieval are promising. \n\nOverall, this paper is well written, and contributions are good. \n\nMinor problems.  \nIn Sec.1 and Sec.2.2, the authors wrote the Grad-CAM has been used for visualization of re-ID (Gordo & Larlus (2017)). However, this paper seems to be not the works of Grad-CAM nor re-ID. \n\nIn my understanding, Decomposition+Bias is a more accurate model than Decomposition. \nIn the experiments of the Sec5.1 and 5.2, the performances of Decompsotion+Bias are lower than Decomposition. However, there are no explanations for this reason. \n", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This submission proposes a method for providing visual explanations for why two images match by highlighting image regions that most contribute to similarity.

Reviewers agreed that the problem is interesting but were divided on the degree of novelty of the proposed approach.

AC shares R1’s concern that localization accuracy is not satisfactory as a quantitative measure of the quality of the explanations. In particular, it pre-supposes what the explanations ought to be, i.e. that a good explanation means good localization. A small user-study would be more convincing. A more convincing evaluation would also include a study of explanation of image pairs with different degrees of similarity (e.g. images that are dissimilar as well as images with the same object).

AC also shares R2’s concern about the validity of the model diagnosis application. This discussion also relies on the assumption that better localization of the whole object means a better explanation. Further, the highlighted regions in Figure 5 are very similar. Once again, a user study would help to indicate whether these results really do improve explainability.

Reviewers also had concerns about missing details and, while the authors did improve this, key details are still missing. For example, the localization method that was used was only referenced but should be described in the paper itself.

Given that several concerns remain, AC recommends rejection.

Decision: Reject