SPA: 3D Spatial-Awareness Enables Effective Embodied Representation

## Abstract

Abstract In this paper, we introduce SPA, a novel representation learning framework that emphasizes the importance of 3D spatial awareness in embodied AI. Our approach leverages differentiable neural rendering on multi-view images to endow a vanilla Vision Transformer (ViT) with intrinsic spatial understanding. We present the most comprehensive evaluation of embodied representation learning to date, covering 268 tasks across 8 simulators with diverse policies in both single-task and language-conditioned multi-task scenarios. The results are compelling: SPA consistently outperforms more than 10 state-of-the-art representation methods, including those specifically designed for embodied AI, vision-centric tasks, and multi-modal applications, while using less training data. Furthermore, we conduct a series of real-world experiments to confirm its effectiveness in practical scenarios. These results highlight the critical role of 3D spatial awareness for embodied representation learning. Our strongest model takes more than 6000 GPU hours to train and we are committed to open-sourcing all code and model weights to foster future research in embodied representation learning. Project Page: https://haoyizhu.github.io/spa/ .

## 1 Introduction

Vision systems have made remarkable progress in understanding 2D images (He et al., ; Chen et al., ; He et al., ; Feichtenhofer et al., ; Tong et al., ; Yang et al., ; Oquab et al., ; Radford et al., ; Fang et al., ; Chen et al., ). However, achieving true visual intelligence necessitates a comprehensive understanding of the 3D world. This is crucial for embodied AI, where agents must perceive, reason, and interact with complex 3D environments.

Existing visual representation learning methods for embodied AI (Nair et al., ; Radosavovic et al., ; Majumdar et al., ; Karamcheti et al., ; Shang et al., ; Yang et al., ) largely rely on paradigms from 2D vision, predominantly employing contrastive-based or masked autoencoder (MAE)-based approaches.
However, they often struggle to fully capture the spatial relationships and 3D structures inherent in the physical world. This limitation arises from their primary emphasis on 2D semantic understanding, which, though valuable, is still insufficient for the sophisticated spatial reasoning required in embodied AI tasks, where agents need to navigate environments, manipulate objects, and make decisions using their 3D spatial awareness.

In this paper, we introduce SPA, a general 3D spatial-aware representation learning framework for embodied AI. SPA leverages neural rendering (Mildenhall et al., ) as the pre-training pre-text task on multi-view images.
Unlike explicit 3D representations like point clouds or meshes—which prior work (Wang et al., ; ; Ze et al., ; Zhu et al., ) has shown to outperform pure 2D inputs in robot learning—multi-view images are easier to process and more readily available, making them ideal for large-scale training, such as from internet videos.
Specifically, given a vanilla 2D image backbone, *e.g*. a Vision Transformer (ViT) (Dosovitskiy et al., ),
we first extract multi-view feature maps from the input images.
Using known camera poses, we then construct a feature volume from these feature maps and sample rays to apply differentiable neural rendering.
This process generates multi-view RGB-D images and semantic maps for supervision without labels, enabling the pre-training of a 2D image backbone to enhance 3D spatial awareness.

To thoroughly validate our assumption and method, we collect 268 embodied tasks across 8 simulators using various policy methods. To our knowledge, this represents the largest scale of embodied evaluation to date. Previous work, such as R3M (Nair et al., ) and VC-1 (Majumdar et al., ), evaluated fewer than 20 tasks, potentially leading to incomplete or biased conclusions. Our evaluation spans both single-task and language-conditioned multi-task learning. We compare over 10 state-of-the-art representation learning methods, categorized as embodied-specific (Nair et al., ; Majumdar et al., ; Radosavovic et al., ), vision-centric (Oquab et al., ; Chen et al., ; He et al., ), and multi-modal (Radford et al., ; Fang et al., ; Chen et al., ). Our method consistently outperforms others, underscoring the importance of 3D spatial awareness for embodied AI. Notably, multi-modal models like CLIP (Radford et al., ), consistently perform poorly. This holds even the vision-language model scales the ViT to 6B parameters (Chen et al., ).
Through a camera pose estimation task and feature map visualization, we demonstrate that SPA has learned superior 3D spatial understanding. Further, we find that 3D awareness shows a positive correlation with embodied performance.
Finally, we conduct several real-world tasks, where SPA also demonstrates superior performance.
Our contribution can be summarized as follows.

- •
We propose a significant spatial hypothesis: 3D spatial awareness is crucial for embodied representation learning. Our experiments provide clear evidence for the hypothesis.
- •
We introduce SPA, a novel paradigm for representation learning in embodied AI. It enhances a vanilla Vision Transformer (ViT) with 3D awareness using differentiable neural rendering as the pre-text task on multi-view images.
- •
We conduct the largest evaluation benchmark for embodied representation learning, significantly larger than previous studies. It involves 268 tasks, 8 simulators, and over 10 SOTA methods with diverse downstream policies and task settings.
- •
Through extensive experiments in both simulators and real-world settings, SPA outperforms more than 10 SOTA representation learning methods, demonstrating its effectiveness.

## 2 Methodology

In this section, we first describe our process for handling multi-view image inputs and feature extraction in Sec. 2.1. Subsequently, we construct an explicit feature volume from these multi-view features, detailed in Sec. 2.2. Finally, we explain the image rendering from the feature volume and loss functions for network optimization in Sec. 2.3 and Sec. 2.4. Our pipeline is visualized in Fig. 2.

### 2.1 Input Process and Feature Extraction

Given a set of multi-view images $\mathbf{I}=\{I_{1},I_{2},\ldots,I_{N}\}$, where each $I_{i}\in\mathbb{R}^{3\times H\times W}$ and $N\in\mathbb{Z}^{+}$, we utilize a 2D image backbone $F$, such as a ViT. The images are processed separately through $F$, yielding latent features $\mathbf{L}=\{l_{1},l_{2},\ldots,l_{N}\}$, where each $l_{i}=F(I_{i})\in\mathbb{R}^{L\times C}$. Following MAE, we apply random masking to input images to enhance robustness, but without a ViT decoder and MAE’s pixel reconstruction objective.
For each $l_{i}$, masked positions are filled with a mask token, and we concatenate the global class token with other patch tokens as read-out tokens similar to DPT (Ranftl et al., ).
We then unpatchify them to obtain a latent feature map of size $\frac{H}{P}\times\frac{W}{P}$, where $P$ is the ViT patch size. Finally, two simple upsampling layers transform this into a feature map $M_{i}$ matching the input resolution. Each upsampling layer includes a convolution, a GELU (Hendrycks & Gimpel, ) activation, and a pixel shuffle layer (Shi et al., ) with an upscale factor of $\sqrt{P}$.

### 2.2 Dynamic Volume Construction

To enable multi-view interaction, we construct a 3D feature volume from multi-view feature maps, $\mathbf{M}$.
Unlike the bird’s-eye view (BEV) construction in autonomous driving (Li et al., ), which usually relies on a fixed scene range around ego vehicle , our method dynamically adjusts the scene range based on the spatial extents of the environment to accommodate varying datasets.
Specifically, the scene’s bounds are first estimated using available depth data, sparse points, or pre-defined rules.
We then partition the scene into a volume of size $X\times Y\times Z$, with voxel size dynamically adjusted to capture either fine object details or larger environments.
Voxel features, $\tilde{\mathcal{V}}$, are initialized with learnable positional embeddings. Each voxel is projected onto the multi-view feature maps using the known transformation matrix $\mathbf{T}$. Deformable attention (Zhu et al., ) is then applied, where the multi-view features act as keys and values, and the voxel features as queries. Finally, a 3D convolution refines the output volume features to obtain $\mathcal{V}$.
The process can be formulated as:

$$ $\mathcal{V}=\operatorname{Conv3D}(\operatorname{DeformAttn}(\tilde{\mathcal{V} },\mathbf{M},\mathbf{T})).$ (1) $$

Figure: Figure 2: Pipeline Overview. Given multi-view images, we randomly mask patches and input the remaining into a Vision Transformer. The upsampled latent features generate multi-view feature maps, from which we construct a feature volume to derive SDF values, SH coefficients, and semantic features. We then render depth, RGB, and semantic maps for loss computation.
Refer to caption: x2.png

### 2.3 Differentiable Volumetric Rendering

After constructing the feature volume, we employ differentiable neural rendering (Mildenhall et al., ) to connect 2D and 3D domains. For better geometry representation, we utilize the implicit signed distance function (SDF) field modeling as in NeuS (Wang et al., ). The SDF represents the 3D distance from a query point to the nearest surface, implicitly capturing the 3D geometry.

Given a feature volume $\mathcal{V}$, we apply a shallow 3D CNN $\phi$ to directly produce three outputs: an SDF feature volume $\mathcal{S}\in\mathbb{R}^{X\times Y\times Z}$, a spherical harmonic (SH) (Yu et al., ; Zhu et al., ) coefficient field $\mathcal{K}\in\mathbb{R}^{D\times X\times Y\times Z}$ (where $D=3\cdot(l_{\mathrm{max}}+1)^{2}$) for color rendering, and a semantic feature volume $\mathcal{F}\in\mathbb{R}^{C_{\mathrm{semantic}}\times X\times Y\times Z}$:

$$ $\mathcal{S}\in\mathbb{R}^{X\times Y\times Z},\quad\mathcal{K}\in\mathbb{R}^{D \times X\times Y\times Z},\quad\mathcal{F}\in\mathbb{R}^{C_{\mathrm{semantic}} \times X\times Y\times Z}=\phi(\mathcal{V}).$ (2) $$

Unlike prior work (Huang et al., ; Zhu et al., ; Yang et al., ), which employs an MLP to compute the attributes of each sampled point individually, we directly apply a 3D CNN to $\mathcal{V}$.
This eliminates the need for pointwise MLP computations, reducing redundant processing and enabling more efficient execution.
Consequently, our approach leads to substantial improvements in both time and memory efficiency, especially when sampling a large number of points during rendering.

To render a 2D pixel $i$, we sample $N$ ray points $\{\mathbf{p}_{j}=\mathbf{o}+t_{j}\mathbf{d}_{i}\mid j=1,\ldots,N,\,t_{j}<t_{j+
1}\}$ from ray $\mathbf{r}_{i}$, where $\mathbf{o}$ is the camera origin and $\mathbf{d}_{i}$ is the viewing direction. Attributes for each point are obtained via trilinear sampling:

$$ $s_{j}=\tau(\mathcal{S},\mathbf{p}_{j}),\quad\mathbf{k}_{j}=\tau(\mathcal{K}, \mathbf{p}_{j}),\quad\mathbf{f}_{j}=\tau(\mathcal{F},\mathbf{p}_{j}).$ (3) $$

The SH vector $\mathbf{k}_{j}=(k_{l}^{m})_{0\leq l\leq l_{\text{max}},-l\leq m\leq l}$, where $k_{l}^{m}\in\mathbb{R}^{3}$, is used to compute view-dependent colors $\hat{\mathbf{c}}_{j}$ by querying the SH basis functions $Y_{l}^{m}:\mathbb{S}^{2}\rightarrow\mathbb{R}$ based on the viewing direction $\mathbf{d}_{j}$:

$$ $\hat{\mathbf{c}}_{j}=\operatorname{Sigmoid}\mathopen{}\mathclose{{}\left(\sum_ {l=0}^{l_{\text{max}}}\sum_{m=-l}^{l}k_{l}^{m}Y_{l}^{m}(\mathbf{d}_{j})}\right).$ (4) $$

Following the formulation in NeuS (Wang et al., ), the RGB color $\hat{\mathbf{C}}_{i}$, depth $\hat{\mathbf{D}}_{i}$, and semantic feature $\hat{\mathbf{F}}_{i}$ for pixel $i$ are computed by integrating the predicted values along the ray:

$$ $\hat{\mathbf{C}}_{i}=\sum_{j=1}^{N}w_{j}\hat{\mathbf{c}}_{j},\quad\hat{\mathbf {D}}_{i}=\sum_{j=1}^{N}w_{j}t_{j},\quad\hat{\mathbf{F}}_{i}=\sum_{j=1}^{N}w_{j }\hat{\mathbf{f}}_{j},$ (5) $$

where $w_{j}=T_{j}\alpha_{j}$ is the occlusion-aware weight, with $T_{j}=\prod_{k=1}^{j-1}(1-\alpha_{k})$ representing the accumulated transmittance and $\alpha_{j}$ being the opacity value. Specifically, $\alpha_{j}$ is computed as:

$$ $\alpha_{j}=\max\mathopen{}\mathclose{{}\left(\frac{\sigma_{s}(s_{j})-\sigma_{s }(s_{j+1})}{\sigma_{s}(s_{j})},0}\right),$ (6) $$

where $\sigma_{s}(x)=(1+e^{-sx})^{-1}$ is the sigmoid function modulated by a learnable parameter $s$.

### 2.4 Loss Functions

During pre-training, we randomly sample $K$ pixels from multi-view inputs in each iteration. The rendering loss is calculated based on the differences between the input pixel values and the predicted values. For the semantic feature map, we use the feature map from AM-RADIO (Ranzinger et al., ) as supervision. Our framework has the capability to distill knowledge from multiple vision foundation models by adding multiple rendering heads. However, this paper does not explore that approach, as it is not the primary focus. The rendering loss is expressed as:

$$ $\mathcal{L}_{\text{render}}=\frac{1}{K}\sum_{i=1}^{K}\mathopen{}\mathclose{{} \left(\lambda_{\text{color}}\cdot\|\mathbf{C}_{i}-\hat{\mathbf{C}}_{i}\|+ \lambda_{\text{depth}}\cdot\|\mathbf{D}_{i}-\hat{\mathbf{D}}_{i}\|+\lambda_{ \text{semantic}}\cdot\|\mathbf{F}_{i}-\hat{\mathbf{F}}_{i}\|}\right).$ (7) $$

Additionally, we incorporate the Eikonal regularization loss $\mathcal{L}_{\text{eikonal}}$, near-surface SDF supervision loss $\mathcal{L}_{\text{sdf}}$, and free space SDF loss $\mathcal{L}_{\text{free}}$, which are standard in neural surface reconstruction. Detailed definitions of these losses are provided in Appendix A.
The total loss is defined as:

$$ $\mathcal{L}_{\text{total}}=\mathcal{L}_{\text{render}}+\lambda_{\text{eikonal} }\cdot\mathcal{L}_{\text{eikonal}}+\lambda_{\text{sdf}}\cdot\mathcal{L}_{\text {sdf}}+\lambda_{\text{free}}\cdot\mathcal{L}_{\text{free}}.$ (8) $$

Figure: Figure 3: Overview of our large-scale embodied evaluation. We conduct the largest-scale evaluation of embodied representation learning to date. Our study encompasses 268 tasks across 8 simulators, including both single-task and language-conditioned multi-task settings. We evaluate diverse policy architectures and assess various state-of-the-art representation methods. This thorough evaluation allows us to provide a comprehensive and unbiased analysis of different representations.
Refer to caption: x3.png

## 3 Large-Scale Embodied Evaluation

Unlike the CV or NLP communities, where large-scale benchmarks are common, embodied representations have not been thoroughly assessed. The largest previous evaluation, VC-1 (Majumdar et al., ), includes only 17 tasks. This may lead to randomness and bias. Therefore, we have created the largest embodied evaluation to date, encompassing 268 tasks across 8 simulators—over 15 times larger than VC-1’s evaluation. Additionally, unlike previous approaches (Majumdar et al., ; Nair et al., ; Radosavovic et al., ) that used a small MLP policy under single-task settings, our evaluation spans multiple policy types (*e.g*. MLP, diffusion, transformer) and includes both single-task and language-conditioned multi-task settings. This unprecedented scale and diversity ensure robust and convincing conclusions. During all evaluations, we adhere to standard practices by freezing the pre-trained representation model.
Our detailed evaluation settings can be found in Appendix B. The overview of our evaluation is shown in Fig. 3.

We have included 3 single-task benchmarks:
1) VC-1 (Majumdar et al., ) involves 4 selected simulators with 14 tasks in total: Adroit (AD) (Kumar, ), Meta-World (MW) (Yu et al., ), DMControl (DMC) (Tunyasuvunakool et al., ), and TriFinger (TF) (Wüthrich et al., ). We use a 3-layer MLP as the policy network.
2) Franka Kitchen (Gupta et al., )
involves 5 selected tasks. Each task spans two camera viewpoints and three random seeds. We utilize 25 demonstrations to train a 2-layer MLP policy.
3) Meta-World (Yu et al., ) involves 48 selected tasks of varying difficulty. We implemented the Diffusion Policy (Chi et al., ) on this benchmark and adhered to the setup in Ze et al. () to generate 10 demonstrations for each single-task training, followed by evaluation through 20 rollouts.

We have also included 2 language-conditioned multi-task benchmarks:
1) RLBench (James et al., ) features 71 selected tasks that can be successfully executed. We divide the tasks into two groups according to their category defined by PolarNet (Chen et al., ). We employ RVT-2 (Goyal et al., ), the SOTA method on this benchmark, as our policy.
2) LIBERO (Liu et al., ) comprises 130 tasks across 5 suites: LIBERO-Spatial, LIBERO-Object, LIBERO-Goal, LIBERO-10, and LIBERO-90. We train a language-conditioned transformer policy provided by the original LIBERO on each suite with only 20 demonstrations per task.

## 4 Training and Implementation Details

In this section, we present the step-by-step implementation and training of our SPA model. We first pre-train a ViT-base (ViT-B) backbone using a small dataset and evaluate this model on the VC-1 benchmark to examine the effects of hyperparameters (Sec. 1). We then compile several multi-view datasets, training ViT-B models on each to assess the impact of different datasets (Sec. 4.2). Finally, we integrate all factors and scale up both data and model size to train the strongest version of SPA using a ViT-large (ViT-L) backbone (Sec. 4.3). More details can be found in Appendix C.

### 4.1 Hyperparameter Investigation

**Table 1: Influence of mask ratio and loss components. C., D., and S. denote the color, depth, and semantic loss components, respectively.**
| Mask<br>Ratio | Loss | VC-1 Benchmark | Mean<br>S.R. |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| C. | D. | S. | AD | MW | DMC | TF |  |  |
| 0.00 | ✓ | ✓ | ✓ | 53.3$\pm$4.6 | 88.5$\pm$5.7 | 57.5$\pm$2.6 | 74.1$\pm$0.6 | 70.36 |
| 0.25 | ✓ | ✓ | ✓ | 52.7$\pm$3.1 | 89.6$\pm$4.5 | 57.6$\pm$3.0 | 70.4$\pm$1.7 | 70.17 |
| 0.50 | ✓ | ✓ | ✓ | 53.3$\pm$4.2 | 88.8$\pm$1.6 | 60.1$\pm$3.1 | 72.6$\pm$0.7 | 71.18 |
| 0.75 | ✓ | ✓ | ✓ | 51.3$\pm$1.2 | 88.0$\pm$3.5 | 61.1$\pm$3.5 | 73.0$\pm$0.8 | 71.01 |
| 0.95 | ✓ | ✓ | ✓ | 51.3$\pm$1.2 | 85.6$\pm$4.0 | 62.5$\pm$5.3 | 73.1$\pm$0.2 | 70.67 |
| 0.50 | ✓ | ✗ | ✓ | 51.3$\pm$1.2 | 90.9$\pm$3.3 | 58.8$\pm$5.6 | 71.5$\pm$1.0 | 71.01 |
| 0.50 | ✗ | ✓ | ✓ | 52.0$\pm$2.0 | 89.3$\pm$3.3 | 53.9$\pm$4.3 | 70.9$\pm$1.3 | 68.71 |
| 0.50 | ✓ | ✓ | ✗ | 52.7$\pm$3.1 | 88.0$\pm$4.5 | 61.5$\pm$3.4 | 71.6$\pm$1.2 | 71.16 |

We conduct hyperparameter tuning with a ViT-B model on ScanNet (Dai et al., ), and evaluate it on VC-1 benchmarks, as shown in Tab. 1.
1) Mask Ratio. Our results indicate that a mask ratio of $0.5$ is the most effective.
2) Loss Components. As discussed in Sec. 2.4, our rendering loss consists of color, depth, and semantic components. We sequentially deactivate each and find that all three are valuable. However, deactivating the semantic loss has the least impact.

### 4.2 Dataset Investigation

We collect several multi-view datasets. To investigate their effectiveness in SPA representation learning, we train a ViT-B model on one or two of the datasets, keeping the total training steps constant, and assess performance on the VC-1 benchmarks. For simplicity, semantic rendering is disabled. The datasets investigated are listed in the first column of Tab. 2.
Most datasets provide ground-truth depth, which we use for supervision.
As our findings above reveal that depth supervision is helpful, for datasets lacking ground-truth depth, we employ a depth estimation model. For instance, Droid (Khazatsky et al., ) only offers binocular images, so we apply CroCo-Stereo (Weinzaepfel et al., ) for dense depth estimation.
Additionally, due to inaccurate camera poses in Droid, we treat its data as single-view inputs.
The results are presented in Tab. 2, with further details in Appendix C. Our analysis reveals that some datasets can be detrimental. For example, although RH20T (Fang et al., ) is a large-scale robotic dataset, its lack of visual diversity—stemming from data collected in the same lab—negatively impacts representation learning.

**Table 2: Influence of different datasets. We present the performance results on the VC-1 benchmark. Mean S.R. refers to the mean success rate across all individual tasks.**
| Datasets | AD | MW | DMC | TF | Mean<br>S.R. |
| --- | --- | --- | --- | --- | --- |
| ScanNet (Dai et al., ) | 52.67$\pm$4.11 | 90.93$\pm$3.22 | 65.11$\pm$1.31 | 70.75$\pm$1.08 | 73.68 |
| ScanNet++ (Yeshwanth et al., ) | 56.00$\pm$2.83 | 89.87$\pm$4.20 | 62.24$\pm$4.51 | 71.28$\pm$0.38 | 72.51 |
| Arkitscenes (Baruch et al., ) | 50.67$\pm$5.73 | 89.87$\pm$4.59 | 60.51$\pm$2.55 | 66.54$\pm$0.13 | 70.45 |
| Droid (Khazatsky et al., ) | 53.33$\pm$5.25 | 90.40$\pm$4.90 | 60.99$\pm$3.72 | 73.28$\pm$0.61 | 72.16 |
| Hypersim (Roberts et al., ) | 52.67$\pm$4.11 | 88.80$\pm$3.27 | 60.84$\pm$2.06 | 72.29$\pm$0.47 | 71.29 |
| Hypersim + ADT (Pan et al., ) | 52.00$\pm$2.83 | 87.20$\pm$2.30 | 63.61$\pm$1.04 | 70.83$\pm$0.13 | 71.41 |
| Hypersim + S3DIS (Armeni et al., ) | 49.33$\pm$0.94 | 94.13$\pm$2.04 | 64.57$\pm$3.91 | 71.74$\pm$0.75 | 73.98 |
| Hypersim + Structured3D (Zheng et al., ) | 46.67$\pm$4.11 | 80.27$\pm$7.72 | 58.02$\pm$ 2.34 | 65.05$\pm$0.40 | 65.35 |
| Hypersim + RH20T (Fang et al., ) | 47.33$\pm$1.89 | 86.93$\pm$4.99 | 57.01$\pm$4.35 | 64.28$\pm$0.46 | 67.35 |
| Hypersim + ASE (Avetisyan et al., ) | 47.33$\pm$4.11 | 87.73$\pm$3.39 | 60.62$\pm$4.14 | 68.59$\pm$0.30 | 69.54 |

### 4.3 Put All Together

Based on the previous analyses, we proceed to pre-train the final version of SPA. We use a mask ratio of $0.5$ and enable all three rendering losses. Following Ponder (Huang et al., ), we set the weight for the RGB loss to $10$, the weights for the depth and semantic losses to $1$, and use $\lambda_{\mathrm{eikonal}}=0.01$, $\lambda_{\mathrm{sdf}}=10$, and $\lambda_{\mathrm{free}}=1$.
The volume size is $128\times 128\times 32$. For stable training, we apply the Exponential Moving Average (EMA) technique with a decay of $0.999$. We use AdamW (Loshchilov et al., ) as the optimizer with a weight decay of $0.04$ and a learning rate of $8e^{-4}$. OneCycle (Smith & Topin, ) learning rate scheduler is adopted. We utilize 80 NVIDIA A100-SXM4-80GB GPUs, each with a batch size of $2$, and accumulate gradients over 8 batches, resulting in a total effective batch size of $2\times 8\times 80=1280$. Training is conducted over $2000$ epochs, sampling each dataset to match the size of ADT per epoch. The datasets used for the final version include ScanNet, ScanNet++, ADT, S3DIS, Hypersim, and Droid.

## 5 Experiment Results

In this section, we present the results of our large-scale evaluation. Our experiments are designed to address the following research questions:
Q1: How does SPA compare to other methods in our large-scale embodied evaluation?
Q2: What insights do we gain about various representation learning approaches from our evaluation?
Q3: Does SPA really learn enhanced 3D awareness that results in improved embodied representation?
Q4: Can SPA facilitate robot learning in real-world environments in a zero-shot manner?

### 5.1 Overall Comparisons (Q1, Q2)

**Table 3: Summary of different representation learning methods. ‘#Param.’ is the total parameters of the encoder, while ‘#Frames’ indicates the total number of image frames used during pre-training.**
| Method | Vision-Centric | Multi-Modal | Embodied-Specific |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| MoCoV3<br>(,<br>) | MAE<br>(,<br>) | DINOV2<br>(,<br>) | CLIP<br>(,<br>) | EVA<br>(,<br>) | InternViT-300M<br>(,<br>) | InternViT-6B<br>(,<br>) | MVP<br>(,<br>) | VC-1<br>(,<br>) | SPA<br>(Ours) |  |
| Is Vanilla? | ✓ | ✓ | ✗ | ✓ | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ |
| Input Size | 224 | 224 | 224 | 224 | 224 | 448 | 224 | 256 | 224 | 224 |
| Patch Size | 16 | 16 | 14 | 14 | 14 | 14 | 14 | 16 | 16 | 16 |
| #Param. | 303M | 303M | 303M | 303M | 303M | 303M | 5.9B | 303M | 303M | 303M |
| #Frames | 1.28M | 1.28M | 1.2B | 400M | 14M | 5.0B | 5.0B | 4.5M | 5.6M | 3.8M |

**Table 4: Comparison of different representation learning methods. ‘OOM’ indicates InternViT-6B encountered an out-of-memory error during evaluation. The best and second-best results are bolded and underlined respectively. The number in parentheses denotes the number of tasks.**
| Method | Vision-Centric | Multi-Modal | Embodied-Specific |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Benchmark | MoCoV3 | MAE | DINOV2 | CLIP | EVA | InternViT-<br>300M | InternViT-<br>6B | MVP | VC-1 | SPA (Ours) |  |
| VC-1 | AD (2) | 58.7$\pm$7.0 | 58.0$\pm$2.0 | 47.3$\pm$3.1 | 48.7$\pm$3.1 | 58.0$\pm$6.0 | 53.3$\pm$3.1 | 60.0$\pm$9.2 | 53.3$\pm$4.2 | 54.0$\pm$4.0 | 60.0$\pm$4.0 |
| MW (5) | 88.8$\pm$5.0 | 90.0$\pm$4.6 | 84.0$\pm$3.7 | 77.1$\pm$3.2 | 90.7$\pm$0.9 | 84.0$\pm$3.7 | 89.1$\pm$1.2 | 93.6$\pm$5.2 | 87.5$\pm$3.8 | 93.3$\pm$2.0 |  |
| DMC (5) | 67.3$\pm$3.3 | 74.4$\pm$1.8 | 64.5$\pm$2.5 | 53.9$\pm$3.6 | 62.7$\pm$2.8 | 53.3$\pm$0.4 | 66.3$\pm$3.2 | 69.4$\pm$2.6 | 65.3$\pm$3.6 | 71.1$\pm$5.0 |  |
| TF (2) | 67.9$\pm$0.2 | 73.0$\pm$0.5 | 68.5$\pm$0.4 | 56.1$\pm$1.6 | 67.2$\pm$0.2 | 65.2$\pm$1.6 | 70.7$\pm$0.9 | 73.2$\pm$0.8 | 70.9$\pm$1.1 | 73.6$\pm$2.0 |  |
| RLBench | Group 1 (35) | 73.7 | 78.3 | 78.2 | 76.8 | 75.2 | 74.1 | OOM | 76.2 | 80.1 | 80.5 |
| Group 2 (36) | 54.2 | 57.7 | 56.1 | 55.7 | 57.0 | 54.9 | OOM | 56.3 | 55.7 | 61.2 |  |
| Meta-World (48) | 69.3$\pm$1.5 | 67.8$\pm$1.7 | 56.3$\pm$0.6 | 66.7$\pm$1.7 | 63.7$\pm$1.3 | 57.5$\pm$1.7 | OOM | 66.4$\pm$1.7 | 68.6$\pm$1.5 | 69.2$\pm$1.7 |  |
| LIBERO | Object (10) | 65.3$\pm$8.0 | 71.7$\pm$13.1 | 64.7$\pm$9.9 | 50.2$\pm$7.0 | 73.2$\pm$6.0 | 67.7$\pm$6.0 | 58.0$\pm$10.6 | 63.7$\pm$4.8 | 69.7$\pm$7.2 | 76.7$\pm$5.3 |
| Spatial (10) | 40.5$\pm$0.9 | 57.2$\pm$2.9 | 36.3$\pm$11.8 | 32.2$\pm$0.6 | 59.3$\pm$7.7 | 48.3$\pm$6.4 | 42.0$\pm$10.3 | 58.0$\pm$6.2 | 50.5$\pm$7.5 | 50.0$\pm$3.8 |  |
| Goal (10) | 49.2$\pm$8.1 | 54.3$\pm$6.0 | 22.2$\pm$2.3 | 30.3$\pm$3.2 | 56.8$\pm$2.9 | 58.8$\pm$4.5 | 33.2$\pm$2.0 | 63.8$\pm$2.8 | 57.5$\pm$6.6 | 65.3$\pm$2.5 |  |
| 10 (10) | 34.2$\pm$3.8 | 41.2$\pm$4.5 | 28.3$\pm$3.0 | 27.5$\pm$3.9 | 43.3$\pm$2.8 | 38.2$\pm$1.3 | 34.3$\pm$4.6 | 39.0$\pm$0.9 | 39.7$\pm$3.5 | 40.2$\pm$3.6 |  |
| 90 (90) | 30.0$\pm$1.4 | 29.9$\pm$2.0 | 27.5$\pm$2.2 | 29.4$\pm$2.0 | 31.3$\pm$2.3 | 23.8$\pm$1.8 | 27.1$\pm$2.1 | 32.1$\pm$3.5 | 30.6$\pm$3.3 | 32.2$\pm$1.6 |  |
| Franka-Kitchen (5) | 48.3$\pm$4.7 | 42.7$\pm$2.6 | 40.9$\pm$6.4 | 30.8$\pm$3.3 | 37.3$\pm$1.3 | 28.5$\pm$1.7 | OOM | 34.3$\pm$6.1 | 37.5$\pm$3.5 | 40.6$\pm$1.9 |  |
| Mean S.R. $\uparrow$ | 81.67 | 85.13 | 75.18 | 77.10 | 83.84 | 75.41 | 30.65 | 84.85 | 84.69 | 88.63 |  |
| Mean Rank $\downarrow$ | 4.51 | 4.07 | 5.61 | 5.17 | 4.37 | 5.92 | 7.57 | 4.24 | 4.13 | 3.20 |  |

Evaluation Metrics. We follow prior work (Majumdar et al., ; Zhu et al., ) in reporting two metrics: Mean Success Rate (Mean S.R.) and Mean Rank. Mean S.R. is the average success rate across all tasks, indicating overall performance, while Mean Rank reflects the average ranking of each method’s success rate across tasks, providing a measure of relative performance. Since RLBench has fixed train and test sets, we report a single result for this benchmark.

Baselines. We evaluate 9 state-of-the-art representation learning models, all using the same ViT-L backbone, categorized into vision-centric, multi-modal, and embodied-specific. This also includes a comparison with a 6B-parameter multi-modal model (Chen et al., ). Details of the models are summarized in Tab. 3.
The results on each benchmark are shown in Tab. 4. For detailed results on each task and each random seed, please refer to Appendix D. We also have visualized the performance radar chart and the per-task rank distributions in Fig. 1.

Finding 1: We observe that SPA demonstrates superior performance in both mean success rate and mean rank. While no method ranks first across all individual benchmarks, consistent with the findings by Majumdar et al. (), SPA achieves the best or second-best mean success rate in 11 out of 13 benchmarks. Additionally, it ranks in the top 3 for over 65.5% of individual tasks, surpassing the second and third highest percentages of 46.8% for MAE and 46.0% for VC-1, respectively. These trends demonstrate the robustness and superiority of SPA.

Finding 2: We observe that for vision-centric methods, superior performance on vision tasks does not necessarily translate to better embodied performance. Despite using 10 times more data, DINOV2 performs worse than MoCoV3 and MAE. Notably, MAE performs exceptionally well, likely due to its reconstruction objective, which enhances 2D spatial awareness. Interestingly, methods like MVP and VC-1, which are MAE models pre-trained on human interaction data, show no clear advantage over ImageNet (Deng et al., ) pre-trained MAE. This suggests that while human activity data may seem more relevant, data diversity and thorough convergence are more critical.

Finding 3: Multimodal methods generally perform poorly in embodied evaluations, except EVA, which combines image-language contrastive techniques with MAE reconstruction. Furthermore, InternViT-6B, despite having significantly more model parameters, does not demonstrate superiority and even performs worse on some benchmarks compared to InternViT-300M. This indicates that current scaling properties of multimodal approaches do not effectively translate to embodied AI.

Finding 4: Focusing on a single benchmark can lead to highly biased conclusions. For instance, ImageNet pre-trained methods (*e.g*. MoCoV3 and MAE) perform exceptionally well on the Franka Kitchen benchmark, suggesting a minimal domain gap between ImageNet and Franka Kitchen observations. Moreover, despite being based on MAE, previous SOTA embodied representations like MVP and VC-1 do not consistently outperform the original ImageNet version. These observations underscore the importance of our large-scale embodied evaluation.

**Table 5: Additional comparisons of ViT-base models on VC-1 benchmarks.**
| Methods | DINOV2-B<br>(,<br>) | MAE-B<br>(,<br>) | R3M-B<br>(,<br>) | VC-1-B<br>(,<br>) | STP-B<br>(,<br>) | Voltron-B<br>(,<br>) | Theia-B<br>(,<br>) | SPA-B<br>(Ours) |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Is Vanilla? | ✗ | ✓ | ✓ | ✓ | ✓ | ✗ | ✓ | ✓ |  |
| Embodied? | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |  |
| VC-1 | AD | 36.67$\pm$2.31 | 52.67$\pm$3.06 | 48.00$\pm$6.93 | 50.00$\pm$5.29 | 52.00$\pm$2.00 | 46.67$\pm$4.62 | 53.33$\pm$5.03 | 52.00$\pm$3.46 |
| MW | 60.80$\pm$0.80 | 88.80$\pm$4.00 | 59.20$\pm$5.60 | 86.67$\pm$0.92 | 92.00$\pm$1.39 | 84.00$\pm$3.20 | 89.07$\pm$3.23 | 92.00$\pm$4.16 |  |
| DMC | 35.19$\pm$4.87 | 62.39$\pm$4.97 | 49.57$\pm$4.85 | 60.92$\pm$0.70 | 61.40$\pm$2.86 | 56.36$\pm$2.01 | 64.98$\pm$3.42 | 64.21$\pm$3.52 |  |
| TF | 54.50$\pm$1.16 | 70.78$\pm$0.17 | 56.18$\pm$7.00 | 72.33$\pm$0.69 | 67.96$\pm$0.95 | 74.26$\pm$1.57 | 69.41$\pm$0.60 | 73.06$\pm$0.51 |  |
| Mean S.R. | 47.31 | 71.63 | 54.37 | 70.19 | 71.92 | 69.50 | 72.55 | 73.66 |  |

### 5.2 Additional Comparisons (Q1)

We primarily compare with SOTA methods using the ViT-L backbone, which is commonly available and pre-trained on large-scale datasets. However, some embodied-specific models are only offered in ViT-B variants. Therefore, we provide additional comparisons with several ViT-B models in Tab. 5.
Our ViT-B version, SPA-B, also outperforms other baselines. Furthermore, when compared to SPA-L on VC-1 benchmarks, the mean success rate increases by 4.16 (73.66 $\rightarrow$ 77.82). This indicates that increasing the model size positively impacts SPA’s performance.

### 5.3 Study on 3D Awareness of SPA (Q3)

**Table 6: Zero-shot camera pose estimation. SPA demonstrates strong 3D awareness.**
| Error | MoCoV3 | MAE | DINOV2 | CLIP | EVA | InternViT-300M | InternViT-6B | MVP | VC-1 | SPA(Ours) |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Trans. ($\times e^{-2}$) | 2.29$\pm$0.07 | 2.15$\pm$0.07 | 6.55$\pm$0.07 | 4.21$\pm$0.37 | 5.49$\pm$0.24 | 4.62$\pm$0.14 | 5.39$\pm$0.41 | 2.15$\pm$0.12 | 2.02$\pm$0.07 | 1.65$\pm$0.09 |
| Rot. ($\times e^{-1}$) | 0.79$\pm$0.07 | 0.73$\pm$0.03 | 2.12$\pm$0.25 | 1.52$\pm$0.08 | 1.83$\pm$0.09 | 1.83$\pm$0.08 | 1.91$\pm$0.12 | 0.77$\pm$0.05 | 0.72$\pm$0.01 | 0.61$\pm$0.01 |

**Table 7: Additional ablations on VC-1.**
| Methods | SPA-B | SPA-MAE | RADIO | E-RADIO |  |
| --- | --- | --- | --- | --- | --- |
| VC-1 | AD | 52.00$\pm$3.46 | 55.33$\pm$3.06 | 55.33$\pm$3.06 | 56.67$\pm$2.31 |
| MW | 92.00$\pm$4.16 | 90.67$\pm$6.00 | 72.00$\pm$9.23 | 83.47$\pm$4.11 |  |
| DMC | 64.21$\pm$3.52 | 63.85$\pm$3.60 | 67.38$\pm$7.35 | 62.92$\pm$4.24 |  |
| TF | 73.06$\pm$0.51 | 70.14$\pm$0.98 | 71.75$\pm$0.14 | 68.44$\pm$1.19 |  |
| Mean S. R. | 73.66 | 73.11 | 67.93 | 70.16 |  |

Firstly, we aim to provide clear evidence that the performance improvements of SPA are due to its 3D awareness. To demonstrate this, we conducted two additional ablation studies on the VC-1 benchmarks: 1) To determine whether the performance gain is due to SPA’s pre-training objectives or the datasets used, we continue pre-training the ImageNet pre-trained MAE-B (the most competitive method besides SPA) on the same datasets used by SPA-B, referring to this model as SPA-MAE. Hyperparameters, including mask ratio and batch size, are kept at their default settings, and both the ImageNet pre-trained encoder and decoder weights are initially loaded. 2) Since SPA uses the feature map of RADIO for semantic rendering supervision, we also evaluate the original RADIO (653M parameters) and its efficient version, E-RADIO (391M parameters). Results are presented in Tab. 7.

Figure: Figure 4: Correlation between mean success rate and camera pose regression error.
Refer to caption: x4.png

Finding 5: The 3D-aware pre-training objective significantly enhances SPA’s performance. It surpasses the single-image naive MAE with the same data. Notably, SPA learns superior representations compared to its semantic rendering teacher by a substantial margin.

Moreover, we provide both quantitative and qualitative evidence to demonstrate that SPA has acquired 3D awareness. For qualitative analysis, we visualize the zero-shot feature maps on multiview images of different encoder outputs, as shown in Fig. 5. The images are taken from the unseen Arkitscenes dataset. For quantitative analysis, we evaluate the zero-shot 3D awareness of various methods using a camera pose estimation task on the NAVI dataset (Jampani et al., ).

Figure: Figure 5: Feature map visualization.
Refer to caption: x5.png

Specifically, given a pair of images from different viewpoints, we use a frozen encoder to extract features and concatenate them.
A small MLP then regresses the relative camera pose and we report rotation and translation errors in Tab. 6. Details are in Appendix E.
While El Banani et al. () has explored 3D awareness of different vision models, their context differs. Their tasks can allow strong semantic models like DINOV2 to ‘cheat’. For example, multiview correspondence can be achieved through semantic matching, and the relative depth estimation task involves transforming normalized values into discrete bins, resembling a per-pixel classification task. Additionally, they emphasize fine-grained dense local context, whereas, embodied AI focuses more on sparse, global information (Nair et al., ). Thus, we believe camera pose estimation, which predicts a global ‘pose’ from observations, is more relevant to embodied AI, where a policy must predict a global ‘action’.

Finding 6: We observe that SPA outperforms all other methods in zero-shot camera pose estimation. It achieved an 18.3% improvement in translation and a 15.3% reduction in rotation error compared to the second-best model. Additionally, we identify a clear positive correlation between camera pose estimation and embodied evaluation performance, as demonstrated in Fig. 4. This finding supports our spatial hypothesis and may offer valuable insights for future research on embodied representation.

Finding 7: The feature map visualization provides clear evidence that SPA has learned multi-view consistent knowledge, demonstrating its 3D awareness. Additionally, the features produced by SPA are cleaner and more coherent. Though VC-1 also generates smooth features, they are not consistent across viewpoints. The feature maps from the multi-modal approach are highly noisy and lack details.

### 5.4 Real-World Experiments (Q4)

Figure: Figure 6: Real-world task illustrations.
Refer to caption: x6.png

We conduct several real-world experiments to further investigate the generalization ability of different representations. Specifically, we utilize the open-sourced Low-Cost Robot Arm (Koch, ) to learn real-world tasks from pixels, with only 50 demonstrations per task using different frozen pre-trained representations. The robot performed two single-arm tasks: (1) picking a cube, and (2) stacking a yellow cube on a pink cube, as well as one dual-arm task: folding a cloth in half. Refer to Fig. 6 for illustrations and Appendix F for more details. We evaluate each task with 25 rollouts, with the results presented in Tab. 8.
SPA consistently performs better on real-world tasks, suggesting that SPA’s pre-trained representations can robustly adapt to real-world environments without finetuning.

**Table 8: Real-world experiment results.**
| Methods | MoCoV3 | MAE | DINOV2 | CLIP | EVA | InternViT-300M | InternViT-6B | MVP | VC-1 | SPA (Ours) |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Picking Cube | 28.00 | 64.00 | 20.00 | 28.00 | 56.00 | 32.00 | 52.00 | 36.00 | 40.00 | 64.00 |
| Stacking Cube | 16.00 | 32.00 | 4.00 | 16.00 | 8.00 | 8.00 | 36.00 | 20.00 | 16.00 | 48.00 |
| Folding Cloth | 48.00 | 64.00 | 32.00 | 24.00 | 28.00 | 48.00 | 44.00 | 64.00 | 60.00 | 84.00 |
| Mean S.R. | 30.67 | 53.33 | 18.67 | 22.67 | 30.67 | 29.33 | 44.00 | 40.00 | 38.67 | 65.33 |

## 6 Related Work

Representation Learning for Computer Vision. Recent advances in computer vision have increasingly focused on unsupervised and self-supervised learning to utilize large amounts of unlabeled data. Techniques like contrastive learning (Chen et al., ; ; ; He et al., ), masked autoencoders (He et al., ; Feichtenhofer et al., ; Bachmann et al., ; Tong et al., ; Wang et al., ), and self-distillation (Caron et al., ; Oquab et al., ; Ranzinger et al., ) have shown that effective representations can be learned without supervision. Moreover, multi-modal pre-training approaches (Radford et al., ; Fang et al., ; Chen et al., ) leverage language to learn more comprehensive representations. These developments have significantly improved transfer learning capabilities while also displaying zero-shot abilities.

Representation Learning for Embodied AI. Inspired by computer vision, recent work has applied methods such as contrastive learning (Nair et al., ; Yang et al., ) and masked autoencoders (Radosavovic et al., ; Majumdar et al., ; Karamcheti et al., ; Yang et al., ) to embodied AI. However, these approaches often overlook the unique challenges of embodied tasks, focusing primarily on semantic knowledge. However, many of these methods primarily adapt techniques from computer vision and focus predominantly on learning semantic knowledge, often overlooking the unique requirements of embodied AI tasks. Prior studies (Zhu et al., ; Ze et al., ; Wang et al., ; ) have highlighted the importance of 3D spatial structure for improving robotic learning, though point clouds are difficult to scale. Despite this, point clouds are challenging to obtain and encode, limiting their scalability. In this work, we propose a spatial hypothesis: while semantic understanding is crucial, 3D spatial awareness is even more important, and we demonstrate how a standard 2D backbone can integrate 3D spatial awareness.

Neural Rendering. Recent advances in 3D vision, particularly in neural rendering (Mildenhall et al., ), have enabled the encoding of scenes using neural networks, which support differentiable rendering and reconstruction. Alongside improvements in neural rendering techniques themselves (Wang et al., ; Zhu et al., ; Gropp et al., ; Ortiz et al., ; Wang et al., ), the Ponder series (Huang et al., ; Zhu et al., ; Yang et al., ) and subsequent works (Wang et al., ; Irshad et al., ) have applied differentiable neural rendering for representation learning. However, they have primarily focused on 3D perception and autonomous driving scenarios. To the best of our knowledge, our work is the first to apply neural rendering for embodied AI representation learning using a standard 2D backbone, marking a novel contribution to this area of research.

## 7 Conclusion and Limitations

In this work, we propose that 3D spatial awareness is crucial for embodied AI and introduce SPA, a novel framework that pre-trains a standard ViT backbone with 3D spatial awareness. To validate our hypothesis, we conduct the largest-scale embodied evaluation to date, over 15 times larger than previous studies. Our experiments demonstrate the clear superiority of SPA and highlight the importance of 3D awareness. Despite strong results across simulated and real robotic tasks, limitations remain. Our evaluation is currently restricted to imitation learning (specifically behavior cloning), and exploring SPA’s performance in other settings, such as reinforcement learning, presents an exciting future direction. Additionally, SPA currently focuses on static multi-view scenes; extending it to dynamic, temporal scenarios could enhance its generality. Lastly, while we use the ViT encoder for fair comparison, the volume decoder’s multi-view interaction knowledge could be leveraged in policy learning, offering further potential for improvement.

## Appendix A Additional Rendering Losses

Here we detail the three additional rendering losses we have applied in Sec. 2.4.

Eikonal Regularization Loss. The Eikonal regularization loss, denoted as $\mathcal{L}_{\text{eikonal}}$, is a widely used loss function for the regularization of signed distance functions (SDFs) (Gropp et al., ). It is defined as:

$$ $\mathcal{L}_{\text{eikonal}}=\frac{1}{N_{r}N_{p}}\sum_{i=1}^{N_{r}}\sum_{j=1}^ {N_{p}}\mathopen{}\mathclose{{}\left(\mathopen{}\mathclose{{}\left\|\nabla s( \mathbf{p}_{i,j})}\right\|-1}\right)^{2},$ (9) $$

where $\nabla s(\mathbf{p}_{i,j})$ represents the gradient of the SDF $s$ at the location $\mathbf{p}_{i,j}$. Since the SDF is a distance measure, $\mathcal{L}_{\text{eikonal}}$ encourages the gradients to have unit norm at the query point.

Near-Surface and Free Space Loss for SDF. To improve SDF estimation, we incorporate additional approximate SDF supervision, similar to iSDF (Ortiz et al., ) and GO-Surf (Wang et al., ). Specifically, for near-surface points, the difference between rendered depth and ground-truth depth serves as pseudo-SDF ground-truth supervision. For points far from the surface, a free space loss is used to further regularize the SDF values.

To compute the approximate SDF supervision, we define an indicator $b(z)$ for each sampled ray point with ray length $z$ and corresponding ground-truth depth $D$:

$$ $b(z)=D-z.$ (10) $$

The value $b(z)$ can be considered a credible approximate SDF value when it is small. Let $t$ be a user-defined threshold, set to $0.05$ in our experiments. For sampled ray points satisfying $b(z)\leq t$, we apply the near-surface SDF loss to constrain the SDF prediction $s(z_{i,j})$:

$$ $\mathcal{L}_{\text{sdf}}=\frac{1}{N_{r}N_{p}}\sum_{i=1}^{N_{r}}\sum_{j=1}^{N_{ p}}\mathopen{}\mathclose{{}\left|s(z_{i,j})-b(z_{i,j})}\right|.$ (11) $$

For the remaining sampled ray points, we utilize a free space loss:

$$ $\mathcal{L}_{\text{free}}=\frac{1}{N_{r}N_{p}}\sum_{i=1}^{N_{r}}\sum_{j=1}^{N_ {p}}\max\mathopen{}\mathclose{{}\left(0,e^{-\alpha\cdot s(z_{i,j})}-1,s(z_{i,j })-b(z_{i,j})}\right),$ (12) $$

where $\alpha$ is set to 5, following Ortiz et al. (); Wang et al. (). Due to the presence of noisy depth images, $\mathcal{L}_{\text{sdf}}$ and $\mathcal{L}_{\text{free}}$ are applied only to rays with valid depth values.

In our experiments, we adopt a similar weighting scheme to GO-Surf (Wang et al., ), setting $\lambda_{C}=10.0$, $\lambda_{D}=1.0$, $\lambda_{\text{sdf}}=10.0$, and $\lambda_{\text{free}}=1.0$. We observe that the Eikonal term can lead to overly smooth reconstructions, so we use a small weight of $0.01$ for the Eikonal loss.

## Appendix B Evaluation Setups

Here we detail the setups of our large-scale evaluation in Sec. 3.

### B.1 Single-Task Benchmarks

VC-1 (Majumdar et al., ). This benchmark includes several simulators. We selected four: Adroit (Kumar, ), Meta-World (Yu et al., ), DMControl (Tunyasuvunakool et al., ), and TriFinger (Wüthrich et al., ). The Adroit subset focuses on dexterous manipulation with 2 tasks. The Meta-World subset addresses two-finger gripper manipulation with 5 tasks. The DMControl subset is for locomotion control, also with 5 tasks. The TriFinger subset targets three-finger manipulation with 2 tasks. For all tasks, we use a 3-layer MLP as the policy network for each single-task training, following the original implementation. Each task is trained with 100 demonstrations, except for 25 on Meta-World, and evaluated 50 times using the specific seeds 100, 200, and 300. The [CLS] token of a frozen pre-trained ViT is used as the observation feature. All hyper-parameters are kept the same with the original implementation.

Franka Kitchen (Gupta et al., ).
Franka-Kitchen is a MuJoCo-modeled simulation environment with a Franka robot in a kitchen scene. Its action space is the 9-dimensional joint velocity with 7 DoF for the arm and 2 DoF for the gripper. Following previous works (Nair et al., ; Karamcheti et al., ), we evaluate five tasks: Sliding Door, Turning Light On, Opening Door, Turning Knob, and Opening Microwave. Each task spans two camera viewpoints and three random seeds. Similar to the evaluation scheme in VC-1, we utilize 25 demonstrations to train a policy model, which is a 2-layer MLP with hidden sizes [256, 256] preceded by a BatchNorm.

Meta-World (Yu et al., ). This benchmark comprises a series of tasks in which an agent directs a Sawyer robot arm to manipulate objects in a tabletop environment. We selected 48 tasks, encompassing easy, medium, and hard levels. We implemented the Diffusion Policy (Chi et al., ) on this benchmark and adhered to the setup in Ze et al. () to generate 10 demonstrations for each single-task training, followed by evaluation through 20 rollouts. The average results across three fixed seeds (100, 200, 300) are reported. The [CLS] token from a frozen pre-trained ViT serves as the observation feature.

### B.2 Language-Conditioned Multi-Task Benchmarks

RLBench (James et al., ). This benchmark is a prominent language-conditioned multi-task robot learning framework. PolarNet (Chen et al., ) has categorized all tasks into 9 groups. We selected 71 tasks from RLBench that can be successfully executed and split them into two groups uniformly on categories: Group 1 with 35 tasks and Group 2 with 36 tasks. Each task includes 100 training demonstrations and 25 testing rollouts. For each group, we train a language-conditioned multi-task agent. We employ RVT-2 (Goyal et al., ), the state-of-the-art (SOTA) method on this benchmark, as our policy. RVT-2 takes multiple images rendered from point clouds as inputs and uses a convolutional block to generate feature maps. We substitute the convolutional block with different pre-trained ViTs, unpatchifying the latent vectors concatenated with the global [CLS] token to obtain feature maps. All other architectures and hyperparameters remain consistent with the original RVT-2 implementation.

LIBERO (Liu et al., ). Built upon Robosuite (Zhu et al., ), LIBERO (Liu et al., ) generates a total of 130 language-conditioned tasks across five suites: LIBERO-Spatial, LIBERO-Object, LIBERO-Goal, LIBERO-10, and LIBERO-90. Each suite contains 10 tasks, except for LIBERO-90, which includes 90 tasks. We train a language-conditioned multi-task policy for each suite, adopting the transformer policy provided by LIBERO. The image encoders are modified from default CNNs to frozen pre-trained ViTs, utilizing the [CLS] token for feature extraction. To expedite policy training, we use only 20 demonstrations per task and forgo augmentations, allowing for pre-extraction of all image features during training. After training for 25 epochs, the checkpoints from the 20th and 25th are evaluated with 20 rollouts per task, and the best checkpoint’s performance is taken. Finally, the results are averaged on 3 random seeds.

## Appendix C More Implementation Details

### C.1 Dataset Details

The datasets used for SPA include ScanNet, ScanNet++, Hypersim, ADT, S3DIS, and Droid.

ScanNet consists of 1.89 million frames in total. Each epoch includes 1.5 times the dataset size. For each scene, a random starting frame is selected, followed by the sampling of 1 to 8 frames at random, with an interval of 8 frames between them.

ScanNet++ comprises 0.11 million frames. Each epoch includes 5 times the dataset size. For each scene, a random starting frame is selected, followed by the sampling of 1 to 8 frames at random, with an interval of 5 frames between them.

Hypersim contains 0.03 million frames. Each epoch includes 8 times the dataset size. For each scene, we randomly select 1 to 8 continuous frames.

ADT consists of 0.0015M frames in total. Each epoch includes 1 times the dataset size. For each scene, 1 to 8 continuous frames are randomly selected.

S3DIS consists of 0.015 million frames. Each epoch includes 5 times the dataset size. For each scene, a random starting frame is selected, followed by the sampling of 1 to 8 frames at random, with an interval of 5 frames between them.

Droid contains a large number of videos, but due to the high similarity between frames, the videos are first downsampled by a factor of 15 during pre-processing, resulting in 1.78 million frames. Since Droid does not provide depth data, we utilize Croco-Stereo Weinzaepfel et al. () to estimate dense depth maps for rendering supervision. Additionally, due to the significant noise in the camera pose data, only a single frame is sampled at a time during training.

During pre-training, we first resize the multi-view input images to slightly larger than $224\times 224$, and then randomly crop them to a final size of $224\times 224$. Random photometric distortions with a probability of $0.5$ are applied for augmentation, including brightness ranging from 0.875 to 1.125, contrast ranging from 0.5 to 1.5, saturation ranging from 0.5 to 1.5, and hue ranging from -0.05 to 0.05. Frames with very small valid depth areas or scene boxes are filtered out.

For semantic rendering supervision, we observe that using larger image sizes improves the quality of feature maps generated by RADIO. Consequently, we resize the images to $1024\times 1024$ before feeding them into RADIO, which outputs a feature map of size $64\times 64$. We then apply bilinear sampling to query the semantic feature labels for each pixel.

### C.2 Pre-Training Details

For stability during pre-training, we apply the Exponential Moving Average (EMA) with a decay rate of 0.999. The model is trained for 2000 epochs on 80 NVIDIA A100-80G GPUs, using a gradient clipping threshold of 1.0. Each GPU processes a batch size of 2, with 8 gradient accumulation steps, resulting in a total effective batch size of $2\times 80\times 8=1280$. We employ the AdamW optimizer with a weight decay of 0.04. The base learning rate is set to $5\times 10^{-6}$, and the actual learning rate is scaled by a factor of 8 times the effective batch size. A OneCycle learning rate scheduler is used, with a percentage start of 0.05, a divide factor of 100, and a final divide factor of 1000.

To facilitate faster convergence and improve stability, we initialize the encoder with ImageNet pre-trained weights from the Masked Autoencoder (MAE), applying a learning rate layer decay of 0.8. This initialization does not affect the validity of our conclusions, as demonstrated by the ablation study of SPA-MAE in Sec. 5.3. The ViT encoder and upsampling layers are trained with FP16 precision, while the volume decoder is trained with FP32 precision.

We set the loss weights to $\lambda_{\text{color}}=10$, $\lambda_{\text{depth}}=1$, $\lambda_{\text{semantic}}=1$, $\lambda_{\text{eikonal}}=0.01$, $\lambda_{\text{free}}=1$, and $\lambda_{\text{sdf}}=10$. For the NeuS sampler, the initial number of samples is set to 72, with 24 importance samples. In each iteration, we randomly sample $512$ pixels per view for rendering and supervision.

## Appendix D Detailed Results of Each Task

We present the results of all individual tasks in Tab. 9, Tab. 10, Tab. 11, Tab. 12, Tab. 13, and Tab. 14.

## Appendix E Camera Pose Estimation Details

We adopt a setup similar to that of El Banani et al. () for camera pose estimation using the NAVI dataset (Jampani et al., ). Given an image pair from different viewpoints, we first extract features from each image using a frozen, pre-trained Vision Transformer (ViT) encoder. Following standard protocols for embodied evaluation, we use the [CLS] token as the feature representation. The two [CLS] tokens are then concatenated and passed through a BatchNorm layer and a Multi-Layer Perceptron (MLP) to regress the camera pose. The MLP consists of four linear layers with three ReLU activations, using hidden sizes of 512, 256, and 128 units, and outputs a 7-dimensional pose vector. The first three dimensions represent the $xyz$ translation, while the last four dimensions correspond to the rotation quaternions.

We employ the Mean Squared Error (MSE) loss function and optimize the model using the AdamW optimizer with a OneCycle learning rate scheduler. The model is trained for 100 epochs with a base learning rate of $1\times 10^{-3}$ and a starting percentage of 0.1. For evaluation, we use Euclidean distance as the translation error metric and geodesic distance as the rotation error metric. The geodesic distance between two quaternions $q_{1}$ and $q_{2}$ is defined as:

$$ $\theta=2\cdot\arccos\mathopen{}\mathclose{{}\left(\mathopen{}\mathclose{{} \left|q_{1}\cdot q_{2}}\right|}\right),$ (13) $$

where $q_{1}$ and $q_{2}$ are normalized quaternions, and $\cdot$ denotes the quaternion dot product.
The Euclidean distance $d$ between two translation vectors $\mathbf{t}_{1}=(x_{1},y_{1},z_{1})$ and $\mathbf{t}_{2}=(x_{2},y_{2},z_{2})$ is given by:

$$ $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}.$ (14) $$

## Appendix F Real-World Experiment Details

Our real-world hardware setup is based on the open-source Low-Cost-Robot project (Koch, ). We utilize two Intel RealSense D415 cameras for image capture. A visualization of our platform is provided in Fig. 7. For teleoperation, policy training, and evaluation, we leverage the open-source RealRobot project (Contributors, ). The policy used is the ACT policy (Zhao et al., ).

For each task, we collect 50 demonstrations, and during evaluation, we conduct 25 rollouts, each with randomized object locations and orientations. The model is trained for 10,000 epochs using four NVIDIA A100 GPUs. We employ the AdamW optimizer with a learning rate of $5\times 10^{-5}$ and a weight decay of 0.05. Additionally, a OneCycle learning rate scheduler is used, with a starting percentage of 0.1, a division factor of 10, and a final division factor of 100.

Figure: Figure 7: Real-world hardware platform.
Refer to caption: x7.png

**Table 9: All results on Vc-1 benchmarks.**
| Benchmark | AD | MW | DMC | TF |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Methods | Seed | Relo-<br>cate | Pen | Button<br>Press<br>Topdown | Drawer<br>Open | Bin<br>Picking | Ham-<br>mer | Assem-<br>bly | Walker<br>Stand | Walker<br>Walk | Reacher<br>Easy | Cheetah<br>Run | Finger<br>Spin | Reach<br>Cube | Move<br>Cube |
| ViT-L Methods |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| MoCoV3 | 100 | 40.00 | 92.00 | 88.00 | 100.00 | 88.00 | 100.00 | 88.00 | 84.88 | 57.59 | 92.29 | 56.28 | 70.49 | 84.37 | 61.20 |
| 200 | 36.00 | 80.00 | 88.00 | 100.00 | 80.00 | 100.00 | 84.00 | 82.95 | 55.02 | 92.08 | 43.17 | 69.49 | 84.20 | 61.26 |  |
| 300 | 28.00 | 76.00 | 84.00 | 100.00 | 68.00 | 92.00 | 72.00 | 81.42 | 53.59 | 91.96 | 41.27 | 68.23 | 84.09 | 64.24 |  |
| MAE | 100 | 36.00 | 84.00 | 84.00 | 100.00 | 88.00 | 100.00 | 100.00 | 951.27 | 680.69 | 976.50 | 482.47 | 703.30 | 85.46 | 59.46 |
| 200 | 36.00 | 80.00 | 84.00 | 100.00 | 76.00 | 96.00 | 96.00 | 933.67 | 676.92 | 952.20 | 49.22 | 695.00 | 86.88 | 59.45 |  |
| 300 | 32.00 | 80.00 | 68.00 | 100.00 | 72.00 | 98.00 | 88.00 | 873.53 | 659.41 | 895.60 | 501.91 | 691.80 | 85.26 | 61.69 |  |
| DINOV2 | 100 | 32.00 | 68.00 | 68.00 | 100.00 | 84.00 | 100.00 | 88.00 | 87.01 | 56.52 | 94.50 | 26.98 | 70.87 | 86.16 | 50.84 |
| 200 | 28.00 | 68.00 | 60.00 | 100.00 | 80.00 | 96.00 | 80.00 | 86.00 | 53.97 | 89.97 | 21.84 | 68.78 | 86.87 | 50.78 |  |
| 300 | 28.00 | 60.00 | 60.00 | 100.00 | 80.00 | 92.00 | 72.00 | 82.41 | 51.69 | 88.36 | 21.34 | 67.41 | 86.05 | 50.17 |  |
| CLIP | 100 | 24.00 | 80.00 | 28.00 | 100.00 | 88.00 | 100.00 | 84.00 | 66.16 | 43.94 | 90.71 | 18.40 | 68.30 | 73.28 | 41.09 |
| 200 | 24.00 | 72.00 | 24.00 | 100.00 | 84.00 | 100.00 | 80.00 | 64.04 | 34.51 | 88.26 | 16.52 | 66.68 | 75.11 | 33.45 |  |
| 300 | 24.00 | 68.00 | 16.00 | 100.00 | 84.00 | 96.00 | 72.00 | 52.70 | 31.60 | 85.17 | 14.51 | 67.49 | 74.73 | 38.95 |  |
| EVA | 100 | 44.00 | 84.00 | 72.00 | 100.00 | 76.00 | 100.00 | 100.00 | 77.92 | 51.64 | 98.17 | 31.04 | 70.17 | 82.56 | 52.04 |
| 200 | 40.00 | 76.00 | 84.00 | 100.00 | 72.00 | 100.00 | 100.00 | 77.63 | 50.81 | 86.66 | 19.37 | 67.43 | 81.72 | 52.07 |  |
| 300 | 32.00 | 72.00 | 96.00 | 100.00 | 68.00 | 96.00 | 96.00 | 77.21 | 47.71 | 88.41 | 29.19 | 67.43 | 82.13 | 52.70 |  |
| InternViT-<br>300M | 100 | 40.00 | 72.00 | 80.00 | 100.00 | 72.00 | 100.00 | 84.00 | 70.04 | 30.44 | 80.80 | 16.70 | 67.05 | 78.59 | 53.67 |
| 200 | 28.00 | 72.00 | 68.00 | 100.00 | 76.00 | 96.00 | 84.00 | 67.63 | 31.55 | 82.33 | 19.39 | 67.57 | 77.07 | 55.21 |  |
| 300 | 28.00 | 80.00 | 60.00 | 100.00 | 72.00 | 96.00 | 72.00 | 66.95 | 29.28 | 81.87 | 18.80 | 68.55 | 78.27 | 48.58 |  |
| InternViT-<br>6B | 100 | 32.00 | 72.00 | 88.00 | 100.00 | 80.00 | 100.00 | 84.00 | 88.53 | 70.02 | 93.09 | 26.54 | 70.62 | 85.96 | 57.52 |
| 200 | 40.00 | 76.00 | 84.00 | 100.00 | 76.00 | 100.00 | 80.00 | 85.28 | 60.09 | 90.86 | 22.84 | 69.04 | 86.30 | 54.11 |  |
| 300 | 60.00 | 80.00 | 80.00 | 100.00 | 88.00 | 100.00 | 76.00 | 81.88 | 59.17 | 87.87 | 21.53 | 67.20 | 85.68 | 54.86 |  |
| MVP | 100 | 32.00 | 84.00 | 96.00 | 100.00 | 96.00 | 100.00 | 100.00 | 84.88 | 57.59 | 92.29 | 56.28 | 70.49 | 84.37 | 61.20 |
| 200 | 28.00 | 76.00 | 92.00 | 100.00 | 84.00 | 100.00 | 96.00 | 82.95 | 55.02 | 92.08 | 43.17 | 69.49 | 84.20 | 61.26 |  |
| 300 | 24.00 | 76.00 | 84.00 | 100.00 | 68.00 | 100.00 | 88.00 | 81.42 | 53.59 | 91.96 | 41.27 | 68.23 | 84.09 | 64.24 |  |
| VC-1 | 100 | 32.00 | 84.00 | 84.00 | 100.00 | 76.00 | 96.00 | 96.00 | 82.36 | 55.33 | 98.09 | 35.31 | 72.60 | 83.36 | 58.00 |
| 200 | 28.00 | 80.00 | 68.00 | 100.00 | 72.00 | 92.00 | 84.00 | 80.21 | 53.90 | 89.83 | 34.10 | 70.15 | 83.17 | 61.00 |  |
| 300 | 24.00 | 76.00 | 76.00 | 100.00 | 96.00 | 88.00 | 84.00 | 68.62 | 50.13 | 87.89 | 31.18 | 70.11 | 82.75 | 57.16 |  |
| SPA-L | 100 | 40.00 | 88.00 | 76.00 | 100.00 | 92.00 | 100.00 | 100.00 | 94.19 | 66.34 | 95.57 | 52.53 | 73.95 | 87.37 | 56.68 |
| 200 | 44.00 | 76.00 | 84.00 | 100.00 | 88.00 | 100.00 | 84.00 | 92.28 | 60.60 | 81.43 | 44.99 | 71.83 | 87.26 | 64.35 |  |
| 300 | 36.00 | 76.00 | 96.00 | 100.00 | 88.00 | 96.00 | 96.00 | 87.87 | 51.75 | 83.86 | 39.10 | 70.91 | 87.62 | 58.02 |  |
| ViT-B Methods and Others |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| STP-B | 100 | 20.00 | 80.00 | 88.00 | 100.00 | 84.00 | 100.00 | 96.00 | 77.02 | 45.34 | 87.97 | 40.01 | 72.72 | 80.41 | 54.66 |
| 200 | 28.00 | 76.00 | 92.00 | 100.00 | 84.00 | 100.00 | 80.00 | 71.50 | 33.60 | 84.08 | 34.30 | 72.18 | 80.13 | 57.97 |  |
| 300 | 32.00 | 76.00 | 88.00 | 100.00 | 72.00 | 100.00 | 96.00 | 71.44 | 42.86 | 79.67 | 39.17 | 69.12 | 80.65 | 53.95 |  |
| R3M-B | 100 | 20.00 | 92.00 | 52.00 | 96.00 | 32.00 | 88.00 | 48.00 | 668.49 | 301.54 | 842.90 | 256.56 | 678.00 | 75.08 | 45.66 |
| 200 | 12.00 | 76.00 | 48.00 | 96.00 | 32.00 | 88.00 | 44.00 | 634.62 | 256.82 | 661.40 | 198.63 | 660.90 | 75..62 | 48.09 |  |
| 300 | 12.00 | 76.00 | 32.00 | 88.00 | 28.00 | 76.00 | 40.00 | 633.39 | 211.90 | 585.50 | 188.15 | 657.30 | 74.54 | 45.59 |  |
| Theia-B | 100 | 32.00 | 76.00 | 88.00 | 100.00 | 80.00 | 96.00 | 96.00 | 72.90 | 43.97 | 82.09 | 37.02 | 70.50 | 84.55 | 55.62 |
| 200 | 36.00 | 80.00 | 60.00 | 100.00 | 84.00 | 100.00 | 84.00 | 79.05 | 56.99 | 94.36 | 39.59 | 70.22 | 83.27 | 54.59 |  |
| 300 | 24.00 | 72.00 | 80.00 | 100.00 | 72.00 | 96.00 | 100.00 | 79.64 | 54.39 | 82.89 | 39.09 | 72.00 | 84.01 | 54.43 |  |
| Voltron-B | 100 | 16.00 | 72.00 | 76.00 | 100.00 | 64.00 | 100.00 | 96.00 | 74.31 | 42.05 | 68.88 | 36.94 | 70.91 | 86.28 | 65.11 |
| 200 | 32.00 | 72.00 | 76.00 | 100.00 | 60.00 | 96.00 | 88.00 | 71.57 | 38.17 | 67.53 | 31.01 | 70.17 | 86.61 | 62.39 |  |
| 300 | 20.00 | 68.00 | 72.00 | 100.00 | 52.00 | 96.00 | 84.00 | 71.25 | 36.50 | 66.14 | 30.11 | 69.88 | 86.16 | 59.02 |  |
| MAE-B | 100 | 24.00 | 88.00 | 88.00 | 100.00 | 84.00 | 96.00 | 96.00 | 88.28 | 42.55 | 95.18 | 44.08 | 69.26 | 85.63 | 55.68 |
| 200 | 28.00 | 76.00 | 84.00 | 100.00 | 84.00 | 88.00 | 88.00 | 77.13 | 38.49 | 88.22 | 32.75 | 69.02 | 85.14 | 56.81 |  |
| 300 | 28.00 | 72.00 | 76.00 | 100.00 | 80.00 | 88.00 | 80.00 | 75.60 | 36.93 | 78.35 | 31.03 | 69.01 | 84.11 | 57.30 |  |
| DINOV2-B | 100 | 8.00 | 60.00 | 40.00 | 100.00 | 44.00 | 96.00 | 20.00 | 45.95 | 16.61 | 63.57 | 13.38 | 60.11 | 74.07 | 36.29 |
| 200 | 8.00 | 68.00 | 40.00 | 100.00 | 64.00 | 88.00 | 16.00 | 37.96 | 15.81 | 51.44 | 12.59 | 59.56 | 74.18 | 32.14 |  |
| 300 | 12.00 | 64.00 | 48.00 | 100.00 | 64.00 | 88.00 | 4.00 | 32.43 | 14.31 | 36.01 | 11.67 | 56.54 | 73.77 | 36.53 |  |
| VC-1-B | 100 | 20.00 | 76.00 | 76.00 | 100.00 | 76.00 | 100.00 | 76.00 | 72.35 | 43.14 | 92.77 | 27.31 | 68.67 | 84.19 | 62.00 |
| 200 | 32.00 | 80.00 | 68.00 | 100.00 | 76.00 | 100.00 | 92.00 | 81.83 | 44.05 | 83.62 | 27.80 | 70.98 | 83.88 | 59.63 |  |
| 300 | 24.00 | 68.00 | 80.00 | 100.00 | 80.00 | 88.00 | 88.00 | 83.01 | 41.25 | 77.60 | 28.53 | 70.89 | 84.76 | 59.51 |  |
| RADIO | 100 | 28.00 | 76.00 | 48.00 | 100.00 | 72.00 | 100.00 | 84.00 | 87.84 | 62.72 | 96.53 | 15.71 | 67.88 | 85.70 | 57.52 |
| 200 | 36.00 | 76.00 | 44.00 | 100.00 | 72.00 | 96.00 | 52.00 | 80.26 | 57.39 | 95.93 | 15.26 | 67.51 | 85.67 | 57.81 |  |
| 300 | 44.00 | 72.00 | 32.00 | 100.00 | 40.00 | 92.00 | 48.00 | 79.62 | 53.51 | 89.16 | 14.80 | 66.57 | 85.64 | 58.14 |  |
| E-RADIO | 100 | 32.00 | 84.00 | 64.00 | 100.00 | 84.00 | 96.00 | 96.00 | 71.47 | 53.41 | 93.01 | 50.19 | 70.75 | 87.17 | 46.97 |
| 200 | 32.00 | 84.00 | 60.00 | 100.00 | 68.00 | 88.00 | 96.00 | 68.80 | 44.56 | 88.54 | 33.19 | 70.46 | 87.39 | 50.72 |  |
| 300 | 28.00 | 80.00 | 60.00 | 100.00 | 72.00 | 88.00 | 80.00 | 65.96 | 33.56 | 98.14 | 32.64 | 69.18 | 87.09 | 51.31 |  |
| SPA-B | 100 | 20.00 | 84.00 | 84.00 | 100.00 | 88.00 | 100.00 | 100.00 | 80.50 | 45.08 | 91.38 | 48.90 | 71.16 | 86.04 | 59.03 |
| 200 | 28.00 | 80.00 | 68.00 | 100.00 | 84.00 | 100.00 | 84.00 | 79.71 | 46.65 | 85.75 | 40.84 | 71.01 | 86.16 | 60.05 |  |
| 300 | 24.00 | 80.00 | 88.00 | 100.00 | 92.00 | 100.00 | 92.00 | 74.70 | 48.97 | 81.60 | 34.92 | 71.16 | 85.16 | 61.94 |  |

**Table 10: All results on Franka Kitchen.**
| Task | View | Seed | MoCoV3 | MAE | DINOV2 | CLIP | EVA | InternViT-<br>300M | MVP | VC-1 | SPA |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Task 1 | Left | 100 | 86.00 | 76.00 | 84.00 | 72.00 | 78.00 | 74.00 | 66.00 | 74.00 | 84.00 |
| 200 | 78.00 | 78.00 | 74.00 | 72.00 | 76.00 | 72.00 | 58.00 | 74.00 | 92.00 |  |  |
| 300 | 80.00 | 80.00 | 78.00 | 62.00 | 82.00 | 70.00 | 64.00 | 74.00 | 80.00 |  |  |
| Right | 100 | 82.00 | 80.00 | 86.00 | 78.00 | 78.00 | 72.00 | 82.00 | 78.00 | 86.00 |  |
| 200 | 88.00 | 62.00 | 90.00 | 70.00 | 86.00 | 86.00 | 86.00 | 84.00 | 72.00 |  |  |
| 300 | 86.00 | 82.00 | 92.00 | 82.00 | 86.00 | 76.00 | 92.00 | 78.00 | 86.00 |  |  |
| Task 2 | Left | 100 | 60.00 | 56.00 | 48.00 | 26.00 | 40.00 | 22.00 | 40.00 | 32.00 | 48.00 |
| 200 | 64.00 | 60.00 | 46.00 | 44.00 | 40.00 | 32.00 | 32.00 | 42.00 | 60.00 |  |  |
| 300 | 58.00 | 54.00 | 40.00 | 26.00 | 32.00 | 34.00 | 30.00 | 50.00 | 66.00 |  |  |
| Right | 100 | 62.00 | 54.00 | 56.00 | 26.00 | 44.00 | 26.00 | 32.00 | 54.00 | 48.00 |  |
| 200 | 64.00 | 54.00 | 60.00 | 36.00 | 40.00 | 24.00 | 28.00 | 56.00 | 42.00 |  |  |
| 300 | 64.00 | 52.00 | 50.00 | 38.00 | 40.00 | 30.00 | 34.00 | 44.00 | 42.00 |  |  |
| Task 3 | Left | 100 | 16.00 | 24.00 | 18.00 | 18.00 | 22.00 | 24.00 | 6.00 | 24.00 | 28.00 |
| 200 | 28.00 | 20.00 | 14.00 | 18.00 | 20.00 | 16.00 | 6.00 | 30.00 | 38.00 |  |  |
| 300 | 22.00 | 16.00 | 14.00 | 10.00 | 26.00 | 22.00 | 8.00 | 26.00 | 30.00 |  |  |
| Right | 100 | 46.00 | 26.00 | 38.00 | 22.00 | 14.00 | 8.00 | 32.00 | 12.00 | 10.00 |  |
| 200 | 48.00 | 22.00 | 38.00 | 24.00 | 18.00 | 4.00 | 32.00 | 12.00 | 12.00 |  |  |
| 300 | 54.00 | 34.00 | 52.00 | 14.00 | 12.00 | 6.00 | 26.00 | 14.00 | 16.00 |  |  |
| Task 4 | Left | 100 | 32.00 | 36.00 | 26.00 | 22.00 | 34.00 | 12.00 | 16.00 | 36.00 | 22.00 |
| 200 | 30.00 | 30.00 | 32.00 | 14.00 | 20.00 | 8.00 | 14.00 | 24.00 | 10.00 |  |  |
| 300 | 24.00 | 46.00 | 28.00 | 14.00 | 32.00 | 4.00 | 20.00 | 36.00 | 16.00 |  |  |
| Right | 100 | 38.00 | 24.00 | 28.00 | 22.00 | 32.00 | 12.00 | 26.00 | 12.00 | 30.00 |  |
| 200 | 42.00 | 24.00 | 24.00 | 24.00 | 24.00 | 12.00 | 30.00 | 8.00 | 38.00 |  |  |
| 300 | 46.00 | 16.00 | 32.00 | 28.00 | 36.00 | 16.00 | 26.00 | 12.00 | 30.00 |  |  |
| Task 5 | Left | 100 | 36.00 | 18.00 | 8.00 | 16.00 | 24.00 | 22.00 | 26.00 | 28.00 | 20.00 |
| 200 | 30.00 | 24.00 | 8.00 | 10.00 | 24.00 | 16.00 | 20.00 | 22.00 | 16.00 |  |  |
| 300 | 22.00 | 22.00 | 10.00 | 12.00 | 16.00 | 14.00 | 28.00 | 30.00 | 18.00 |  |  |
| Right | 100 | 24.00 | 46.00 | 20.00 | 4.00 | 14.00 | 10.00 | 26.00 | 22.00 | 30.00 |  |
| 200 | 24.00 | 30.00 | 16.00 | 8.00 | 18.00 | 18.00 | 22.00 | 22.00 | 26.00 |  |  |
| 300 | 14.00 | 36.00 | 16.00 | 12.00 | 10.00 | 12.00 | 20.00 | 16.00 | 22.00 |  |  |

**Table 11: All results on Meta-World.**
| Method | MoCoV3 | MAE | DINOV2 | CLIP | EVA | InternViT-<br>300M | MVP | VC-1 | SPA |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Seed | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 |
| ButtonPressWall | 100 | 100 | 100 | 100 | 100 | 100 | 95 | 90 | 95 | 100 | 100 | 100 | 95 | 95 | 100 | 95 | 100 | 95 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| DoorClose | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| DoorUnlock | 70 | 65 | 80 | 70 | 65 | 85 | 35 | 35 | 30 | 60 | 50 | 60 | 85 | 85 | 90 | 80 | 65 | 75 | 75 | 70 | 85 | 80 | 75 | 90 | 80 | 75 | 80 |
| DrawerClose | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| DrawerOpen | 80 | 70 | 85 | 85 | 65 | 75 | 60 | 40 | 60 | 90 | 80 | 80 | 60 | 55 | 75 | 70 | 75 | 75 | 95 | 75 | 85 | 85 | 85 | 80 | 90 | 60 | 75 |
| FaucetClose | 70 | 80 | 55 | 60 | 80 | 60 | 55 | 65 | 35 | 70 | 80 | 50 | 65 | 75 | 60 | 50 | 65 | 50 | 70 | 75 | 60 | 65 | 75 | 100 | 70 | 80 | 65 |
| PlateSlide | 90 | 95 | 100 | 95 | 100 | 100 | 65 | 70 | 80 | 85 | 95 | 80 | 100 | 100 | 100 | 85 | 95 | 90 | 100 | 100 | 100 | 100 | 95 | 100 | 95 | 95 | 95 |
| PlateSlideBack | 80 | 65 | 85 | 85 | 65 | 85 | 90 | 75 | 90 | 85 | 75 | 90 | 80 | 65 | 90 | 85 | 80 | 90 | 85 | 70 | 90 | 80 | 70 | 90 | 80 | 70 | 85 |
| PlateSlideSide | 85 | 90 | 95 | 95 | 90 | 95 | 90 | 85 | 85 | 80 | 85 | 95 | 100 | 95 | 100 | 90 | 95 | 90 | 80 | 90 | 95 | 100 | 95 | 90 | 90 | 90 | 95 |
| WindowClose | 100 | 100 | 100 | 100 | 100 | 100 | 70 | 90 | 100 | 100 | 100 | 95 | 95 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| Basketball | 85 | 95 | 95 | 95 | 100 | 100 | 70 | 55 | 65 | 85 | 85 | 70 | 95 | 85 | 80 | 90 | 80 | 95 | 95 | 100 | 95 | 90 | 100 | 95 | 95 | 100 | 100 |
| BinPicking | 30 | 45 | 40 | 20 | 10 | 35 | 10 | 15 | 10 | 30 | 30 | 25 | 20 | 5 | 45 | 10 | 10 | 10 | 25 | 20 | 15 | 30 | 30 | 30 | 40 | 25 | 30 |
| BoxClose | 80 | 80 | 80 | 75 | 80 | 70 | 35 | 45 | 30 | 80 | 70 | 60 | 55 | 70 | 55 | 60 | 65 | 40 | 80 | 80 | 65 | 80 | 95 | 60 | 80 | 80 | 65 |
| CoffeePush | 45 | 50 | 40 | 40 | 55 | 30 | 30 | 25 | 15 | 45 | 40 | 55 | 45 | 35 | 40 | 45 | 30 | 25 | 25 | 45 | 25 | 30 | 45 | 55 | 35 | 40 | 30 |
| Assembly | 70 | 60 | 55 | 55 | 65 | 45 | 30 | 35 | 25 | 45 | 55 | 50 | 45 | 50 | 40 | 30 | 25 | 30 | 60 | 60 | 45 | 60 | 60 | 50 | 50 | 55 | 50 |
| Disassemble | 40 | 55 | 50 | 30 | 45 | 45 | 30 | 20 | 45 | 55 | 50 | 60 | 30 | 50 | 50 | 40 | 45 | 50 | 40 | 45 | 45 | 40 | 30 | 35 | 40 | 45 | 55 |
| PushWall | 25 | 35 | 30 | 20 | 30 | 40 | 40 | 30 | 45 | 35 | 30 | 35 | 25 | 35 | 30 | 15 | 15 | 25 | 30 | 35 | 35 | 55 | 55 | 60 | 30 | 40 | 45 |
| ShelfPlace | 35 | 35 | 20 | 25 | 45 | 20 | 30 | 30 | 35 | 30 | 35 | 30 | 25 | 20 | 15 | 15 | 15 | 15 | 25 | 25 | 15 | 25 | 15 | 15 | 15 | 35 | 15 |
| DoorOpen | 95 | 90 | 90 | 100 | 95 | 95 | 95 | 80 | 95 | 85 | 75 | 90 | 80 | 90 | 100 | 50 | 55 | 60 | 80 | 75 | 95 | 95 | 95 | 95 | 85 | 100 | 95 |
| ButtonPress | 75 | 85 | 85 | 85 | 100 | 100 | 80 | 95 | 85 | 55 | 70 | 75 | 80 | 90 | 90 | 85 | 90 | 80 | 85 | 90 | 95 | 80 | 90 | 85 | 100 | 95 | 100 |
| SweepInto | 45 | 45 | 40 | 55 | 55 | 45 | 50 | 50 | 40 | 45 | 45 | 40 | 45 | 25 | 30 | 35 | 25 | 30 | 45 | 50 | 40 | 55 | 50 | 50 | 50 | 50 | 45 |
| DoorLock | 100 | 85 | 85 | 90 | 100 | 100 | 95 | 90 | 85 | 85 | 85 | 75 | 95 | 100 | 95 | 80 | 90 | 95 | 85 | 100 | 95 | 100 | 100 | 90 | 80 | 95 | 85 |
| ReachWall | 70 | 70 | 80 | 75 | 85 | 70 | 85 | 80 | 85 | 90 | 90 | 80 | 65 | 75 | 85 | 60 | 55 | 55 | 75 | 65 | 75 | 75 | 80 | 80 | 75 | 80 | 70 |
| Hammer | 25 | 45 | 30 | 30 | 30 | 30 | 40 | 45 | 35 | 25 | 35 | 25 | 30 | 35 | 20 | 20 | 20 | 20 | 30 | 35 | 30 | 45 | 40 | 55 | 30 | 40 | 30 |
| StickPush | 95 | 95 | 100 | 80 | 90 | 95 | 90 | 90 | 90 | 75 | 85 | 85 | 90 | 85 | 100 | 60 | 80 | 85 | 90 | 95 | 90 | 85 | 85 | 95 | 90 | 90 | 85 |
| ButtonPressTopdown | 80 | 80 | 75 | 80 | 85 | 80 | 80 | 90 | 90 | 80 | 90 | 70 | 55 | 65 | 55 | 45 | 55 | 55 | 80 | 85 | 80 | 75 | 80 | 70 | 80 | 85 | 80 |
| HandlePressSide | 100 | 100 | 100 | 100 | 100 | 100 | 95 | 100 | 90 | 80 | 100 | 90 | 100 | 100 | 95 | 85 | 100 | 90 | 95 | 100 | 100 | 75 | 100 | 80 | 90 | 100 | 100 |
| PlateSlideBackSide | 100 | 100 | 100 | 100 | 95 | 95 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| Sweep | 50 | 80 | 70 | 35 | 60 | 60 | 65 | 85 | 95 | 60 | 85 | 75 | 35 | 50 | 55 | 15 | 60 | 35 | 35 | 70 | 65 | 35 | 65 | 65 | 30 | 65 | 55 |
| ButtonPressTopdownWall | 45 | 70 | 80 | 45 | 75 | 75 | 70 | 75 | 75 | 45 | 60 | 70 | 30 | 45 | 65 | 20 | 55 | 45 | 30 | 60 | 70 | 50 | 85 | 80 | 45 | 65 | 75 |
| HandlePress | 85 | 95 | 95 | 80 | 100 | 75 | 75 | 100 | 80 | 90 | 100 | 90 | 85 | 100 | 85 | 65 | 90 | 75 | 80 | 95 | 75 | 85 | 100 | 90 | 85 | 100 | 80 |
| Push | 25 | 30 | 30 | 25 | 30 | 30 | 30 | 25 | 40 | 25 | 15 | 30 | 30 | 25 | 20 | 25 | 20 | 20 | 25 | 20 | 25 | 40 | 30 | 25 | 30 | 15 | 35 |
| CoffeePull | 55 | 55 | 55 | 40 | 45 | 40 | 20 | 30 | 20 | 50 | 70 | 40 | 40 | 45 | 45 | 40 | 40 | 25 | 55 | 55 | 40 | 55 | 55 | 60 | 55 | 55 | 55 |
| DialTurn | 80 | 65 | 80 | 85 | 75 | 75 | 40 | 30 | 35 | 80 | 95 | 90 | 65 | 65 | 80 | 70 | 70 | 55 | 70 | 65 | 75 | 80 | 95 | 75 | 85 | 85 | 75 |
| Reach | 90 | 75 | 80 | 90 | 75 | 80 | 70 | 75 | 85 | 95 | 95 | 100 | 85 | 80 | 75 | 95 | 80 | 90 | 80 | 70 | 75 | 70 | 80 | 80 | 85 | 70 | 85 |
| CoffeeButton | 85 | 95 | 75 | 100 | 100 | 95 | 85 | 80 | 60 | 95 | 100 | 85 | 90 | 100 | 95 | 90 | 85 | 85 | 100 | 100 | 90 | 90 | 100 | 80 | 100 | 100 | 100 |
| PickPlaceWall | 45 | 35 | 65 | 40 | 25 | 45 | 15 | 10 | 20 | 35 | 40 | 50 | 20 | 25 | 35 | 30 | 25 | 25 | 25 | 35 | 40 | 35 | 20 | 45 | 40 | 35 | 55 |
| StickPull | 35 | 35 | 25 | 15 | 40 | 20 | 25 | 10 | 5 | 45 | 40 | 45 | 25 | 35 | 15 | 25 | 25 | 15 | 15 | 30 | 25 | 30 | 30 | 30 | 25 | 35 | 30 |
| HandInsert | 35 | 30 | 30 | 30 | 25 | 25 | 20 | 20 | 20 | 45 | 45 | 40 | 20 | 25 | 20 | 25 | 30 | 25 | 40 | 40 | 35 | 40 | 30 | 40 | 40 | 50 | 40 |
| PegInsertSide | 40 | 35 | 40 | 50 | 35 | 45 | 25 | 15 | 10 | 45 | 30 | 20 | 45 | 25 | 30 | 30 | 20 | 25 | 45 | 45 | 30 | 50 | 25 | 35 | 55 | 45 | 60 |
| PickPlace | 35 | 30 | 30 | 25 | 45 | 15 | 15 | 10 | 10 | 25 | 15 | 30 | 25 | 30 | 25 | 30 | 10 | 30 | 20 | 35 | 25 | 25 | 20 | 20 | 25 | 30 | 40 |
| FaucetOpen | 95 | 95 | 100 | 100 | 100 | 100 | 80 | 80 | 100 | 100 | 95 | 100 | 95 | 95 | 100 | 80 | 85 | 95 | 100 | 100 | 100 | 100 | 100 | 100 | 95 | 100 | 100 |
| PushBack | 65 | 70 | 60 | 40 | 55 | 40 | 15 | 15 | 25 | 30 | 45 | 25 | 35 | 35 | 45 | 15 | 35 | 25 | 40 | 45 | 45 | 45 | 55 | 25 | 35 | 55 | 50 |
| LeverPull | 70 | 80 | 80 | 80 | 70 | 75 | 15 | 30 | 35 | 55 | 85 | 80 | 70 | 65 | 70 | 60 | 55 | 55 | 65 | 80 | 65 | 65 | 80 | 70 | 85 | 70 | 80 |
| HandlePull | 85 | 85 | 80 | 85 | 80 | 85 | 45 | 55 | 40 | 75 | 75 | 80 | 80 | 60 | 65 | 45 | 70 | 65 | 80 | 90 | 80 | 70 | 85 | 75 | 100 | 90 | 90 |
| Soccer | 25 | 40 | 35 | 50 | 30 | 25 | 15 | 10 | 15 | 45 | 40 | 30 | 35 | 35 | 25 | 20 | 20 | 30 | 30 | 30 | 35 | 20 | 20 | 20 | 25 | 50 | 25 |
| WindowOpen | 65 | 80 | 80 | 55 | 80 | 85 | 60 | 50 | 65 | 50 | 65 | 60 | 65 | 80 | 75 | 55 | 75 | 75 | 60 | 70 | 70 | 60 | 70 | 75 | 55 | 85 | 65 |
| PickOutOfHole | 65 | 75 | 80 | 65 | 65 | 60 | 60 | 55 | 60 | 70 | 70 | 50 | 60 | 55 | 50 | 60 | 55 | 55 | 65 | 55 | 60 | 70 | 75 | 60 | 65 | 60 | 75 |

**Table 12: All results on RLBench.**
| Method | MoCoV3 | MAE | DINOV2 | CLIP | EVA | InternViT<br>300M | MVP | VC-1 | SPA |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Group 1 |  |  |  |  |  |  |  |  |  |
| basketball in hoop | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| put rubbish in bin | 100 | 100 | 96 | 96 | 96 | 100 | 96 | 100 | 100 |
| meat off grill | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| meat on grill | 80 | 76 | 76 | 68 | 80 | 72 | 68 | 76 | 80 |
| slide block to target | 0 | 84 | 96 | 24 | 4 | 0 | 100 | 100 | 4 |
| reach and drag | 100 | 96 | 88 | 100 | 96 | 100 | 96 | 100 | 100 |
| take frame off hanger | 88 | 88 | 92 | 88 | 84 | 84 | 88 | 88 | 96 |
| water plants | 64 | 60 | 28 | 64 | 60 | 44 | 52 | 60 | 68 |
| hang frame on hanger | 8 | 4 | 0 | 4 | 8 | 8 | 12 | 4 | 4 |
| wipe desk | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| stack blocks | 60 | 72 | 72 | 68 | 56 | 60 | 84 | 68 | 68 |
| reach target | 60 | 96 | 88 | 100 | 96 | 80 | 92 | 96 | 92 |
| push button | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| lamp on | 88 | 68 | 84 | 88 | 52 | 80 | 28 | 88 | 64 |
| toilet seat down | 100 | 100 | 100 | 100 | 100 | 100 | 96 | 96 | 100 |
| close laptop lid | 96 | 96 | 96 | 96 | 84 | 80 | 80 | 96 | 100 |
| open box | 12 | 12 | 20 | 4 | 16 | 4 | 0 | 12 | 16 |
| open drawer | 88 | 96 | 92 | 100 | 88 | 88 | 92 | 96 | 96 |
| pick up cup | 92 | 92 | 88 | 96 | 96 | 88 | 96 | 96 | 96 |
| turn tap | 88 | 84 | 84 | 96 | 88 | 92 | 96 | 100 | 100 |
| take usb out of computer | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 88 | 100 |
| play jenga | 96 | 96 | 96 | 100 | 96 | 100 | 96 | 96 | 96 |
| insert onto square peg | 28 | 84 | 80 | 44 | 88 | 40 | 64 | 92 | 84 |
| take umbrella out of umbrella stand | 92 | 100 | 100 | 92 | 100 | 96 | 100 | 100 | 100 |
| insert usb in computer | 12 | 20 | 20 | 24 | 24 | 20 | 16 | 8 | 68 |
| straighten rope | 56 | 44 | 72 | 80 | 48 | 72 | 52 | 60 | 84 |
| turn oven on | 96 | 96 | 96 | 96 | 96 | 96 | 100 | 100 | 100 |
| change clock | 64 | 68 | 48 | 68 | 64 | 72 | 64 | 60 | 68 |
| close microwave | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| close fridge | 80 | 92 | 92 | 88 | 92 | 96 | 88 | 92 | 100 |
| close grill | 96 | 96 | 96 | 96 | 96 | 96 | 100 | 100 | 96 |
| open grill | 100 | 100 | 100 | 100 | 100 | 100 | 96 | 100 | 100 |
| unplug charger | 44 | 32 | 48 | 36 | 48 | 40 | 40 | 44 | 44 |
| press switch | 92 | 92 | 88 | 72 | 76 | 84 | 76 | 88 | 92 |
| take money out safe | 100 | 96 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| Group 2 |  |  |  |  |  |  |  |  |  |
| change channel | 0 | 8 | 4 | 0 | 0 | 4 | 0 | 0 | 4 |
| tv on | 4 | 8 | 0 | 4 | 4 | 8 | 4 | 4 | 8 |
| push buttons | 12 | 4 | 4 | 0 | 0 | 0 | 0 | 12 | 4 |
| stack wine | 12 | 16 | 40 | 4 | 12 | 0 | 28 | 8 | 28 |
| scoop with spatula | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| place hanger on rack | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| move hanger | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| sweep to dustpan | 92 | 96 | 96 | 96 | 92 | 100 | 100 | 88 | 96 |
| take plate off colored dish rack | 96 | 100 | 96 | 92 | 84 | 96 | 88 | 92 | 96 |
| screw nail | 52 | 36 | 36 | 36 | 36 | 52 | 32 | 32 | 48 |
| take shoes out of box | 20 | 28 | 24 | 36 | 40 | 12 | 32 | 36 | 36 |
| slide cabinet open and place cups | 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 4 |
| lamp off | 100 | 96 | 96 | 100 | 96 | 96 | 100 | 100 | 100 |
| pick and lift | 88 | 96 | 92 | 96 | 92 | 80 | 96 | 96 | 96 |
| take lid off saucepan | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| close drawer | 100 | 100 | 100 | 100 | 96 | 100 | 100 | 100 | 100 |
| close box | 92 | 92 | 96 | 96 | 100 | 96 | 100 | 96 | 100 |
| phone on base | 100 | 100 | 100 | 100 | 100 | 96 | 100 | 100 | 100 |
| toilet seat up | 80 | 88 | 100 | 88 | 88 | 80 | 88 | 92 | 96 |
| put books on bookshelf | 12 | 24 | 24 | 28 | 28 | 20 | 20 | 28 | 16 |
| beat the buzz | 88 | 92 | 96 | 88 | 92 | 84 | 88 | 88 | 100 |
| stack cups | 40 | 56 | 52 | 52 | 48 | 56 | 64 | 68 | 64 |
| put knife on chopping board | 72 | 76 | 68 | 72 | 80 | 88 | 80 | 76 | 80 |
| place shape in shape sorter | 20 | 36 | 32 | 28 | 36 | 20 | 44 | 36 | 56 |
| take toilet roll off stand | 100 | 92 | 76 | 96 | 92 | 88 | 84 | 92 | 96 |
| put umbrella in umbrella stand | 8 | 0 | 12 | 12 | 0 | 4 | 12 | 8 | 12 |
| setup checkers | 76 | 80 | 68 | 68 | 88 | 92 | 92 | 80 | 80 |
| open window | 96 | 96 | 100 | 100 | 96 | 100 | 96 | 100 | 100 |
| open wine bottle | 80 | 100 | 88 | 92 | 92 | 88 | 96 | 88 | 88 |
| open microwave | 100 | 100 | 88 | 96 | 100 | 80 | 96 | 100 | 100 |
| put money in safe | 96 | 100 | 88 | 92 | 100 | 96 | 100 | 100 | 100 |
| open door | 100 | 96 | 96 | 96 | 96 | 96 | 84 | 96 | 96 |
| close door | 32 | 68 | 56 | 60 | 80 | 20 | 24 | 20 | 60 |
| open fridge | 44 | 52 | 48 | 44 | 36 | 64 | 52 | 32 | 64 |
| open oven | 8 | 4 | 12 | 8 | 4 | 20 | 4 | 4 | 16 |
| plug charger in power supply | 32 | 36 | 32 | 24 | 44 | 36 | 24 | 32 | 60 |

**Table 13: All results on LIBERO-OBJECT, LIBERO-SPATIAL, LIBERO-GOAL, LIBERO-10.**
|  | MoCoV3 | MAE | DINOV2 | CLIP | EVA | InternViT-<br>300M | InternViT-<br>6B | MVP | VC-1 | SPA |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Seed | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 |
| LIBERO-OBJECT |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| 0 | 0.65 | 0.60 | 0.65 | 0.65 | 0.45 | 0.55 | 0.65 | 0.80 | 0.85 | 0.80 | 0.75 | 0.65 | 1.00 | 0.70 | 0.95 | 0.80 | 0.65 | 0.60 | 0.70 | 0.85 | 0.50 | 0.80 | 0.90 | 0.65 | 0.80 | 0.50 | 0.60 | 0.90 | 0.95 | 0.95 |
| 1 | 0.35 | 0.35 | 0.55 | 0.90 | 0.75 | 0.80 | 0.30 | 0.50 | 0.75 | 0.40 | 0.30 | 0.05 | 0.65 | 0.30 | 0.70 | 0.15 | 0.40 | 0.20 | 0.60 | 0.25 | 0.45 | 0.05 | 0.80 | 0.60 | 0.40 | 0.65 | 0.45 | 0.65 | 0.70 | 0.45 |
| 2 | 0.90 | 0.85 | 0.95 | 0.90 | 0.40 | 0.95 | 0.85 | 0.50 | 0.90 | 0.70 | 0.80 | 0.75 | 0.85 | 0.75 | 0.75 | 0.90 | 0.85 | 0.80 | 0.85 | 0.45 | 0.85 | 0.80 | 0.85 | 0.90 | 1.00 | 0.95 | 0.95 | 0.90 | 0.95 | 0.80 |
| 3 | 0.55 | 0.70 | 0.65 | 0.90 | 0.15 | 0.90 | 0.30 | 0.65 | 0.90 | 0.25 | 0.45 | 0.60 | 0.80 | 0.80 | 0.90 | 0.75 | 0.70 | 0.40 | 1.00 | 0.50 | 0.55 | 0.70 | 0.65 | 0.85 | 0.95 | 0.75 | 0.60 | 0.70 | 0.90 | 0.90 |
| 4 | 0.65 | 0.85 | 0.85 | 0.80 | 0.90 | 0.75 | 0.75 | 0.55 | 0.75 | 0.35 | 0.75 | 0.65 | 0.95 | 0.75 | 1.00 | 0.90 | 1.00 | 0.85 | 0.90 | 0.70 | 0.80 | 0.80 | 0.75 | 0.70 | 0.90 | 0.85 | 0.90 | 0.90 | 1.00 | 0.95 |
| 5 | 0.50 | 0.70 | 0.80 | 0.70 | 0.35 | 0.60 | 0.55 | 0.75 | 0.60 | 0.25 | 0.70 | 0.45 | 0.75 | 0.75 | 0.65 | 0.85 | 0.60 | 0.75 | 0.60 | 0.35 | 0.50 | 0.55 | 0.40 | 0.80 | 0.65 | 0.70 | 0.70 | 0.25 | 0.15 | 0.65 |
| 6 | 0.35 | 0.50 | 0.65 | 0.60 | 0.65 | 0.65 | 0.55 | 0.70 | 0.70 | 0.35 | 0.55 | 0.60 | 0.40 | 0.35 | 0.25 | 0.65 | 0.60 | 0.55 | 0.30 | 0.10 | 0.35 | 0.25 | 0.50 | 0.65 | 0.50 | 0.50 | 0.30 | 0.50 | 0.70 | 0.80 |
| 7 | 0.75 | 0.75 | 0.80 | 0.90 | 0.40 | 0.75 | 0.55 | 0.30 | 0.70 | 0.40 | 0.35 | 0.40 | 0.55 | 0.75 | 0.70 | 0.80 | 0.40 | 0.60 | 0.60 | 0.65 | 0.70 | 0.60 | 0.45 | 0.65 | 0.80 | 0.75 | 0.50 | 0.80 | 0.75 | 0.65 |
| 8 | 0.50 | 0.95 | 0.90 | 1.00 | 0.95 | 1.00 | 0.50 | 0.35 | 0.50 | 0.45 | 0.45 | 0.35 | 1.00 | 0.75 | 0.85 | 0.70 | 0.65 | 0.75 | 0.50 | 0.40 | 0.75 | 0.65 | 0.55 | 0.70 | 0.80 | 0.90 | 0.50 | 0.85 | 0.95 | 0.90 |
| 9 | 0.45 | 0.50 | 0.40 | 0.60 | 0.65 | 0.95 | 0.80 | 0.90 | 0.95 | 0.50 | 0.70 | 0.30 | 0.85 | 0.75 | 0.75 | 0.85 | 0.95 | 0.65 | 0.90 | 0.60 | 0.15 | 0.65 | 0.60 | 0.30 | 0.70 | 0.70 | 0.65 | 0.60 | 0.95 | 0.90 |
| LIBERO-SPATIAL |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| 0 | 0.35 | 0.55 | 0.45 | 0.45 | 0.40 | 0.70 | 0.65 | 0.50 | 0.60 | 0.25 | 0.20 | 0.35 | 0.70 | 0.75 | 0.65 | 0.55 | 0.65 | 0.55 | 0.55 | 0.50 | 0.30 | 0.75 | 0.75 | 0.60 | 0.35 | 0.55 | 0.60 | 0.45 | 0.50 | 0.35 |
| 1 | 0.65 | 0.70 | 0.70 | 0.80 | 0.80 | 0.50 | 0.55 | 0.30 | 0.35 | 0.75 | 0.75 | 0.70 | 0.55 | 0.70 | 0.25 | 0.35 | 0.50 | 0.50 | 1.00 | 1.00 | 0.90 | 0.60 | 0.40 | 0.60 | 0.45 | 0.65 | 0.80 | 0.65 | 0.65 | 0.85 |
| 2 | 0.55 | 0.50 | 0.50 | 0.35 | 0.60 | 0.40 | 0.20 | 0.05 | 0.55 | 0.10 | 0.00 | 0.40 | 0.70 | 0.80 | 0.50 | 0.70 | 0.75 | 0.60 | 0.75 | 0.60 | 0.20 | 0.85 | 0.55 | 0.75 | 0.45 | 0.45 | 0.70 | 0.50 | 0.50 | 0.40 |
| 3 | 0.50 | 0.70 | 0.75 | 0.55 | 0.60 | 0.75 | 0.80 | 0.70 | 0.95 | 0.15 | 0.40 | 0.30 | 0.85 | 0.90 | 0.85 | 0.35 | 0.50 | 0.40 | 0.40 | 0.30 | 0.15 | 0.95 | 0.55 | 0.60 | 0.50 | 0.70 | 0.65 | 0.55 | 0.85 | 0.60 |
| 4 | 0.15 | 0.15 | 0.20 | 0.55 | 0.70 | 0.80 | 0.50 | 0.05 | 0.45 | 0.35 | 0.30 | 0.20 | 0.45 | 0.55 | 0.40 | 0.35 | 0.25 | 0.40 | 0.25 | 0.15 | 0.15 | 0.60 | 0.50 | 0.70 | 0.60 | 0.60 | 0.80 | 0.70 | 0.70 | 0.50 |
| 5 | 0.45 | 0.10 | 0.10 | 0.65 | 0.40 | 0.30 | 0.30 | 0.20 | 0.35 | 0.55 | 0.45 | 0.45 | 0.65 | 0.50 | 0.45 | 0.40 | 0.30 | 0.70 | 0.55 | 0.60 | 0.60 | 0.55 | 0.30 | 0.25 | 0.05 | 0.05 | 0.15 | 0.35 | 0.35 | 0.30 |
| 6 | 0.30 | 0.35 | 0.45 | 0.55 | 0.25 | 0.95 | 0.40 | 0.30 | 0.40 | 0.20 | 0.25 | 0.10 | 0.75 | 0.70 | 0.85 | 0.45 | 0.55 | 0.55 | 0.40 | 0.35 | 0.05 | 0.45 | 0.75 | 0.65 | 0.60 | 0.70 | 0.35 | 0.35 | 0.45 | 0.30 |
| 7 | 0.10 | 0.20 | 0.25 | 0.50 | 0.35 | 0.45 | 0.05 | 0.00 | 0.10 | 0.30 | 0.15 | 0.25 | 0.30 | 0.30 | 0.20 | 0.30 | 0.60 | 0.65 | 0.15 | 0.05 | 0.05 | 0.60 | 0.65 | 0.60 | 0.10 | 0.20 | 0.40 | 0.40 | 0.15 | 0.45 |
| 8 | 0.55 | 0.70 | 0.50 | 0.35 | 0.65 | 0.70 | 0.40 | 0.15 | 0.55 | 0.30 | 0.55 | 0.30 | 0.85 | 0.70 | 0.60 | 0.30 | 0.55 | 0.60 | 0.65 | 0.40 | 0.35 | 0.70 | 0.40 | 0.55 | 0.70 | 0.60 | 0.70 | 0.75 | 0.70 | 0.40 |
| 9 | 0.55 | 0.05 | 0.10 | 0.85 | 0.75 | 0.50 | 0.20 | 0.05 | 0.25 | 0.20 | 0.20 | 0.20 | 0.55 | 0.50 | 0.30 | 0.35 | 0.50 | 0.30 | 0.45 | 0.40 | 0.35 | 0.45 | 0.45 | 0.30 | 0.50 | 0.55 | 0.65 | 0.35 | 0.50 | 0.45 |
| LIBERO-GOAL |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| 0 | 0.45 | 0.70 | 0.75 | 0.70 | 0.85 | 0.80 | 0.15 | 0.10 | 0.30 | 0.25 | 0.40 | 0.35 | 0.70 | 0.60 | 0.60 | 0.75 | 0.65 | 0.75 | 0.25 | 0.35 | 0.35 | 0.75 | 0.60 | 0.95 | 0.45 | 0.85 | 1.00 | 0.85 | 1.00 | 0.85 |
| 1 | 0.70 | 0.60 | 0.80 | 0.65 | 0.50 | 0.90 | 0.25 | 0.55 | 0.25 | 0.20 | 0.15 | 0.25 | 0.70 | 0.80 | 0.80 | 0.90 | 0.90 | 1.00 | 0.40 | 0.15 | 0.15 | 0.90 | 0.80 | 0.95 | 0.65 | 0.65 | 0.65 | 1.00 | 0.85 | 0.90 |
| 2 | 0.50 | 0.20 | 0.15 | 0.10 | 0.40 | 0.35 | 0.10 | 0.05 | 0.15 | 0.30 | 0.25 | 0.30 | 0.65 | 0.75 | 0.75 | 0.40 | 0.75 | 0.45 | 0.50 | 0.35 | 0.35 | 0.45 | 0.25 | 0.65 | 0.40 | 0.60 | 0.35 | 0.50 | 0.55 | 0.35 |
| 3 | 0.75 | 0.45 | 0.60 | 0.40 | 0.75 | 0.55 | 0.20 | 0.10 | 0.10 | 0.05 | 0.20 | 0.55 | 0.30 | 0.15 | 0.15 | 0.30 | 0.50 | 0.65 | 0.20 | 0.25 | 0.25 | 0.70 | 0.70 | 0.15 | 0.75 | 0.55 | 0.50 | 0.65 | 0.35 | 0.80 |
| 4 | 0.20 | 0.25 | 0.05 | 0.35 | 0.40 | 0.25 | 0.10 | 0.00 | 0.05 | 0.40 | 0.30 | 0.15 | 0.15 | 0.10 | 0.10 | 0.20 | 0.15 | 0.10 | 0.15 | 0.20 | 0.20 | 0.55 | 0.60 | 0.25 | 0.15 | 0.30 | 0.30 | 0.30 | 0.35 | 0.35 |
| 5 | 0.10 | 0.75 | 0.80 | 0.60 | 0.85 | 0.80 | 0.65 | 0.50 | 0.50 | 0.35 | 0.45 | 0.50 | 0.80 | 0.75 | 0.75 | 0.70 | 0.55 | 0.45 | 0.55 | 0.45 | 0.45 | 0.80 | 0.75 | 0.85 | 0.65 | 0.75 | 0.80 | 0.80 | 0.65 | 0.65 |
| 6 | 0.45 | 0.05 | 0.15 | 0.00 | 0.10 | 0.05 | 0.00 | 0.05 | 0.00 | 0.10 | 0.10 | 0.00 | 0.00 | 0.65 | 0.65 | 0.50 | 0.40 | 0.30 | 0.00 | 0.00 | 0.00 | 0.15 | 0.35 | 0.70 | 0.25 | 0.50 | 0.45 | 0.40 | 0.30 | 0.35 |
| 7 | 0.25 | 0.75 | 0.90 | 0.80 | 0.65 | 1.00 | 0.45 | 0.45 | 0.35 | 0.50 | 0.65 | 0.80 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.95 | 0.70 | 0.85 | 0.85 | 0.95 | 1.00 | 0.95 | 1.00 | 0.95 | 0.70 | 0.95 | 1.00 | 1.00 |
| 8 | 0.50 | 0.80 | 0.75 | 0.85 | 0.55 | 0.90 | 0.45 | 0.40 | 0.20 | 0.60 | 0.25 | 0.50 | 0.90 | 0.35 | 0.35 | 0.95 | 0.65 | 0.55 | 0.65 | 0.25 | 0.25 | 0.70 | 0.65 | 0.70 | 0.50 | 0.75 | 0.55 | 0.80 | 0.65 | 0.80 |
| 9 | 0.10 | 0.65 | 0.60 | 0.50 | 0.20 | 0.50 | 0.10 | 0.00 | 0.10 | 0.10 | 0.10 | 0.00 | 0.15 | 0.70 | 0.70 | 0.60 | 0.40 | 0.20 | 0.15 | 0.35 | 0.35 | 0.30 | 0.50 | 0.55 | 0.20 | 0.35 | 0.70 | 0.55 | 0.60 | 0.45 |
| LIBERO-10 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| 0 | 0.15 | 0.20 | 0.10 | 0.15 | 0.25 | 0.10 | 0.00 | 0.05 | 0.10 | 0.00 | 0.05 | 0.05 | 0.25 | 0.35 | 0.10 | 0.35 | 0.10 | 0.25 | 0.15 | 0.15 | 0.00 | 0.05 | 0.15 | 0.20 | 0.10 | 0.45 | 0.25 | 0.05 | 0.10 | 0.05 |
| 1 | 0.25 | 0.20 | 0.20 | 0.30 | 0.15 | 0.25 | 0.15 | 0.15 | 0.15 | 0.40 | 0.30 | 0.15 | 0.65 | 0.10 | 0.60 | 0.15 | 0.50 | 0.45 | 0.00 | 0.25 | 0.35 | 0.15 | 0.10 | 0.15 | 0.20 | 0.40 | 0.15 | 0.25 | 0.05 | 0.45 |
| 2 | 0.70 | 0.60 | 0.75 | 0.30 | 0.60 | 0.75 | 0.55 | 0.45 | 0.50 | 0.25 | 0.45 | 0.40 | 0.75 | 0.55 | 0.65 | 0.45 | 0.80 | 0.55 | 0.70 | 0.80 | 0.75 | 0.75 | 0.65 | 0.55 | 0.85 | 1.00 | 0.90 | 0.70 | 0.80 | 0.50 |
| 3 | 0.50 | 0.80 | 0.55 | 0.55 | 0.60 | 0.80 | 0.40 | 0.45 | 0.45 | 0.60 | 0.65 | 0.60 | 0.80 | 0.90 | 0.75 | 0.75 | 0.65 | 0.50 | 0.75 | 0.60 | 0.60 | 0.75 | 0.70 | 0.65 | 0.80 | 0.70 | 0.70 | 0.70 | 0.90 | 0.70 |
| 4 | 0.25 | 0.20 | 0.05 | 0.35 | 0.25 | 0.30 | 0.10 | 0.10 | 0.05 | 0.20 | 0.05 | 0.05 | 0.15 | 0.10 | 0.15 | 0.15 | 0.15 | 0.05 | 0.15 | 0.20 | 0.15 | 0.25 | 0.20 | 0.35 | 0.30 | 0.25 | 0.30 | 0.40 | 0.30 | 0.25 |
| 5 | 0.40 | 0.60 | 0.75 | 0.55 | 0.70 | 0.80 | 0.50 | 0.65 | 0.75 | 0.40 | 0.40 | 0.30 | 0.85 | 0.65 | 0.75 | 0.75 | 0.55 | 0.75 | 0.45 | 0.55 | 0.45 | 0.60 | 0.70 | 0.75 | 0.80 | 0.90 | 0.60 | 0.70 | 0.70 | 0.45 |
| 6 | 0.20 | 0.25 | 0.10 | 0.40 | 0.35 | 0.40 | 0.05 | 0.20 | 0.05 | 0.25 | 0.15 | 0.15 | 0.20 | 0.30 | 0.35 | 0.10 | 0.15 | 0.20 | 0.20 | 0.25 | 0.05 | 0.40 | 0.30 | 0.35 | 0.30 | 0.10 | 0.20 | 0.20 | 0.20 | 0.15 |
| 7 | 0.40 | 0.30 | 0.25 | 0.50 | 0.50 | 0.50 | 0.10 | 0.30 | 0.60 | 0.30 | 0.40 | 0.20 | 0.45 | 0.30 | 0.25 | 0.40 | 0.35 | 0.35 | 0.35 | 0.70 | 0.25 | 0.35 | 0.30 | 0.25 | 0.30 | 0.25 | 0.30 | 0.50 | 0.45 | 0.40 |
| 8 | 0.10 | 0.10 | 0.15 | 0.10 | 0.30 | 0.20 | 0.35 | 0.20 | 0.05 | 0.10 | 0.10 | 0.10 | 0.15 | 0.20 | 0.10 | 0.20 | 0.00 | 0.25 | 0.05 | 0.20 | 0.05 | 0.10 | 0.30 | 0.20 | 0.25 | 0.30 | 0.25 | 0.25 | 0.05 | 0.15 |
| 9 | 0.20 | 0.60 | 0.35 | 0.40 | 0.65 | 0.30 | 0.35 | 0.25 | 0.45 | 0.45 | 0.45 | 0.30 | 0.40 | 0.70 | 0.50 | 0.50 | 0.45 | 0.60 | 0.50 | 0.25 | 0.40 | 0.40 | 0.55 | 0.50 | 0.00 | 0.00 | 0.00 | 0.50 | 0.65 | 0.50 |

**Table 14: All results on LIBERO-90.**
|  | MoCoV3 | MAE | DINOV2 | CLIP | EVA | InternViT-<br>300M | InternViT-<br>6B | MVP | VC-1 | SPA |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Seed | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 | 100 | 200 | 300 |
| LIBERO-90 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| 0 | 0.95 | 0.85 | 0.90 | 1.00 | 0.90 | 0.80 | 0.80 | 1.00 | 0.60 | 0.90 | 0.80 | 0.80 | 1.00 | 1.00 | 1.00 | 0.90 | 0.80 | 0.85 | 0.75 | 0.80 | 0.95 | 0.95 | 0.95 | 1.00 | 0.95 | 1.00 | 0.95 | 1.00 | 1.00 | 0.95 |
| 1 | 0.60 | 0.35 | 0.60 | 0.35 | 0.50 | 0.15 | 0.50 | 0.55 | 0.30 | 0.40 | 0.65 | 0.35 | 0.70 | 0.50 | 0.25 | 0.30 | 0.45 | 0.40 | 0.25 | 0.35 | 0.55 | 0.80 | 0.55 | 0.30 | 0.40 | 0.50 | 0.05 | 0.65 | 0.40 | 0.50 |
| 2 | 0.85 | 0.50 | 0.80 | 0.55 | 0.55 | 0.20 | 0.65 | 0.60 | 0.30 | 0.45 | 0.30 | 0.50 | 0.35 | 0.50 | 0.70 | 0.85 | 0.65 | 0.80 | 0.25 | 0.35 | 0.30 | 0.45 | 0.70 | 0.70 | 0.75 | 0.55 | 0.35 | 0.70 | 0.85 | 0.60 |
| 3 | 0.10 | 0.10 | 0.00 | 0.05 | 0.00 | 0.00 | 0.05 | 0.00 | 0.00 | 0.15 | 0.00 | 0.00 | 0.00 | 0.10 | 0.15 | 0.00 | 0.05 | 0.05 | 0.00 | 0.00 | 0.05 | 0.10 | 0.00 | 0.05 | 0.05 | 0.10 | 0.00 | 0.10 | 0.10 | 0.00 |
| 4 | 0.40 | 0.05 | 0.20 | 0.30 | 0.25 | 0.30 | 0.15 | 0.40 | 0.55 | 0.40 | 0.40 | 0.35 | 0.10 | 0.25 | 0.15 | 0.40 | 0.05 | 0.25 | 0.20 | 0.45 | 0.40 | 0.30 | 0.40 | 0.15 | 0.25 | 0.05 | 0.15 | 0.15 | 0.15 | 0.35 |
| 5 | 0.05 | 0.05 | 0.05 | 0.10 | 0.05 | 0.20 | 0.00 | 0.20 | 0.00 | 0.05 | 0.05 | 0.20 | 0.25 | 0.25 | 0.10 | 0.10 | 0.05 | 0.30 | 0.20 | 0.10 | 0.25 | 0.05 | 0.15 | 0.10 | 0.10 | 0.05 | 0.05 | 0.35 | 0.00 | 0.15 |
| 6 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.05 | 0.05 | 0.10 | 0.05 | 0.10 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.00 | 0.00 | 0.05 | 0.10 | 0.10 | 0.00 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.05 |
| 7 | 0.35 | 0.30 | 0.65 | 0.20 | 0.60 | 0.30 | 0.35 | 0.25 | 0.40 | 0.50 | 0.60 | 0.35 | 0.60 | 0.10 | 0.20 | 0.15 | 0.25 | 0.10 | 0.40 | 0.25 | 0.45 | 0.50 | 0.20 | 0.40 | 0.20 | 0.30 | 0.25 | 0.30 | 0.30 | 0.65 |
| 8 | 0.10 | 0.15 | 0.00 | 0.05 | 0.20 | 0.10 | 0.15 | 0.25 | 0.10 | 0.20 | 0.10 | 0.10 | 0.10 | 0.05 | 0.00 | 0.05 | 0.00 | 0.10 | 0.20 | 0.15 | 0.20 | 0.10 | 0.00 | 0.20 | 0.05 | 0.15 | 0.20 | 0.05 | 0.05 | 0.15 |
| 9 | 0.30 | 0.25 | 0.35 | 0.50 | 0.25 | 0.30 | 0.35 | 0.60 | 0.70 | 0.25 | 0.20 | 0.50 | 0.25 | 0.10 | 0.50 | 0.10 | 0.10 | 0.25 | 0.60 | 0.25 | 0.30 | 0.25 | 0.15 | 0.45 | 0.25 | 0.05 | 0.35 | 0.25 | 0.20 | 0.25 |
| 10 | 0.50 | 0.75 | 0.50 | 0.50 | 0.60 | 0.55 | 0.65 | 0.60 | 0.60 | 0.90 | 0.45 | 0.55 | 0.40 | 0.85 | 0.35 | 0.35 | 0.05 | 0.25 | 0.45 | 0.45 | 0.65 | 0.40 | 0.50 | 0.55 | 0.45 | 0.75 | 0.40 | 0.40 | 0.35 | 0.35 |
| 11 | 0.45 | 0.35 | 0.75 | 0.45 | 0.70 | 0.65 | 0.35 | 0.20 | 0.15 | 0.40 | 0.70 | 0.55 | 0.80 | 0.25 | 0.70 | 0.50 | 0.50 | 0.10 | 0.35 | 0.25 | 0.45 | 0.80 | 0.60 | 0.95 | 0.70 | 0.75 | 0.60 | 0.60 | 0.60 | 0.65 |
| 12 | 0.15 | 0.15 | 0.10 | 0.15 | 0.15 | 0.05 | 0.20 | 0.20 | 0.15 | 0.10 | 0.05 | 0.05 | 0.10 | 0.25 | 0.05 | 0.05 | 0.00 | 0.00 | 0.25 | 0.30 | 0.10 | 0.15 | 0.10 | 0.10 | 0.20 | 0.25 | 0.10 | 0.05 | 0.10 | 0.15 |
| 13 | 0.20 | 0.35 | 0.30 | 0.15 | 0.30 | 0.20 | 0.30 | 0.35 | 0.10 | 0.30 | 0.40 | 0.35 | 0.30 | 0.10 | 0.45 | 0.20 | 0.35 | 0.40 | 0.25 | 0.15 | 0.55 | 0.30 | 0.30 | 0.15 | 0.45 | 0.10 | 0.10 | 0.10 | 0.20 | 0.10 |
| 14 | 0.05 | 0.10 | 0.00 | 0.30 | 0.30 | 0.20 | 0.10 | 0.10 | 0.15 | 0.15 | 0.40 | 0.20 | 0.25 | 0.35 | 0.10 | 0.15 | 0.15 | 0.05 | 0.20 | 0.15 | 0.10 | 0.20 | 0.35 | 0.10 | 0.20 | 0.10 | 0.20 | 0.15 | 0.15 | 0.10 |
| 15 | 0.60 | 0.75 | 0.45 | 0.70 | 0.50 | 0.65 | 0.35 | 0.50 | 0.55 | 0.45 | 0.65 | 0.40 | 0.70 | 0.75 | 0.40 | 0.40 | 0.65 | 0.50 | 0.35 | 0.55 | 0.45 | 0.70 | 0.60 | 0.55 | 0.80 | 0.80 | 0.70 | 0.65 | 0.80 | 0.55 |
| 16 | 0.05 | 0.20 | 0.00 | 0.30 | 0.15 | 0.05 | 0.10 | 0.10 | 0.05 | 0.10 | 0.00 | 0.10 | 0.20 | 0.20 | 0.15 | 0.15 | 0.15 | 0.20 | 0.05 | 0.00 | 0.10 | 0.15 | 0.05 | 0.10 | 0.00 | 0.15 | 0.15 | 0.05 | 0.10 | 0.15 |
| 17 | 0.05 | 0.15 | 0.15 | 0.10 | 0.25 | 0.05 | 0.05 | 0.10 | 0.05 | 0.05 | 0.00 | 0.05 | 0.05 | 0.20 | 0.15 | 0.10 | 0.10 | 0.15 | 0.00 | 0.10 | 0.00 | 0.20 | 0.10 | 0.20 | 0.15 | 0.10 | 0.00 | 0.25 | 0.10 | 0.10 |
| 18 | 0.45 | 0.40 | 0.60 | 0.40 | 0.75 | 0.65 | 0.30 | 0.35 | 0.40 | 0.45 | 0.25 | 0.35 | 0.25 | 0.35 | 0.60 | 0.40 | 0.05 | 0.70 | 0.60 | 0.50 | 0.35 | 0.35 | 0.25 | 0.45 | 0.30 | 0.60 | 0.35 | 0.60 | 0.35 | 0.55 |
| 19 | 0.30 | 0.30 | 0.25 | 0.35 | 0.40 | 0.20 | 0.20 | 0.05 | 0.35 | 0.45 | 0.45 | 0.30 | 0.30 | 0.35 | 0.25 | 0.15 | 0.25 | 0.20 | 0.35 | 0.30 | 0.15 | 0.55 | 0.30 | 0.40 | 0.40 | 0.45 | 0.35 | 0.45 | 0.20 | 0.35 |
| 20 | 0.85 | 0.75 | 0.80 | 1.00 | 1.00 | 0.95 | 0.95 | 1.00 | 1.00 | 0.75 | 0.85 | 0.30 | 1.00 | 1.00 | 1.00 | 0.95 | 0.95 | 0.90 | 1.00 | 0.50 | 0.80 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| 21 | 0.40 | 0.20 | 0.40 | 0.35 | 0.25 | 0.30 | 0.25 | 0.40 | 0.20 | 0.25 | 0.10 | 0.45 | 0.30 | 0.70 | 0.05 | 0.00 | 0.05 | 0.10 | 0.35 | 0.10 | 0.30 | 0.40 | 0.15 | 0.30 | 0.30 | 0.70 | 0.60 | 0.65 | 0.40 | 0.60 |
| 22 | 0.90 | 0.95 | 0.95 | 1.00 | 0.85 | 0.95 | 0.25 | 0.60 | 0.40 | 0.75 | 0.75 | 0.75 | 0.95 | 1.00 | 0.95 | 0.85 | 0.95 | 0.60 | 0.45 | 0.25 | 0.25 | 0.90 | 1.00 | 1.00 | 0.90 | 0.90 | 0.95 | 1.00 | 0.95 | 1.00 |
| 23 | 0.15 | 0.05 | 0.15 | 0.05 | 0.10 | 0.00 | 0.05 | 0.10 | 0.05 | 0.00 | 0.00 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.25 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 24 | 0.80 | 0.30 | 0.85 | 0.85 | 0.50 | 0.80 | 0.60 | 0.50 | 0.65 | 0.70 | 0.45 | 0.60 | 0.70 | 0.70 | 0.80 | 0.40 | 0.65 | 0.60 | 0.55 | 0.80 | 0.45 | 0.65 | 0.60 | 0.90 | 0.90 | 0.80 | 0.80 | 0.90 | 0.80 | 0.75 |
| 25 | 1.00 | 0.80 | 0.85 | 1.00 | 1.00 | 0.90 | 0.75 | 0.90 | 0.90 | 0.80 | 0.95 | 0.90 | 0.90 | 1.00 | 0.95 | 0.70 | 0.70 | 0.85 | 0.95 | 0.60 | 0.65 | 1.00 | 0.85 | 1.00 | 1.00 | 1.00 | 0.90 | 1.00 | 1.00 | 1.00 |
| 26 | 0.15 | 0.20 | 0.25 | 0.25 | 0.40 | 0.40 | 0.05 | 0.30 | 0.40 | 0.45 | 0.05 | 0.15 | 0.05 | 0.30 | 0.15 | 0.25 | 0.40 | 0.20 | 0.25 | 0.15 | 0.20 | 0.20 | 0.30 | 0.60 | 0.25 | 0.45 | 0.25 | 0.25 | 0.20 | 0.20 |
| 27 | 0.30 | 0.15 | 0.20 | 0.35 | 0.35 | 0.10 | 0.05 | 0.10 | 0.00 | 0.35 | 0.05 | 0.10 | 0.05 | 0.20 | 0.05 | 0.05 | 0.15 | 0.00 | 0.10 | 0.10 | 0.05 | 0.35 | 0.20 | 0.30 | 0.10 | 0.45 | 0.40 | 0.10 | 0.40 | 0.20 |
| 28 | 0.90 | 0.90 | 1.00 | 0.95 | 0.70 | 0.70 | 0.80 | 0.50 | 0.80 | 0.90 | 0.75 | 0.90 | 0.95 | 1.00 | 0.85 | 0.90 | 0.85 | 1.00 | 0.50 | 0.60 | 0.45 | 0.85 | 0.75 | 0.90 | 0.75 | 0.95 | 0.60 | 0.90 | 0.65 | 0.90 |
| 29 | 0.15 | 0.50 | 0.35 | 0.60 | 0.55 | 0.20 | 0.50 | 0.50 | 0.40 | 0.50 | 0.50 | 0.30 | 0.65 | 0.30 | 0.30 | 0.15 | 0.30 | 0.40 | 0.25 | 0.35 | 0.25 | 0.35 | 0.50 | 0.25 | 0.60 | 0.60 | 0.10 | 0.30 | 0.35 | 0.70 |
| 30 | 0.15 | 0.25 | 0.15 | 0.60 | 0.35 | 0.35 | 0.35 | 0.10 | 0.50 | 0.25 | 0.20 | 0.45 | 0.30 | 0.70 | 0.20 | 0.10 | 0.15 | 0.20 | 0.50 | 0.20 | 0.25 | 0.00 | 0.05 | 0.20 | 0.10 | 0.25 | 0.10 | 0.40 | 0.25 | 0.40 |
| 31 | 0.70 | 0.60 | 0.80 | 0.70 | 0.75 | 0.60 | 0.45 | 0.70 | 0.75 | 0.95 | 0.65 | 0.95 | 0.80 | 0.75 | 0.45 | 0.50 | 0.55 | 0.35 | 0.95 | 0.80 | 0.85 | 0.80 | 0.70 | 0.75 | 0.75 | 0.75 | 0.45 | 0.70 | 0.90 | 0.80 |
| 32 | 0.30 | 0.05 | 0.20 | 0.05 | 0.10 | 0.05 | 0.00 | 0.00 | 0.05 | 0.35 | 0.10 | 0.10 | 0.20 | 0.10 | 0.15 | 0.10 | 0.15 | 0.10 | 0.05 | 0.15 | 0.05 | 0.20 | 0.25 | 0.10 | 0.05 | 0.10 | 0.05 | 0.20 | 0.10 | 0.05 |
| 33 | 0.50 | 0.55 | 0.40 | 0.15 | 0.30 | 0.30 | 0.10 | 0.20 | 0.35 | 0.30 | 0.25 | 0.30 | 0.00 | 0.50 | 0.40 | 0.35 | 0.20 | 0.25 | 0.25 | 0.25 | 0.30 | 0.20 | 0.35 | 0.40 | 0.35 | 0.45 | 0.65 | 0.15 | 0.15 | 0.15 |
| 34 | 0.30 | 0.35 | 0.30 | 0.40 | 0.40 | 0.25 | 0.35 | 0.40 | 0.15 | 0.40 | 0.40 | 0.50 | 0.10 | 0.40 | 0.10 | 0.15 | 0.05 | 0.25 | 0.35 | 0.30 | 0.50 | 0.25 | 0.30 | 0.30 | 0.55 | 0.25 | 0.05 | 0.05 | 0.30 | 0.10 |
| 35 | 0.65 | 0.40 | 0.60 | 0.85 | 0.95 | 0.75 | 0.80 | 0.80 | 0.60 | 0.65 | 0.55 | 0.90 | 0.90 | 1.00 | 0.80 | 0.10 | 0.20 | 0.55 | 0.85 | 0.75 | 0.70 | 0.85 | 0.80 | 0.85 | 0.25 | 0.80 | 0.55 | 1.00 | 0.70 | 1.00 |
| 36 | 0.05 | 0.10 | 0.15 | 0.05 | 0.00 | 0.00 | 0.00 | 0.25 | 0.05 | 0.05 | 0.05 | 0.00 | 0.15 | 0.20 | 0.10 | 0.15 | 0.10 | 0.25 | 0.00 | 0.00 | 0.10 | 0.20 | 0.00 | 0.15 | 0.30 | 0.05 | 0.20 | 0.05 | 0.20 | 0.10 |
| 37 | 0.35 | 0.30 | 0.40 | 0.55 | 0.20 | 0.25 | 0.65 | 0.50 | 0.35 | 0.30 | 0.60 | 0.60 | 0.70 | 0.80 | 0.60 | 0.45 | 0.55 | 0.45 | 0.50 | 0.55 | 0.55 | 0.45 | 0.45 | 0.50 | 0.45 | 0.75 | 0.35 | 0.75 | 0.50 | 0.55 |
| 38 | 0.50 | 0.30 | 0.45 | 0.55 | 0.50 | 0.35 | 0.25 | 0.15 | 0.30 | 0.50 | 0.45 | 0.30 | 0.50 | 0.20 | 0.35 | 0.35 | 0.55 | 0.45 | 0.35 | 0.50 | 0.35 | 0.70 | 0.40 | 0.55 | 0.70 | 0.65 | 0.30 | 0.70 | 0.45 | 0.45 |
| 39 | 0.80 | 0.80 | 0.75 | 0.45 | 0.70 | 0.60 | 0.60 | 0.55 | 0.65 | 0.60 | 0.65 | 0.70 | 0.65 | 0.85 | 0.55 | 0.60 | 0.15 | 0.60 | 0.65 | 0.60 | 0.60 | 0.45 | 0.40 | 0.70 | 0.30 | 0.65 | 0.35 | 0.60 | 0.55 | 0.60 |
| 40 | 0.40 | 0.50 | 0.20 | 0.40 | 0.30 | 0.40 | 0.30 | 0.45 | 0.55 | 0.50 | 0.25 | 0.30 | 0.70 | 0.65 | 0.30 | 0.25 | 0.60 | 0.25 | 0.55 | 0.40 | 0.25 | 0.65 | 0.70 | 0.80 | 0.35 | 0.45 | 0.25 | 0.55 | 0.35 | 0.30 |
| 41 | 0.20 | 0.60 | 0.40 | 0.50 | 0.45 | 0.60 | 0.35 | 0.25 | 0.55 | 0.20 | 0.45 | 0.50 | 0.85 | 0.45 | 0.50 | 0.45 | 0.65 | 0.45 | 0.20 | 0.30 | 0.35 | 0.55 | 0.80 | 0.20 | 0.35 | 0.50 | 0.65 | 0.65 | 0.80 | 0.40 |
| 42 | 0.20 | 0.40 | 0.20 | 0.35 | 0.15 | 0.05 | 0.30 | 0.30 | 0.55 | 0.35 | 0.05 | 0.20 | 0.70 | 0.45 | 0.20 | 0.40 | 0.65 | 0.60 | 0.25 | 0.10 | 0.05 | 0.30 | 0.50 | 0.65 | 0.35 | 0.60 | 0.50 | 0.60 | 0.60 | 0.40 |
| 43 | 0.50 | 0.50 | 0.50 | 0.35 | 0.40 | 0.30 | 0.35 | 0.35 | 0.15 | 0.35 | 0.25 | 0.45 | 0.20 | 0.60 | 0.50 | 0.35 | 0.35 | 0.05 | 0.30 | 0.30 | 0.15 | 0.30 | 0.60 | 0.40 | 0.55 | 0.40 | 0.20 | 0.55 | 0.70 | 0.40 |
| 44 | 0.90 | 0.90 | 0.95 | 1.00 | 1.00 | 0.85 | 0.80 | 0.90 | 0.95 | 0.75 | 0.85 | 0.85 | 0.95 | 0.80 | 1.00 | 1.00 | 0.95 | 0.85 | 0.85 | 0.65 | 0.95 | 0.85 | 0.95 | 0.90 | 0.95 | 0.95 | 0.95 | 0.95 | 1.00 | 0.95 |
| 45 | 0.55 | 0.40 | 0.60 | 0.80 | 0.75 | 0.60 | 0.45 | 0.55 | 0.60 | 0.70 | 0.70 | 0.55 | 0.45 | 0.40 | 0.30 | 0.55 | 0.15 | 0.55 | 0.40 | 0.65 | 0.30 | 0.65 | 0.50 | 0.35 | 0.55 | 0.65 | 0.45 | 0.60 | 0.75 | 0.60 |
| 46 | 0.00 | 0.00 | 0.00 | 0.05 | 0.35 | 0.10 | 0.00 | 0.15 | 0.00 | 0.10 | 0.10 | 0.05 | 0.05 | 0.10 | 0.00 | 0.00 | 0.00 | 0.10 | 0.10 | 0.00 | 0.05 | 0.05 | 0.05 | 0.20 | 0.00 | 0.05 | 0.10 | 0.10 | 0.00 | 0.10 |
| 47 | 0.45 | 0.35 | 0.25 | 0.25 | 0.20 | 0.20 | 0.10 | 0.20 | 0.15 | 0.60 | 0.25 | 0.45 | 0.45 | 0.30 | 0.30 | 0.15 | 0.30 | 0.30 | 0.15 | 0.35 | 0.20 | 0.40 | 0.40 | 0.30 | 0.20 | 0.25 | 0.10 | 0.55 | 0.45 | 0.30 |
| 48 | 0.00 | 0.15 | 0.30 | 0.10 | 0.00 | 0.15 | 0.20 | 0.05 | 0.20 | 0.10 | 0.10 | 0.25 | 0.05 | 0.10 | 0.25 | 0.15 | 0.00 | 0.25 | 0.20 | 0.10 | 0.20 | 0.05 | 0.10 | 0.10 | 0.15 | 0.20 | 0.10 | 0.10 | 0.05 | 0.20 |
| 49 | 0.05 | 0.05 | 0.25 | 0.25 | 0.30 | 0.15 | 0.10 | 0.20 | 0.25 | 0.25 | 0.40 | 0.30 | 0.15 | 0.25 | 0.05 | 0.05 | 0.00 | 0.15 | 0.25 | 0.30 | 0.00 | 0.00 | 0.00 | 0.15 | 0.15 | 0.05 | 0.25 | 0.15 | 0.05 | 0.10 |
| 50 | 0.25 | 0.05 | 0.25 | 0.00 | 0.05 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.10 | 0.05 | 0.05 | 0.00 | 0.00 | 0.05 | 0.00 | 0.05 | 0.05 | 0.05 | 0.10 | 0.00 | 0.00 | 0.05 | 0.15 | 0.05 |
| 51 | 0.05 | 0.15 | 0.05 | 0.10 | 0.15 | 0.05 | 0.15 | 0.15 | 0.20 | 0.15 | 0.20 | 0.15 | 0.15 | 0.10 | 0.05 | 0.05 | 0.20 | 0.05 | 0.35 | 0.15 | 0.35 | 0.15 | 0.20 | 0.30 | 0.15 | 0.00 | 0.10 | 0.05 | 0.10 | 0.10 |
| 52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.05 | 0.10 | 0.00 | 0.00 | 0.05 | 0.05 | 0.10 | 0.00 | 0.15 | 0.10 | 0.00 | 0.00 | 0.05 | 0.05 | 0.00 | 0.05 | 0.15 | 0.10 | 0.00 | 0.00 | 0.10 | 0.15 | 0.00 | 0.05 |
| 53 | 0.05 | 0.05 | 0.10 | 0.15 | 0.00 | 0.05 | 0.20 | 0.20 | 0.05 | 0.00 | 0.10 | 0.20 | 0.05 | 0.25 | 0.05 | 0.05 | 0.00 | 0.00 | 0.25 | 0.15 | 0.25 | 0.00 | 0.00 | 0.00 | 0.05 | 0.15 | 0.10 | 0.10 | 0.05 | 0.15 |
| 54 | 0.05 | 0.20 | 0.05 | 0.05 | 0.05 | 0.00 | 0.05 | 0.05 | 0.05 | 0.25 | 0.05 | 0.05 | 0.05 | 0.05 | 0.10 | 0.20 | 0.10 | 0.00 | 0.20 | 0.20 | 0.05 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.15 | 0.05 |
| 55 | 0.10 | 0.05 | 0.05 | 0.00 | 0.00 | 0.00 | 0.10 | 0.05 | 0.00 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.00 | 0.00 | 0.05 | 0.05 | 0.05 | 0.00 | 0.05 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| 56 | 0.05 | 0.15 | 0.10 | 0.10 | 0.10 | 0.05 | 0.15 | 0.15 | 0.30 | 0.20 | 0.10 | 0.25 | 0.10 | 0.10 | 0.05 | 0.10 | 0.20 | 0.00 | 0.25 | 0.15 | 0.10 | 0.05 | 0.00 | 0.05 | 0.20 | 0.15 | 0.10 | 0.10 | 0.15 | 0.20 |
| 57 | 0.10 | 0.00 | 0.05 | 0.10 | 0.10 | 0.05 | 0.05 | 0.20 | 0.00 | 0.15 | 0.10 | 0.05 | 0.10 | 0.15 | 0.00 | 0.05 | 0.05 | 0.10 | 0.20 | 0.25 | 0.10 | 0.00 | 0.00 | 0.20 | 0.10 | 0.00 | 0.20 | 0.20 | 0.05 | 0.05 |
| 58 | 0.05 | 0.10 | 0.20 | 0.00 | 0.05 | 0.10 | 0.10 | 0.25 | 0.10 | 0.25 | 0.20 | 0.15 | 0.20 | 0.15 | 0.15 | 0.05 | 0.05 | 0.15 | 0.05 | 0.15 | 0.05 | 0.15 | 0.10 | 0.10 | 0.05 | 0.10 | 0.20 | 0.15 | 0.05 | 0.10 |
| 59 | 0.05 | 0.10 | 0.10 | 0.05 | 0.10 | 0.10 | 0.05 | 0.15 | 0.00 | 0.05 | 0.10 | 0.05 | 0.05 | 0.10 | 0.25 | 0.05 | 0.15 | 0.25 | 0.05 | 0.10 | 0.05 | 0.10 | 0.00 | 0.10 | 0.15 | 0.15 | 0.00 | 0.00 | 0.20 | 0.05 |
| 60 | 0.55 | 0.65 | 0.70 | 0.30 | 0.60 | 0.45 | 0.50 | 0.50 | 0.40 | 0.40 | 0.35 | 0.65 | 0.20 | 0.75 | 0.55 | 0.35 | 0.35 | 0.50 | 0.40 | 0.40 | 0.50 | 0.45 | 0.50 | 0.75 | 0.20 | 0.50 | 0.55 | 0.45 | 0.65 | 0.90 |
| 61 | 0.05 | 0.15 | 0.05 | 0.00 | 0.10 | 0.00 | 0.00 | 0.10 | 0.05 | 0.05 | 0.10 | 0.10 | 0.05 | 0.10 | 0.05 | 0.00 | 0.00 | 0.10 | 0.15 | 0.05 | 0.20 | 0.10 | 0.15 | 0.20 | 0.05 | 0.15 | 0.05 | 0.15 | 0.05 | 0.15 |
| 62 | 0.45 | 0.40 | 0.40 | 0.45 | 0.20 | 0.20 | 0.25 | 0.30 | 0.25 | 0.55 | 0.15 | 0.70 | 0.40 | 0.50 | 0.45 | 0.30 | 0.10 | 0.50 | 0.40 | 0.15 | 0.05 | 0.20 | 0.15 | 0.35 | 0.25 | 0.35 | 0.50 | 0.40 | 0.10 | 0.35 |
| 63 | 0.10 | 0.00 | 0.05 | 0.15 | 0.05 | 0.00 | 0.15 | 0.20 | 0.15 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 64 | 0.10 | 0.05 | 0.05 | 0.00 | 0.05 | 0.00 | 0.00 | 0.05 | 0.05 | 0.00 | 0.05 | 0.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.05 | 0.00 |
| 65 | 0.05 | 0.00 | 0.15 | 0.20 | 0.05 | 0.10 | 0.00 | 0.05 | 0.05 | 0.10 | 0.05 | 0.05 | 0.05 | 0.00 | 0.05 | 0.00 | 0.05 | 0.05 | 0.05 | 0.10 | 0.10 | 0.10 | 0.00 | 0.10 | 0.15 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 |
| 66 | 0.20 | 0.35 | 0.05 | 0.05 | 0.30 | 0.15 | 0.40 | 0.40 | 0.50 | 0.20 | 0.15 | 0.25 | 0.10 | 0.20 | 0.05 | 0.25 | 0.10 | 0.25 | 0.15 | 0.20 | 0.30 | 0.20 | 0.20 | 0.20 | 0.10 | 0.10 | 0.20 | 0.35 | 0.40 | 0.25 |
| 67 | 0.00 | 0.00 | 0.05 | 0.05 | 0.00 | 0.15 | 0.05 | 0.05 | 0.05 | 0.05 | 0.00 | 0.05 | 0.05 | 0.00 | 0.00 | 0.10 | 0.05 | 0.00 | 0.00 | 0.05 | 0.00 | 0.00 | 0.10 | 0.00 | 0.05 | 0.10 | 0.10 | 0.00 | 0.00 | 0.00 |
| 68 | 0.05 | 0.40 | 0.20 | 0.30 | 0.25 | 0.15 | 0.30 | 0.40 | 0.60 | 0.25 | 0.20 | 0.25 | 0.20 | 0.25 | 0.15 | 0.20 | 0.25 | 0.15 | 0.40 | 0.50 | 0.40 | 0.35 | 0.30 | 0.35 | 0.15 | 0.15 | 0.35 | 0.30 | 0.15 | 0.30 |
| 69 | 0.15 | 0.00 | 0.20 | 0.10 | 0.25 | 0.05 | 0.00 | 0.00 | 0.00 | 0.10 | 0.05 | 0.10 | 0.30 | 0.05 | 0.50 | 0.20 | 0.20 | 0.00 | 0.10 | 0.20 | 0.10 | 0.30 | 0.15 | 0.25 | 0.30 | 0.30 | 0.10 | 0.25 | 0.35 | 0.10 |
| 70 | 0.20 | 0.45 | 0.05 | 0.20 | 0.20 | 0.20 | 0.30 | 0.35 | 0.20 | 0.20 | 0.30 | 0.25 | 0.20 | 0.20 | 0.30 | 0.20 | 0.30 | 0.25 | 0.20 | 0.20 | 0.20 | 0.25 | 0.55 | 0.40 | 0.25 | 0.15 | 0.50 | 0.40 | 0.20 | 0.40 |
| 71 | 0.35 | 0.25 | 0.10 | 0.20 | 0.20 | 0.35 | 0.35 | 0.20 | 0.15 | 0.15 | 0.30 | 0.05 | 0.15 | 0.15 | 0.30 | 0.25 | 0.10 | 0.30 | 0.35 | 0.05 | 0.45 | 0.35 | 0.10 | 0.15 | 0.05 | 0.10 | 0.25 | 0.20 | 0.45 | 0.30 |
| 72 | 0.10 | 0.35 | 0.25 | 0.05 | 0.10 | 0.40 | 0.05 | 0.05 | 0.25 | 0.05 | 0.20 | 0.10 | 0.20 | 0.35 | 0.35 | 0.10 | 0.10 | 0.30 | 0.05 | 0.20 | 0.05 | 0.25 | 0.25 | 0.50 | 0.15 | 0.40 | 0.30 | 0.05 | 0.30 | 0.25 |
| 73 | 0.20 | 0.05 | 0.25 | 0.10 | 0.05 | 0.15 | 0.05 | 0.00 | 0.10 | 0.20 | 0.15 | 0.15 | 0.00 | 0.15 | 0.00 | 0.25 | 0.10 | 0.25 | 0.15 | 0.05 | 0.15 | 0.05 | 0.05 | 0.25 | 0.20 | 0.25 | 0.05 | 0.10 | 0.10 | 0.30 |
| 74 | 0.30 | 0.40 | 0.25 | 0.20 | 0.25 | 0.40 | 0.20 | 0.30 | 0.15 | 0.40 | 0.15 | 0.25 | 0.35 | 0.30 | 0.25 | 0.15 | 0.10 | 0.25 | 0.45 | 0.35 | 0.15 | 0.40 | 0.25 | 0.45 | 0.40 | 0.50 | 0.20 | 0.50 | 0.15 | 0.25 |
| 75 | 0.20 | 0.30 | 0.15 | 0.20 | 0.10 | 0.25 | 0.10 | 0.20 | 0.10 | 0.05 | 0.20 | 0.15 | 0.20 | 0.20 | 0.20 | 0.25 | 0.15 | 0.20 | 0.10 | 0.10 | 0.10 | 0.20 | 0.35 | 0.55 | 0.20 | 0.20 | 0.15 | 0.10 | 0.20 | 0.25 |
| 76 | 0.15 | 0.15 | 0.40 | 0.75 | 0.50 | 0.20 | 0.40 | 0.40 | 0.35 | 0.45 | 0.25 | 0.30 | 0.00 | 0.30 | 0.05 | 0.00 | 0.00 | 0.00 | 0.60 | 0.20 | 0.30 | 0.05 | 0.25 | 0.40 | 0.10 | 0.05 | 0.10 | 0.10 | 0.05 | 0.05 |
| 77 | 0.35 | 0.35 | 0.10 | 0.05 | 0.05 | 0.30 | 0.25 | 0.50 | 0.35 | 0.15 | 0.00 | 0.40 | 0.15 | 0.15 | 0.50 | 0.30 | 0.00 | 0.10 | 0.15 | 0.20 | 0.20 | 0.15 | 0.25 | 0.30 | 0.55 | 0.45 | 0.55 | 0.35 | 0.15 | 0.40 |
| 78 | 0.10 | 0.20 | 0.25 | 0.00 | 0.20 | 0.15 | 0.10 | 0.00 | 0.00 | 0.10 | 0.10 | 0.05 | 0.10 | 0.40 | 0.20 | 0.05 | 0.00 | 0.10 | 0.05 | 0.05 | 0.00 | 0.20 | 0.05 | 0.05 | 0.20 | 0.30 | 0.10 | 0.15 | 0.00 | 0.25 |
| 79 | 0.15 | 0.40 | 0.35 | 0.25 | 0.20 | 0.40 | 0.15 | 0.45 | 0.40 | 0.35 | 0.35 | 0.20 | 0.35 | 0.25 | 0.35 | 0.35 | 0.00 | 0.20 | 0.30 | 0.15 | 0.30 | 0.25 | 0.15 | 0.60 | 0.50 | 0.65 | 0.25 | 0.35 | 0.05 | 0.25 |
| 80 | 0.15 | 0.30 | 0.40 | 0.20 | 0.40 | 0.45 | 0.25 | 0.20 | 0.35 | 0.10 | 0.05 | 0.15 | 0.40 | 0.20 | 0.20 | 0.20 | 0.00 | 0.15 | 0.30 | 0.25 | 0.50 | 0.25 | 0.40 | 0.45 | 0.60 | 0.20 | 0.30 | 0.40 | 0.00 | 0.30 |
| 81 | 0.15 | 0.10 | 0.15 | 0.00 | 0.05 | 0.20 | 0.25 | 0.15 | 0.05 | 0.10 | 0.05 | 0.10 | 0.05 | 0.20 | 0.05 | 0.15 | 0.00 | 0.05 | 0.00 | 0.00 | 0.05 | 0.25 | 0.25 | 0.25 | 0.00 | 0.15 | 0.15 | 0.20 | 0.25 | 0.20 |
| 82 | 0.20 | 0.35 | 0.45 | 0.55 | 0.30 | 0.45 | 0.15 | 0.45 | 0.25 | 0.40 | 0.60 | 0.65 | 0.70 | 0.45 | 0.60 | 0.20 | 0.00 | 0.15 | 0.35 | 0.45 | 0.50 | 0.25 | 0.45 | 0.65 | 0.45 | 0.65 | 0.15 | 0.40 | 0.30 | 0.45 |
| 83 | 0.10 | 0.35 | 0.40 | 0.10 | 0.15 | 0.20 | 0.10 | 0.15 | 0.10 | 0.30 | 0.00 | 0.10 | 0.20 | 0.15 | 0.20 | 0.05 | 0.10 | 0.15 | 0.40 | 0.20 | 0.15 | 0.15 | 0.00 | 0.25 | 0.15 | 0.25 | 0.20 | 0.15 | 0.10 | 0.20 |
| 84 | 0.05 | 0.20 | 0.20 | 0.15 | 0.25 | 0.05 | 0.20 | 0.15 | 0.40 | 0.35 | 0.20 | 0.10 | 0.30 | 0.20 | 0.05 | 0.05 | 0.05 | 0.10 | 0.50 | 0.25 | 0.20 | 0.20 | 0.05 | 0.20 | 0.20 | 0.05 | 0.20 | 0.05 | 0.15 | 0.00 |
| 85 | 0.05 | 0.00 | 0.05 | 0.00 | 0.10 | 0.05 | 0.05 | 0.20 | 0.00 | 0.20 | 0.10 | 0.15 | 0.00 | 0.05 | 0.05 | 0.00 | 0.00 | 0.00 | 0.20 | 0.10 | 0.05 | 0.00 | 0.00 | 0.05 | 0.10 | 0.05 | 0.00 | 0.05 | 0.05 | 0.00 |
| 86 | 0.05 | 0.25 | 0.15 | 0.20 | 0.60 | 0.25 | 0.00 | 0.05 | 0.00 | 0.15 | 0.25 | 0.30 | 0.25 | 0.25 | 0.30 | 0.20 | 0.05 | 0.15 | 0.15 | 0.20 | 0.10 | 0.10 | 0.00 | 0.45 | 0.05 | 0.20 | 0.05 | 0.40 | 0.30 | 0.30 |
| 87 | 0.40 | 0.65 | 0.65 | 0.25 | 0.55 | 0.40 | 0.30 | 0.20 | 0.20 | 0.40 | 0.30 | 0.35 | 0.55 | 0.65 | 0.55 | 0.25 | 0.50 | 0.40 | 0.45 | 0.30 | 0.30 | 0.30 | 0.45 | 0.90 | 0.35 | 0.65 | 0.70 | 0.50 | 0.45 | 0.55 |
| 88 | 0.40 | 0.20 | 0.55 | 0.20 | 0.55 | 0.35 | 0.45 | 0.65 | 0.65 | 0.55 | 0.60 | 0.55 | 0.45 | 0.50 | 0.50 | 0.40 | 0.20 | 0.50 | 0.55 | 0.25 | 0.20 | 0.75 | 0.45 | 0.40 | 0.35 | 0.65 | 0.30 | 0.45 | 0.55 | 0.50 |
| 89 | 0.10 | 0.00 | 0.05 | 0.05 | 0.10 | 0.10 | 0.05 | 0.20 | 0.05 | 0.20 | 0.05 | 0.05 | 0.00 | 0.10 | 0.00 | 0.10 | 0.25 | 0.05 | 0.10 | 0.15 | 0.05 | 0.00 | 0.25 | 0.30 | 0.30 | 0.05 | 0.10 | 0.20 | 0.20 | 0.10 |

## Peer Reviews

confidence: 4
contribution: 3
initial_rating: 5
presentation: 2
questions: 1. SPA currently focuses on static multi-view scenes. How does the model generalize to dynamic environments, especially where temporal information is critical?
2. The evaluation is focused solely on imitation learning. How would SPA perform in a reinforcement learning setting?
3. Are there any optimizations or lightweight versions of SPA that could reduce computational costs?
soundness: 3
strengths: 1. The paper conducts one of the most extensive evaluations in embodied AI representation learning to date, covering 268 tasks across 8 different simulators. This large-scale evaluation provides a thorough comparison with multiple state-of-the-art methods showing a significant level of empirical rigor.
2. SPA uses neural rendering and multi-view images to enhance the 3D spatial awareness of the ViT, which is an effective way to give the model a better understanding of depth information and spatial relationships in 3D scenes.
3. The paper makes an important conceptual contribution by proposing and validating the spatial awareness hypothesis, which could guide future research in embodied AI representation learning.
summary: This paper propose a representation learning framework named SPA to incopriate the 3D spatial awarness in embodied AI. SPA represents an advancement in embodied representation learning by enhancing a standard ViT with intrinsic 3D spatial understanding through neural rendering. The comprehensive evaluation and consistent empirical success show the effectiveness of spatial awareness in embodied AI tasks.
weaknesses: 1. SPA simply extends and adapts the ViT by adding neural rendering and 3D spatial features to enhance expressiveness, but the underlying architecture is still the same ViT that already exists; in contrast, many new model architectures make more independent innovations at the algorithmic level. This paper is lack sufficient groundbreaking innovations in model architecture.
2. The evaluation of SPA focuses primarily on imitative learning and does not fully explore reinforcement learning or other complex learning paradigms. This limits the scope of understanding the generalizability and performance of the model under different real-world conditions.
3. SPA is designed for static multi-view images, which constrains the ability to model dynamics and temporal changes that are essential in many embodied AI scenarios. And the paper proposes 3D spatial awareness is critical, however it does not consider temporal relationships.
4. While the paper claims that SPA has achieved significant improvements in 3D spatial perception, there is a lack of independent comparative experiments to validate the contribution of neural rendering for the overall performance improvement. The specific effects of multi-view learning and 3D spatial understanding are not isolated. This makes it impossible to determine whether the improvements come from 3D spatial awareness or from better data or other improvements in training strategies, etc.

---

confidence: 3
contribution: 3
initial_rating: 6
presentation: 3
questions: Could the authors clarify if Section 2.2 represents a novel contribution or builds on existing methods?

I believe the DROID dataset consists of dynamic scenes, which is not explicitly handled by the NeuS volume rendering.
Did the authors do anything special to handle this?

Minor suggestions:

Table 1 appears to be structured more like an ablation study than a main result.
For reading flow, it might be helpful to move this to a later section.

Figure 1 is a bit hard to read due to choice of colors.
soundness: 3
strengths: Method addresses an important gap in current representation learning approaches by explicitly incorporating 3D spatial understanding through differentiable rendering.

Comprehensive evaluation across a large number of tasks and simulators demonstrates the broad applicability of their approach.

The self-supervised nature of their training signal (generated RGBD and semantic maps) is an interesting direction that reduces the need for expensive labeled data.
summary: This work introduces SPA, a representation learning method that incorporates 3D spatial awareness into Vision Transformers using differentiable rendering as a pretraining objective.
Starting with multi-view images and camera poses, the method constructs feature volumes using deformable attention and employs NeuS-based volume rendering to generate self-supervised RGBD and semantic maps for pretraining.
The authors claim their 3D pre-training objective better captures the 3D spatial relationships for embodied tasks.
They benchmark their approach through an extensive evaluation, spanning five existing benchmarks (VC-1, Franka, Meta-World, RLBench and LIBERO).
The results demonstrate consistent improvements over both vision-centric and embodied-specific baselines, with particularly strong performance on zero-shot camera pose estimation tasks.
weaknesses: The paper's performance on LIBERO-spatial (Table 4) is somewhat counterintuitive.
This seems like quite an important benchmark out of all the evaluation tasks, and given SPA's neural rendering pretraining objective, one would expect stronger results on spatial tasks.

It seems to me that AM-RADIO should be a baseline comparison in Table 3, given that the feature maps are in used as supervision during pre-training.

---

confidence: 4
contribution: 3
initial_rating: 8
presentation: 3
questions: 1. What are the mask tokens that are used to fill the masked patches in section 2.1? are they learnt?

2. Can you describe the tasks and what they entail properly? It is not much clear from the paper itself what the single and multi task benchmarks are about. 

3. Can you provide results for proper established real world tasks (object detection or vision language based spatial aware tasks)? You can check the OpenEQA dataset, or the paper "Spatial VLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities" for this.
soundness: 3
strengths: 1. The paper is very nicely written

2. The architecture is quite well thought out, tying several components effectively, a feat not easy to achieve or make it work.

3. The evaluation benchmark has 268 tasks, which is quite extensive and a big improvement over previous benchmarks.

4. Thorough ablations (mask ratio importance, dataset impact, etc) are very informative

5. Results are quite nice, showing the potential of SPA
summary: This paper introduces a new way of incorporating 3D spatial awareness into 2D visual setting to be used in embodied AI. The authors achieve this by first extracting 2D features from images via a ViT, then construct a 3D feature volume from the multi-view feature maps, then employs differentiable neural rendering to connect the 2D and 3D domains, predict color, depth and semantic features per pixel and then trains the whole model with rendering loss along with some regularizations. This paper also presents an extensive embodied evaluation benchmark.
weaknesses: 1. Benchmark descriptions are not well written. Not clear what the tasks are supposed to be.

2. Tables do not have sufficient captions, and is a bit difficult to understand the metrics from the tables themselves.

3. It is not clear from the tables which methods are adapted from vision community to solve embodied AI tasks, thus making it difficult to assess the fairness of the comparison.

4. Real world task setting is missing the most common vision language tasks which might benefit from spatial awareness. How well does this perform for tasks solved by papers like "Spatial VLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities"?

---

confidence: 3
contribution: 2
initial_rating: 5
presentation: 3
questions: My questions are listed in weakness section.
soundness: 2
strengths: The paper is well-written. The method named SPA is simple yet effective. The authors have carefully designed their experiments, showcasing SPA's impressive performance across a wide range of task types, including both single-task and language-conditioned multi-task scenarios. This level of comprehensive evaluation highlights the versatility and robustness of SPA. I greatly appreciate the extensive efforts the authors have invested in the evaluation process, as they rigorously compared SPA against multiple state-of-the-art representation methods.
summary: The paper presents SPA, an innovative framework for representation learning that enhances 3D spatial awareness in embodied AI. SPA integrates differentiable neural rendering on multi-view images to give a ViT a strong sense of spatial understanding, enabling it to excel in various embodied tasks. The author conducted an extensive evaluation across 268 tasks in 8 different simulators, addressing both single-task and language-conditioned multi-task scenarios. SPA achieves superior performance with less training data. Real-world experiments confirm SPA’s practical effectiveness, underscoring the importance of 3D spatial awareness in representation learning for embodied AI. Overall, the paper is well-written and the experiments are extensive.
weaknesses: My main concerns about this paper are listed below.
1) The author claims that the paper proposes a significant spatial hypothesis that 3D spatial awareness is crucial for embodied representation learning. However, I believe this hypothesis is clear long before and that is also why many work try to use 3D features for embodied tasks. I appreciate the authors' efforts to demonstrate this, but I do not think it is a significant 'new' hypothesis.

2) About the methodology. Previous work have tried to generate 3D representations from 2D images and use them for embodied tasks. But here, the author randomly mask patches across multi-view images. So I'm worried about the quality of the volume construction. MAE leverages a high ratio of mask and I'm wondering whether the quality of construction will be affected, and then make the training objective too easy during the volume rendering.

3) As the paper is about how to integrate 3D spatial awareness into 2D backbones, I believe some work about learning 3D features from 2D images should be further discussed. However, in section "Representation Learning for Embodied AI", I didn't see too much about this.

Overall, I think there are still some questions in this paper, both on writing and methodology. But I may consider raise the score if the authors can explain more about question 2. And I would like to know the attitude of the authors towards question 1&3

Meta-review: The paper introduces SPA, a framework that integrates 3D spatial awareness into Vision Transformers (ViTs) for embodied AI tasks. SPA uses differentiable neural rendering on multi-view images to improve the ViT’s understanding of 3D spatial relationships. The authors evaluate SPA across 268 tasks in 8 simulators, showing that it outperforms over 10 state-of-the-art methods while using less training data. Real-world experiments further confirm its practical utility, highlighting the importance of 3D spatial awareness in embodied AI.

Strengths of the Paper:

-- The paper presents a large-scale evaluation of SPA across 268 tasks in diverse simulators, providing strong empirical evidence of its effectiveness in both single-task and multi-task scenarios.

-- By integrating neural rendering, SPA improves the ViT’s spatial understanding, which is crucial for embodied AI tasks involving 3D scenes.

-- The paper includes real-world experiments and a commitment to open-source the code, promoting further research in embodied AI.

Weaknesses of the Paper:

-- The paper focuses primarily on imitation learning, without exploring reinforcement learning or dynamic environments, which are critical for many real-world applications.

-- SPA only works with static multi-view images and doesn’t handle temporal dynamics. Additionally, the paper doesn’t isolate the impact of its key components, making it unclear if improvements are due to the 3D spatial features or other factors.

-- The evaluation lacks commonly used real-world benchmarks like object detection or vision-language tasks that could better demonstrate SPA’s broader applicability.

After carefully reading the paper, reviews and rebuttal discussions, the AC agrees with the majority of the reviewers on accepting the paper.

Decision: Accept (Poster)