Volume-Aware Distance for Robust Similarity Learning
A new volume-aware distance for the better similarity learning
摘要
评审与讨论
This paper presents Volume-Aware Distance (VAD), a novel metric for similarity learning that extends traditional point-wise distances to field-to-field distances by introducing volume-aware data representations. The authors propose a measure-head network for volume prediction and a volume expansion regularizer to improve generalization. The method is mathematically well-grounded, providing strong theoretical guarantees, and is empirically validated across multiple domains.
给作者的问题
See the weakness.
论据与证据
The main contributions of the paper are: A new similarity metric (VAD) that enhances generalization by incorporating volume-awareness. A theoretical framework demonstrating VAD’s tighter generalization bounds. Empirical results showing VAD’s superiority over state-of-the-art similarity learning methods.
方法与评估标准
The proposed VAD framework, including the measure-head network and regularizer, is well-motivated. The evaluation includes multiple supervised and unsupervised tasks, making the results highly convincing.
理论论述
The authors present rigorous mathematical proofs for generalization error bounds and sample-space coverage, which validate the effectiveness of VAD.
实验设计与分析
The experiments are well-structured, covering both metric learning and contrastive learning. The baselines used for comparison are strong, ensuring credibility. Ablation studies demonstrate the necessity of each component.
补充材料
I reviewed the supplementary material.
与现有文献的关系
The work is well-grounded in existing literature and makes a meaningful contribution to the field of similarity learning.
遗漏的重要参考文献
No critical references appear to be missing.
其他优缺点
Strengths:
Novel and impactful contribution to similarity learning.
Solid theoretical underpinnings.
Comprehensive empirical evaluation.
Weakness:
The computational complexity of the method could be further analyzed in large-scale settings.
其他意见或建议
None
Thank you for your positive and constructive comments! Our responses are given below.
Comment_1: The computational complexity of the method could be further analyzed in large-scale settings.
Response_1: Thank you for your suggestion! Here we would like to provide the training time comparison of our VADSL and the baseline methods (SimCLR and SwAV) on the large-scale ImageNet-1K dataset. Specifically, we use eight NVIDIA TeslaV100 GPUs to train our models based on SimCLR and SwAV with 100 epochs, respectively. For each case, we set the batch size to 512, 1024, and 1536.
| Method | ImageNet-1K (ba. si. = 512) | ImageNet-1K (ba. si. = 1024) | ImageNet-1K (ba. si. = 1536) |
|---|---|---|---|
| SimCLR | 70.1 | 35.2 | 23.1 |
| SwAV | 71.2 | 36.7 | 24.2 |
| VADSL (SimCLR + VAD) | 71.5 | 35.6 | 23.5 |
| VADSL (SwAV + VAD) | 72.1 | 36.9 | 24.6 |
The table above reveals that the introduction of the proposed VAD component causes very little increase in time consumption (less than 2%). This is because the gradient calculation of VAD is independent of the size of the training data, thereby keeping the training time well within practical limits. We will also add the above time comparison in the camera-ready version if this paper is finally accepted.
The paper introduces Volume-Aware Distance (VAD), a novel metric for robust similarity learning. Unlike conventional point-level similarity measures, VAD models instances as volume-aware data balls, improving generalization by capturing field-to-field geometric relationships. The paper also proposes a measure-head network to learn instance volumes and a volume expansion regularizer to further enhance generalization. Theoretical analysis shows that VAD tightens generalization bounds and preserves topological properties, while extensive experiments on supervised and unsupervised tasks demonstrate clear advantages over state-of-the-art methods.
给作者的问题
i). How sensitive is VAD to the choice of the measure-head network’s architecture?
ii). Would VAD work in few-shot learning settings where data volume is extremely limited?
论据与证据
The key claims in the paper include: VAD generalizes better than conventional similarity learning methods, supported by theoretical proofs. VAD outperforms baseline models across multiple tasks, shown via strong empirical results.
方法与评估标准
The measure-head network and volume expansion regularizer are well-designed and logically justified. The proposed method is evaluated comprehensively across various datasets and baselines, making the results reliable.
理论论述
I examined the proofs for generalization bounds and distance flexibility. The claims are mathematically sound, and the derivations align with existing principles in similarity learning.
实验设计与分析
Experiments cover multiple learning paradigms (metric learning and contrastive learning). Baseline comparisons are thorough, ensuring fairness. Ablation studies validate the necessity of each proposed component.
补充材料
I reviewed the supplementary material, including additional experiments and theoretical proofs. The additional insights further solidify the validity of the approach.
与现有文献的关系
The paper clearly situates itself within the literature on metric learning, contrastive learning, and regularization methods. The citations are appropriate and comprehensive.
遗漏的重要参考文献
No.
其他优缺点
Strengths: Well-motivated and novel approach to similarity learning. Strong theoretical backing with comprehensive analysis. Extensive empirical validation across diverse datasets.
Weaknesses: Computational overhead due to volume estimation, though the authors argue it remains manageable.
其他意见或建议
None
Thank you for your positive and constructive comments! Our point-by-point responses are provided below.
Comment_1: Computational overhead due to volume estimation, though the authors argue it remains manageable.
Response_1: Thanks for your comments! We agree with the reviewer that the volume estimation does indeed introduce additional computation burden due to the necessary feedforward of the head network. However, we want to clarify that such additional computation cost is actually necessary to achieve better performance and is negligible in real-world use. Specifically, as shown in Appendix A.3 of our manuscript, the baseline method SimCLR and our method VADSL spend 2.3 hours and 2.4 hours, respectively, to train 100 epochs on CIFAR-10 (batch size = 512). It implies that the calculation of volume estimation only adds less than 5% of the time consumption. Similarly, on ImageNet-100, the time cost of the baseline method and our method are 10.9 hours and 11.2 hours, respectively, which means that the volume estimation merely requires an additional 3% time consumption. In summary, we believe that the additional time cost of our method is relatively small and acceptable in practice.
Comment_2: How sensitive is VAD to the choice of the measure-head network’s architecture?
Response_2: Thanks for your comments! Since the measure-head network is implemented by the classical MLP with a single hidden layer, the only human-tuned parameter is the dimensionality of the hidden layer (because the input-feature dimensionality is usually fixed and the output-layer dimensionality is always 1). Therefore, here we want to investigate the robustness of our method by changing the hidden-layer dimensionality.
| Dataset | 32-dim | 64-dim | 128-dim | 256-dim | 512-dim |
|---|---|---|---|---|---|
| CIFAR-10 (400-eps, 512-bs) | 86.3 | 93.5 | 94.9 | 93.5 | 91.2 |
| STL-10 (400-eps, 512-bs) | 79.4 | 85.2 | 85.6 | 85.8 | 81.1 |
In above table, we vary the hidden-layer dimensionality from 32 to 512 to record the final performance of our method on STL-10 and CIFAR-10. We can easily observe that the hidden-layer dimensionality indeed affects the classification accuracy to some extent, because VAD needs a certain amount of hidden nodes to ensure its nonlinearity. However, it is also obvious that the performance of our method is relatively stable around 128 (e.g., from 64 to 256), which means that such a hyper-parameter can be easily tuned in practical use. Meanwhile, we would like to further investigate the sensitivity of VAD by setting different number of hidden layers (including 1-layer, 2-layers, and 3-layer). For each case, we let the dimensionalities of all hidden layers be the same (i.e., 128-dim). The following table records the corresponding accuracy rates of our method on CIFAR-10 and STL-10.
| Dataset | 1-layer hidden | 2-layers hidden | 3-layers hidden |
|---|---|---|---|
| CIFAR-10 (400-eps, 512-bs) | 94.9 | 93.6 | 94.5 |
| STL-10 (400-eps, 512-bs) | 85.6 | 85.6 | 85.5 |
We can clearly observe that the results on both datasets are relatively stable when the layer number changes, and this means that our method is robust to the choice of network architectures.
Comment_3: Would VAD work in few-shot learning settings where data volume is extremely limited?
Response_3: Thanks for your comments! Actually, VAD is able to work well for few-shot recognition tasks. To be specific, for the four datasets (i.e., CAR-196, CUB-200, SOP, and In-Shop) used in the metric learning task, no classes of the test data are involved in the training phase, and only very few reference examples are provided for classification during the test phase. In such a few-shot setting, our VAD effectively improves the NMI and Recall@K scores of the baseline methods, and our final performance can surpass SOTA methods in most cases (Tab. 2). We believe that the effectiveness of our VAD in few-shot learning settings is well validated.
This paper introduces a novel approach to similarity learning with the Volume-Aware Distance (VAD) metric. Instead of relying on traditional point-level similarity measures, VAD models data instances as volume-aware data spheres, allowing it to capture both observed and unobserved neighbor relationships. To improve generalization, the method utilizes a measure-head network for estimating instance volumes and incorporates a volume expansion regularizer. Theoretical analysis confirms its enhanced error bounds and topological properties, while extensive experiments across multiple domains demonstrate its effectiveness compared to existing methods.
给作者的问题
a. Can VAD be extended beyond similarity learning, e.g., in clustering?
b. How does the measure-head network perform when used with transformers instead of CNNs?
论据与证据
This paper asserts that VAD enhances generalization by encompassing a wider sample space while maintaining essential topological properties, as substantiated by theoretical analysis. Furthermore, VAD surpasses leading methods in both supervised metric learning and unsupervised contrastive learning. These conclusions are reinforced by rigorous mathematical derivations and comprehensive experimental evaluations, highlighting its robustness and broad applicability.
方法与评估标准
The experimental setup is thorough, covering multiple datasets (e.g., CIFAR-10, ImageNet, SOP, CUB-200) and different learning paradigms. The proposed method makes sense in similarity learning, particularly in contrastive learning and metric learning.
理论论述
The proofs related to generalization error bounds and distance flexibility looks fine. They are mathematically sound, and the theoretical contribution is clear.
实验设计与分析
The experimental design covers both supervised and unsupervised settings. The baselines are well-selected, and results consistently show the advantage of the proposed VAD. The t-SNE visualizations and ablation studies further strengthen the empirical support.
补充材料
The supplementary material provides additional experiments and proofs, which reinforces the claims in the main paper.
与现有文献的关系
The paper effectively connects its contributions to prior work in metric learning, contrastive learning, and regularization techniques. The citations are comprehensive and demonstrate a good understanding of the field.
遗漏的重要参考文献
Not obvious
其他优缺点
Strengths:
- Novel extension of distance metric learning and comprehensive theoretical guarantees.
- Comprehensive empirical evaluation. Well-written and clearly structured.
Weaknesses:
Some details are unclear:
a. Can VAD be extended beyond similarity learning, e.g., in clustering?
b. How does the measure-head network perform when used with transformers instead of CNNs?
其他意见或建议
N/A
Thank you for your appreciation of the novelty, theoretical analyses, and experimental results of our paper! Thanks also for your very insightful and constructive suggestions! Our point-by-point responses are as follows.
Comment_1: Can VAD be extended beyond similarity learning, e.g., in clustering?
Response_1: Thanks for your comments! Yes, VAD is also applicable to clustering task. Actually, in our manuscript, we have already evaluated the clustering performance of VAD by showing the NMI scores on CAR-196, CUB-200, SOP, and In-Shop, where our VAD can successfully improve the baseline methods Npair and ProxyAnchor with at least 3 percentages (see Tab. 2). Here we also want to follow the reviewer’s suggestion to further validate the effectiveness of our VAD on the deep clustering model “contrastive clustering (CC)” (Li et al., Contrastive Clustering, AAAI’21). We simply implement our measure-head network by replacing the contrastive head in CC, so that we can calculate the corresponding VAD similarity values. We record the clustering accuracy and NMI scores of compared approaches on CIFAR-10 and CIFAR-100, and the following table reveals that our method still improves the strong baseline upon CC itself.
| Setting | CIFAR-10 (Acc) | CIFAR-10 (NMI) | CIFAR-100 (Acc) | CIFAR-100 (NMI) |
|---|---|---|---|---|
| CC (baseline) | 79.0 | 70.5 | 42.9 | 43.1 |
| VADSL (ours) | 79.4 | 71.2 | 43.6 | 43.8 |
Comment_2: How does the measure-head network perform when used with transformers instead of CNNs?
Response_2: Thanks for your comments! We agree with the reviewer that transformer has shown very promising reliability in lots of vision tasks. As our Tab. 4 has provided the detailed performance results (i.e., k-NN, Top-1, Top-5), we would like to discuss here again the superiority of our method when it is equipped with the ViT model (ViT.16/48MB). Specifically, for both ImageNet-100 and ImageNet-1K, we implement our method on the cluster-free method BYOL as well as the cluster-based method SwAV, and the encoder networks of all compared methods are ViT.16. It can be observed that our method consistently improves the two baseline methods on all cases of the two datasets. Furthermore, we also compare our method with SOTA methods including DINO, iBOT, and MTE, and we can find that our VADSL outperforms the SOTA in most cases (see the bottom of Tab. 4). This implies that our method works well with the vision transformer in the feature extraction, and also shows that our VAD is a fairly general technique that can be used in different frameworks.
The paper introduces Volume-Aware Distance (VAD), a new similarity metric that generalizes conventional point-wise distance by incorporating volume information. The authors propose a measure-head network to learn instance volumes and a volume expansion regularizer to improve generalization. Theoretical analyses prove a tighter generalization bound, and experimental results show superior performance in metric learning and contrastive learning tasks.
给作者的问题
(1) Can VAD be applied to NLP tasks such as sentence similarity?
(2) How does VAD behave in extremely high-dimensional spaces?
论据与证据
The authors claim:VAD provides better generalization (supported by theoretical proofs).VAD outperforms state-of-the-art methods in supervised and unsupervised tasks (validated via extensive experiments). These claims are well-supported by rigorous proofs and strong empirical evidence.
方法与评估标准
The method is well-motivated and logically sound. Evaluation is extensive, with results on various domains and datasets, ensuring robustness.
理论论述
The proofs for error bounds, flexibility, and sample-space coverage are well-structured and mathematically valid.
实验设计与分析
Experiments are comprehensive, covering both supervised and unsupervised learning. Ablation studies clearly show the importance of each component. Comparison with strong baselines ensures credibility.
补充材料
The appendix provides additional theoretical proofs and more experimental results, further strengthening the contributions.
与现有文献的关系
The paper relates well to existing literature in metric learning and contrastive learning.
遗漏的重要参考文献
No major missing references.
其他优缺点
Strengths: 1) Well-motivated and novel approach. 2) Strong theoretical guarantees. 3) Impressive empirical results.
Weaknesses: Slightly higher computational cost due to volume estimation.
其他意见或建议
NA
伦理审查问题
NA
Thanks for your positive and insightful comments! Our explanation and clarification can be found as follows.
Comment_1: Slightly higher computational cost due to volume estimation.
Response_1: Thanks for your comments! We agree with the reviewer that the volume estimation does indeed introduce additional computation burden due to the necessary feedforward of the head network. However, we want to clarify that such additional computation cost is actually necessary to achieve better performance and is negligible in real-world use. Specifically, as shown in Appendix A.3 of our manuscript, the baseline method SimCLR and our method VADSL spend 2.3 hours and 2.4 hours, respectively, to train 100 epochs on CIFAR-10 (batch size = 512). It implies that the calculation of volume estimation only adds less than 5% of the time consumption. Similarly, on ImageNet-100, the time cost of the baseline method and our method are 10.9 hours and 11.2 hours, respectively, which means that the volume estimation merely requires an additional 3% time consumption. In summary, we believe that the additional time cost of our method is relatively small and acceptable in practice.
Comment_2: Can VAD be applied to NLP tasks such as sentence similarity?
Response_2: Thanks for your comments! Yes, VAD can be applied to NLP tasks. In fact, we have already validated the effectiveness of our method on two sentence embedding related datasets including STS and BookCorpus. As the reviewer considered, for each dataset, we construct the positive (similar) pairs by aligning each sentence with its contextual sentences in the same paragraph, while we build the negative (dissimilar) pairs by combining those sentences from different paragraphs. For both datasets, our method can consistently improve the baseline methods and outperform the SOTA methods in most cases (see Tab. 5 and Fig. A1), so we believe that our method is applicable to the sentence embedding tasks.
Comment_3: How does VAD behave in extremely high-dimensional spaces?
Response_3: Thanks for your comments! Here we follow the reviewer’s suggestion to investigate the reliability of VAD for high-dimensional features. Specifically, we increase the output-layer dimensionality of the feature encoder from 512 to 4096, and record the corresponding accuracy of our method on STL-10 (batch size = 512). From the following table, we can clearly observe that the high-dimensional space indeed weakens the feature discriminability, where the accuracy decreases when the feature dimensionality is higher than 1024. However, in these high-dimensional cases, our VAD can still successfully improve the final performance on STL-10, which demonstrates the usefulness of VAD even in the high-dimensional space.
| Setting | STL_100-eps (w/o VAD) | STL_400-eps (w/o VAD) | STL_100-eps (w/ VAD) | STL_400-eps (w/ VAD) |
|---|---|---|---|---|
| 512-dimension | 71.1±1.2 | 78.2±3.3 | 77.1±2.9 ✔ | 85.6±3.2 ✔ |
| 1024-dimension | 70.4±4.2 | 78.2±2.1 | 77.2±3.6 ✔ | 85.9±1.6 ✔ |
| 2048-dimension | 68.3±2.3 | 76.5±1.3 | 73.3±1.2 ✔ | 82.3±2.3 ✔ |
| 4096-dimension | 68.9±4.1 | 77.2±1.6 | 75.4±3.2 ✔ | 83.2±2.9 ✔ |
This paper introduces Volume-Aware Distance (VAD), a novel metric for robust similarity learning. Unlike conventional point-level similarity measures, VAD models instances as volume-aware data balls, improving generalization by capturing field-to-field geometric relationships.
This paper received universal positive scores after the rebuttal period. All reviewers agreed that the approach is novel and that the empirical results were very solid.