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Volume-Aware Distance for Robust Similarity Learning
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Proposes a volume-aware distance (VAD) that represents each instance as a predicted-volume data ball and scales point distances by the volumes, trained via a measure-head and volume expansion regularizer for similarity learning.
Problem
Point-level distances in similarity learning (metric and contrastive learning) generalize poorly because finitely many training points cannot cover the infinite sample space, leading to bumpy decision boundaries.
Approach
Extend each data point to a data ball with a learned volume predicted by a measure-head MLP, and define a volume-aware distance that divides the Euclidean feature distance by exp(V(x)+V(x')), so large-volume balls capture unsampled neighbors; a volume expansion regularizer pushes volumes up.
Key results
- On CUB-200 with 512-dim embeddings and Npair, VADSL-NP reaches R@1 ~77.36 vs Npair baseline 65.38 on R@1 row (metric learning gains reported across datasets).
- On ImageNet-1K with ViT-B/16 (800 epochs), VADSL cluster-used reports 80.5 k-NN top-1 versus MTE w/ iBOT 78.3 in the table.
- Ablation shows increasing lambda from 0.1 to 0.5 gives noticeable gains (e.g., CAR-196 128-dim Npair R@1 68.39 to 70.23).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add VAD to ProxyAnchor | ProxyAnchor with ResNet-50 · CAR-196 | R@1: 92.31 -> 94.13 | Helped |
| Add VAD to ProxyAnchor | ProxyAnchor with ResNet-50 · CUB-200 | R@1: 74.42 -> 78.69 | Helped |
| Add VAD to ProxyAnchor | ProxyAnchor with ResNet-50 · SOP | R@1: 83.32 -> 86.23 | Helped |
| Add VAD to ProxyAnchor | ProxyAnchor with ResNet-50 · In-Shop | R@1: 92.78 -> 93.82 | Helped |
| Add VAD to Arcface | Arcface with ResNet-50 · AgeDB30 | accuracy: 93.93 -> 95.21 | Helped |
| Add VAD to Arcface | Arcface with ResNet-50 · CFP-FP | accuracy: 94.77 -> 96.24 | Helped |
| Add VAD to Arcface | Arcface with ResNet-50 · MegaFace (M.-106) | accuracy: 90.68 -> 91.78 | Helped |
| Use VAD with clustering instead of cluster-free VADSL (ablation) | VADSL with ResNet-50 · ImageNet-100, 100 epochs | Top-1: 77.6 -> 77.8 | Helped |
| Use VAD with clustering instead of cluster-free VADSL (ablation) | VADSL with ResNet-50 · ImageNet-100, 400 epochs | Top-1: 76.5 -> 77.8 | Helped |
| Use VAD with clustering instead of cluster-free VADSL (ablation) | VADSL with ResNet-50 · ImageNet-1K, 300 epochs | Top-1: 73.7 -> 74.9 | Helped |
| Use VAD with clustering instead of cluster-free VADSL (ablation) | VADSL with ResNet-50 · ImageNet-1K, 800 epochs | Top-1: 76.3 -> 77.6 | Helped |
| Add VAD to SimCLR with negative samples | SimCLR transfer learning with ResNet-50 · COCO val2017 object detection | APbb: 40.3 -> 43.1 | Helped |
Surprising findings
- VAD is not a metric: it violates the triangle inequality in general, which the authors present as a feature for flexible similarity relations.
Limitations
- Generalization bound and coverage results are asymptotic/loose and rely on assumptions (e.g., feature normalization, bounded volumes).
- Only one extra hyperparameter lambda but its gains are sensitive to choice; experiments run on TeslaV100 with limited reported seeds.
Experimental setup
Datasets: CUB-200 CAR-196 SOP In-Shop CASIA-WebFace CIFAR-10 STL-10 ImageNet-100 ImageNet-1K STS12-16 BookCorpus DD
Benchmarks: CUB-200 CAR-196 SOP In-Shop AgeDB30 CFP-FP MegaFace CIFAR-10 STL-10 ImageNet-100 ImageNet-1K STS12-16
Metrics: Recall@K NMI accuracy k-NN accuracy linear probing Top-1/Top-5 AP
Baselines: Npair ProxyAnchor JDR IBC ContextSimilarity MetricFormer MFC DASL SimCLR BYOL HCL SwAV
Builds on: SimCLR Npair loss ProxyAnchor SimCSE InfoGraph
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