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Potential Field Based Deep Metric Learning
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Proposes PFML, a deep metric learning framework that models sample and proxy interactions as superposed attractive/repulsive potential fields whose strength decays with distance, and evaluates it on Cars-196, CUB-200-2011 and SOP.
Problem
Deep metric learning typically relies on tuplet mining and proxy-sample losses that discard interactions or strengthen inter-sample forces with distance, making them sensitive to label noise and limiting intra-class feature learning.
Approach
Represent each embedding's influence as a continuous potential field (attraction for same class, repulsion for different class) that decays with distance, superpose all fields with proxies, and train the network by minimizing total potential energy via gradient descent.
Key results
- Achieves 73.4% R@1 on CUB-200-2011 with ResNet-50 (512 dim), outperforming HIST's 71.4%.
- Under 20% label noise, improves R@1 over Proxy Anchor by 6% on CUB-200-2011 and 7.6% on Cars-196.
- Proxies have lower average W2 distance to their data (0.16) than SoftTriple (0.24) on CUB-200-2011.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use potential-field metric learning instead of HIST | Image retrieval with ResNet-50 · CUB-200-2011 | R@1: 71.4 -> 73.4 ± 0.3 | Helped |
| Use potential-field metric learning instead of HIST | Image retrieval with ResNet-50 · Cars-196 | R@1: 89.6 -> 92.7± 0.3 | Helped |
| Use potential-field metric learning instead of HIST | Image retrieval with ResNet-50 · SOP | R@1: 81.4 -> 82.9 ± 0.2 | Helped |
| Use potential-field metric learning with 20% training-label noise instead of PA | ResNet-50 metric learning · CUB-200-2011 with 20% training-label noise | R@1: 60.7 -> 66.7 ± 0.6 | Helped |
| Use potential-field metric learning with 20% training-label noise instead of PA | ResNet-50 metric learning · Cars-196 with 20% training-label noise | R@1: 76.9 -> 84.5± 0.5 | Helped |
| Add proxies to augment the potential field (ablation) | Potential Field · Cars-196 and CUB-200-2011 | R@1 | Helped |
| Vary the number of proxies per class over [0, 30] (ablation) | Potential Field · Cars-196 and CUB-200-2011 | R@1 | Mixed |
| Vary the radius parameter δ over [0.1, 0.35] (ablation) | Potential Field · Cars-196 and CUB-200-2011 | R@1 | No clear effect |
| Remove potential-field decay by setting α = 0 (ablation) | Potential Field · Cars-196 and CUB-200-2011 | R@1 | Hurt |
| Use strong potential-field decay (α ∈ [3, 6]) instead of milder decay (α ∈ [1, 2]) (ablation) | Potential Field · Cars-196 and CUB-200-2011 | R@1 | Helped |
| Extend repulsion beyond the attraction radius by setting δrep > δatt (ablation) | Potential Field · Cars-196 and CUB-200-2011 | R@1 | Hurt |
Surprising findings
- Removing distance decay (alpha=0) degrades performance, while strongly decaying fields (alpha in [3,6]) work best.
Limitations
- Proxy count scales linearly with number of classes, increasing training cost for large class counts.
- Hyperparameters (delta, alpha, M) are selected via cross-validation and sensitive to choice of decay rate.
Experimental setup
Datasets: Cars-196 CUB-200-2011 Stanford Online Products
Benchmarks: Cars-196 CUB-200-2011 SOP
Metrics: Recall@K Wasserstein distance W2
Baselines: Proxy Anchor ProxyGML SoftTriple Multi-Similarity loss HIST HIER Hyp CPML ProxyNCA Triplet loss
Builds on: ProxyNCA Proxy Anchor contrastive loss triplet loss
Closest papers by meaning
- Mean Field Theory in Deep Metric Learning (ICLR 2024 · similarity 0.89)
- Revisiting Training Strategies and Generalization Performance in Deep Metric Learning (ICML 2020 · similarity 0.88)
- Deep Compositional Metric Learning (CVPR 2021 · similarity 0.87)
- Learning Semantic Proxies from Visual Prompts for Parameter-Efficient Fine-Tuning in Deep Metric Learning (ICLR 2024 · similarity 0.87)
- Deep Disentangled Metric Learning (AAAI 2025 · similarity 0.86)
- Towards Improved Proxy-Based Deep Metric Learning via Data-Augmented Domain Adaptation (AAAI 2024 · similarity 0.86)
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