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The Balanced-Pairwise-Affinities Feature Transform
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Supplementary material for the Balanced-Pairwise-Affinities (BPA) feature transform, giving a PyTorch-style implementation, ablations (Sinkhorn iterations, lambda, scalability, naive baselines), and insertion into PT-MAP, SPICE, and TopDBNet plus a synthetic sphere clustering study.
Problem
Upgrading the features of a set of input items so that downstream matching or grouping (few-shot classification, clustering, person re-ID) benefits from high-order pairwise relations among the items.
Approach
A transductive feature transform that computes cosine-distance self-affinities, sets the diagonal to infinity, runs Sinkhorn optimal transport to obtain a balanced fractional matching, and restores unit self-affinity; the resulting affinity matrix serves as the new feature set.
Key results
- ProtoNet-BPA with 5 Sinkhorn iterations reaches 71.20% 5-way 1-shot and 84.10% 5-way 5-shot on MiniImageNet validation, with gains saturating after a few iterations.
- On synthetic sphere clustering, k-means on BPA features is reported to give gains over original features across dimensions 10 to 1234 and noise levels 0.1 to 0.75.
- Lambda=0.1 is used for few-shot classification and lambda=0.25 for re-ID; BPA is reported to outperform the no-transform baseline consistently, unlike row-softmax or raw cosine affinity variants.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase Sinkhorn iterations from 1 to 2 (ablation) | ProtoNet-BPA_p · MiniImagenet validation, 5-way-1-shot | accuracy: 70.71 -> 71.10 | Helped |
| Increase Sinkhorn iterations from 1 to 2 (ablation) | ProtoNet-BPA_p · MiniImagenet validation, 5-way-5-shot | accuracy: 83.79 -> 84.01 | Helped |
| Increase Sinkhorn iterations from 2 to 4 (ablation) | ProtoNet-BPA_p · MiniImagenet validation, 5-way-1-shot | accuracy: 71.10 -> 71.18 | Helped |
| Increase Sinkhorn iterations from 2 to 4 (ablation) | ProtoNet-BPA_p · MiniImagenet validation, 5-way-5-shot | accuracy: 84.01 -> 84.08 | Helped |
| Increase Sinkhorn iterations from 4 to 8 (ablation) | ProtoNet-BPA_p · MiniImagenet validation, 5-way-1-shot | accuracy: 71.18 -> 71.20 | Helped |
| Increase Sinkhorn iterations from 4 to 8 (ablation) | ProtoNet-BPA_p · MiniImagenet validation, 5-way-5-shot | accuracy: 84.08 -> 84.10 | Helped |
| Increase Sinkhorn iterations from 8 to 16 (ablation) | ProtoNet-BPA_p · MiniImagenet validation, 5-way-1-shot | accuracy: 71.20 -> 71.20 | No clear effect |
| Increase Sinkhorn iterations from 8 to 16 (ablation) | ProtoNet-BPA_p · MiniImagenet validation, 5-way-5-shot | accuracy: 84.10 -> 84.10 | No clear effect |
| Add BPA rather than applying no transform (ablation) | PTMAP · MiniImagenet few-shot classification | accuracy | Helped |
| Vary Sinkhorn entropy regularization λ (ablation) | Few-shot classification with BPA · MiniImagenet validation | accuracy | Mixed |
| Vary Sinkhorn entropy regularization λ (ablation) | BPA for person re-identification · Market-1501 validation | mAP | Mixed |
| Vary Sinkhorn entropy regularization λ (ablation) | BPA for person re-identification · Market-1501 validation | rank-1 | Mixed |
Surprising findings
- The main paper mistakenly reported lambda=1.0 for re-ID, whereas all results used lambda=0.25.
Limitations
- Transductive module whose cost is quadratic in the number of input items per batch.
- Optimal lambda depends on the number of shots and task type, requiring per-setting tuning for best results.
Experimental setup
Datasets: MiniImageNet Tiered-ImageNet Market-1501
Benchmarks: MiniImageNet Tiered-ImageNet Market-1501
Metrics: accuracy mAP rank-1 ARI NMI
Baselines: PT-MAP ProtoNet SPICE TopDBNet k-means on original features softmax-normalized affinity cosine affinity
Builds on: Sinkhorn-Knopp PT-MAP SPICE ProtoNet TopDBNet
Closest papers by meaning
- Pairwise Matching Through Max-Weight Bipartite Belief Propagation (CVPR 2016 · similarity 0.85)
- Generalizable Person Re-identification via Balancing Alignment and Uniformity (NeurIPS 2024 · similarity 0.82)
- Exploring the Camera Bias of Person Re-identification (ICLR 2025 · similarity 0.82)
- MATCHA: Towards Matching Anything (CVPR 2025 · similarity 0.82)
- FairDD: Fair Dataset Distillation (NeurIPS 2025 · similarity 0.81)
- PairDETR : Joint Detection and Association of Human Bodies and Faces (CVPR 2024 · similarity 0.81)
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