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Not All Classes Stand on Same Embeddings: Calibrating a Semantic Distance with Metric Tensor
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Proposes metric-tensor-based consistency regularization for semi-supervised image classification, learning a global and class-wise local metric tensor on embeddings to measure semantic distance between weak and strong views.
Problem
Existing consistency-training SSL methods measure distances between augmented views with Euclidean distance, ignoring non-Euclidean geometry and class-wise variation of embedding spaces.
Approach
Replace the Euclidean distance in consistency regularization with a learned metric tensor: a global metric tensor estimated from all embeddings (class-invariant) plus class-wise local metric tensors estimated via pseudo-labels on projected embeddings (class-variant), tied together by an MSE consistency loss and a trace regularizer.</ntml:parameter>
Key results
- Achieves average top-1 error of 4.33% on CIFAR-10 (40/250/4000 labels) versus 4.59% for SoftMatch and 5.60% for FixMatch, per Table 1.
- On STL-10 with 40 labels, error drops to 20.47% vs 21.42% for SoftMatch (Table 2 as reported).
- Ablation shows each loss term contributes; global-only metric tensor gives poor performance until local tensors are added (Table 3).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the local metric loss LMT-L to the global metric loss LMT-G (ablation) | Metric-tensor consistency regularization · CIFAR-10 (40 labels) | top-1 classification error rate (%): 7.87 -> 5.19 | Helped |
| Add the consistency loss LMT-C to the global and local metric losses (ablation) | Metric-tensor consistency regularization · CIFAR-10 (40 labels) | top-1 classification error rate (%): 5.19 -> 4.88 | Helped |
| Add the informative local metric loss LMT-N to LMT-G, LMT-L, and LMT-C (ablation) | Metric-tensor consistency regularization · CIFAR-10 (40 labels) | top-1 classification error rate (%): 4.88 -> 4.34 | Helped |
| Set EMA momentum to 0.97 instead of 0.99 (ablation) | Proposed method · CIFAR-10 (40 labels) | top-1 classification error rate (%): 4.37 -> 4.42 | Hurt |
| Set EMA momentum to 0.95 instead of 0.99 (ablation) | Proposed method · CIFAR-10 (40 labels) | top-1 classification error rate (%): 4.37 -> 4.61 | Hurt |
| Use the proposed method instead of ConMatch | Semi-supervised image classification · CIFAR-10, Avg. | top-1 classification error rate (%): 4.34±0.15 -> 4.33±0.12 | Helped |
| Use the proposed method instead of SimMatch | Semi-supervised image classification · CIFAR-100, Avg. | top-1 classification error rate (%): 27.82±0.87 -> 27.70±0.74 | Helped |
| Use the proposed method instead of SoftMatch | Semi-supervised image classification · SVHN, Avg. | top-1 classification error rate (%): 2.18±0.08 -> 2.10±0.12 | Helped |
| Use the proposed method instead of SoftMatch | Semi-supervised image classification · STL-10, Avg. | top-1 classification error rate (%): 12.12±1.24 -> 11.39±1.95 | Helped |
Surprising findings
- Using only the global metric tensor (L_MT-G) gives poor classification performance, while adding class-wise local tensors substantially improves it.
Limitations
- Difficult to introduce metric tensors for manifold analysis due to heuristic nature of the manifold hypothesis.
- Pseudo-labeling used is simple and close to naive techniques.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 SVHN STL-10
Benchmarks: CIFAR-10 CIFAR-100 SVHN STL-10
Metrics: top-1 classification error rate inter/intra-class distance ratio
Baselines: Pseudo-Labeling Mean Teacher VAT UDA DASH FixMatch ReMixMatch FlexMatch SimMatch ConMatch SoftMatch ShrinkMatch
Builds on: FixMatch Virtual adversarial training Mean Teacher FlexMatch USB
Closest papers by meaning
- Deep Metric Learning with Graph Consistency (AAAI 2021 · similarity 0.87)
- On Data-Augmentation and Consistency-Based Semi-Supervised Learning (ICLR 2021 · similarity 0.86)
- Stabilizing Sample Similarity in Representation via Mitigating Random Consistency (ICML 2025 · similarity 0.85)
- Euclidean Embedding of Data Using Local Distances (NeurIPS 2026 · similarity 0.83)
- Relaxed Class-consensus Consistency for Semi-supervised Semantic Segmentation (AAAI 2025 · similarity 0.83)
- Deep Disentangled Metric Learning (AAAI 2025 · similarity 0.83)
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