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Protected Test-Time Adaptation via Online Entropy Matching: A Betting Approach
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Proposes POEM, an online test-time adaptation method that uses betting-martingale drift detection on classifier entropy and matches the target entropy distribution to the source via an optimal-transport-style mapping, updating only normalization layers.
Problem
Test-time adaptation via self-training with entropy minimization is unstable: it yields overconfident predictions, noisy updates, and collapse to trivial predictions under distribution shift and can harm accuracy and calibration without shift.
Approach
Instead of minimizing entropy, detect shifts by sequentially testing whether the test entropy CDF-transformed values are uniform (betting martingale with online SF-OGD betting), and use the martingale-derived adapted quantile mapped through the source entropy CDF as a target for an entropy-matching loss, so the adapted model's test entropy distribution matches the source's.
Key results
- Single-shift ImageNet-C severity 5 with ViT: POEM 67.36% average accuracy vs. EATA 64.14% (3.22 point gap), vs. no-adapt 51.65%.
- Single-shift ImageNet-C severity 5 with ResNet50 (GN): POEM 38.90% vs. EATA 38.63%, vs. no-adapt 31.44%.
- In-distribution ImageNet: POEM keeps ECE and parameter change minimal, while baseline methods increase ECE and modify parameters more.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use POEM instead of EATA | ResNet50 (GN) · ImageNet-C severity 5, 15-corruption average | accuracy: 38.63 -> 38.90 | Helped |
| Use POEM instead of EATA | ViT (LN) · ImageNet-C severity 5, 15-corruption average | accuracy: 64.14 -> 67.36 | Helped |
| Use POEM instead of entropy minimization | ImageNet validation, all evaluated methods · ImageNet validation | expected calibration error | Helped |
| Replace the entropy matching loss ℓmatch with the filtered and weighted ℓmatch++ loss (ablation) | POEM · ImageNet-C severity 5, 15-corruption average | accuracy | Helped |
Surprising findings
- TENT with ResNet50 (25.46%) and COTTA (23.90%) fall below the no-adapt baseline (31.44%) in the single-shift setting.
Limitations
- Requires holdout unlabeled source data to estimate the source entropy CDF.
- Hyperparameters such as learning rate eta and threshold choices need tuning; sensitivity to label shift is not handled.
- Long-horizon stability relies on no explicit stabilizers, so comparable rather than superior to EATA/SAR in extended streams.
Experimental setup
Datasets: ImageNet ImageNet-C CIFAR10-C CIFAR100-C OfficeHome
Benchmarks: ImageNet-C ImageNet CIFAR10-C CIFAR100-C OfficeHome
Metrics: accuracy expected calibration error parameter deviation norm
Baselines: TENT EATA SAR COTTA no adapt
Builds on: TENT EATA SAR COTTA testing by betting SF-OGD
Closest papers by meaning
- COME: Test-time Adaption by Conservatively Minimizing Entropy (ICLR 2025 · similarity 0.87)
- Unified Entropy Optimization for Open-Set Test-Time Adaptation (CVPR 2024 · similarity 0.87)
- Ranked Entropy Minimization for Continual Test-Time Adaptation (ICML 2025 · similarity 0.87)
- Active Test-Time Adaptation: Theoretical Analyses and An Algorithm (ICLR 2024 · similarity 0.87)
- Entropy is not Enough for Test-Time Adaptation: From the Perspective of Disentangled Factors (ICLR 2024 · similarity 0.86)
- A Layer Selection Approach to Test Time Adaptation (AAAI 2025 · similarity 0.86)
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