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TTVD: Towards a Geometric Framework for Test-Time Adaptation Based on Voronoi Diagram
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Frames test-time adaptation geometrically via Voronoi diagrams, proposing TTVD with a cluster-induced Voronoi diagram (self-supervised rotation sites plus entropy) and a power diagram for filtering noisy samples, evaluated on CIFAR-10/100-C, ImageNet-C and ImageNet-R.
Problem
Test-time adaptation under distribution shift: neighbor-based TTA methods (prototype/Voronoi-style) learn too little from test data, and entropy minimization and self-supervision suffer from noisy samples and conflicting gradients.
Approach
Recasts neighbor-based TTA as a Voronoi diagram over class-mean sites, then extends it to a cluster-induced Voronoi diagram (rotation-augmented sites giving a joint self-supervision and entropy objective) and a power diagram (weighted cells used to filter samples near boundaries).
Key results
- TTVD reaches 20.5% average error on CIFAR-10-C level 5 versus 21.3% for the best baseline TTT (oracle selection), and 49.1% on CIFAR-100-C and 59.8% on ImageNet-C.
- On ImageNet-C, TTVD achieves 21.0% ECE versus 32.8% for BN_Adapt and 36.4% for SHOT, and 67.5% error on ImageNet-R versus 68.2% for NOTE.
- Ablation on CIFAR-10-C: VD 28.4% error, CIVD 22.7%, CIPD 20.5% average error.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use TTVD instead of TTT | CIFAR-10-C · CIFAR-10-C level 5 | error (%): 21.3 -> 20.5 | Helped |
| use TTVD instead of T3A | CIFAR-10-C · CIFAR-10-C level 5 | ECE (%): 19.5 -> 11.8 | Helped |
| use TTVD instead of SHOT | CIFAR-100-C · CIFAR-100-C level 5 | error (%): 49.8 -> 49.1 | Helped |
| use TTVD instead of SAR | CIFAR-100-C · CIFAR-100-C level 5 | ECE (%): 18.1 -> 17.0 | Helped |
| use TTVD instead of SAR | ImageNet-C · ImageNet-C level 5 | error (%): 61.4 -> 59.8 | Helped |
| use TTVD instead of T3A | ImageNet-C · ImageNet-C level 5 | ECE (%): 26.3 -> 21.0 | Helped |
| use TTVD instead of TENT | ImageNet-R · ImageNet-R | error (%): 68.3 -> 67.5 | Helped |
| use TTVD instead of T3A | ImageNet-R · ImageNet-R | ECE (%): 20.5 -> 16.8 | Helped |
| add CIVD multi-site influence to standard VD (ablation) | TTVD · CIFAR-10-C | error (%): 28.4 -> 22.7 | Helped |
| add Power Diagram to CIVD, forming CIPD (ablation) | TTVD · CIFAR-10-C | error (%): 22.7 -> 20.5 | Helped |
| calculate class means using 5% instead of 10% of ImageNet data (ablation) | TTVD · ImageNet-C level 5 | error (%): 59.8 -> 59.8 | No clear effect |
| calculate class means using 1% instead of 10% of ImageNet data (ablation) | TTVD · ImageNet-C level 5 | error (%): 59.8 -> 59.9 | Hurt |
Surprising findings
- Tent and SAR show no clear overfitting in adaptation curves under the rigid grid-searched setting, contrary to earlier claims in the TTA literature.
- TTVD's performance is largely insensitive to the amount of data used to compute class means (10%, 5%, 1% of ImageNet give 59.8, 59.8, 59.9 error).
Limitations
- Relies on oracle model-selection numbers for some baseline comparisons; the paper notes these may overfit to online batches.
- Requires offline computation of class-mean Voronoi sites during pre-training, which may be costly at larger scale.
- Evaluated only on image classification corruption benchmarks.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 ImageNet CIFAR-10-C CIFAR-100-C ImageNet-C ImageNet-R MNIST-C MNIST
Benchmarks: CIFAR-10-C CIFAR-100-C ImageNet-C ImageNet-R
Metrics: classification error expected calibration error
Baselines: T3A TAST BN_Adapt SHOT TTT TENT NOTE Conjugate_PL SAR AdaNPC
Builds on: T3A Tent TTAB SHOT Balestriero power diagram theory
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