Measuring the Symmetry--Data Exchange Rate
Equivariance theory predicts that an architectural symmetry prior reduces sample complexity by a factor of |G|; this is widely cited but rarely measured as a scaling law with controls that separate the prior from its confounds. On a controlled C_n-symmetric task, we report three findings. First, a wrong-group control with identical orbit size and matched compute is worse than no constraint (joint pairwise CI [+0.79, +3.26] excludes zero, robust across estimators); misaligned constraint is actively harmful, not merely unhelpful. Second, an augmentation baseline equipped with test-time orbit averaging matches the equivariant model exactly -- bit-identical per-epoch validation curves across ...
| Authors | Ahmed M. Adly |
|---|---|
| Primary category | stat.ME |
| Published | 31 May 2026 |
| Last updated at source | 31 May 2026 |
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