Measuring Learned Equivariance: An Information Theoretic Approach
Learning symmetries through data augmentation offers an alternative to architectural equivariance, but does not guarantee that a network respects those symmetries. Measuring learned equivariance is especially difficult for intermediate representations, whose group actions are not specified. In a finite discrete setting, we show that equivariance requires representations of original and transformed inputs to determine one another exactly, yielding a test based on normalized mutual information (NMI). For high-dimensional activations, we use centered kernel alignment (CKA) as a scalable test, with an exact guarantee for orthogonal feature transformations. Across architectures and tasks, augm...
| Authors | Claire Schlesinger, Wolfgang Gatterbauer, Robin Walters |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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