Measuring Learned Equivariance: An Information Theoretic Approach

Key points

• Measuring learned equivariance is especially difficult for intermediate representations, whose group actions are not specified.1
• 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).1
• For high-dimensional activations, we use centered kernel alignment (CKA) as a scalable test, with an exact guarantee for orthogonal feature transformations.1
• Across architectures and tasks, augmentation usually increases transformation consistency, showing that learned equivariance can be probed directly from representations without recovering the hidden transformation rules that relate them.1

Sources (1)

• [1]Measuring Learned Equivariance: An Information Theoretic Approach
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 12, 06:24 PM

  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.

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