Group Symmetry in PAC LearningDownload PDF

02 Mar 2022, 12:21 (edited 25 Apr 2022)GTRL 2022 SpotlightReaders: Everyone
  • Keywords: Invariance, Equivariance, Symmetry, Learning Theory, Geometry
  • TL;DR: Sample Complexity Bounds for Equivariant Learning In Terms of Geometry of Spaces
  • Abstract: In this paper we show rigorously how learning in the PAC framework with invariant or equivariant hypotheses reduces to learning in a space of orbit representatives. Our results hold for any compact group, including infinite groups such as rotations. In addition, we show how to use these equivalences to derive generalisation bounds for invariant/equivariant models in terms of the geometry of the input and output spaces. To the best of our knowledge, our results are the most general of their kind to date.
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