Barriers to Learning Symmetries

Abstract: Given the success of equivariant models, there has been increasing interest in models which can learn a symmetry from data, rather than it being imposed a priori. We present work which formalizes a tradeoff between (a) the simultaneous learnability of symmetries and equivariant functions, and (b) universal approximation of equivariant functions. The work is motivated by an experiment which modifies the Equivariant Multilayer Perceptron (EMLP) of Finzi et al. (2021) in an attempt to learn a group together with an equivariant function. Additionally, the tradeoff is shown to not exist for group-convolutional networks.

machine learningmathematical physicscommutative algebraalgebraic geometryalgebraic topologycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html