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arXiv · 2410.03989

Symmetry From Scratch: Group Equivariance as a Supervised Learning Task

Haozhe Huang·Leo Kaixuan Cheng·Kaiwen Chen·Alán Aspuru-Guzik
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Abstract

In machine learning datasets with symmetries, the paradigm for backward compatibility with symmetry-breaking has been to relax equivariant architectural constraints, engineering extra weights to differentiate symmetries of interest. However, this process becomes increasingly over-engineered as models are geared towards specific symmetries/asymmetries hardwired of a particular set of equivariant basis functions. In this work, we introduce symmetry-cloning, a method for inducing equivariance in machine learning models. We show that general machine learning architectures (i.e., MLPs) can learn symmetries directly as a supervised learning task from group equivariant architectures and retain/break the learned symmetry for downstream tasks. This simple formulation enables machine learning models with group-agnostic architectures to capture the inductive bias of group-equivariant architectures.

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Haozhe Huang, Leo Kaixuan Cheng, Kaiwen Chen, Alán Aspuru-Guzik. 2024-10-05. Symmetry From Scratch: Group Equivariance as a Supervised Learning Task. https://arxiv.org/abs/2410.03989

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