Learning Probabilistic Symmetrization for Architecture Agnostic Equivariance

TL;DR

This paper introduces a probabilistic symmetrization framework that enables arbitrary base models to learn equivariant functions across diverse symmetry groups, improving flexibility and performance over traditional equivariant architectures.

Contribution

It proposes a novel probabilistic symmetrization method that allows non-equivariant models to learn equivariant functions, enhancing versatility and reducing sample complexity.

Findings

Competitive results against specialized equivariant architectures

Effective on various symmetry groups including permutation and Euclidean groups

Improved learning in symmetric modalities like graphs

Abstract

We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and symmetrize it to be equivariant to the given group by employing a small equivariant network that parameterizes the probabilistic distribution underlying the symmetrization. The distribution is end-to-end trained with the base model which can maximize performance while reducing sample complexity of symmetrization. We show that this approach ensures not only equivariance to given group but also universal approximation capability in expectation. We implement our method on various base models, including patch-based transformers that can be initialized from pretrained vision transformers, and test them for a wide range of symmetry groups including permutation and Euclidean groups and their combinations. Empirical tests show competitive results against tailored equivariant architectures, suggesting the potential for learning equivariant functions for diverse groups using a non-equivariant universal base architecture. We further show evidence of enhanced learning in symmetric modalities, like graphs, when pretrained from non-symmetric modalities, like vision. Code is available at https://github.com/jw9730/lps.