Meta-Learning Symmetries by Reparameterization

TL;DR

This paper introduces a method for neural networks to automatically learn and encode symmetries from data, enabling equivariance without manual architecture design, applicable to various transformations in image tasks.

Contribution

It proposes a data-driven approach to learn equivariance-inducing parameter sharing patterns, generalizing to any finite symmetry group, reducing manual design effort.

Findings

Successfully learns equivariances for common image transformations

Can represent any finite group of symmetries

Improves generalization by encoding learned symmetries

Abstract

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only works when practitioners know the symmetries of the task and can manually construct an architecture with the corresponding equivariances. Our goal is an approach for learning equivariances from data, without needing to design custom task-specific architectures. We present a method for learning and encoding equivariances into networks by learning corresponding parameter sharing patterns from data. Our method can provably represent equivariance-inducing parameter sharing for any finite group of symmetry transformations. Our experiments suggest that it can automatically learn to encode equivariances to common transformations used in image processing tasks. We provide our experiment code at https://github.com/AllanYangZhou/metalearning-symmetries.