Noether Networks: Meta-Learning Useful Conserved Quantities

TL;DR

This paper introduces Noether Networks, a novel architecture that uses meta-learning to discover conserved quantities, thereby automatically identifying useful symmetries to enhance sequential prediction tasks.

Contribution

It proposes a new architecture that meta-learns conservation laws inspired by Noether's theorem to improve inductive biases in sequential prediction.

Findings

Noether Networks improve prediction accuracy in sequential tasks.

The framework effectively discovers useful symmetries.

Theoretical analysis supports the method's generality.

Abstract

Progress in machine learning (ML) stems from a combination of data availability, computational resources, and an appropriate encoding of inductive biases. Useful biases often exploit symmetries in the prediction problem, such as convolutional networks relying on translation equivariance. Automatically discovering these useful symmetries holds the potential to greatly improve the performance of ML systems, but still remains a challenge. In this work, we focus on sequential prediction problems and take inspiration from Noether's theorem to reduce the problem of finding inductive biases to meta-learning useful conserved quantities. We propose Noether Networks: a new type of architecture where a meta-learned conservation loss is optimized inside the prediction function. We show, theoretically and experimentally, that Noether Networks improve prediction quality, providing a general framework for discovering inductive biases in sequential problems.