Noether Networks: meta-learning useful conserved quantities

Ferran Alet, Dylan Doblar, Allan Zhou, Joshua B. Tenenbaum, Kenji Kawaguchi, Chelsea Finn

Keywords: meta-learning, sequential prediction, physics, video prediction

TL;DR: We meta-learn inductive biases in the form of useful conserved quantities that improve predictions when optimized inside the prediction function.

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.

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Code: https://lis.csail.mit.edu/noether

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2112.03321/code)