Optimizing Likelihood-free Inference using Self-supervised Neural Symmetry Embeddings

TL;DR

This paper introduces a method to accelerate likelihood-free inference by learning physical symmetries through self-supervised neural embeddings, leading to faster convergence in parameter estimation tasks.

Contribution

It presents a novel approach that incorporates learned symmetry embeddings into normalizing flows to improve inference speed and efficiency.

Findings

Faster convergence in physical problems using symmetry-informed embeddings.

Reduced number of parameters needed for effective inference.

Demonstrated effectiveness on two simple physical problems.

Abstract

Likelihood-free inference is quickly emerging as a powerful tool to perform fast/effective parameter estimation. We demonstrate a technique of optimizing likelihood-free inference to make it even faster by marginalizing symmetries in a physical problem. In this approach, physical symmetries, for example, time-translation are learned using joint-embedding via self-supervised learning with symmetry data augmentations. Subsequently, parameter inference is performed using a normalizing flow where the embedding network is used to summarize the data before conditioning the parameters. We present this approach on two simple physical problems and we show faster convergence in a smaller number of parameters compared to a normalizing flow that does not use a pre-trained symmetry-informed representation.