Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent

TL;DR

This paper introduces an equivariant Stein Variational Gradient Descent algorithm that efficiently samples from symmetric densities and uses it to train energy-based models for various complex data types.

Contribution

It proposes a novel equivariant SVGD algorithm and integrates it with energy-based models to improve sampling efficiency and scalability for symmetric data.

Findings

Efficient sampling from symmetric densities using equivariant SVGD.

Improved training and scalability of energy-based models with symmetry considerations.

Successful application to image, particle, and molecular data modeling.

Abstract

We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling method based on Stein's identity for sampling from densities with symmetries. Equivariant SVGD explicitly incorporates symmetry information in a density through equivariant kernels which makes the resultant sampler efficient both in terms of sample complexity and the quality of generated samples. Subsequently, we define equivariant energy based models to model invariant densities that are learned using contrastive divergence. By utilizing our equivariant SVGD for training equivariant EBMs, we propose new ways of improving and scaling up training of energy based models. We apply these equivariant energy models for modelling joint densities in regression and classification tasks for image datasets, many-body particle systems and molecular structure generation.