Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent
This work addresses the problem of scaling and improving energy-based models for researchers in machine learning, particularly for applications with symmetries, but it is incremental as it builds on existing methods like SVGD and EBMs.
The paper tackled efficient sampling and learning of probability densities by incorporating symmetries, introducing an equivariant Stein Variational Gradient Descent algorithm and equivariant energy-based models, which improved training and were applied to tasks like image datasets and molecular structure generation, achieving better sample quality and efficiency.
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.