Adaptive Sampling for Continuous Group Equivariant Neural Networks

TL;DR

This paper introduces an adaptive sampling method for continuous group equivariant neural networks that reduces computational costs while maintaining or improving model performance and equivariance.

Contribution

We propose a novel adaptive sampling technique that dynamically adjusts sampling in continuous groups, enhancing efficiency without sacrificing accuracy or symmetry properties.

Findings

Improved model performance with fewer samples

Reduced computational costs compared to fixed sampling methods

Marginal increase in memory efficiency

Abstract

Steerable networks, which process data with intrinsic symmetries, often use Fourier-based nonlinearities that require sampling from the entire group, leading to a need for discretization in continuous groups. As the number of samples increases, both performance and equivariance improve, yet this also leads to higher computational costs. To address this, we introduce an adaptive sampling approach that dynamically adjusts the sampling process to the symmetries in the data, reducing the number of required group samples and lowering the computational demands. We explore various implementations and their effects on model performance, equivariance, and computational efficiency. Our findings demonstrate improved model performance, and a marginal increase in memory efficiency.