GLGENN: A Novel Parameter-Light Equivariant Neural Networks Architecture Based on Clifford Geometric Algebras

TL;DR

GLGENN introduces a parameter-efficient, Clifford algebra-based neural network architecture that is equivariant to all pseudo-orthogonal transformations, outperforming or matching existing models on benchmark tasks.

Contribution

The paper presents a novel, parameter-light equivariant neural network architecture based on Clifford geometric algebras, capable of handling all pseudo-orthogonal transformations.

Findings

Outperforms or matches competitors on benchmark tasks

Uses significantly fewer parameters than baseline models

Less prone to overfitting due to weight-sharing parametrization

Abstract

We propose, implement, and compare with competitors a new architecture of equivariant neural networks based on geometric (Clifford) algebras: Generalized Lipschitz Group Equivariant Neural Networks (GLGENN). These networks are equivariant to all pseudo-orthogonal transformations, including rotations and reflections, of a vector space with any non-degenerate or degenerate symmetric bilinear form. We propose a weight-sharing parametrization technique that takes into account the fundamental structures and operations of geometric algebras. Due to this technique, GLGENN architecture is parameter-light and has less tendency to overfitting than baseline equivariant models. GLGENN outperforms or matches competitors on several benchmarking equivariant tasks, including estimation of an equivariant function and a convex hull experiment, while using significantly fewer optimizable parameters.