ICML 2025

GLGENN: A Novel Parameter-Light Equivariant Neural Networks
Architecture Based on Clifford Geometric Algebras
Ekaterina Filimoshina 1 2 Dmitry Shirokov 1 3
Abstract
We propose, implement, and compare with com-
petitors a new architecture of equivariant neural
networks based on geometric (Clifford) algebras:
Generalized Lipschitz Group Equivariant Neu-
ral Networks (GLGENN). These networks are
equivariant to all pseudo-orthogonal transforma-
tions, including rotations and reflections, of a vec-
tor 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 equiv-
ariant models. GLGENN outperforms or matches
competitors on several benchmarking equivariant
tasks, including estimation of an equivariant func-
tion and a convex hull experiment, while using
significantly fewer optimizable parameters.
1. Introduction
Equivariant neural networks are a class of neural networks
that explicitly incorporate symmetries into their architec-
ture, making them well-suited for tasks that inherently re-
quire equivariance to transformations with respect to some
group’s action (e.g., rotations, permutations, translations,
etc.). Equivariant neural networks were introduced in Cohen
& Welling, 2016 and have since been extensively developed
and applied in a wide range of tasks in computer and natural
sciences. These applications include modeling dynamical
systems (Finzi et al., 2021), particle physics (Ruhe et al.,
2023; Finzi et al., 2021), analyzing molecular properties and
1HSE University, Moscow, Russia 2 Skolkovo Institute of
Science and Technology, Moscow, Russia 3 Institute for In-
formation Transmission Problems of the Russian Academy
of Sciences, Moscow, Russia.
Correspondence to:
Ekate-
rina Filimoshina <filimoshinae...