Clifford-Steerable Convolutional Neural Networks	

Maksim Zhdanov-- University of Amsterdam

Clifford algebras provide a convenient framework for handling geometric relationships. Recently adapted in deep learning, they enable a new class of group equivariant architectures thanks to their inherent connection to orthogonal transformations. 

In this talk, I will examine the properties of group equivariant architectures based on the Clifford algebra formalism. Ruhe et al. (2023) suggested a framework for building MLP-like neural networks equivariant to (pseudo-)orthogonal transformations. Zhdanov et al. (2024) further suggested a way to generalize this framework to convolutional neural networks (CNNs), which enjoy equivariance to full isometries of pseudo-Euclidean spaces, which was not achieved before. 

From the application point of view, equivariant models proved superior for PDE modelling. They also allowed for modelling relativistic data living in space-time, such as electromagnetic fields."