Related papers: Geometric Clifford Algebra Networks

Geometric Clifford Algebra Networks

URL: http://arxiv.org/abs/2302.06594v2
Date: Mon, 29 May 2023 16:51:59 GMT
Title: Geometric Clifford Algebra Networks
Authors: David Ruhe, Jayesh K. Gupta, Steven de Keninck, Max Welling, Johannes Brandstetter
Abstract summary: We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras.
Score: 53.456211342585824
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the $\mathrm{Pin}(p,q,r)$ group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable $\textit{geometric templates}$ that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

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