Clifford-Steerable Convolutional Neural Networks

2024/02/22 by Maksim Zhdanov, Zhdanov, Maksim, David Ruhe +9 · 3 citations
Computer Science · Neuroscience · #Artificial Intelligence (cs.AI) #Brain Tumor Detection and Classification #FOS: Computer and information sciences #Machine Learning (cs.LG) #Neural Networks and Applications

paper · doi:10.48550/arxiv.2402.14730

openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of E(p, q)-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces ℝ^p,q. They cover, for instance, E(3)-equivariance on ℝ³ and Poincaré-equivariance on Minkowski spacetime ℝ^1,3. Our approach is based on an implicit parametrization of O(p,q)-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.

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• The State-Operator Clifford Compatibility: A Real Algebraic Framework for Quantum Information
• Equivariant Neural Networks for General Linear Symmetries on Lie Algebras
• Conditional Clifford-Steerable CNNs with Complete Kernel Basis for PDE Modeling

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