Geometric Algebra for Neural Networks: A Survey
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arXiv:2607. 06634v1 Announce Type: new Abstract: Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples.
arXiv:2607. 01449v1 Announce Type: new Abstract: We propose a novel hybrid neural architecture, the Geometry-aware R-Structured Kolmogorov-Arnold Network (GRS-KAN), which integrates V.
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...
The paper introduces Product Interactions, an algebraic framework that unifies modern neural architectures by treating data as algebraic elements and multiplication as a core operation. It shows how convolutional, equivariant, state‑space, and attention models arise from different orders of product interactions and symmetry constraints, and demonstrates that a simplified algebraic dynamical layer can outperform Mamba on CIFAR‑10. The framework positions architecture design as a systematic algebraic construction problem, enabling both analysis of existing models and generation of new ones.
arXiv:2607. 28755v1 Announce Type: new Abstract: Over the last decade, neural networks have been applied to an increasingly diverse range of applications, including data with rich geometric, topological, or symmetry-related structure.
arXiv:2602. 22895v2 Announce Type: replace-cross Abstract: Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages.