arXiv AI
Oct 16

Product Interaction: An Algebraic Formalism for Deep Learning Architectures

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.

By Haonan Dong, Chun-Wun Cheng, Angelica I. Aviles-Rivero
arXiv Machine Learning
Aug 11

SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization

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.

By Bruno Aristimunha, Ce Ju, Antoine Collas, Florent Bouchard, Ammar Mian, Bertrand Thirion, Sylvain Chevallier, Reinmar Kobler