In this paper we discuss the results recently published in~[1] about algebraic signal models (ASMs) based on non commutative algebras and their use in convolutional neural networks. Relying on the general tools from algebraic signal processing (ASP), we study the filtering and stability properties of non commutative convolutional filters. We show how non commutative filters can be stable to small perturbations on the space of operators. We also show that although the spectral components of the Fourier representation in a non commutative signal model are associated to spaces of dimension larger than one, there is a trade-off between stability and selectivity similar to that observed for commutative models. Our results have direct implications for group neural networks, multigraph neural networks and quaternion neural networks, among other non commutative architectures. We conclude by corroborating these results through numerical experiments.

基于非交换代数的代数信号模型在卷积神经网络中的应用，探讨了非交换卷积滤波器的滤波和稳定性特性，以及稳定性与选择性之间的权衡关系。通过数值实验验证了这些结果。

神经网络中的非交换卷积信号模型：对微小变形的稳定性