提出更宽松的约束方法，让群卷积网络更高效且适用范围更广。
Group Cross-Correlations with Faintly Constrained Filters
- 引入弱化约束，保持节点数优势的同时兼容非紧稳定子的群作用
- 突破传统限制，使群卷积网络适用于非传递群作用和非单模群
- 适合研究群对称性建模与高效神经网络设计的读者
针对群 $G$ 的群卷积层通常通过卷积或互相关操作实现，是群卷积神经网络的基础模块。当滤波器完全无约束且 $G$ 为非阿贝尔群时，此类网络的任意隐藏层所需节点数与 $G$ 的精细离散化顶点数相当。为减少节点数，文献中提出了若干滤波器约束。本文提出更弱的约束，在保留节点数优势的同时，解决了先前约束在群作用具有非紧稳定子时的不相容性问题。此外，我们还将已有结果推广至非传递群作用情形，并弱化了 $G$ 必须单模的常见假设。
原文摘要 · Abstract (English)
Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained filters and $G$ a non-abelian group, any hidden layer of such a network requires as many nodes as vertices in a fine enough discretization of $G$. In order to reduce the necessary number of nodes, certain constraints on filters were proposed in the literature. We propose weaker constraints retaining this benefit while also resolving an incompatibility previous constraints have for group actions with non-compact stabilizers. Moreover, we generalize previous results to group actions that are not necessarily transitive, and we weaken the common assumption that $G$ is unimodular.
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