Group equivariant non-expansive operators have been recently proposed as basic components in topological data analysis and deep learning. In this paper we study some geometric properties of the spaces of group equivariant operators and show how a space $\mathcal{F}$ of group equivariant non-expansive operators can be endowed with the structure of a Riemannian manifold, so making available the use of gradient descent methods for the minimization of cost functions on $\mathcal{F}$. As an application of this approach, we also describe a procedure to select a finite set of representative group equivariant non-expansive operators in the considered manifold.

翻译：最近有人提议将集团间不扩大操作员作为表层数据分析和深层学习的基本组成部分。我们在本文件中研究了集团间等操作员空间的一些几何特性,并展示了如何将集团间不扩大操作员的空间$\mathcal{F}美元与里曼尼多元结构相容,从而可以使用梯度下降法将成本函数最小化为$\mathcal{F}美元。作为这一方法的一种应用,我们还描述了在考虑的多元中选择一组有一定代表性的具有代表性的集团间等离性非扩大操作员的程序。