The purpose of this paper is to employ the language of Cartan moving frames to study the geometry of the data manifolds and its Riemannian structure, via the data information metric and its curvature at data points. Using this framework and through experiments, explanations on the response of a neural network are given by pointing out the output classes that are easily reachable from a given input. This emphasizes how the proposed mathematical relationship between the output of the network and the geometry of its inputs can be exploited as an explainable artificial intelligence tool.

翻译：本文旨在运用Cartan活动标架的语言，通过数据信息度量及其在数据点处的曲率，研究数据流形的几何结构及其黎曼结构。利用该框架并通过实验，我们通过指出从给定输入容易到达的输出类别，对神经网络的响应进行了解释。这强调了所提出的网络输出与其输入几何之间的数学关系如何可作为可解释人工智能工具加以利用。