Title: Cartan moving frames and the data manifolds Show Chinese title

Title: 嘉当活动框架与数据流形

Abstract: 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. Show Chinese abstract

Abstract: 本文的目的是利用嘉当活动标架的语言，通过数据信息度量及其在数据点处的曲率来研究数据流形及其黎曼结构的几何性质。利用这一框架并通过实验，通过对从给定输入容易到达的输出类别加以指明，给出了神经网络响应的解释。这强调了如何将网络输出与输入几何之间的所提出的数学关系作为可解释的人工智能工具加以利用。