用微分几何揭示神经网络输入输出的可解释关系
Cartan moving frames and the data manifolds
- 引入卡坦运动标架研究数据流形的黎曼结构
- 通过信息度量曲率定位易达输出类别
- 为神经网络决策提供几何解释，适合可解释AI研究者
本文采用卡坦运动标架的语言，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与黎曼性质。基于该框架并结合实验，论文解释了神经网络对输入的响应：指出从给定输入出发，哪些输出类别易于到达。这凸显了网络输出与输入几何之间存在的数学关联，可作为可解释人工智能工具加以利用。
原文摘要 · Abstract (English)
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.
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