Cartan moving frames and the data manifolds
This work addresses the need for explainability in AI for researchers and practitioners, though it appears incremental by applying existing mathematical frameworks to neural networks.
The paper tackles the problem of explaining neural network responses by studying the geometry of data manifolds using Cartan moving frames, resulting in a method that identifies easily reachable output classes from a given input as an explainable AI tool.
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.