Cartan moving frames and the data manifolds - ENAC - École nationale de l'aviation civile
Pré-Publication, Document De Travail Année : 2024

Cartan moving frames and the data manifolds

Résumé

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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Dates et versions

hal-04701811 , version 1 (18-09-2024)

Identifiants

  • HAL Id : hal-04701811 , version 1

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Eliot Tron, Rita Fioresi, Nicolas Couellan, Stéphane Puechmorel. Cartan moving frames and the data manifolds. 2024. ⟨hal-04701811⟩
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