Cartan moving frames and the data manifolds
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 10 of its 26 references that are in the map. First posted on arXiv 18 Sep 2024.
Builds on
10 of 26 references.
References · 10
- 2015Automatic differentiation in machine learning: a surveycited by 846
- 2017Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methodscited by 542
- 2018An elementary introduction to information geometrycited by 76
- 2018The Adversarial Attack and Detection under the Fisher Information Metriccited by 18
- 2019Defending Against Adversarial Attacks by Suppressing the Largest Eigenvalue of Fisher Information Matrixcited by 9
- 2021Model-centric Data Manifold: the Data Through the Eyes of the Modelcited by 9
- 2019Inspecting adversarial examples using the Fisher informationcited by 7
- 2022Adversarial attacks on neural networks through canonical Riemannian foliationscited by 5
- 2014Two-Stage Metric Learningcited by 1
- 2024Geometry of Singular Foliations and Learning Manifolds in ReLU Networks via the Data Information Matrixcited by 1
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Citing papers per year: 2026: 1.
1 paper.