Riemannian Integrated Gradients: A Geometric View of Explainable AI

Federico Costanza, Lachlan Simpson
3/2/2025
cs.LGmath.DG

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Abstract

We introduce Riemannian Integrated Gradients (RIG); an extension of Integrated Gradients (IG) to Riemannian manifolds. We demonstrate that RIG restricts to IG when the Riemannian manifold is Euclidean space. We show that feature attribution can be phrased as an eigenvalue problem where attributions correspond to eigenvalues of a symmetric endomorphism.

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Cite this paper

@article{costanza2025riemannian,
  title  = {Riemannian Integrated Gradients: A Geometric View of Explainable AI},
  author = {Federico Costanza and Lachlan Simpson},
  year   = {2025},
  eprint = {2503.00892},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2503.00892v1}
}

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