Riemannian Integrated Gradients: A Geometric View of Explainable AI

Federico Costanza; Lachlan Simpson

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arXiv · 2503.00892

Riemannian Integrated Gradients: A Geometric View of Explainable AI

Federico Costanza·Lachlan Simpson

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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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Federico Costanza, Lachlan Simpson. 2025-03-02. Riemannian Integrated Gradients: A Geometric View of Explainable AI. https://arxiv.org/abs/2503.00892

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