Riemannian Integrated Gradients: A Geometric View of Explainable AI

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.

@article{costanza2025_2503.00892,
  title={ Riemannian Integrated Gradients: A Geometric View of Explainable AI },
  author={ Federico Costanza and Lachlan Simpson },
  journal={arXiv preprint arXiv:2503.00892},
  year={ 2025 }
}