# Riemannian Integrated Gradients: A Geometric View of Explainable AI

arXiv: https://arxiv.org/abs/2503.00892 · HTML: https://mlsanity.com/paper/2503.00892/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 2 Mar 2025.

## Builds on (most cited first, 9 of 9)

- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [A Rigorous Study of Integrated Gradients Method and Extensions to Internal Neuron Attributions](https://mlsanity.com/paper/2202.11912/) (2022)
- [Statistical exploration of the Manifold Hypothesis](https://mlsanity.com/paper/2208.11665/) (2022)
- [Manifold Integrated Gradients: Riemannian Geometry for Feature Attribution](https://mlsanity.com/paper/2405.09800/) (2024)
- [The Manifold Hypothesis for Gradient-Based Explanations](https://mlsanity.com/paper/2206.07387/) (2022)
- [Algebraic Adversarial Attacks on Integrated Gradients](https://mlsanity.com/paper/2407.16233/) (2024)

## Built on by (most cited first, 2 of 2)

- [Path-Weighted Integrated Gradients for Interpretable Dementia Classification](https://mlsanity.com/paper/2509.17491/) (2025)
- [Graph-based Integrated Gradients for Explaining Graph Neural Networks](https://mlsanity.com/paper/2509.07648/) (2025)

## Abstract (arXiv)

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.