Riemannian Integrated Gradients: A Geometric View of Explainable AI

2025-03-02

AI Summary

The lack of interpretability for AI models operating on Riemannian manifolds hinders trust and adoption in non-Euclidean deep learning. Method: We propose Riemannian Integrated Gradients (RIG), the first geometric attribution method extending Integrated Gradients to non-Euclidean spaces. RIG defines path-integral attribution on manifolds via geodesic integration and covariant differentiation, and formulates feature attribution as an eigenvalue assignment problem over symmetric endomorphisms. Contribution/Results: Theoretically, we establish the first Riemannian geometry–driven attribution framework, rigorously proving that RIG satisfies completeness, sensitivity, and geometric covariance, and recovers standard IG in the Euclidean limit. Empirically, RIG significantly improves attribution plausibility and robustness on spherical embeddings and symmetric positive-definite (SPD) matrix data, offering a novel interpretability paradigm for non-Euclidean deep learning.

Technology Category

Machine Learning: Learning with ManifoldsComputer Vision: Interpretability, Explainability, and TransparencyKnowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Extends Integrated Gradients to Riemannian manifolds.
• Shows RIG reduces to IG in Euclidean space.
• Formulates feature attribution as an eigenvalue problem.

Innovation

• Extends Integrated Gradients to Riemannian manifolds
• Links feature attribution to eigenvalue problems
• Reduces to Euclidean space in special cases