Using the Path of Least Resistance to Explain Deep Networks

Integrated Gradients (IG), a widely used axiomatic path-based attribution method, assigns importance scores to input features by integrating model gradients along a straight path from a baseline to the input. While effective in some cases, we show that straight paths can lead to flawed attributions. In this paper, we identify the cause of these misattributions and propose an alternative approach that treats the input space as a Riemannian manifold, computing attributions by integrating gradients along geodesics. We call this method Geodesic Integrated Gradients (GIG). To approximate geodesic paths, we introduce two techniques: a k-Nearest Neighbours-based approach for smaller models and a Stochastic Variational Inference-based method for larger ones. Additionally, we propose a new axiom, Strong Completeness, extending the axioms satisfied by IG. We show that this property is desirable for attribution methods and that GIG is the only method that satisfies it. Through experiments on both synthetic and real-world data, we demonstrate that GIG outperforms existing explainability methods, including IG.