Diffeomorphic Explanations with Normalizing Flows

Abstract

Normalizing flows are diffeomorphisms which are parameterized by neural networks. As a result, they can induce coordinate transformations in the tangent space of the data manifold. In this work, we demonstrate that such transformations can be used to generate interpretable explanations for decisions of neural networks. More specifically, we perform gradient ascent in the base space of the flow to generate counterfactuals which are classified with great confidence as a specified target class. We analyze this generation process theoretically using Riemannian differential geometry and establish a rigorous theoretical connection between gradient ascent on the data manifold and in the base space of the flow.