From Baselines to Transport Geodesics: Axiomatic Attribution via Optimal Generative Flows

TL;DR

This paper introduces a transport-geodesic attribution method that selects data-driven paths for feature attribution, leading to more stable and structured explanations in model interpretability.

Contribution

It proposes a novel axiomatic framework for feature attribution based on optimal transport and geodesic paths, improving stability and interpretability of explanations.

Findings

Transport-consistent paths yield more stable explanations.

Lower-action paths preserve deletion faithfulness.

The method is implemented with Rectified Flow and Reflow.

Abstract

Feature attributions often hide a critical modeling choice: they explain a prediction along a counterfactual path from a reference state to an input. Different baselines, interpolations, and generative trajectories define different paths and can therefor produce different explanations. We study this path ambiguity as a modeling problem. Our central question is whether the path can be chosen by the data-generating transport process, rather than by a hand-designed interpolation or by the sensitivity geometry of the model being explained. We separate attribution into fixed-path credit allocation and path selection. For a fixed path, we prove that the Aumann-Shapley line integral is the unique attribution rule under standard fixed-path axioms and explicit coordinate-trace regularity. For path selection, we minimize kinetic action over flows that transport a reference distribution to the data distribution, yielding a transport-geodesic attribution principle. We approximate this ideal with Rectified Flow and Reflow and derive stability bounds linking vector-field error to attribution error. Experiments show that lower-action, transport-consistent paths produce more stable and structured explanations, preserving competitive deletion faithfulness, without claiming data-manifold membership. Our code is available at https://github.com/cenweizhang/OTFlowSHAP.