Path-Sampled Integrated Gradients

TL;DR

Path-sampled integrated gradients (PS-IG) is a novel feature attribution method that improves accuracy and reduces variance by sampling baselines along interpolation paths, with theoretical guarantees.

Contribution

We introduce PS-IG, a framework that generalizes integrated gradients, proves its mathematical equivalence to path-weighted variants, and demonstrates improved error convergence and variance reduction.

Findings

PS-IG improves error convergence from O(m^{-1/2}) to O(m^{-1}) for smooth models.

PS-IG reduces attribution variance by a factor of 1/3 under uniform sampling.

PS-IG preserves key axiomatic properties like linearity and invariance.

Abstract

We introduce path-sampled integrated gradients (PS-IG), a framework that generalizes feature attribution by computing the expected value over baselines sampled along the linear interpolation path. We prove that PS-IG is mathematically equivalent to path-weighted integrated gradients, provided the weighting function matches the cumulative distribution function of the sampling density. This equivalence allows the stochastic expectation to be evaluated via a deterministic Riemann sum, improving the error convergence rate from $O(m^{-1/2})$ to $O(m^{-1})$ for smooth models. Furthermore, we demonstrate analytically that PS-IG functions as a variance-reducing filter against gradient noise - strictly lowering attribution variance by a factor of 1/3 under uniform sampling - while preserving key axiomatic properties such as linearity and implementation invariance.