Path-Sampled Integrated Gradients

arXiv cs.LG / 4/17/2026

📰 NewsIdeas & Deep AnalysisModels & Research

共有:

Key Points

The paper proposes Path-Sampled Integrated Gradients (PS-IG), a framework for feature attribution that estimates integrated-gradients expectations using baselines sampled along a linear interpolation path.
It proves PS-IG is mathematically equivalent to path-weighted integrated gradients when the weighting function matches the cumulative distribution function of the sampling density.
Using this equivalence, PS-IG’s stochastic expectation can be computed with a deterministic Riemann sum, improving approximation error convergence from O(m^-1/2) to O(m^-1) for smooth models.
The authors show PS-IG also acts as a variance-reducing filter against gradient noise, reducing attribution variance by a factor of 1/3 under uniform sampling while maintaining attribution axioms like linearity and implementation 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})

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.