Path-Sampled Integrated Gradients

2026-04-15

AI Summary

This work addresses the high variance and poor stability of feature attribution methods caused by gradient noise. To overcome these limitations, the authors propose a deterministic attribution framework based on linear interpolation path sampling. By establishing the equivalence between path sampling and weighted integrated gradients, the method reformulates stochastic estimation as a Riemann sum, enabling efficient and stable attribution computation. Theoretical analysis demonstrates that, under smooth models, the proposed approach improves the error convergence rate from $O(m^{-1/2})$ to $O(m^{-1})$. Moreover, under uniform sampling, it rigorously reduces attribution variance by one-third while preserving both linearity and implementation invariance.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Interpretability, Explainability, and Transparency
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• feature attribution
• variance reduction
• error convergence
• gradient noise
• integrated gradients

Innovation

• Path-Sampled Integrated Gradients
• feature attribution
• variance reduction
• error convergence rate
• axiomatic properties