SmoothHess: ReLU Network Feature Interactions via Stein's Lemma

2023/11/01 by Max Torop, Torop, Max, Aria Masoomi +9 · 2 citations
Computer Science · #Domain Adaptation and Few-Shot Learning #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning in Healthcare

paper · pdf · doi:10.48550/arxiv.2311.00858

openalex publication_date 2023/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several recent methods for interpretability model feature interactions by looking at the Hessian of a neural network. This poses a challenge for ReLU networks, which are piecewise-linear and thus have a zero Hessian almost everywhere. We propose SmoothHess, a method of estimating second-order interactions through Stein's Lemma. In particular, we estimate the Hessian of the network convolved with a Gaussian through an efficient sampling algorithm, requiring only network gradient calls. SmoothHess is applied post-hoc, requires no modifications to the ReLU network architecture, and the extent of smoothing can be controlled explicitly. We provide a non-asymptotic bound on the sample complexity of our estimation procedure. We validate the superior ability of SmoothHess to capture interactions on benchmark datasets and a real-world medical spirometry dataset.

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