SmoothHess: ReLU Network Feature Interactions via Stein's Lemma

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

Bibtex Paper Supplemental


Max Torop, Aria Masoomi, Davin Hill, Kivanc Kose, Stratis Ioannidis, Jennifer Dy


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.