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Several recent methods for interpretability model feature interactions bylooking at the Hessian of a neural network. This poses a challenge for ReLUnetworks, which are piecewise-linear and thus have a zero Hessian almosteverywhere. We propose SmoothHess, a method of estimating second-orderinteractions through Stein's Lemma. In particular, we estimate the Hessian ofthe network convolved with a Gaussian through an efficient sampling algorithm,requiring only network gradient calls. SmoothHess is applied post-hoc, requiresno modifications to the ReLU network architecture, and the extent of smoothingcan be controlled explicitly. We provide a non-asymptotic bound on the samplecomplexity of our estimation procedure. We validate the superior ability ofSmoothHess to capture interactions on benchmark datasets and a real-worldmedical spirometry dataset.

SmoothHess: ReLU Network Feature Interactions via Stein's Lemma