Bayesian Influence Functions for Hessian-Free Data Attribution

Authors

Philipp Alexander Kreer
Timaeus, Technical University of Munich
Wilson Wu
University of Colorado Boulder
Maxwell Adam
Timaeus, University of Melbourne
Zach Furman
University of Melbourne
Jesse Hoogland
Timaeus

Publication Details

Published:
September 30, 2025

Abstract

Classical influence functions face significant challenges when applied to deep neural networks, primarily due to non-invertible Hessians and high-dimensional parameter spaces. We propose the local Bayesian influence function (BIF), an extension of classical influence functions that replaces Hessian inversion with loss landscape statistics that can be estimated via stochastic-gradient MCMC sampling. This Hessian-free approach captures higher-order interactions among parameters and scales efficiently to neural networks with billions of parameters. We demonstrate state-of-the-art results on predicting retraining experiments.