ICLR 2026poster0 citations
Bayesian Influence Functions for Hessian-Free Data Attribution
Philipp Alexander Kreer, Wilson Wu, Maxwell Adam, Zach Furman, Jesse Hoogland
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.
Training Data AttributionInterpretabilitySGMCMCInfluence FunctionsMCMCLoss LandscapeGeometrySingular Learning TheoryRobustness
BibTeX
@inproceedings{
kreer2026bayesian,
title={Bayesian Influence Functions for Hessian-Free Data Attribution},
author={Philipp Alexander Kreer and Wilson Wu and Maxwell Adam and Zach Furman and Jesse Hoogland},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=YEBpZVm70i}
}