Bayesian Influence Functions for Hessian-Free Data Attribution
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.
Cite
Text
Kreer et al. "Bayesian Influence Functions for Hessian-Free Data Attribution." International Conference on Learning Representations, 2026.Markdown
[Kreer et al. "Bayesian Influence Functions for Hessian-Free Data Attribution." International Conference on Learning Representations, 2026.](https://mlanthology.org/iclr/2026/kreer2026iclr-bayesian/)BibTeX
@inproceedings{kreer2026iclr-bayesian,
title = {{Bayesian Influence Functions for Hessian-Free Data Attribution}},
author = {Kreer, Philipp Alexander and Wu, Wilson and Adam, Maxwell and Furman, Zach and Hoogland, Jesse},
booktitle = {International Conference on Learning Representations},
year = {2026},
url = {https://mlanthology.org/iclr/2026/kreer2026iclr-bayesian/}
}