[2509.26544] Bayesian Influence Functions for Hessian-Free Data Attribution

Computer Science > Machine Learning arXiv:2509.26544 (cs) [Submitted on 30 Sep 2025 (v1), last revised 27 Feb 2026 (this version, v2)] Title:Bayesian Influence Functions for Hessian-Free Data Attribution Authors:Philipp Alexander Kreer, Wilson Wu, Maxwell Adam, Zach Furman, Jesse Hoogland View a PDF of the paper titled Bayesian Influence Functions for Hessian-Free Data Attribution, by Philipp Alexander Kreer and 4 other authors View PDF HTML (experimental) 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. Comments: Subjects: Machine Learning (cs.LG) Cite as: arXiv:2509.26544 [cs.LG]   (or arXiv:2509.26544v2 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2509.26544 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Philipp Alexander Kreer [view email] [v1] Tue, 30 Sep 2025 17:17:37 UTC (25,513 KB) [v2] Fri, 27 Feb 2026 20:52:56 UTC (23,011 KB) Full-text links: ...