[Submitted on 23 Oct 2026]
Title:Lower expected Fisher rank implies better PAC generalization
View a PDF of the paper titled Lower expected Fisher rank implies better PAC generalization, by Marco Miani and 4 other authors
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Abstract:Deep learning architectures tend to generalize well to unseen data, but explaining this capability is still an open area of research. Under the assumption of i.i.d. data, PAC-Bayes provides a bound on generalization error, and its tightness relies on a parameter distribution that covers a large volume of low-loss solutions. The Fisher information metric endows the parameter space with a geometry for which distances reflect functional changes, and whose zero-component captures functional invariances. We define and study a Fisher-aligned parameter distribution for which we can simultaneously guarantee (1) a low-loss, thanks to the exploration constrained on the functional invariances and (2) a large log-volume of parameters, proportional to the number of zero eigenvalues. This distribution results in a high-probability generalization error bound, which scales with the expected rank of the Fisher information matrix, shedding light on the relevance of this quantity.
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2610.33208 [cs.LG]
(or arXiv:2610.33208v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.33208
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Marco Miani [view email] [v1] Fri, 23 Oct 2026 18:56:03 UTC (242 KB)
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