AI4SLT: Empirical Processes in Lean 4 for Formal Statistical Learning Theory

Abstract:We present the first comprehensive Lean 4 formalization of statistical learning theory (SLT) grounded in empirical process theory. Our en-to-end formal infrastructure implement the missing contents in latest Lean library, including a complete development of Gaussian Lipschitz concentration, Dudley's entropy integral theorem for sub-Gaussian processes, and an application to least-squares (sparse) regression with a sharp rate. The project was carried out using a human-AI collaborative workflow, in which humans design proof strategies and AI agents execute tactical proof construction, leading to the human-verified Lean 4 toolbox for SLT. Beyond implementation, the formalization process exposes and resolves implicit assumptions and missing details in standard SLT textbooks, enforcing a granular, line-by-line understanding of the theory. This work establishes a reusable formal foundation and opens the door for future developments in machine learning theory. The code is provided in this https URL.

Machine Learning (cs.LG); Computation and Language (cs.CL); Statistics Theory (math.ST)

arXiv:2602.02285 [cs.LG]

(or arXiv:2602.02285v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2602.02285 Focus to learn more arXiv-issued DOI via DataCite

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