Statistical Learning Theory in Lean 4: Empirical Processes from Scratch

Yuanhe Zhang, Jason D. Lee, Fanghui Liu

Statistical Learning Theory in Lean 4: Empirical Processes from Scratch: 0 upvotes on Hugging Face Daily Papers, #55 of 58 papers on 2026-02-10. Day-by-day upvote history.

We present the first comprehensive Lean 4 formalization of statistical learning theory (SLT) grounded in empirical process theory. Our end-to-end formal infrastructure implement the missing contents in latest Lean 4 Mathlib library, including a complete development of Gaussian Lipschitz concentration, the first formalization of 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 available at https://github.com/YuanheZ/lean-stat-learning-theory

Paper page on Hugging Face · arXiv

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