arXiv:2602.02285v2 Announce Type: replace-cross 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
The proliferation of advanced AI systems necessitates rigorous formal verification of AI and statistical learning theory to ensure reliability and trustworthiness.
Formal verification of AI algorithms, particularly at the foundational statistical learning theory level, is crucial for building robust, auditable, and safe AI systems.
The availability of comprehensive formalizations in Lean 4 provides a foundational infrastructure for developing provably correct AI architectures and statistical models.
- · AI safety researchers
- · High-assurance AI developers
- · Formal methods community
- · Critical infrastructure relying on AI
- · Developers of unverified AI
- · AI systems lacking transparency
This work directly enables the development of more trustworthy and formally verified AI algorithms and statistical models.
Increased trust in AI systems could accelerate deployment in sensitive domains like finance, healthcare, and autonomous systems.
Formal verification could become a standard requirement for critical AI applications, influencing regulation and industry best practices.
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Read at arXiv cs.CL