GenLimitLib: A Formal Library for Language Generation in the Limit and AI-Assisted Mathematical Research

Abstract:We present GenLimitLib, a source-aligned Lean 4 library for language generation in the limit. Introduced by Kleinberg and Mullainathan at NeurIPS 2024, language generation in the limit studies a theoretical question motivated by LLMs: how to generate valid new strings from observed examples. This young and rapidly evolving field offers a natural testbed for studying large-scale formalization. GenLimitLib contains formal developments for 30 papers. It extracts shared definitions and reusable proof components while preserving paper-specific assumptions and statements, and records relationships across papers. In this way, GenLimitLib provides a concrete and structured view of the literature. We show through mathematical case studies and LLM experiments how our library can support both human mathematical research and AI-assisted research. Our Library: this https URL.

Machine Learning (cs.LG); Logic in Computer Science (cs.LO)

arXiv:2609.36663 [cs.LG]

(or arXiv:2609.36663v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.36663 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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