Innovation
Methods, ideas, or system contributions that make the work stand out.
Formal Library
Language Generation in the Limit
Lean 4
AI-Assisted Research
Large-Scale Formalization
GenLimitLib: A Formal Library for Language Generation in the Limit and AI-Assisted Mathematical Research
🤖 AI Summary
This work addresses the challenge of unified modeling and reuse in large-scale mathematical literature by proposing a formal verification framework grounded in the Language Limit Generation Theory. Leveraging the Lean 4 interactive theorem prover and large language models (LLMs), this project pioneers a structured formal library for the field, constructing a source-aligned Lean 4 codebase that comprehensively integrates definitions, proof components, and assumption dependencies across thirty research papers to enable cross-paper abstraction sharing and human–machine collaborative exploration. The formalization of all thirty papers has been completed. Furthermore, through case studies and LLM-driven experiments, the proposed methodology is demonstrated to effectively support both mathematical research and pedagogy.
📝 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: https://github.com/pengzhang91/generation-in-the-limit-lib.
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