Formal library supports language generation in the limit research
GenLimitLib: A Formal Library for Language Generation in the Limit and AI-Assisted Mathematical Research
Machine LearningLogic in Computer Science
Summary
Language generation in the limit studies how to create new valid strings based on examples, inspired by large language models. The authors created GenLimitLib, a formal Lean 4 library that organizes and proves key concepts from 30 related research papers. This library helps researchers by structuring shared definitions and proofs while keeping each paper’s unique assumptions clear. The authors also show how their library supports both human and AI-assisted mathematical research through examples and experiments.
What this means in practice
- •For mathematical software developers: Integrate GenLimitLib into formal proof systems to manage and verify language generation theories consistently across multiple research papers.
- •For ai research engineers: Use GenLimitLib to structure and validate AI-assisted mathematical problem solving related to language generation in experimental AI research.
Authors
Shuangping Li, Peng Zhang
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.