2024/10/08 by Adarsh Kumarappan, Mo Tiwari, Kumarappan, Adarsh +10 · 3 voices · 3 citations
Business, Management and Accounting · Computer Science · Engineering · #Artificial Intelligence (cs.AI) #Business Process Modeling and Analysis #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Machine Learning (cs.LG) #Manufacturing Process and Optimization #cs.AI #cs.LG #cs.LO
paper · pdf · doi:10.48550/arxiv.2410.06209
openalex publication_date 2024/10/08 · arxiv published 2024/10/08 · arxiv updated 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a specific dataset to perform well on particular domains, such as undergraduate-level mathematics. These methods struggle with generalizability to advanced mathematics. A fundamental limitation is that these approaches operate on static domains, failing to capture how mathematicians often work across multiple domains and projects simultaneously or cyclically. We present LeanAgent, a novel lifelong learning framework for formal theorem proving that continuously generalizes to and improves on ever-expanding mathematical knowledge without forgetting previously learned knowledge. LeanAgent introduces several key innovations, including a curriculum learning strategy that optimizes the learning trajectory in terms of mathematical difficulty, a dynamic database for efficient management of evolving mathematical knowledge, and progressive training to balance stability and plasticity. LeanAgent successfully generates formal proofs for 155 theorems across 23 diverse Lean repositories where formal proofs were previously missing, many from advanced mathematics. It performs significantly better than the static LLM baseline, proving challenging theorems in domains like abstract algebra and algebraic topology while showcasing a clear progression of learning from basic concepts to advanced topics. In addition, we analyze LeanAgent's superior performance on key lifelong learning metrics. LeanAgent achieves exceptional scores in stability and backward transfer, where learning new tasks improves performance on previously learned tasks. This emphasizes LeanAgent's continuous generalizability and improvement, explaining its superior theorem-proving performance.