Artificial Intelligence (AI) and Machine Learning (ML) are popular fields that are revolutionizing the way humans interact with machines. In AI, reasoning plays a significant role, and researchers have explored various approaches such as Automated theorem proving (ATP) to produce proofs for theorems. However, ATP faces challenges due to its massive search space. To address this, Interactive theorem proving (ITP) has emerged as an alternative paradigm where human experts interact with software tools called proof assistants.
To overcome the limitations faced by Large language models (LLMs) in theorem proving, a team of researchers from Caltech, NVIDIA, MIT, UC Santa Barbara, and UT Austin has developed LeanDojo. It is an open-source toolkit built around the Lean proof assistant, which is popular among mathematicians. LeanDojo enables models to communicate with Lean programmatically, allowing them to view proof states, perform proof actions, and receive feedback from Lean.
LeanDojo also offers resources for data extraction from proof trees and intermediate proof states. This data extraction capability is valuable for premise selection, a critical bottleneck in theorem proving. The researchers have used LeanDojo’s data extraction capabilities to develop ReProver, the first LLM-based prover with retrieval for selecting premises from a large math library. Unlike previous methods that relied on private datasets and extensive computing resources, ReProver is designed to be accessible and cost-effective. It requires less computing power and can be trained with just one GPU per week.
The combination of LeanDojo’s program analysis capacity and ReProver’s retrieval mechanism enhances the prover’s performance and the effectiveness of the retrieval procedure. To evaluate ReProver and enable further research, the team has created a benchmark dataset comprising thousands of theorems and proofs extracted from Lean’s math library. This benchmark dataset challenges the prover to generalize to theorems that rely on novel premises not used during training. Experimental results have shown that ReProver performs well compared to non-retrieval baselines and GPT-4 when using this benchmark dataset.
In conclusion, LeanDojo and ReProver offer promising solutions for LLM-based theorem proving. They provide accessible toolkits, data, models, and benchmarks, overcoming the barriers of private code, data, and large computing requirements.
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**About the Author**
Tanya Malhotra is a final year undergraduate student from the University of Petroleum & Energy Studies, pursuing a degree in Computer Science Engineering with a specialization in Artificial Intelligence and Machine Learning. She is passionate about Data Science, with strong analytical and critical thinking skills. Tanya is always eager to acquire new skills, lead groups, and manage work efficiently.