Theorem proving in arithmetic faces rising challenges resulting from rising proof complexity. Formalized programs like Lean, Isabelle, and Coq supply computer-verifiable proofs, however creating these calls for substantial human effort. Giant language fashions (LLMs) present promise in fixing high-school-level math issues utilizing proof assistants, but their efficiency nonetheless wants to enhance resulting from knowledge shortage. Formal languages require vital experience, leading to restricted corpora. In contrast to typical programming languages, formal proof languages comprise hidden intermediate data, making uncooked language corpora unsuitable for coaching. This shortage persists regardless of the existence of priceless human-written corpora. Auto-formalization efforts, whereas useful, can not absolutely substitute human-crafted knowledge in high quality and variety.
Present makes an attempt to handle theorem-proving challenges have developed considerably with fashionable proof assistants like Coq, Isabelle, and Lean having expanded formal programs past first-order logic, rising curiosity in automated theorem proving (ATP). The current integration of huge language fashions has additional superior this area. Early ATP approaches used conventional strategies like KNN or GNN, with some using reinforcement studying. Latest efforts make the most of deep transformer-based strategies, treating theorems as plain textual content. Many learning-based programs (e.g., GPT-f, PACT, Llemma) prepare language fashions on (proof state, next-tactic) pairs and use tree seek for theorem proving. Different approaches contain LLMs producing total proofs independently or primarily based on human-provided proofs. Knowledge extraction instruments are essential for ATP, capturing intermediate states invisible in code however seen throughout runtime. Instruments exist for varied proof assistants, however Lean 4 instruments face challenges in huge extraction throughout a number of initiatives resulting from single-project design limitations. Some strategies additionally discover incorporating casual proofs into formal proofs, broadening the scope of ATP analysis.
Researchers from The Chinese language College of Hong Kong suggest LEAN-GitHub, a large-scale Lean dataset that enhances the well-utilized Mathlib dataset. This modern method supplies an open-source Lean repositories on GitHub, considerably increasing the accessible knowledge for coaching theorem-proving fashions. The researchers developed a scalable pipeline to boost extraction effectivity and parallelism, enabling the exploitation of priceless knowledge from beforehand uncompiled and unextracted Lean corpus. Additionally, they supply an answer to the state duplication drawback frequent in tree-proof search strategies.
The LEAN-GitHub dataset development course of concerned a number of key steps and improvements:
- Repository Choice: The researchers recognized 237 Lean 4 repositories (GitHub doesn’t differentiate between Lean 3 and Lean 4) on GitHub, estimating roughly 48,091 theorems. After discarding 90 repositories with deprecated Lean 4 variations, 147 remained. Solely 61 of those could possibly be compiled with out modifications.
- Compilation Challenges: The group developed automated scripts to search out the closest official releases for initiatives utilizing non-official Lean 4 variations. Additionally they addressed the difficulty of remoted information inside empty Lean initiatives.
- Supply Code Compilation: As a substitute of utilizing the Lake instrument, they known as the Leanc compiler immediately. This method allowed for compiling non-compliant Lean initiatives and remoted information, which Lake couldn’t deal with. They prolonged Lake’s import graph and created a customized compiling script with elevated parallelism.
- Extraction Course of: Constructing upon LeanDojo, the group carried out knowledge extraction for remoted information and restructured the implementation to extend parallelism. This method overcame bottlenecks in community connection and computational redundancies.
- Outcomes: Out of 8,639 Lean supply information, 6,352 and 42,000 theorems had been efficiently extracted. The ultimate dataset consists of 2,133 information and 28,000 theorems with legitimate tactic data.
The ensuing LEAN-GitHub dataset is various, protecting varied mathematical fields together with logic, first-order logic, matroid principle, and arithmetic. It accommodates cutting-edge mathematical matters, knowledge constructions, and Olympiad-level issues. In comparison with present datasets, LEAN-GitHub provides a novel mixture of human-written content material, intermediate states, and various complexity ranges, making it a priceless useful resource for advancing automated theorem proving and formal arithmetic.
InternLM2-StepProver, skilled on the various LEAN-GitHub dataset, demonstrates distinctive formal reasoning talents throughout varied benchmarks. It achieves state-of-the-art efficiency on miniF2F (63.9% on Legitimate, 54.5% on Check), surpassing earlier fashions. On ProofNet, it attains an 18.1% Move@1 charge, outperforming the earlier chief. For PutnamBench, it solves 5 issues in a single move, together with the beforehand unsolved Putnam 1988 B2. These outcomes span high-school to superior undergraduate-level arithmetic, showcasing InternLM2-StepProver’s versatility and the effectiveness of the LEAN-GitHub dataset in coaching superior theorem-proving fashions.
LEAN-GitHub, a large-scale dataset extracted from open Lean 4 repositories, accommodates 28,597 theorems and 218,866 ways. This various dataset was used to coach InternLM2-StepProver, attaining state-of-the-art efficiency in Lean 4 formal reasoning. Fashions skilled on LEAN-GitHub show improved efficiency throughout varied mathematical fields and problem ranges, highlighting the dataset’s effectiveness in enhancing reasoning capabilities. By open-sourcing LEAN-GitHub, the researchers purpose to assist the group higher make the most of under-exploited data in uncooked corpora and advance mathematical reasoning. This contribution may considerably speed up progress in automated theorem proving and formal arithmetic.
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