TheoremLlama An End-To-End Framework to Train a General-Purpose Large Language Model to Become a Lean4 Expert
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llm, lean4, theorem-proving, theorem-llama, stub, abstract, citation
Abstract
Proving mathematical theorems using computer-verifiable formal languages like Lean significantly impacts mathematical reasoning. One approach to formal theorem proving involves generating complete proofs using Large Language Models (LLMs) based on Natural Language (NL) proofs. Similar methods have shown promising results in code generation. However, most modern LLMs exhibit suboptimal performance due to the scarcity of aligned NL and Formal Language (FL) theorem-proving data. This scarcity results in a paucity of methodologies for training LLMs and techniques to fully utilize their capabilities in composing formal proofs. To address the challenges, this paper proposes TheoremLlama, an end-to-end framework to train a general-purpose LLM to become a Lean4 expert. This framework encompasses NL-FL aligned dataset generation methods, training approaches for the LLM formal theorem prover, and techniques for LLM Lean4 proof writing. Using the dataset generation method, we provide Open Bootstrapped Theorems (OBT), an NL-FL aligned and bootstrapped dataset. A key innovation in this framework is the NL-FL bootstrapping method, where NL proofs are integrated into Lean4 code for training datasets, leveraging the NL reasoning ability of LLMs for formal reasoning. The TheoremLlama framework achieves cumulative accuracies of 36.48% and 33.61% on MiniF2F-Valid and Test datasets respectively, surpassing the GPT-4 baseline of 22.95% and 25.41%. We have also open-sourced our model checkpoints and generated dataset1, and will soon make all the code publicly available2.
Introduction
(Wang et al. 2024) the authors present an end-to-end framework to train a Large Language Model (LLM) to become a Lean4 expert. 1 The framework includes NL-FL aligned dataset generation methods, training approaches for the LLM formal theorem prover, and techniques for LLM Lean4 proof writing. The authors demonstrate the effectiveness of TheoremLlama by achieving cumulative accuracies of 36.48% and 33.61% on MiniF2F-Valid and Test datasets respectively, surpassing the GPT-4 baseline of 22.95% and 25.41%.2
TheoremLlama is a significant step towards using LLMs’ natural language abilities to formalize theorem proving in Lean4, improving mathematical reasoning, and tackling major issues with data alignment and training approaches.
However, the lack of aligned NL and Formal Language (FL) theorem-proving data frequently makes it difficult for contemporary LLMs to operate efficiently. The lack of available resources impedes the advancement of efficient training approaches and strategies to fully utilize LLMs’ potential in creating formal mathematical proofs. In order to overcome these limitations, a team of researchers from The Hong Kong University of Science and Technology and the University of Illinois Urban-Champagin has introduced TheoremLlama, an end-to-end framework created to specialize a general-purpose LLM in Lean4 theorem proving.
TheoremLlama is made up of various important parts, which are as follows:
NL-FL Aligned Dataset Generation: TheoremLlama presents techniques for creating an NL-FL-aligned dataset in order to get over data shortage. This dataset, called Open Bootstrapped Theorems (OBT), uses a bootstrapping technique to include NL proofs into Lean4 code. By integrating NL reasoning into Lean4 scenarios, the framework improves LLMs’ comprehension and execution of formal reasoning.
Formal Training for LLM Theorem Provers: The system applies new training strategies to help LLMs become successful Lean4 theorem provers. Methods like block training and curriculum data sorting have been utilized to enhance the LLM’s in-context learning and guarantee reliable training on the OBT dataset. LLM Lean4 Proof Writing: This part is about improving the LLM’s capacity to write formal proofs in Lean4 on its own. The LLM refines its formal reasoning abilities iteratively by using correctly generated proofs as examples.
TheoremLlama’s NL-FL bootstrapping approach is a significant invention that enables efficient training by coordinating natural language reasoning with formal mathematical language constraints. The framework’s efficiency has been demonstrated by experimental findings, which on the MiniF2F-Valid and Test datasets, respectively, yielded cumulative accuracies of 36.48% and 33.61%. These outcomes outperformed GPT-4’s baseline findings, which on the same datasets yielded accuracies of 22.95% and 25.41%.
In conclusion, TheoremLlama is an important step towards using LLMs’ natural language abilities to formalize theorem proving in Lean4, improving mathematical reasoning, and tackling major issues with data alignment and training approaches
See also:
- paper
- https://www.marktechpost.com/2024/07/10/theoremllama-an-end-to-end-framework-to-train-a-general-purpose-large-language-model-to-become-a-lean4-expert/