Efficient Neural Theorem Proving via Fine-grained Proof Structure Analysis

• URL: http://arxiv.org/abs/2501.18310v1
• Date: Thu, 30 Jan 2025 12:37:06 GMT
• Title: Efficient Neural Theorem Proving via Fine-grained Proof Structure Analysis
• Authors: Haoxiong Liu, Jiacheng Sun, Zhenguo Li, Andrew C Yao,
• Abstract summary: We propose ProofAug, a novel theorem proving method that enjoys superior sample efficiency. Our method is validated on the miniF2F-test benchmark using the open-source deepseek-math-7b-base model and the Isabelle proof assistant.
• Score: 50.020850767257095
• License:
• Abstract: The synergy between deep learning models and traditional automation tools plays a pivotal role in developing robust neural theorem provers (NTPs). However, for proof synthesis with LLMs, previous work applies automation tools either only when the model explicitly calls the method, or only at a single granularity level, failing to fully exploit the power of built-in tactics and off-the-shelf automated theorem provers. In this work, we propose ProofAug, a novel theorem proving method that enjoys superior sample efficiency through equipping proof-generation LLMs with automation methods in different granularities via fine-grained structure analysis of model-generated proof proposals. Furthermore, ProofAug serves as a versatile plug-and-play module that seamlessly integrates with any tree-search algorithm, enabling our construction of an efficient recursive proving (ERP) module to further enhance performance. The superiority of our method is validated on the miniF2F-test benchmark using the open-source deepseek-math-7b-base model and the Isabelle proof assistant. Notably, by additionally employing a mixed prompting strategy, we achieve a cumulative pass rate of 66.0% after curation of the dataset (61.9% for the original version), setting a new SOTA across all proof languages with a total sample budget of only 2100. Our code is available at https://github.com/haoxiongliu/ProofAug.

Related papers

• Reasoning with Reinforced Functional Token Tuning [70.96651128307985]
  We propose Reinforced Functional Token Tuning (RFTT) to empower Large Language Models (LLMs) with self-play learn-to-reason capabilities. RFTT embeds a rich set of learnable functional tokens directly into the model vocabulary, enabling chain-of-thought construction with diverse human-like reasoning behaviors.
  arXiv  Detail & Related papers  (2025-02-19T02:59:42Z)
• CorrectBench: Automatic Testbench Generation with Functional Self-Correction using LLMs for HDL Design [6.414167153186868]
  We propose CorrectBench, an automatic testbench generation framework with functional self-validation and self-correction. The proposed approach can validate the correctness of the generated testbenches with a success rate of 88.85%. Our work's performance is 62.18% higher than previous work in sequential tasks and almost 5 times the pass ratio of the direct method.
  arXiv  Detail & Related papers  (2024-11-13T10:45:19Z)
• Cobblestone: Iterative Automation for Formal Verification [11.445689801392657]
  Formal verification using proof assistants, such as Coq, is an effective way of improving software quality, but it is expensive. Recent research has used machine learning to automatically synthesize proofs, reducing verification effort, but these tools are able to prove only a fraction of the desired software properties. We introduce Cobblestone, a new proof-synthesis approach that improves on the state of the art by taking advantage of partial progress in proof synthesis attempts.
  arXiv  Detail & Related papers  (2024-10-25T19:25:00Z)
• Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning [55.96599486604344]
  We introduce an approach aimed at enhancing the reasoning capabilities of Large Language Models (LLMs) through an iterative preference learning process. We use Monte Carlo Tree Search (MCTS) to iteratively collect preference data, utilizing its look-ahead ability to break down instance-level rewards into more granular step-level signals. The proposed algorithm employs Direct Preference Optimization (DPO) to update the LLM policy using this newly generated step-level preference data.
  arXiv  Detail & Related papers  (2024-05-01T11:10:24Z)
• Towards Large Language Models as Copilots for Theorem Proving in Lean [81.94024084598598]
  We introduce Lean Copilot, a framework for running Lean inference in large language models. We build tools for suggesting proof steps, completing intermediate proof goals, and selecting relevant premises. Experimental results demonstrate the effectiveness of our method in assisting humans and theorem proving process.
  arXiv  Detail & Related papers  (2024-04-18T22:54:08Z)
• MUSTARD: Mastering Uniform Synthesis of Theorem and Proof Data [85.50740598523818]
  MUSTARD is a framework that masters uniform synthesis of theorem and proof data of high quality and diversity. We present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data.
  arXiv  Detail & Related papers  (2024-02-14T05:57:58Z)
• Enhancing Neural Theorem Proving through Data Augmentation and Dynamic Sampling Method [1.8130068086063336]
  We introduce DS-Prover, a novel dynamic sampling method for theorem proving. We augment the training dataset by decomposing simplification and rewrite tactics with multiple premises into tactics with single premises. We achieve a state-of-the-art performance (Pass@1) of 14.2% on the ProofNet dataset and a performance of 29.8% on MiniF2F.
  arXiv  Detail & Related papers  (2023-12-20T09:55:21Z)
• LeanDojo: Theorem Proving with Retrieval-Augmented Language Models [72.54339382005732]
  Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. Existing methods are difficult to reproduce or build on, due to private code, data, and compute requirements. This paper introduces LeanDojo: an open-source Lean toolkit consisting of toolkits, data, models. We develop ReProver: an LLM-based prover augmented with retrieval for selecting premises from a vast math library.
  arXiv  Detail & Related papers  (2023-06-27T17:05:32Z)
• Baldur: Whole-Proof Generation and Repair with Large Language Models [8.100054850290507]
  We use large language models, trained on natural language text and code and fine-tuned on proofs, to generate whole proofs for theorems at once. We combine this proof generation model with a fine-tuned repair model to repair generated proofs, further increasing proving power. We evaluate our method in a prototype, Baldur, and evaluate it on a benchmark of 6,336 Isabelle/HOL theorems and their proofs.
  arXiv  Detail & Related papers  (2023-03-08T22:00:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.