EvolProver: Advancing Automated Theorem Proving by Evolving Formalized Problems via Symmetry and Difficulty
EvolProver enhances automated theorem proving by evolving problems via symmetry and difficulty, achieving 53.8% pass@32.
Key Findings
Methodology
This study introduces a novel data augmentation pipeline to enhance model robustness through symmetry and difficulty. EvolAST targets syntactic symmetry, EvolDomain addresses semantic symmetry, and EvolDifficulty adjusts difficulty to generate diverse problem data.
Key Results
- EvolProver achieved a 53.8% pass@32 rate on the FormalMATH-Lite dataset, surpassing all models of comparable size, including reasoning models.
- On MiniF2F-Test, EvolProver achieved a 69.8% pass@32 rate, setting a new record for non-reasoning models.
- On Ineq-Comp-Seed and Ineq-Comp-Transformed, it achieved 52.2% and 34.0% pass@32 rates respectively.
Significance
This research significantly enhances the robustness and generalizability of automated theorem proving models by addressing the fragility of existing models to minor problem statement transformations.
Technical Contribution
Introduced EvolAST, EvolDomain, and EvolDifficulty methods for data augmentation, significantly improving model performance and data diversity.
Novelty
First to combine symmetry and difficulty for data augmentation, generating syntactically and semantically diverse problems, overcoming limitations of existing data synthesis methods.
Limitations
- EvolProver may struggle with extremely complex theorems, especially those requiring deep reasoning.
- The data augmentation process may introduce semantic errors, affecting model training effectiveness.
Future Work
Future research could explore more complex theorem proving scenarios and further optimize data augmentation strategies to enhance model robustness and generalizability.
AI Executive Summary
Automated theorem proving is a crucial research area in AI, but existing models often struggle with minor changes in problem statements. EvolProver introduces an innovative data augmentation pipeline that combines symmetry and difficulty adjustments to generate diverse problem data, significantly enhancing model robustness. Core technologies include EvolAST, EvolDomain, and EvolDifficulty, each targeting syntactic and semantic symmetry and difficulty adjustments. Experimental results show that EvolProver sets new records across multiple benchmarks, notably achieving a 53.8% pass@32 rate on FormalMATH-Lite. Despite these achievements, the model still faces limitations in handling extremely complex theorems, and future research will focus on further optimizing data augmentation strategies.
Deep Analysis
Background
Automated theorem proving is a key area of AI research, with recent advancements in large language models prompting exploration of their application in mathematical reasoning. Notable works include DeepSeek-Prover and Goedel-Prover, but these models often struggle with minor problem statement changes.
Core Problem
Existing automated theorem proving models struggle with minor changes in problem statements, lacking generalizability, which leads to insufficient robustness across different scenarios.
Innovation
EvolProver introduces an innovative data augmentation pipeline that combines symmetry and difficulty adjustments to generate diverse problem data, significantly enhancing model robustness. EvolAST, EvolDomain, and EvolDifficulty each target syntactic and semantic symmetry and difficulty adjustments.
Methodology
- �� EvolAST: Uses Abstract Syntax Tree for syntactic symmetry transformation. • EvolDomain: Achieves semantic symmetry through cross-domain translation. • EvolDifficulty: Adjusts problem difficulty to generate diverse data.
Experiments
Experiments use datasets like FormalMATH-Lite, MiniF2F-Test, and Ineq-Comp, comparing EvolProver's performance with other models, focusing on the impact of data augmentation on model robustness.
Results
EvolProver sets new records across multiple benchmarks, notably achieving a 53.8% pass@32 rate on FormalMATH-Lite, significantly surpassing other models of comparable size.
Applications
EvolProver can be directly applied in mathematical theorem proving, automated problem generation in education, and complex problem-solving in scientific research.
Limitations & Outlook
Despite EvolProver's strong performance across benchmarks, it still faces limitations in handling extremely complex theorems, and future research will focus on further optimizing data augmentation strategies.
Plain Language Accessible to non-experts
Imagine you're in a kitchen, and EvolProver is like a smart chef assistant. It can create new recipes based on different ingredient combinations. Even if you change just a little, it ensures the taste and quality remain consistent. This way, it helps you tackle various challenges in the kitchen, ensuring every dish is perfectly presented.
ELI14 Explained like you're 14
Hey there! Imagine you're playing a game, and EvolProver is like a super game assistant. It helps you solve all kinds of puzzles, even if the game rules change a bit, it finds the best strategy. Just like solving math problems at school, it helps you find the easiest way to solve them. Isn't that cool?
Glossary
Abstract Syntax Tree (AST)
A tree model used to represent program structure, aiding in code parsing and transformation.
Used in EvolAST method for syntactic symmetry transformation.
Symmetry
A property of invariance in mathematics, helping generate equivalent problems.
Used in EvolAST and EvolDomain methods.
Difficulty Adjustment
Generating diverse data by changing problem complexity.
Used in EvolDifficulty method.
FormalMATH-Lite
A dataset containing 425 mathematical problems for evaluating theorem proving models.
EvolProver sets new records on this dataset.
pass@32
A metric for evaluating model performance, indicating the success rate in 32 attempts.
Used to measure EvolProver's performance.
Open Questions Unanswered questions from this research
- 1 How to further improve model performance on extremely complex theorems? Current methods still lack in handling deep reasoning.
- 2 How to reduce semantic errors potentially introduced during data augmentation? A stricter verification mechanism is needed.
Applications
Immediate Applications
Mathematics Education
Assists teachers in generating diverse exercises, enhancing students' mathematical thinking skills.
Long-term Vision
Scientific Research
Provides more powerful automated tools in solving complex scientific problems, driving scientific progress.
Abstract
Large Language Models (LLMs) for formal theorem proving have shown significant promise, yet they often lack generalizability and are fragile to even minor transformations of problem statements. To address this limitation, we introduce a novel data augmentation pipeline designed to enhance model robustness from two perspectives: symmetry and difficulty. From the symmetry perspective, we propose two complementary methods: EvolAST, an Abstract Syntax Tree (AST) based approach that targets syntactic symmetry to generate semantically equivalent problem variants, and EvolDomain, which leverages LLMs to address semantic symmetry by translating theorems across mathematical domains. From the difficulty perspective, we propose EvolDifficulty, which uses carefully designed evolutionary instructions to guide LLMs in generating new theorems with a wider range of difficulty. We then use the evolved data to train EvolProver, a 7B-parameter non-reasoning theorem prover. EvolProver establishes a new state-of-the-art (SOTA) on FormalMATH-Lite with a 53.8% pass@32 rate, surpassing all models of comparable size, including reasoning-based models. It also sets new SOTA records for non-reasoning models on MiniF2F-Test (69.8% pass@32), Ineq-Comp-Seed (52.2% pass@32), and Ineq-Comp-Transformed (34.0% pass@32). Ablation studies further confirm our data augmentation pipeline's effectiveness across multiple benchmarks.