HomeAI PapersUnlocking the Potential of Large Language Models for Formal Theorem Proving

    Unlocking the Potential of Large Language Models for Formal Theorem Proving

    Exploring Failure Cases to Enhance Performance and Accessibility of AI-driven Proof Automation

    • Large language models, such as GPT-3.5 Turbo and GPT-4, have the potential to revolutionize formal theorem proving by simplifying the process and making it more accessible.
    • Researchers have conducted a fine-grained analysis of model outputs to identify failure cases, aiming to learn from them to improve AI-driven proof automation techniques.
    • The study provides recommendations to enhance language models’ theorem-proving capabilities, including better access to information, utilizing the chat API, and learning from errors.

    Formal theorem proving is a vital yet challenging task, well-suited for automation. Recent advances in large language models, such as GPT-3.5 Turbo and GPT-4, present opportunities to enhance formal proof automation. By examining the failure cases of these models, researchers aim to learn how to improve AI-driven proof automation techniques and make them more accessible.

    To better understand the capabilities of these state-of-the-art models, researchers conducted a fine-grained analysis of their outputs when tasked with proving theorems using common prompting-based techniques. The focus of the study was on failure cases and how these instances can provide valuable insights into getting more out of these language models.

    Based on the analysis, researchers provided several recommendations for improving the performance of AI-driven theorem proving:

    • Allow the model to prompt the proof assistant for more information, enabling the model to gather details as it generates proof in steps.
    • Give the model access to proof states to emulate the interactive conversation between human proof engineers and the proof assistant.
    • Provide the model access to information in file dependencies to avoid incorrect assumptions and errors.
    • Grant the model access to proofs preceding the current proof, allowing the model to learn from context and improve its output.
    • Encourage models to learn from errors, utilizing error messages as feedback to guide improvements in theorem proving.
    • Introduce diversity through prompt engineering to boost performance by generating different prompts for Coq proofs.

    The study’s findings offer valuable insights into enhancing the theorem-proving capabilities of large language models. By addressing these failure cases, AI-driven proof automation can become more efficient, accessible, and reliable, ultimately transforming the field of formal theorem proving.


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