DeepTheorem-qwen-7b-rl

DeepTheorem: Advancing LLM Reasoning for Theorem Proving Through Natural Language and Reinforcement Learning 🚀

Welcome to the GitHub repository for DeepTheorem 🎉, a comprehensive framework for enhancing large language model (LLM) mathematical reasoning through informal, natural language-based theorem proving. This project introduces a novel approach to automated theorem proving (ATP) by leveraging the informal reasoning strengths of LLMs, moving beyond traditional formal proof systems 🌟.

Overview 📖

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Theorem proving is a critical benchmark for evaluating complex reasoning in LLMs 🧠. However, formal proof systems often misalign with the informal, natural language knowledge LLMs acquire during pre-training. DeepTheorem addresses this gap by introducing:

1. A Large-Scale Theorem Proving Dataset 📊:

   • Contains high-quality, IMO-level informal theorems and proofs across diverse mathematical domains 📚.
   • Rigorously annotated for correctness, difficulty, and topic categories ✅.
   • Includes systematically constructed verifiable theorem variants for robust evaluation 🔍.

2. RL-Zero 🤖:

   • A novel reinforcement learning strategy tailored for informal theorem proving ⚙️.
   • Utilizes verified theorem variants to incentivize robust mathematical inference 💡.

Deeptheorem demonstrates its superior performance over both opensource and commercial models (i.e Gemini and o1)

Performance 🚀

Deeptheorem achieves the #Rank 5 position along all the commerical models and open source models.

DeepTheorem Dataset 📊

The DeepTheorem dataset comprises 121K IMO-level informal theorems and proofs spanning diverse mathematical domains 🌐. Each theorem-proof pair is rigorously annotated for:

• o3-mini Proofs 🖋️: Ensuring mathematical accuracy through proofs generated or verified by the o3-mini model ✅.
• Truth Value 🔍: The truth value of the theorem extracted from the o3-mini proofs, indicating whether the theorem is true or false ✔️.
• Difficulty 🎚️: Categorized by complexity to suit various LLM capabilities 🧩.
• Topic Categories 🗂️: Covering algebra, geometry, number theory, and more 📘.
• Variants 🔄: Positive or negative variants of the theorem that share the same or inverse truth value of the original theorem 🔀.