102 lines
3.1 KiB
Markdown
102 lines
3.1 KiB
Markdown
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---
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pipeline_tag: text-generation
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license: other
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language:
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- en
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tags:
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- math
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---
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# InternLM-Step-Prover
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<div align="center">
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<img src="https://raw.githubusercontent.com/InternLM/InternLM/main/assets/logo.svg" width="200"/>
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<div> </div>
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<div align="center">
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<b><font size="5">InternLM-Math</font></b>
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<sup>
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<a href="https://internlm.intern-ai.org.cn/">
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<i><font size="4">HOT</font></i>
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</a>
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</sup>
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<div> </div>
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</div>
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A state-of-the-art LEAN4 step prover.
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[💻 Github](https://github.com/InternLM/InternLM-Math) [📊Dataset](https://huggingface.co/datasets/internlm/Lean-Github) [📖 Paper](https://arxiv.org/abs/2407.17227)
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</div>
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InternLM-Step-Prover is a 7B language model trained on Lean-Github and multiple sythesis datasets. InternLM-Step-Prover achieves state-of-the-art performances on MiniF2F, ProofNet, and Putnam math benchmarks, showing its formal math proving ability in multiple domains.
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# Dialogue Example
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```
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### Input Example
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DECL MyNat.mul_pow
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GOAL a b n : N
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⊢ (a * b) ^ n = a ^ n * b ^ n
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### Output Example
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PROOFSTEP induction n with t Ht
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```
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# Performance
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## MiniF2F
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| Method | Model size | Pass | miniF2F-valid | miniF2F-test |
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|--------|------------|------|---------------|--------------|
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| **Whole-Proof Generation Methods** |
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| GPT-4-turbo 0409 | - | 64 | 25.4% | 23.0% |
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| DeepSeekMath-Base | 7B | 128 | 25.4% | 27.5% |
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| DeepSeek-Prover | 7B | 1 | - | 30.0% |
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| | | 64 | - | 46.3% |
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| | | 128 | - | 46.3% |
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| | | 8192 | - | 48.8% |
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| | | 65536 | - | 50.0% |
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| | | cumulative | *60.2%* | *52.0%* |
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| TheoremLlama | - | cumulative | 36.5% | 33.6% |
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| **Tree Search Methods** |
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| COPRA (GPT-3.5) | - | 1 | - | 9.0% |
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| COPRA (GPT-4) | - | 1 | - | 26.6% |
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| DSP(Isabelle) | 540B | 100 | 42.6% | 38.9% |
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| Proof Artifact Co-Training | 837M | 1 | 23.9% | 24.6% |
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| | | 8 | 29.3% | 29.2% |
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| ReProver | 229M | 1 | - | 25.0% |
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| Llemma | 7B | 1 | 26.2% | 26.2% |
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| Llemma | 34B | 1 | 27.9% | 25.8% |
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| Curriculum Learning | 837M | 1 | 33.6% | 29.6% |
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| | | 8 | 41.2% | 34.5% |
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| | | 64 | 47.3% | 36.6% |
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| Hypertree Proof Search | 600M | cumulative | 58.6% | - |
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| | | 64 | - | 41.0% |
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| Lean-STaR | 7B | 64 | - | 46.3% |
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| InternLM2-Math | 7B | 1 | 29.9% | 30.3% |
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| InternLM2-Math-Plus | 7B | 1 | - | 43.4% |
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| InternLM2-Step-Prover | 7B | 1 | 59.8% | 48.8% |
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| InternLM2-Step-Prover | 7B | 64 | **63.9%** | **54.5%** |
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## Proofnet & Putnam
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| Method | Model size | Pass | result |
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|--------|------------|------|--------|
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| **ProofNet benchmark** |
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| ReProver | 229M | 1 | 13.8% |
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| InternLM2-Step-Prover | 7B | 1 | **18.1%** |
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| **Putnam benchmark** |
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| GPT-4 | - | 10 | 1/640 |
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| COPRA (GPT-4) | - | 10 | 1/640 |
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| DSP(Isabelle) | 540B | 10 | 4/640 |
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| ReProver | 229M | 1 | 0/640 |
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| InternLM2-Step-Prover | 7B | 1 | **5/640** |
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# Citation and Tech Report
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```
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@misc{wu2024leangithubcompilinggithublean,
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title={LEAN-GitHub: Compiling GitHub LEAN repositories for a versatile LEAN prover},
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author={Zijian Wu and Jiayu Wang and Dahua Lin and Kai Chen},
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year={2024},
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eprint={2407.17227},
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archivePrefix={arXiv},
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primaryClass={cs.AI},
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url={https://arxiv.org/abs/2407.17227},
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}
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```
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