metadata
pipeline_tag: text-generation
license: other
language:
- en
tags:
- math
InternLM-Step-Prover
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.
Dialogue Example
### Input Example
DECL MyNat.mul_pow
GOAL a b n : N
⊢ (a * b) ^ n = a ^ n * b ^ n
### Output Example
PROOFSTEP induction n with t Ht
Performance
MiniF2F
| Method | Model size | Pass | miniF2F-valid | miniF2F-test |
|---|---|---|---|---|
| Whole-Proof Generation Methods | ||||
| GPT-4-turbo 0409 | - | 64 | 25.4% | 23.0% |
| DeepSeekMath-Base | 7B | 128 | 25.4% | 27.5% |
| DeepSeek-Prover | 7B | 1 | - | 30.0% |
| 64 | - | 46.3% | ||
| 128 | - | 46.3% | ||
| 8192 | - | 48.8% | ||
| 65536 | - | 50.0% | ||
| cumulative | 60.2% | 52.0% | ||
| TheoremLlama | - | cumulative | 36.5% | 33.6% |
| Tree Search Methods | ||||
| COPRA (GPT-3.5) | - | 1 | - | 9.0% |
| COPRA (GPT-4) | - | 1 | - | 26.6% |
| DSP(Isabelle) | 540B | 100 | 42.6% | 38.9% |
| Proof Artifact Co-Training | 837M | 1 | 23.9% | 24.6% |
| 8 | 29.3% | 29.2% | ||
| ReProver | 229M | 1 | - | 25.0% |
| Llemma | 7B | 1 | 26.2% | 26.2% |
| Llemma | 34B | 1 | 27.9% | 25.8% |
| Curriculum Learning | 837M | 1 | 33.6% | 29.6% |
| 8 | 41.2% | 34.5% | ||
| 64 | 47.3% | 36.6% | ||
| Hypertree Proof Search | 600M | cumulative | 58.6% | - |
| 64 | - | 41.0% | ||
| Lean-STaR | 7B | 64 | - | 46.3% |
| InternLM2-Math | 7B | 1 | 29.9% | 30.3% |
| InternLM2-Math-Plus | 7B | 1 | - | 43.4% |
| InternLM2-Step-Prover | 7B | 1 | 59.8% | 48.8% |
| InternLM2-Step-Prover | 7B | 64 | 63.9% | 54.5% |
Proofnet & Putnam
| Method | Model size | Pass | result |
|---|---|---|---|
| ProofNet benchmark | |||
| ReProver | 229M | 1 | 13.8% |
| InternLM2-Step-Prover | 7B | 1 | 18.1% |
| Putnam benchmark | |||
| GPT-4 | - | 10 | 1/640 |
| COPRA (GPT-4) | - | 10 | 1/640 |
| DSP(Isabelle) | 540B | 10 | 4/640 |
| ReProver | 229M | 1 | 0/640 |
| InternLM2-Step-Prover | 7B | 1 | 5/640 |
Citation and Tech Report
@misc{wu2024leangithubcompilinggithublean,
title={LEAN-GitHub: Compiling GitHub LEAN repositories for a versatile LEAN prover},
author={Zijian Wu and Jiayu Wang and Dahua Lin and Kai Chen},
year={2024},
eprint={2407.17227},
archivePrefix={arXiv},
primaryClass={cs.AI},
url={https://arxiv.org/abs/2407.17227},
}