internlm/internlm2-math-plus-1_8b

InternLM-Math-Plus

InternLM-Math ^Plus

State-of-the-art bilingual open-sourced Math reasoning LLMs. A solver, prover, verifier, augmentor.

💻 Github 🤗 Demo

News

• [2024.05.24] We release updated version InternLM2-Math-Plus with 4 sizes and state-of-the-art performances including 1.8B, 7B, 20B, and 8x22B. We improve informal math reasoning performance (chain-of-thought and code-intepreter) and formal math reasoning performance (LEAN 4 translation and LEAN 4 theorem proving) significantly.
• [2024.02.10] We add tech reports and citation reference.
• [2024.01.31] We add MiniF2F results with evaluation codes!
• [2024.01.29] We add checkpoints from ModelScope. Update results about majority voting and Code Intepreter. Tech report is on the way!
• [2024.01.26] We add checkpoints from OpenXLab, which ease Chinese users to download!

Performance

Formal Math Reasoning

We evaluate the performance of InternLM2-Math-Plus on formal math reasoning benchmark MiniF2F-test. The evaluation setting is same as Llemma with LEAN 4.

Models	MiniF2F-test
ReProver	26.5
LLMStep	27.9
GPT-F	36.6
HTPS	41.0
Llemma-7B	26.2
Llemma-34B	25.8
InternLM2-Math-7B-Base	30.3
InternLM2-Math-20B-Base	29.5
InternLM2-Math-Plus-1.8B	38.9
InternLM2-Math-Plus-7B	43.4
InternLM2-Math-Plus-20B	42.6
InternLM2-Math-Plus-Mixtral8x22B	37.3

Informal Math Reasoning

We evaluate the performance of InternLM2-Math-Plus on informal math reasoning benchmark MATH and GSM8K. InternLM2-Math-Plus-1.8B outperforms MiniCPM-2B in the smallest size setting. InternLM2-Math-Plus-7B outperforms Deepseek-Math-7B-RL which is the state-of-the-art math reasoning open source model. InternLM2-Math-Plus-Mixtral8x22B achieves 68.5 on MATH (with Python) and 91.8 on GSM8K.

Model	MATH	MATH-Python	GSM8K
MiniCPM-2B	10.2	-	53.8
InternLM2-Math-Plus-1.8B	37.0	41.5	58.8
InternLM2-Math-7B	34.6	50.9	78.1
Deepseek-Math-7B-RL	51.7	58.8	88.2
InternLM2-Math-Plus-7B	53.0	59.7	85.8
InternLM2-Math-20B	37.7	54.3	82.6
InternLM2-Math-Plus-20B	53.8	61.8	87.7
Mixtral8x22B-Instruct-v0.1	41.8	-	78.6
Eurux-8x22B-NCA	49.0	-	-
InternLM2-Math-Plus-Mixtral8x22B	58.1	68.5	91.8

We also evaluate models on MathBench-A. InternLM2-Math-Plus-Mixtral8x22B has comparable performance compared to Claude 3 Opus.

Model	Arithmetic	Primary	Middle	High	College	Average
GPT-4o-0513	77.7	87.7	76.3	59.0	54.0	70.9
Claude 3 Opus	85.7	85.0	58.0	42.7	43.7	63.0
Qwen-Max-0428	72.3	86.3	65.0	45.0	27.3	59.2
Qwen-1.5-110B	70.3	82.3	64.0	47.3	28.0	58.4
Deepseek-V2	82.7	89.3	59.0	39.3	29.3	59.9
Llama-3-70B-Instruct	70.3	86.0	53.0	38.7	34.7	56.5
InternLM2-Math-Plus-Mixtral8x22B	77.5	82.0	63.6	50.3	36.8	62.0
InternLM2-Math-20B	58.7	70.0	43.7	24.7	12.7	42.0
InternLM2-Math-Plus-20B	65.8	79.7	59.5	47.6	24.8	55.5
Llama3-8B-Instruct	54.7	71.0	25.0	19.0	14.0	36.7
InternLM2-Math-7B	53.7	67.0	41.3	18.3	8.0	37.7
Deepseek-Math-7B-RL	68.0	83.3	44.3	33.0	23.0	50.3
InternLM2-Math-Plus-7B	61.4	78.3	52.5	40.5	21.7	50.9
MiniCPM-2B	49.3	51.7	18.0	8.7	3.7	26.3
InternLM2-Math-Plus-1.8B	43.0	43.3	25.4	18.9	4.7	27.1

Citation and Tech Report

@misc{ying2024internlmmath,
      title={InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning}, 
      author={Huaiyuan Ying and Shuo Zhang and Linyang Li and Zhejian Zhou and Yunfan Shao and Zhaoye Fei and Yichuan Ma and Jiawei Hong and Kuikun Liu and Ziyi Wang and Yudong Wang and Zijian Wu and Shuaibin Li and Fengzhe Zhou and Hongwei Liu and Songyang Zhang and Wenwei Zhang and Hang Yan and Xipeng Qiu and Jiayu Wang and Kai Chen and Dahua Lin},
      year={2024},
      eprint={2402.06332},
      archivePrefix={arXiv},
      primaryClass={cs.CL}
}