[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

QuantFactory/internlm2-math-plus-1_8b-GGUF

InternLM-Math-Plus-GGUF

Model Description

News

Performance

Formal Math Reasoning

Informal Math Reasoning

QuantFactory/
internlm2-math-plus-1_8b-GGUF