francis-llgg / mathbench

MathBench: A Comprehensive Multi-Level Difficulty Mathematics Evaluation Dataset

MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmark

[🏰Project Page] [📚LeaderBoard]

☀️Introduction

MathBench is an All in One math dataset for language model evaluation, with:

• A Sophisticated Five-Stage Difficulty Mechanism: Unlike the usual mathematical datasets that can only evaluate a single difficulty level or have a mix of unclear difficulty levels, MathBench provides 3709 questions with a gradient difficulty division by education stages, ranging from basic arithmetic to primary, middle, high school, and college levels, allowing you to get a clear overview of the comprehensive difficulty evaluation results.
• Bilingual Gradient Evaluation: Apart from the basic calculation part which is language-independent, MathBench provides questions in both Chinese and English for the four-stage difficulty datasets from primary to college.
• Implementation of the Robust Circular Evaluation (CE) Method: MathBench use CE as the main evaluation method for questions. Compared to the general Accuracy evaluation method, CE requires the model to answer the same multiple-choice question multiple times, with the order of the options changing each time. The model is considered correct on this question only if all answers are correct. The results of CE can reflect the model's capabilities more realistically, providing more valuable evaluation results.
• Support for Basic Theory Questions: For every stage, MathBench provides questions that cover the basic theory knowledge points of the corresponding stage, to ascertain whether the model has genuinely mastered the fundamental concepts of each stage or merely memorized the answers.

🚀 What's New

• [2024.3.14] We release the complete version of MathBench, which includes a total of 3,709 problems in both Chinese and English. The dataset covers both applied and theoretical math problems. Each problem is labeled with a three-level taxonomy. 🎉🎉🎉
• [2024.1.26] We release the Application questions of MathBench. 🎉🎉🎉

🌲Dataset Structure

📒Model Performance

We use zero-shot CoT set for multiple-choice questions and few-shot (8) CoT set for all textual questions. The results are shown in the following table, we present the results with common Accuracy and Circular Evaluation (CE) metrics.

Here is the overall average result of MathBench:

Models	ACC Average	CE Average
API Models
GPT-3.5	66.1	48.1
Qwen-Max	75.2	62.9
GLM4	73.0	60.3
Claude-3-Opus	77.4	64.2
GPT-4	78.8	68.9
Open-Source Chat Models
ChatGLM3-6B	43.7	24.3
Yi-6B-Chat	42.5	23.5
InternLM2-Chat-7B	59.3	42.7
Qwen-7B-Chat	51.8	34.3
Deepseek-7B-Chat	43.5	23.9
Baichuan2-13B-Chat	49.5	32.1
Qwen-14B-Chat	64.1	44.4
InternLM2-Chat-20B	64.7	47.4
Yi-34B-Chat	54.9	39.0
Deepseek-67B-Chat	65.3	52.0
Qwen-72B-Chat	72.2	61.1
Mathematical Models
MammoTH-7B	28.5	11.7
Metamath-Llemma-7B	39.4	25.1
InternLM2-Chat-Math-7B	64.0	46.0
Deepseek-Math-7B-Instruct	63.9	48.3
Deepseek-Math-7B-RL	69.6	58.7
MammoTH-13B	38.9	20.2
InternLM2-Chat-Math-20B	64.6	51.8
MammoTH-70B	49.9	34.2

Here is the CE result of MathBench with 5-level difficulty divisions🪜:

Models	Arithmetic	Primary	Middle	High	College
API Models
GPT-3.5	70.3	67.9	39.3	30.6	32.2
Qwen-Max	69.3	84.2	62.7	51.4	47.0
GLM4	61.3	83.0	64.0	52.1	41.2
Claude-3-Opus	84.7	86.1	63.5	48.2	38.7
GPT-4	76.3	82.9	69.8	56.6	59.0
Open-Source Chat Models
ChatGLM3-6B	41.0	40.5	21.4	11.5	6.3
Yi-6B-Chat	35.7	41.1	20.3	11.5	9.1
InternLM2-Chat-7B	53.0	67.5	41.0	29.6	22.6
Qwen-7B-Chat	51.3	50.2	32.6	20.2	17.3
Deepseek-7B-Chat	46.0	39.3	15.5	9.6	9.2
Baichuan2-13B-Chat	46.0	54.2	29.5	16.6	14.3
Qwen-14B-Chat	64.7	66.1	49.2	32.8	27.2
InternLM2-Chat-20B	62.7	70.0	47.4	33.7	23.3
Yi-34B-Chat	51.0	64.8	38.0	23.2	17.8
Deepseek-67B-Chat	61.3	77.2	48.4	36.3	36.8
Qwen-72B-Chat	72.0	80.1	64.8	47.8	40.8
Mathematical Models
MammoTH-7B	26.7	18.1	5.3	4.8	3.7
Metamath-Llemma-7B	48.7	35.3	16.1	15.5	10.1
InternLM2-Chat-Math-7B	53.7	66.0	49.0	34.3	26.9
Deepseek-Math-7B-Instruct	61.0	73.7	42.2	34.9	29.9
Deepseek-Math-7B-RL	67.7	80.8	57.2	45.4	42.7
MammoTH-13B	35.0	34.8	10.7	9.9	10.6
InternLM2-Chat-Math-20B	58.7	71.1	55.5	41.8	31.9
MammoTH-70B	35.7	59.3	28.1	23.6	24.5

🔊Application Scores with Stages

Models exhibit similar performances in Arithmetic and Primary stages, while demonstrating a clear performance decline from Primary to College stages.

🖋Inference MathBench with OpenCompass

OpenCompass is a toolkit for evaluating the performance of large language models (LLMs). There are steps for inference MathBench with OpenCompass:

1. Install OpenCompass

conda create --name opencompass python=3.10 pytorch torchvision pytorch-cuda -c nvidia -c pytorch -y
conda activate opencompass
git clone https://github.com/open-compass/opencompass opencompass
cd opencompass
pip install -e .

2. Prepare the dataset

# Download dataset from release file and copy to data/ folder
mkdir data
cp -rf mathbench ./data/ 

3. Inference MathBench

# Inference MathBench with hf_llama2_7b_chat model
python run.py --models hf_llama2_7b_chat --datasets mathbench_gen

You can also evaluate HuggingFace models via command line.

python run.py --datasets mathbench_gen \
--hf-path meta-llama/Llama-2-7b-chat-hf \  # HuggingFace model path
--model-kwargs device_map='auto' \  # Arguments for model construction
--tokenizer-kwargs padding_side='left' truncation='left' use_fast=False \  # Arguments for tokenizer construction
--max-seq-len 2048 \  # Maximum sequence length the model can accept
--batch-size 8 \  # Batch size
--no-batch-padding \  # Don't enable batch padding, infer through for loop to avoid performance loss
--num-gpus 1  # Number of minimum required GPUs
--summarizer summarizers.mathbench_v1 # Summarizer for MathBench

Citation and Tech Report

To be appended.