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Datasets:
nlile
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math_benchmark_test_saturation

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Tags:
math
llm
benchmarks
saturation
evaluation
leaderboard
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pandas
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float64
10.6
89.7
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1.5
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1
Gemini 2.0 Flash Experimental
89.7
null
No
No
No
2,024
[]
2
Qwen2.5-Math-72B-Instruct (TIR,Greedy)
88.1
72
Yes
Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement
No
Yes
2,024
[]
3
GPT-4 Turbo (MACM, w/code, voting)
87.92
null
No
MACM: Utilizing a Multi-Agent System for Condition Mining in Solving Complex Mathematical Problems
Yes
Yes
2,024
[ "code environment", "majority voting", "multi-agent" ]
4
Qwen2.5-Math-72B-Instruct (COT,Greedy)
85.9
72
Yes
Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement
No
Yes
2,024
[]
5
Qwen2.5-Math-7B-Instruct (TIR,Greedy)
85.2
7
Yes
Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement
No
Yes
2,024
[]
6
GPT-4-code model (CSV, w/ code, SC, k=16)
84.3
null
No
Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification
Yes
Yes
2,023
[ "multi-agent", "majority voting", "code environment" ]
7
Qwen2-Math-72B-Instruct (greedy)
84
72
Yes
Qwen2 Technical Report
Yes
Yes
2,024
[]
8
Qwen2.5-Math-7B-Instruct (COT,Greedy)
83.6
7
Yes
Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement
No
Yes
2,024
[]
9
Qwen2.5-Math-1.5B-Instruct (TIR,Greedy)
79.9
1.5
Yes
Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement
No
Yes
2,024
[]
10
OpenMath2-Llama3.1-70B (majority@256)
79.6
null
Yes
OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data
Yes
Yes
2,024
[]
11
OpenMath2-Llama3.1-8B (majority@256)
76.1
null
Yes
OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data
Yes
Yes
2,024
[]
12
Qwen2.5-Math-1.5B-Instruct (COT,Greedy)
75.8
1.5
Yes
Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement
No
Yes
2,024
[]
13
GPT-4-code model (CSV, w/ code)
73.5
null
No
Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification
Yes
Yes
2,023
[ "code environment" ]
14
CR (GPT-4-turbo model, w/ code)
72.2
null
No
Cumulative Reasoning with Large Language Models
Yes
Yes
2,023
[ "code environment" ]
15
OpenMath2-Llama3.1-70B
71.9
null
Yes
OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data
Yes
Yes
2,024
[]
16
LogicNet (with code interpreter)
71.2
null
Yes
Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification
Yes
Yes
2,023
[]
17
Qwen2-72B-Instruct-Step-DPO (0-shot CoT, w/o code)
70.8
null
Yes
Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs
Yes
Yes
2,024
[]
18
GPT-4-code model (w/ code)
69.7
null
No
Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification
Yes
Yes
2,023
[ "code environment" ]
19
OpenMath2-Llama3.1-8B
67.8
null
Yes
OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data
Yes
Yes
2,024
[]
20
AlphaMath-7B-SBS@3
66.3
null
No
AlphaMath Almost Zero: Process Supervision without Process
Yes
Yes
2,024
[ "code environment" ]
21
Minerva 62B (maj5@256)
64.9
62
No
Solving Quantitative Reasoning Problems with Language Models
Yes
Yes
2,022
[]
22
DAMOMath-7B
64.5
7
Yes
2,024
[]
23
MMOS-DeepSeekMath-7B (0-shot,k=50)
63.7
7
Yes
An Empirical Study of Data Ability Boundary in LLMs' Math Reasoning
Yes
Yes
2,024
[ "code environment", "zero-shot", "majority voting" ]
24
GPT-4-code model (w/o code)
60.8
null
No
Solving Challenging Math Word Problems Using GPT-4 Code Interpreter with Code-based Self-Verification
Yes
Yes
2,023
[]
25
OpenMath-CodeLlama-70B (w/ code, SC, k=50)
60.4
70
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
Yes
2,024
[ "code environment", "majority voting" ]
26
OpenMath-CodeLlama-34B (w/ code, SC, k=50)
60.2
34
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
Yes
2,024
[ "code environment", "majority voting" ]
27
ToRA-Code 34B model (w/ code, SC, k=50)
60
34
Yes
ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving
Yes
Yes
2,023
[ "majority voting", "code environment", "gpt-4 distillation" ]
28
DeepSeekMATH-RL-7B (w/ code, greedy decoding)
58.8
7
Yes
DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
Yes
Yes
2,024
[]
29
OpenMath-Llama2-70B (w/ code, SC, k=50)
58.3
70
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
Yes
2,024
[ "code environment", "majority voting" ]
30
CR (GPT-4 model, w/o code)
58
null
No
Cumulative Reasoning with Large Language Models
Yes
Yes
2,023
[]
31
OpenMath-CodeLlama-13B (w/ code, SC, k=50)
57.6
13
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
Yes
2,024
[ "code environment", "majority voting" ]
32
OpenMath-Mistral-7B (w/ code, SC, k=50)
57.2
7
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
Yes
2,024
[ "code environment", "majority voting" ]
33
ToRA 70B (w/ code, SC, k=50)
56.9
70
Yes
ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving
Yes
Yes
2,023
[ "majority voting", "code environment", "gpt-4 distillation" ]
34
SKiC (GPT-4 model)
56.4
null
No
Skills-in-Context Prompting: Unlocking Compositionality in Large Language Models
No
Yes
2,023
[ "code environment" ]
35
DART-Math-Llama3-70B-Prop2Diff (0-shot CoT, w/o code)
56.1
70
Yes
DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
Yes
Yes
2,024
[]
36
OpenMath-CodeLlama-7B (w/ code, SC, k=50)
55.6
7
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
Yes
2,024
[ "code environment", "majority voting" ]
37
MMOS-DeepSeekMath-7B (0-shot)
55
7
Yes
An Empirical Study of Data Ability Boundary in LLMs' Math Reasoning
Yes
Yes
2,024
[]
38
DART-Math-Llama3-70B-Uniform (0-shot CoT, w/o code)
54.9
70
Yes
DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
Yes
Yes
2,024
[]
39
PHP (GPT-4 model)
53.9
null
No
Progressive-Hint Prompting Improves Reasoning in Large Language Models
Yes
Yes
2,023
[]
40
DART-Math-DSMath-7B-Prop2Diff (0-shot CoT, w/o code)
53.6
7
Yes
DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
Yes
Yes
2,024
[]
41
Gemini Ultra (4-shot)
53.2
null
No
Gemini: A Family of Highly Capable Multimodal Models
Yes
Yes
2,023
[]
42
DART-Math-DSMath-7B-Uniform (0-shot CoT, w/o code)
52.9
7
Yes
DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
Yes
Yes
2,024
[]
43
GPT-4 model (w/ code, PAL)
51.8
null
No
PAL: Program-aided Language Models
Yes
Yes
2,022
[ "code environment" ]
44
DeepSeekMATH-RL-7B (greedy decoding)
51.7
7
Yes
DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
Yes
Yes
2,024
[]
45
AlphaLLM (with MCTS)
51
null
No
Toward Self-Improvement of LLMs via Imagination, Searching, and Criticizing
Yes
Yes
2,024
[]
46
ToRA-Code 34B (w/ code)
50.8
34
Yes
ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving
Yes
Yes
2,023
[ "code environment", "gpt-4 distillation" ]
47
OpenMath-CodeLlama-70B (w/ code)
50.7
70
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
No
2,024
[ "code environment" ]
48
Minerva 540B (maj1@k, k=64)
50.3
null
No
Solving Quantitative Reasoning Problems with Language Models
Yes
Yes
2,022
[ "majority voting" ]
49
ToRA 70B (w/ code)
49.7
70
Yes
ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving
Yes
Yes
2,023
[ "code environment", "gpt-4 distillation" ]
50
MMOS-CODE-34B (0-shot)
49.5
34
Yes
An Empirical Study of Data Ability Boundary in LLMs' Math Reasoning
Yes
Yes
2,024
[]
51
DeepSeekMath-7B-KPMath-Plus
48.8
7
No
Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning
2,024
[]
52
PaLM 2 (few-shot, k=4, SC)
48.8
null
No
PaLM 2 Technical Report
Yes
No
2,023
[ "majority voting" ]
53
Llemma-34B-KPMath-Plus
48.6
34
No
Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning
2,024
[]
54
OpenMath-CodeLlama-34B (w/ code)
48.3
34
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
Yes
2,024
[ "code environment" ]
55
Shepherd + DeepSeek-67B (SFT on MetaMATH + PRM rerank, k=256)
48.1
67
Yes
Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations
Yes
No
2,023
[ "rerank" ]
56
ToRA-Code 13B (w/ code)
48.1
13
Yes
ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving
Yes
Yes
2,023
[ "code environment", "gpt-4 distillation" ]
57
Minerva 8B (maj5@256)
47.6
8
No
Solving Quantitative Reasoning Problems with Language Models
Yes
Yes
2,022
[]
58
Mistral-7B-KPMath-Plus
46.8
7
Yes
Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning
2,024
[]
59
DART-Math-Llama3-8B-Prop2Diff (0-shot CoT, w/o code)
46.6
8
Yes
DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
Yes
Yes
2,024
[]
60
OpenMath-Llama2-70B (w/ code)
46.3
70
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
No
2,024
[]
61
OpenMath-CodeLlama-13B (w/ code)
45.5
13
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
No
2,024
[]
62
DART-Math-Mistral-7B-Prop2Diff (0-shot CoT, w/o code)
45.5
7
Yes
DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
No
Yes
2,024
[]
63
DART-Math-Llama3-8B-Uniform (0-shot CoT, w/o code)
45.3
8
Yes
DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
Yes
Yes
2,024
[]
64
MathCoder-CL-34B
45.2
34
Yes
MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning
Yes
No
2,023
[]
65
MathCoder-L-34B
45.1
34
Yes
MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning
Yes
No
2,023
[]
66
MMIQC-72B
45
72
Yes
Augmenting Math Word Problems via Iterative Question Composing
Yes
Yes
2,024
[]
67
ToRA-Code 7B (w/ code)
44.6
7
Yes
ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving
Yes
Yes
2,023
[ "code environment", "gpt-4 distillation" ]
68
OpenMath-Mistral-7B (w/ code)
44.5
7
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
No
2,024
[]
69
MMOS-CODE-7B (0-shot)
44.3
7
Yes
An Empirical Study of Data Ability Boundary in LLMs' Math Reasoning
Yes
Yes
2,024
[]
70
OpenMath-CodeLlama-7B (w/ code)
43.6
7
Yes
OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset
Yes
No
2,024
[]
71
Shepherd+Mistral-7B (SFT on MetaMATH + PRM RL+ PRM rerank, k=256)
43.5
7
Yes
Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations
Yes
No
2,023
[ "rerank" ]
72
DART-Math-Mistral-7B-Uniform (0-shot CoT, w/o code)
43.5
7
Yes
DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving
Yes
Yes
2,024
[]
73
Minerva 62B (maj1@k, k=64)
43.4
62
No
Solving Quantitative Reasoning Problems with Language Models
Yes
Yes
2,022
[ "majority voting" ]
74
ToRA 13B (w/ code)
43
13
Yes
ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving
Yes
Yes
2,023
[ "code environment", "gpt-4 distillation" ]
75
GPT-4
42.5
null
No
Sparks of Artificial General Intelligence: Early experiments with GPT-4
Yes
Yes
2,023
[]
76
SFT-Mistral-7B
41.8
7
Yes
2,024
[]
77
Llama2-13B-KPMath-Plus
41
13
No
Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning
2,024
[]
78
ToRA 7B (w/ code)
40.1
7
Yes
ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving
Yes
Yes
2,023
[ "code environment", "gpt-4 distillation" ]
79
MathCoder-CL-13B
35.9
13
Yes
MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning
Yes
No
2,023
[]
80
MuggleMATH-70B
35.6
70
Yes
MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning
Yes
No
2,023
[]
81
PaLM 2 (few-shot, k=4, CoT)
34.3
null
No
PaLM 2 Technical Report
Yes
No
2,023
[]
82
Minerva 540B
33.6
540
No
Solving Quantitative Reasoning Problems with Language Models
Yes
No
2,022
[]
83
Minerva 540B (5-shot)
33.6
540
No
Galactica: A Large Language Model for Science
Yes
No
2,022
[]
84
Shepherd + Mistral-7B (SFT on MetaMATH + PRM RL)
33
7
Yes
Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations
Yes
No
2,023
[]
85
WizardMath-7B-V1.1
33
7
Yes
WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct
Yes
No
2,023
[]
86
Gemini Pro (4-shot)
32.6
null
No
Gemini: A Family of Highly Capable Multimodal Models
Yes
Yes
2,023
[]
87
MuggleMATH-13B
30.7
13
Yes
MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning
Yes
No
2,023
[]
88
MathCoder-CL-7B
30.2
7
Yes
MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning
Yes
No
2,023
[]
89
MathCoder-L-13B
29.9
13
Yes
MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning
Yes
No
2,023
[]
90
Qwen2idae-16x14B (4-shot)
29.9
null
Yes
Parameter-Efficient Sparsity Crafting from Dense to Mixture-of-Experts for Instruction Tuning on General Tasks
Yes
No
2,024
[]
91
OpenChat-3.5-1210 7B
28.9
7
No
OpenChat: Advancing Open-source Language Models with Mixed-Quality Data
Yes
No
2,023
[]
92
OpenChat-3.5 7B
28.6
7
No
OpenChat: Advancing Open-source Language Models with Mixed-Quality Data
Yes
No
2,023
[]
93
Mixtral 8x7B (maj@4)
28.4
null
No
Mixtral of Experts
Yes
Yes
2,024
[]
94
Minerva 62B (4-shot)
27.6
62
No
Solving Quantitative Reasoning Problems with Language Models
Yes
Yes
2,022
[]
95
MetaMath 70B
26
70
Yes
MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models
Yes
No
2,023
[ "fine-tuned" ]
96
MuggleMATH 7B
25.8
7
Yes
MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning
Yes
No
2,023
[]
97
Minerva 8B (maj1@k, k=64)
25.4
8
No
Solving Quantitative Reasoning Problems with Language Models
Yes
Yes
2,022
[ "majority voting" ]
98
MathCoder-L-7B
23.3
7
Yes
MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning
Yes
No
2,023
[]
99
WizardMath-70B-V1.0
22.7
70
Yes
WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct
Yes
No
2,023
[]
100
Camelidae-8×34B (4-shot)
22.6
null
Yes
Parameter-Efficient Sparsity Crafting from Dense to Mixture-of-Experts for Instruction Tuning on General Tasks
Yes
No
2,024
[]
End of preview. Expand in Data Studio

LLM Leaderboard Data for Hendrycks MATH Dataset (2022–2024)

This dataset aggregates yearly performance (2022–2024) of large language models (LLMs) on the Hendrycks MATH benchmark. It is specifically compiled to explore performance evolution, benchmark saturation, parameter scaling trends, and evaluation metrics of foundation models solving complex math word problems.

Original source data: Math Word Problem Solving on MATH (Papers with Code)

About Hendrycks' MATH Benchmark

Introduced by Hendrycks et al., the MATH dataset includes 12,500 challenging competition math problems, each accompanied by detailed solutions. These problems provide an ideal setting for evaluating and training AI models in advanced mathematical reasoning.

Dataset Highlights

  • Performance Evolution: Significant increase in accuracy over three years (benchmark saturation analysis).
  • Parameter Scaling: Insight into how model size (parameters) correlates with accuracy improvements.
  • Benchmark Saturation: Clear evidence of performance brackets becoming saturated, indicating the need for new and more challenging mathematical reasoning benchmarks.

Key Insights from the Dataset (2022–2024)

  • Rapid Accuracy Gains: Top model accuracy jumped dramatically—from approximately 65% in 2022 to nearly 90% in 2024.
  • Performance Bracket Saturation: Models achieving over 80% accuracy increased significantly, illustrating benchmark saturation and highlighting a potential ceiling in current dataset challenges.
  • Efficiency in Parameter Scaling: Smaller parameter models now perform tasks previously requiring large parameter counts, emphasizing efficiency gains alongside increased accuracy.

Dataset Structure

  • Number of Examples: 112
  • Data Format: CSV (converted from Papers with Code)
  • Features include:
    • Model ranking and year-specific accuracy
    • Parameter counts and extra training data
    • Direct links to relevant academic papers and model code

Practical Usage

Here's how to quickly load and interact with the dataset:

from datasets import load_dataset

data = load_dataset("your_dataset_name_here")
df = data['train'].to_pandas()
df.head()

Visualizations

Model Accuracy Improvement (2022–2024)

Model Accuracy Trends Rapid growth in top accuracy indicating approaching benchmark saturation.

Accuracy Distribution Among Top 20%

Top 20% Model Accuracy Sharp increase in the number of high-performing models over three years.

Parameter Scaling and Model Accuracy

Standard Deviation vs Median Accuracy Visualizing consistency in accuracy improvements and the diminishing returns from scaling model parameters.

Citation

Please cite the original Hendrycks MATH dataset paper and this dataset aggregation/analysis:

MATH Dataset:

@article{hendrycks2021math,
  title={Measuring Mathematical Problem Solving With the MATH Dataset},
  author={Hendrycks, Dan and Burns, Collin and Basart, Steven and Zou, Andy and Mazeika, Mantas and Song, Dawn and Steinhardt, Jacob},
  journal={arXiv preprint arXiv:2103.03874},
  year={2021}
}

@misc{nlile2024mathbenchmark,
  author = {nlile},
  title = {LLM Leaderboard Data for Hendrycks MATH Dataset (2022-2024): Benchmark Saturation and Performance Trends},
  year = {2024},
  publisher = {Hugging Face},
  url = {https://huggingface.co/datasets/nlile/math_benchmark_test_saturation/}
}
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