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Mathematical Reasoning on GSM

94AccuracyQwenPRM
-2.40822.62147.6572.679May 16, 2023Nov 17, 2023May 20, 2024Nov 22, 2024May 26, 2025Nov 27, 2025Jun 1, 2026

Evaluation results

MethodLinks
QwenPRMModel Size=7B2026.0394
MCNIGModel Size=8B2026.0393.8
ORMModel Size=8B2026.0393.7
IGModel Size=8B2026.0393.3
IDPOModel=Qwen3-8B2025.0593
SAI-DPOModel=Qwen3-8B2025.0592.9
GPT-4Shots=8-shot, Method=CoT2023.0692.5
Base ModelModel=Qwen3-8B2025.0592.1
OVM2026.0392
SAI-DPOModel=Qwen2.5-7B-Math-SFT2025.0591.7
IDPOModel=Qwen2.5-7B-Math-SFT2025.0591.3
Majority voting2026.0391.2
Granite PRM v22026.0390.9
Base ModelModel=Qwen2.5-7B-Math-SFT2025.0590.8
ImplicitPRM2026.0389.9
MathShepherd2026.0389.5
SAI-DPOModel=Qwen2.5-7B-Math-Base2025.0589.1
IDPOModel=Qwen2.5-7B-Math-Base2025.0588.4
SATLMLanguage Model=code-davinci-002, Decoding Method=self-consistency decoding2023.0584.8
PROGLMLanguage Model=code-davinci-002, Decoding Method=self-consistency decoding2023.0582.4
SAI-DPOModel=Llama3.1-8B-Instruct2025.0577.4
COTLanguage Model=code-davinci-002, Decoding Method=self-consistency decoding2023.0577.3
IDPOModel=Llama3.1-8B-Instruct2025.0576.9
ChatGPTShots=8-shot, Method=CoT2023.0676
DPSLLM Backbone=GPT-3.5 Turbo2025.0275.5
OPROLLM Backbone=GPT-3.5 Turbo2025.0273.4
Single sampling2026.0373.3
DPSLLM Backbone=Gemini-1.5 Flash2025.0272.9
PROGLMLanguage Model=code-davinci-002, Decoding Method=greedy decoding2023.0572.7
APELLM Backbone=GPT-3.5 Turbo2025.0272.1
SATLMLanguage Model=code-davinci-002, Decoding Method=greedy decoding2023.0571.8
DPSLLM Backbone=Llama-3.1 70B2025.0271.8
OPROLLM Backbone=Gemini-1.5 Flash2025.0270.4
APELLM Backbone=Gemini-1.5 Flash2025.0269.8
OPROLLM Backbone=Llama-3.1 70B2025.0269.3
Base ModelModel=Llama3.1-8B-Instruct2025.0569.1
APELLM Backbone=Llama-3.1 70B2025.0267.5
Base ModelModel=Qwen2.5-7B-Math-Base2025.0566.7
COTLanguage Model=code-davinci-002, Decoding Method=greedy decoding2023.0562.7
Human mix. 65BShots=8-shot, Method=CoT2023.0660
ShareGPT 65BShots=8-shot, Method=CoT2023.0659
TÜLU 65BShots=8-shot, Method=CoT2023.0659
DenseMixerBackbone=Qwen1.5-MoE-A2.7B, Top-k=42026.0654.97
Frozen RouterBackbone=Qwen1.5-MoE-A2.7B, Top-k=42026.0653.37
ConventionalBackbone=Qwen1.5-MoE-A2.7B, Top-k=42026.0653.3
ProbMoEBackbone=Qwen1.5-MoE-A2.7B, Top-k=42026.0653.29
TÜLU 30BShots=8-shot, Method=CoT2023.0653
TÜLU-1.1 13BShots=8-shot, Method=CoT2023.0653
DefaultMoEBackbone=Qwen1.5-MoE-A2.7B, Top-k=42026.0651
ProbMoEBackbone=OLMoE-1B-7B, Top-k=82026.0650.19
LLaMa 65BShots=8-shot, Method=CoT2023.0650
DenseMixerBackbone=OLMoE-1B-7B, Top-k=82026.0647
ReMoEBackbone=Qwen1.5-MoE-A2.7B, Top-k=42026.0646.3
ConventionalBackbone=OLMoE-1B-7B, Top-k=82026.0645.94
Frozen RouterBackbone=OLMoE-1B-7B, Top-k=82026.0644.88
TÜLU 13BShots=8-shot, Method=CoT2023.0640.5
Base ModelBackbone=Qwen1.5-MoE-A2.7B, Top-k=42026.0638.69
TÜLU-1.1 7BShots=8-shot, Method=CoT2023.0637
LLaMa 30BShots=8-shot, Method=CoT2023.0636
N/ALLM Backbone=Gemini-1.5 Flash2025.0229.9
N/ALLM Backbone=GPT-3.5 Turbo2025.0228.5
N/ALLM Backbone=Llama-3.1 70B2025.0228.1
LLaMa-2 13BShots=8-shot, Method=CoT2023.0625
TÜLU 7BShots=8-shot, Method=CoT2023.0625
STANDARDLanguage Model=code-davinci-002, Decoding Method=greedy decoding2023.0522.2
Base ModelBackbone=OLMoE-1B-7B, Top-k=82026.0615.85
LLaMa 13BShots=8-shot, Method=CoT2023.0614.5
LLaMa-2 7BShots=8-shot, Method=CoT2023.0612
LLaMa 7BShots=8-shot, Method=CoT2023.0610
SparseMixerBackbone=Qwen1.5-MoE-A2.7B, Top-k=42026.061.3