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Mathematical Reasoning on Minerva Math

63.2AccuracyPass@8 (Upper Bound)
33.76841.40949.0556.691May 20, 2025Jul 12, 2025Sep 4, 2025Oct 28, 2025Dec 20, 2025Feb 12, 2026Apr 7, 2026

Evaluation results

MethodLinks
Pass@8 (Upper Bound)Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-8, Bound=Upper Bound2026.0163.2
Pass@8 (Upper Bound)Policy Model=Qwen2.5-7B-Instruct2026.0157.7
Qwen2.5-Math-PRM-7BTraining Samples=1500K, Aggregation Method=Mean, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0154
Majority Vote@8Policy Model=Qwen2.5-14B-Instruct, Strategy=Majority Voting, Samples=82026.0153.3
Qwen2.5-Math-7B-NAITTraining Samples=128K, Aggregation Method=Mean, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0152.7
EurusPRM-Stage1Training Samples=463K, Aggregation Method=Min, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0152.6
EurusPRM-Stage2Training Samples=693K, Aggregation Method=Sum, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0151.5
Skywork-PRM-Qwen2.5-7BTraining Samples=N/A, Aggregation Method=Mean, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0151.1
Qwen2.5-Math-7B-MCRDTraining Samples=128K, Aggregation Method=Mean, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0150.8
RLHFlow-PRM-Mistral-8BTraining Samples=273K, Aggregation Method=Mean, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0150.4
RLHFlow-PRM-DeepSeek-8BTraining Samples=253K, Aggregation Method=Mean, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0150
Math-Shepherd-PRM-7BTraining Samples=445K, Aggregation Method=Mean, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0149.6
Qwen2.5-Math-7B-MCTraining Samples=128K, Aggregation Method=Mean, Policy Model=Qwen2.5-14B-Instruct, Strategy=Best-of-82026.0149.3
SkyWork-OR1-Math-7BTeacher Model=SkyWork-OR1-Math-7B2026.0349.3
GreedyPolicy Model=Qwen2.5-14B-Instruct, Strategy=Greedy Search2026.0149.2
Skywork-PRM-Qwen2.5-7BPolicy Model=Qwen2.5-7B-Instruct, Training Samples=-, Aggregation Method=Mean2026.0148.5
SkyWork-OR1-7BTeacher Model=SkyWork-OR1-7B2026.0347.1
Pass@8 (Upper Bound)Decoding Strategy=Pass@82025.0546.7
Majority Vote@8Policy Model=Qwen2.5-7B-Instruct2026.0146.7
Qwen2.5-Math-PRM-7BPolicy Model=Qwen2.5-7B-Instruct, Training Samples=1500K, Aggregation Method=Mean2026.0146.7
Qwen3-235B-A22BModel Category=Large Language Models, Model Scale=235B-A22B, Reasoning Strategy=Thinking2025.1246.69
Pass@8 (Upper Bound)Policy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Pass@82026.0146
Qwen2.5-Math-7B-NAITPolicy Model=Qwen2.5-7B-Instruct, Training Samples=128K, Aggregation Method=Mean2026.0145.8
EurusPRM-Stage2Policy Model=Qwen2.5-7B-Instruct, Training Samples=693K, Aggregation Method=Sum2026.0145.6
Qwen3-32BModel Category=Large Language Models, Model Scale=32B, Reasoning Strategy=Thinking2025.1245.22
Qwen2.5-Math-7B-MCRDPolicy Model=Qwen2.5-7B-Instruct, Training Samples=128K, Aggregation Method=Mean2026.0145.1
Math-Shepherd-PRM-7BPolicy Model=Qwen2.5-7B-Instruct, Training Samples=445K, Aggregation Method=Mean2026.0144.8
RLHFlow-PRM-DeepSeek-8BPolicy Model=Qwen2.5-7B-Instruct, Training Samples=253K, Aggregation Method=Mean2026.0144.8
EurusPRM-Stage1Policy Model=Qwen2.5-7B-Instruct, Training Samples=463K, Aggregation Method=Min-Max2026.0144.8
FIGR2025.1244.49
Qwen2.5-Math-7B-MCPolicy Model=Qwen2.5-7B-Instruct, Training Samples=128K, Aggregation Method=Mean2026.0144.2
Reasoning Palette (Linear Decay)Backbone=Qwen3-8B-Base, RL Algorithm=RLOO2025.1243.77
Text-only RLMode=Text-only, Reasoning Strategy=RL2025.1243.38
GreedyPolicy Model=Qwen2.5-7B-Instruct2026.0143
R1-Qwen-1.5B + EvoCoTBackbone=R1-Qwen-1.5B, Algorithm=EvoCoT2025.0842.8
Reasoning Palette (Linear Decay)Backbone=Qwen3-4B-Base, RL Algorithm=RLOO2025.1242.67
Reasoning Palette (Two-Phase)Backbone=Qwen3-8B-Base, RL Algorithm=RLOO2025.1242.57
Reasoning Palette (Linear Decay)Backbone=Qwen3-4B-Base, RL Algorithm=GRPO2025.1242.53
RLHFlow-PRM-Mistral-8BPolicy Model=Qwen2.5-7B-Instruct, Training Samples=273K, Aggregation Method=Mean2026.0142.3
Reasoning Palette (Two-Phase)Backbone=Qwen3-4B-Base, RL Algorithm=GRPO2025.1242.2
Reasoning Palette (Two-Phase)Backbone=Qwen3-8B-Base, RL Algorithm=GRPO2025.1241.37
Qwen3-VL-32B-InstructModel Category=Large Vision-Language Models, Model Scale=32B, Reasoning Strategy=Instruct2025.1241.18
Reasoning Palette (Linear Decay)Backbone=Qwen3-8B-Base, RL Algorithm=GRPO2025.1240.91
Majority @8Decoding Strategy=Majority @82025.0540.1
Qwen3-VL-8B-InstructModel Category=Large Vision-Language Models, Model Scale=8B, Reasoning Strategy=Instruct2025.1240.07
Hi-CoTModel=DeepSeek-R1-Distill-Qwen-32B2026.0339.7
Qwen2.5-7B + PRIME (380K)Backbone=Qwen2.5-7B, Algorithm=PRIME, Training Data Size=380K2025.0839.7
RLOOBackbone=Qwen3-8B-Base, RL Algorithm=RLOO2025.1239.48
GRPOBackbone=Qwen3-4B-Base, RL Algorithm=GRPO2025.1239.39
Qwen3-32BModel Category=Large Language Models, Model Scale=32B, Reasoning Strategy=Non-Thinking2025.1239.34
UNLOCKModel Family=Qwen3, Target Model (TL)=14B, Unlock/Instruction-tuning Configuration (SU)=+UNLOCK from 4B, Transfer Setting=Second Setting (Red Shading)2026.0439.2
Skywork-PRM-7BDecoding Strategy=Best-of-8 strategy, Training Data=automatically constructed2025.0539.1
GRPOBackbone=Qwen3-8B-Base, RL Algorithm=GRPO2025.1239.07
Reasoning Palette (Two-Phase)Backbone=Qwen3-4B-Base, RL Algorithm=RLOO2025.1238.75
Majority Vote@8Policy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Majority Vote@82026.0138.6
GLM-4.5VModel Category=Large Vision-Language Models, Model Scale=108B2025.1238.6
REOPOLDTeacher Model=SkyWork-OR1-Math-7B2026.0338.6
Hi-CoT (format-relaxed)Model=DeepSeek-R1-Distill-Qwen-32B2026.0338.6
RLHFlow-PRM-Deepseek-8BDecoding Strategy=Best-of-8 strategy, Training Data=automatically constructed2025.0538.2
Skywork-PRM-1.5BDecoding Strategy=Best-of-8 strategy, Training Data=automatically constructed2025.0538.2
SCOPEDecoding Strategy=Best-of-8 strategy, Training Data=automatically constructed2025.0538.2
SCOPE (w/o AST normalization)Decoding Strategy=Best-of-8 strategy, Ablation=w/o AST normalization2025.0538.2
Skywork-PRM-Qwen2.5-7BPolicy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Best-of-8, Aggregation Method=Mean2026.0138.2
R1-Qwen-1.5B + DeepScaleR(GRPO)Backbone=R1-Qwen-1.5B, Algorithm=DeepScaleR(GRPO)2025.0838.2
Qwen2.5-Math-7B-PRM800KDecoding Strategy=Best-of-8 strategy, Training Data=manually annotated (PRM800K)2025.0538.1
EurusPRM-Stage1Decoding Strategy=Best-of-8 strategy, Training Data=automatically constructed2025.0537.9
PRISMModel=Qwen2.5-7B, Data=DAPO-17k2026.0137.9
EurusPRM-Stage2Decoding Strategy=Best-of-8 strategy, Training Data=automatically constructed2025.0537.7
RLHFlow-PRM-Mistral-8BDecoding Strategy=Best-of-8 strategy, Training Data=automatically constructed2025.0537.5
Qwen2.5-Math-PRM-7BPolicy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Best-of-8, Training Samples=1500K, Aggregation Method=Mean2026.0137.5
UNLOCKModel Family=Ministral-3, Target Model (TL)=8B, Unlock/Instruction-tuning Configuration (SU)=+UNLOCK from 3B, Transfer Setting=Task-Conditioned Transfer With Limited Data2026.0437.4
Token-ALPevaluation_protocol=average@32, temperature=1.0, max_tokens=4096, setting=Single-turn2026.0337.27
SCOPE (Step Replacement)Decoding Strategy=Best-of-8 strategy, Ablation=Step Replacement2025.0537.1
SCOPE (Step Skipping)Decoding Strategy=Best-of-8 strategy, Ablation=Step Skipping2025.0537.1
Qwen2.5-Math-7B-NAITPolicy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Best-of-8, Training Samples=128K, Aggregation Method=Mean2026.0137.1
Hi-CoTModel=Qwen3-32B2026.0337.1
Qwen2.5-7B + EvoCoTBackbone=Qwen2.5-7B, Algorithm=EvoCoT2025.0837.1
Seq-ALPevaluation_protocol=average@32, temperature=1.0, max_tokens=4096, setting=Single-turn2026.0337.06
LLaDA RCDModel=LLaDA, Sequence length=512, Decoding strategy=single-token-per-step2026.0137
INT.Model=Qwen2.5-7B, Data=DAPO-17k2026.0136.8
Seq-MISevaluation_protocol=average@32, temperature=1.0, max_tokens=4096, setting=Single-turn2026.0336.75
Qwen2.5-Math-7B-MCRDPolicy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Best-of-8, Training Samples=128K, Aggregation Method=Mean2026.0136.7
GRPOevaluation_protocol=average@32, temperature=1.0, max_tokens=4096, setting=Single-turn2026.0336.43
SCOPE (w/o code translation)Decoding Strategy=Best-of-8 strategy, Ablation=w/o code translation2025.0536.4
RLHFlow-PRM-Mistral-8BPolicy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Best-of-8, Training Samples=273K, Aggregation Method=Mean2026.0136.4
EurusPRM-Stage1Policy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Best-of-8, Training Samples=463K, Aggregation Method=Min-Max2026.0136.4
SFTTeacher Model=SkyWork-OR1-Math-7B2026.0336.4
RLOOBackbone=Qwen3-4B-Base, RL Algorithm=RLOO2025.1236.07
Hi-CoTModel=Qwen3-4B-Instruct-25072026.0336
StandardModel=DeepSeek-R1-Distill-Qwen-14B2026.0336
Token-MISevaluation_protocol=average@32, temperature=1.0, max_tokens=4096, setting=Single-turn2026.0335.94
Hi-CoT (format-relaxed)Model=Qwen3-4B-Thinking-25072026.0335.7
Hi-CoT (format-relaxed)Model=Qwen3-32B2026.0335.7
Hi-CoTModel=DeepSeek-R1-Distill-Qwen-14B2026.0335.7
EurusPRM-Stage2Policy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Best-of-8, Training Samples=693K, Aggregation Method=Sum2026.0135.6
CoTModel=Qwen3-4B-Instruct-25072026.0335.3
Hi-CoTModel=Qwen3-4B-Thinking-25072026.0335.3
Hi-CoT (format-relaxed)Model=DeepSeek-R1-Distill-Qwen-14B2026.0335.3
Seq-Bypassevaluation_protocol=average@32, temperature=1.0, max_tokens=4096, setting=Single-turn2026.0335.23
RLHFlow-PRM-DeepSeek-8BPolicy Model=Qwen2.5-3B-Instruct, Evaluation Protocol=Best-of-8, Training Samples=253K, Aggregation Method=Mean2026.0134.9