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Mathematical Reasoning on MATH500 (Performance (%))

98.6Performance (%)Gemini-2.5-pro
17.27238.38659.580.614Aug 5, 2025Sep 27, 2025Nov 20, 2025Jan 13, 2026Mar 8, 2026May 1, 2026Jun 24, 2026

Evaluation results

MethodLinks
Gemini-2.5-proCategory=Proprietary LLMs2026.0698.6
MiniMax-M2.5Category=Proprietary LLMs2026.0698.4
Qwen3-8B-OPERACategory=Our Methods, Technique=OPERA2026.0696.2
Qwen3-8BCategory=Our Methods2026.0695.6
Qwen3-8B-SFTCategory=Our Methods2026.0694.8
Ouro 2.6B R4Architecture=LoopLM, # Total Params=2.6B, # Trained Tokens=7.7T2025.1090.85
VRPOModel Scale=Qwen3-8B, Optimization Method=VRPO2025.0890.2
VRPOBase Model=Qwen3-8B2025.0890.2
λ-GRPOModel Scale=Qwen3-8B, Optimization Method=λ-GRPO2025.0890
λ-GRPOBase Model=Qwen3-8B2025.0890
GRPOModel Scale=Qwen3-8B, Optimization Method=GRPO2025.0889.2
Reinforce++Model Scale=Qwen3-8B, Optimization Method=Reinforce++2025.0889
Dr.GRPOModel Scale=Qwen3-8B, Optimization Method=Dr.GRPO2025.0887.8
BaseModel Scale=Qwen3-8B, Optimization Method=Base2025.0887.4
BaseBase Model=Qwen3-8B2025.0887.4
PPOModel Scale=Qwen3-8B, Optimization Method=PPO2025.0886.4
KTAEModel Scale=Qwen3-8B, Optimization Method=KTAE2025.0886
KTAEBase Model=Qwen3-8B2025.0886
VRPOModel Scale=Qwen3-1.7B, Optimization Method=VRPO2025.0885.4
BaseModel Scale=Qwen3-1.7B, Optimization Method=Base2025.0884.8
Reinforce++Model Scale=Qwen3-1.7B, Optimization Method=Reinforce++2025.0884.4
GRPOModel Scale=Qwen3-1.7B, Optimization Method=GRPO2025.0884.2
PPOModel Scale=Qwen3-1.7B, Optimization Method=PPO2025.0883.8
Dr.GRPOModel Scale=Qwen3-1.7B, Optimization Method=Dr.GRPO2025.0883.4
Gemma3Architecture=Dense, # Total Params=12.0B, # Trained Tokens=12T2025.1083.2
λ-GRPOModel Scale=Qwen3-1.7B, Optimization Method=λ-GRPO2025.0882.8
DeepWriter-8BCategory=Open-source LLMs2026.0680.4
Entropy-Cut MHModel=Qwen3-8B-Base2026.0580.2
TMCModel=Qwen3-8B-Base2026.0579.7
Uniform-Cut MHModel=Qwen3-8B-Base2026.0579.5
SMCModel=Qwen3-8B-Base2026.0579.3
Entropy-Cut MHModel=Qwen2.5-Math-7B2026.0579
SMCModel=Qwen2.5-Math-7B2026.0578.9
TMCModel=Qwen2.5-Math-7B2026.0578.2
GPT-4o-0513Category=Proprietary LLMs2026.0678
Low-TemperatureModel=Qwen3-8B-Base2026.0577.3
λ-GRPOBase Model=Qwen2.5-7B-Cold Start2025.0874
CAREBackbone=Phi4-mini-instruct2026.0573.77
LongWriter-Zero-32BCategory=Open-source LLMs2026.0673.4
GTBackbone=Phi4-mini-instruct2026.0573.25
Uniform-Cut MHModel=Qwen2.5-Math-7B2026.0573.1
VRPOBase Model=Qwen2.5-7B-Cold Start2025.0872.2
Entropy-Cut MHModel=Qwen2.5-7B2026.0571.9
BaseBase Model=Qwen2.5-7B-Cold Start2025.0871.6
TMCModel=Qwen2.5-7B2026.0570.4
SMCModel=Qwen2.5-7B2026.0569.8
OracleBackbone=Phi4-mini-instruct2026.0569.73
Entropy-Cut MHModel=Phi-4-mini-instruct2026.0568.8
Uniform-Cut MHModel=Phi-4-mini-instruct2026.0568.7
KTAEBase Model=Qwen2.5-7B-Cold Start2025.0868.6
Gemma3Architecture=Dense, # Total Params=4.0B, # Trained Tokens=4T2025.1068.6
Low-TemperatureModel=Qwen2.5-Math-7B2026.0568.3
SMCModel=Phi-4-mini-instruct2026.0568.1
ProbBackbone=Phi4-mini-instruct2026.0567.83
RandomBackbone=Phi4-mini-instruct2026.0567.7
Uniform-Cut MHModel=Qwen2.5-7B2026.0567.4
Low-TemperatureModel=Phi-4-mini-instruct2026.0566.4
TTRLBackbone=Phi4-mini-instruct2026.0566.3
TMCModel=Phi-4-mini-instruct2026.0566.1
KTAEModel Scale=Qwen3-1.7B, Optimization Method=KTAE2025.0864.4
EntropyBackbone=Phi4-mini-instruct2026.0563.95
Low-TemperatureModel=Qwen2.5-7B2026.0562.3
Qwen3Architecture=Dense, # Total Params=8.0B, # Trained Tokens=36T2025.1062.3
Qwen2.5Architecture=Dense, # Total Params=7.0B, # Trained Tokens=18T2025.1061.2
Qwen3Architecture=Dense, # Total Params=4.0B, # Trained Tokens=36T2025.1059.6
StandardModel=Qwen3-8B-Base2026.0558.5
Llama3.1-8B-SFTCategory=Our Methods2026.0658.2
Llama3.1-8B-OPERACategory=Our Methods, Technique=OPERA2026.0656.8
StandardModel=Phi-4-mini-instruct2026.0555.5
Llama3.1Architecture=Dense, # Total Params=8.0B, # Trained Tokens=15T2025.1052.9
Llama3.1-8BCategory=Our Methods2026.0652.4
StandardModel=Qwen2.5-Math-7B2026.0550.1
SMCModel=Phi-3.5-mini-instruct2026.0549.8
Entropy-Cut MHModel=Phi-3.5-mini-instruct2026.0549.7
TMCModel=Phi-3.5-mini-instruct2026.0549.3
Uniform-Cut MHModel=Phi-3.5-mini-instruct2026.0549.1
Low-TemperatureModel=Phi-3.5-mini-instruct2026.0545.3
StandardModel=Phi-3.5-mini-instruct2026.0542.9
Qwen2.5Architecture=Dense, # Total Params=3.0B, # Trained Tokens=18T2025.1042.6
Llama3.2Architecture=Dense, # Total Params=3.0B, # Trained Tokens=9T2025.1040.8
VanillaBackbone=Phi4-mini-instruct2026.0539.93
StandardModel=Qwen2.5-7B2026.0535.9
LongWriter-8BCategory=Open-source LLMs2026.0620.4