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Mathematical Reasoning on MATH 500 (Pass@1, Avg tokens)

6,749Average TokensBaseline
427.92162,068.97083,710.025,351.0692Aug 6, 2025Sep 27, 2025Nov 18, 2025Jan 10, 2026Mar 3, 2026Apr 24, 2026Jun 16, 2026

Evaluation results

MethodLinks
BaselineBackbone=Qwen3-4B-Thinking-25072026.066,74996.2
OriginalModel Scale=Qwen3-4B-Thinking-2507, # Data=–2026.056,51797.8
DyConBackbone=Qwen3-4B-Thinking-25072026.066,09296.2
DEERBackbone=Qwen3-4B-Thinking-25072026.065,50894.6
Budget PromptModel Scale=Qwen3-4B-Thinking-2507, # Data=–2026.055,45797.2
Qwen3-8BType=BASE LLM2025.105,10492.3
NoWaitBackbone=Qwen3-4B-Thinking-25072026.065,06292.6
O1-PrunerType=SHORT COT2025.104,96892.43
BaselineBackbone=Qwen3-14B2026.064,96295
CoDBackbone=Qwen3-4B-Thinking-25072026.064,48495.6
NothinkingBackbone=Qwen3-4B-Thinking-25072026.064,36295.2
BaselineBackbone=QwQ-32B2026.064,26796
DeepSeek-R1-DistillModel Scale=1.5B, Base Model=Qwen2.5-Math2026.064,260—
SFT-S1.1Model Scale=DeepSeek-R1-Distill-Qwen-14B, # Data=1K2026.054,25595.3
BeConciseType=SHORT COT2025.104,23291.55
SFT-S1.1Model Scale=DeepSeek-R1-Distill-Qwen-7B, # Data=1K2026.054,10193.4
OriginalModel Scale=DeepSeek-R1-Distill-Qwen-7B, # Data=–2026.054,09892.6
Dynasor-CoTBackbone=Qwen3-14B2026.064,02393.8
NothinkingBackbone=QwQ-32B2026.063,98995.6
OriginalBackbone=DeepSeek-R1-Distill-Qwen-1.5B, Zero-shot Chain-of-Thought (CoT)=true2025.083,97883
NoWaitType=SHORT COT2025.103,97692.25
BaselineBackbone=DeepSeek-R1-Distill-Qwen-7B2026.063,95592
SFT-S1.1Model Scale=DeepSeek-R1-Distill-Qwen-32B, # Data=1K2026.053,89196
TrimRBackbone=QwQ-32B2026.063,83093.8
OriginalModel Scale=DeepSeek-R1-Distill-Qwen-14B, # Data=–2026.053,80094.1
SEALBackbone=QwQ-32B2026.063,66793
CoDBackbone=QwQ-32B2026.063,66294.8
DyConBackbone=Qwen3-14B2026.063,64595
OriginalModel Scale=DeepSeek-R1-Distill-Qwen-32B, # Data=–2026.053,61194.8
CoDBackbone=Qwen3-14B2026.063,53593.8
MixReasoningType=ADAPTIVE2025.103,48392.76
OriginalBackbone=DeepSeek-R1-Distill-Qwen-7B, Zero-shot Chain-of-Thought (CoT)=true2025.083,42286.9
DyConBackbone=QwQ-32B2026.063,34595.8
DEERBackbone=QwQ-32B2026.063,31694.6
DEERBackbone=Qwen3-14B2026.063,31694
NoWaitBackbone=Qwen3-14B2026.063,30594.6
DEERType=SHORT COT2025.103,25991.34
SFT-S1.1Model Scale=Qwen3-4B-Thinking-2507, # Data=1K2026.053,25095.3
DyConBackbone=DeepSeek-R1-Distill-Qwen-7B2026.063,21692
DASTBackbone=DeepSeek-R1-Distill-Qwen-1.5B, Zero-shot Chain-of-Thought (CoT)=true2025.083,15583.4
FlashThinkBackbone=QwQ-32B2026.063,14493.2
DeepSeek-R1-DistillModel Scale=7B, Base Model=Qwen2.5-Math2026.063,126—
Budget PromptModel Scale=DeepSeek-R1-Distill-Qwen-7B, # Data=–2026.052,97991
SEALBackbone=DeepSeek-R1-Distill-Qwen-7B2026.062,94391.6
ThinkpilotBackbone=Qwen3-4B-Thinking-25072026.062,91188.6
FCS+Ref.Backbone=DeepSeek-R1-Distill-Qwen-7B, Zero-shot Chain-of-Thought (CoT)=true2025.082,90987.8
NoWaitBackbone=QwQ-32B2026.062,90293.6
No WaitBackbone=DeepSeek-R1-Distill-Qwen-1.5B, Zero-shot Chain-of-Thought (CoT)=true2025.082,89481.6
FCS+Ref.Backbone=DeepSeek-R1-Distill-Qwen-1.5B, Zero-shot Chain-of-Thought (CoT)=true2025.082,88382.9
DASTBackbone=DeepSeek-R1-Distill-Qwen-7B, Zero-shot Chain-of-Thought (CoT)=true2025.082,87688.6
EfficientRModel Scale=DeepSeek-R1-Distill-Qwen-7B, # Data=3.2K†, Alpha=0.12026.052,86992.2
OriginalBackbone=DeepSeek-R1-Distill-Qwen-14B, Zero-shot Chain-of-Thought (CoT)=true2025.082,83287.4
Controlling Thinking SpeedBackbone=DeepSeek-R1-Distill-Qwen-7B2026.062,81890
Budget PromptModel Scale=DeepSeek-R1-Distill-Qwen-14B, # Data=–2026.052,81393.4
NoWaitBackbone=DeepSeek-R1-Distill-Qwen-7B2026.062,70289.6
LCPOBackbone=DeepSeek-R1-Distill-Qwen-1.5B, Zero-shot Chain-of-Thought (CoT)=true2025.082,68480.5
O1-PrunerBackbone=DeepSeek-R1-Distill-Qwen-7B, Zero-shot Chain-of-Thought (CoT)=true2025.082,67889
VeriThinkerModel Scale=DeepSeek-R1-Distill-Qwen-7B, # Data=340K2026.052,67492.8
No WaitBackbone=DeepSeek-R1-Distill-Qwen-7B, Zero-shot Chain-of-Thought (CoT)=true2025.082,57987.2
ThinklessType=HYBRID2025.102,55581.84
LCPOBackbone=DeepSeek-R1-Distill-Qwen-7B, Zero-shot Chain-of-Thought (CoT)=true2025.082,53984.7
Budget PromptModel Scale=DeepSeek-R1-Distill-Qwen-32B, # Data=–2026.052,48193.6
O1-PrunerBackbone=DeepSeek-R1-Distill-Qwen-1.5B, Zero-shot Chain-of-Thought (CoT)=true2025.082,44682.3
EfficientRModel Scale=DeepSeek-R1-Distill-Qwen-7B, # Data=3.2K†, Alpha=0.42026.052,43290.6
LCPOBackbone=DeepSeek-R1-Distill-Qwen-14B, Zero-shot Chain-of-Thought (CoT)=true2025.082,42686.8
DEERBackbone=DeepSeek-R1-Distill-Qwen-1.5B, Zero-shot Chain-of-Thought (CoT)=true2025.082,39884.1
CoT-ValveType=SHORT COT2025.102,37585.45
Manifold SteeringBackbone=DeepSeek-R1-Distill-Qwen-7B2026.062,23988.4
MERABackbone=DeepSeek-R1-Distill-Qwen-1.5B, Zero-shot Chain-of-Thought (CoT)=true2025.082,23986
HINT TUNINGModel Scale=Qwen3-4B-Thinking-2507, # Data=1K2026.052,19095.7
DEERBackbone=DeepSeek-R1-Distill-Qwen-7B2026.062,14389.8
AdaptThinkModel Scale=DeepSeek-R1-Distill-Qwen-7B, # Data=40K†2026.052,09592
O1-PrunerBackbone=DeepSeek-R1-Distill-Qwen-14B, Zero-shot Chain-of-Thought (CoT)=true2025.082,01590.2
CoDBackbone=DeepSeek-R1-Distill-Qwen-7B2026.061,97681.8
HINT TUNINGModel Scale=DeepSeek-R1-Distill-Qwen-7B, # Data=1K2026.051,94492.5
DASTBackbone=DeepSeek-R1-Distill-Qwen-14B, Zero-shot Chain-of-Thought (CoT)=true2025.081,94388.9
FCS+Ref.Backbone=DeepSeek-R1-Distill-Qwen-14B, Zero-shot Chain-of-Thought (CoT)=true2025.081,93789.3
No WaitBackbone=DeepSeek-R1-Distill-Qwen-14B, Zero-shot Chain-of-Thought (CoT)=true2025.081,93188.7
HINT TUNINGModel Scale=DeepSeek-R1-Distill-Qwen-32B, # Data=1K2026.051,92795.9
HINT TUNINGModel Scale=DeepSeek-R1-Distill-Qwen-14B, # Data=1K2026.051,90893.4
DEERBackbone=DeepSeek-R1-Distill-Qwen-7B, Zero-shot Chain-of-Thought (CoT)=true2025.081,90888.9
MERABackbone=DeepSeek-R1-Distill-Qwen-7B, Zero-shot Chain-of-Thought (CoT)=true2025.081,73991
DEERBackbone=DeepSeek-R1-Distill-Qwen-14B, Zero-shot Chain-of-Thought (CoT)=true2025.081,72987.7
AdaptThinkModel Scale=1.5B, Base Model=Qwen2.5-Math2026.061,564—
AdaCoTModel Scale=1.5B, Base Model=Qwen2.5-Math2026.061,479—
AdaptThinkModel Scale=7B, Base Model=Qwen2.5-Math2026.061,424—
AdaCoTModel Scale=7B, Base Model=Qwen2.5-Math2026.061,387—
S-GRPOModel Scale=1.5B, Base Model=Qwen2.5-Math2026.061,377—
MERABackbone=DeepSeek-R1-Distill-Qwen-14B, Zero-shot Chain-of-Thought (CoT)=true2025.081,35992.5
LHRMsModel Scale=1.5B, Base Model=Qwen2.5-Math2026.061,252—
NothinkingBackbone=DeepSeek-R1-Distill-Qwen-7B2026.061,02080
S-GRPOModel Scale=7B, Base Model=Qwen2.5-Math2026.06988—
NothinkingBackbone=Qwen3-14B2026.0694087.4
ThinkpilotBackbone=Qwen3-14B2026.0685486.8
ThinkpilotBackbone=DeepSeek-R1-Distill-Qwen-7B2026.0671578
PROGRS-8 (No Centering)rollout_budget=8, centering=none2026.02699.6867.78
PROGRS-4rollout_budget=42026.02694.774.14
PROGRS-8rollout_budget=82026.02683.7474.92
DAPO-8rollout_budget=82026.02673.8668.4
DAPO-16rollout_budget=162026.02671.0469.66