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Mathematical Reasoning on Minerva (pass@1 accuracy %)

74.8Pass@1 AccuracyQwen2.5-32B + SimpleRL
32.36843.38454.465.416May 20, 2025Jul 20, 2025Sep 19, 2025Nov 19, 2025Jan 19, 2026Mar 21, 2026May 21, 2026

Evaluation results

MethodLinks
Qwen2.5-32B + SimpleRLEvaluation Approach=LLM-as-a-judge (Ours), Model Size=32B, Training Strategy=SimpleRL2026.0474.8
Qwen2.5-14B + SimpleRLEvaluation Approach=LLM-as-a-judge (Ours), Model Size=14B, Training Strategy=SimpleRL2026.0474.3
Qwen2.5-7B + SimpleRLEvaluation Approach=LLM-as-a-judge (Ours), Model Size=7B, Training Strategy=SimpleRL2026.0465.7
Qwen2.5-7B + SimpleRL (Lighteval)Evaluation Approach=LLM-as-a-judge (Ours), Model Size=7B, Training Strategy=SimpleRL, Evaluation Framework=Lighteval2026.0465.3
Qwen2.5-32BEvaluation Approach=LLM-as-a-judge (Ours), Model Size=32B2026.0456
Qwen3Model Category=Original Models2026.0552.9
HiPO-Mt-biasBackbone=Qwen2.5-7B-Instruct2026.0451.02
TEPOBackbone=Qwen3-14B, Method Variant=TEPO2026.0449.26
DPOBackbone=Qwen2.5-7B-Instruct2026.0448.81
Qwen3-14B w. Entropy-based TermBackbone=Qwen3-14B, Method Variant=Entropy-based Term2026.0448.52
Qwen3-14B w. GSPOBackbone=Qwen3-14B, Method Variant=GSPO2026.0448.52
BaseBackbone=Qwen2.5-7B-Instruct2026.0448.26
Qwen3-14B w. GRPO/DAPOBackbone=Qwen3-14B, Method Variant=GRPO/DAPO2026.0447.79
Qwen3-14B w. KL-CovBackbone=Qwen3-14B, Method Variant=KL-Cov2026.0447.79
HiPO-Rq-biasBackbone=Qwen2.5-7B-Instruct2026.0447.66
HiPO-Rq+Mt-biasBackbone=Qwen2.5-7B-Instruct2026.0447.65
Qwen2.5-14BEvaluation Approach=LLM-as-a-judge (Ours), Model Size=14B2026.0447.6
Qwen2.5-7BEvaluation Approach=LLM-as-a-judge (Ours), Model Size=7B2026.0447.4
Qwen3-8192Model Category=Original Models, Max Generation Length=81922026.0547.4
Qwen3-14B w. GPGBackbone=Qwen3-14B, Method Variant=GPG2026.0447.05
Qwen2.5-7B (Lighteval)Evaluation Approach=LLM-as-a-judge (Ours), Model Size=7B, Evaluation Framework=Lighteval2026.0446.4
Qwen3-14BBackbone=Qwen3-14B, Method Variant=Base2026.0445.95
Qwen3-14B w. CLIP-CovBackbone=Qwen3-14B, Method Variant=CLIP-Cov2026.0445.58
DeepSeek-R1-Distill-32BModel Name=DeepSeek-R1-Distill-32B, Model Size=32B, Method Type=Baseline2026.0445.1
Qwen2.5-7B-Math + SFT + RL-TCERBase Model=Qwen2.5-7B-Math, Training Strategy=SFT + RL-TCER2026.0444.5
RL-PLUSBase Model=Qwen2.5-Math-7B, Training Method=RL-PLUS2025.0743.8
RL-PLUSBase Model=Qwen2.5-Math-7B2025.0743.8
Qwen2.5-32B + SimpleRLEvaluation Approach=Symbolic (Baseline), Model Size=32B, Training Strategy=SimpleRL2026.0443.5
SCRLCandidate responses=64, Training samples=32, Backbone=Qwen2.5-Math-7B2026.0343.1
Qwen2.5-7B-Math + SFT + RL-EndoRBase Model=Qwen2.5-7B-Math, Training Strategy=SFT + RL-EndoR2026.0442.6
HölderPOModel Scale=7B, Base Architecture=R1-Distill-Qwen-7B, Training Phase/Objective=RL Post-Trained, p-Scheduling Strategy=Linear Des: 2 → -22026.0542.3
SFTModel Category=Off-Policy and Mixed-Policy2026.0542.3
Qwen2.5-14B + SimpleRLEvaluation Approach=Symbolic (Baseline), Model Size=14B, Training Strategy=SimpleRL2026.0441.7
SCRLCandidate responses=32, Training samples=16, Backbone=Qwen2.5-Math-7B2026.0341.6
PieceHint-Qwen3-1.7BModel Name=Qwen3-1.7B, Model Size=1.7B, Method Type=PieceHint2026.0441.6
Re-Schedule_sigmoidBackbone=Qwen2.5-7B, Weight Function=sigmoid2025.1041.5
Re-Schedule_linearBackbone=Qwen2.5-7B, Weight Function=linear2025.1041.2
Qwen2.5-7B-Math + SFTBase Model=Qwen2.5-7B-Math, Training Strategy=SFT2026.0440.8
SFTBase Model=Qwen2.5-Math-7B, Training Method=SFT2025.0740.8
SFTBase Model=Qwen2.5-Math-7B2025.0740.8
Qwen3-4BModel Name=Qwen3-4B, Model Size=4B, Method Type=Baseline2026.0440.4
TGPO-annealingModel Category=On-Policy Methods2026.0540.4
DAPOBase Model=Qwen2.5-Math-7B2025.0740.1
ReLIFTBase Model=Qwen2.5-Math-7B2025.0740.1
DeepSeek-R1-Distill-7BModel Name=DeepSeek-R1-Distill-7B, Model Size=7B, Method Type=Baseline2026.0440
SFT+GRPOBase Model=Qwen2.5-Math-7B2025.0739.7
PRIMEFine-tuning base=Qwen2.5-Math-7B, Comparison Group=Non-comparable Baselines2025.0839.7
GRPOModel Scale=7B, Base Architecture=R1-Distill-Qwen-7B, Training Phase/Objective=RL Post-Trained, Hölder Parameter (p)=12026.0539.7
GRPOBase Model=Qwen2.5-Math-7B, Training Method=GRPO2025.0739.3
GRPOBase Model=Qwen2.5-Math-7B2025.0739.3
PMPOModel Scale=7B, Base Architecture=R1-Distill-Qwen-7B, Training Phase/Objective=RL Post-Trained2026.0539.3
PRIMEBase Model=Qwen2.5-Math-7B2025.0739
PRIME-ZeroModel Category=On-Policy Methods2026.0539
GRPOBackbone=Qwen2.5-7B, Category=Classical RLVR Methods2025.1038.6
LUFFYModel Category=Off-Policy and Mixed-Policy2026.0538.6
TAPOBase Model=Qwen2.5-Math-7B2025.0738.2
GMPOModel Scale=7B, Base Architecture=R1-Distill-Qwen-7B, Training Phase/Objective=RL Post-Trained, p-Scheduling Strategy=p → 02026.0537.9
TGPOModel Category=On-Policy Methods2026.0537.9
Qwen2.5-7B w. CLIP-CovBackbone=Qwen2.5-7B, Method Variant=CLIP-Cov2026.0437.86
Eurus-2-7B-PRIMEZero-shot=true, Model Category=Qwen 7B Models, Training Samples=230K + 150K2025.0537.5
LUFFYBase Model=Qwen2.5-Math-7B2025.0737.5
HölderPOTraining Stage=RL Post-Trained Models, Backbone=Qwen3-8B-Base, Training Objective=Linear Des: 2 → -22026.0537.5
Dr.GRPOModel Scale=7B, Base Architecture=R1-Distill-Qwen-7B, Training Phase/Objective=RL Post-Trained2026.0537.5
GRPO++Model Category=On-Policy Methods2026.0537.5
Self-Instruct + CoT-Self-InstructBackbone=Qwen3-8B-Base, # Train=63882025.1137.27
InstructFine-tuning base=Qwen2.5-Math-7B, Comparison Group=Non-comparable Baselines2025.0837.1
PieceHint-DeepSeek-1.5BModel Name=DeepSeek-R1-Distill-1.5B, Model Size=1.5B, Method Type=PieceHint2026.0436.7
Qwen2.5-7B w. Entropy-based TermBackbone=Qwen2.5-7B, Method Variant=Entropy-based Term2026.0436.02
GPG-7BZero-shot=true, Model Category=Qwen 7B Models, Training Samples=8,5232025.0536
DPO-LoRRFine-tuning base=Qwen2.5-Math-7B, Iteration=iter32025.0836
PRIME-Zero-7BModel Scale=7B, Base Architecture=Qwen2.5-Math, Training Phase/Objective=RL Post-Trained2026.0536
Eurus-7BModel Scale=7B, Base Architecture=Qwen2.5-Math, Training Phase/Objective=RL Post-Trained2026.0536
KDRLModel Category=On-Policy Methods2026.0536
Self-InstructBackbone=Qwen3-8B-Base, # Train=59902025.1135.79
CoT Cold-Start + Solver FeedbackBackbone=Qwen3-8B-Base, # Train=68012025.1135.79
Qwen2.5-7B w. GSPOBackbone=Qwen2.5-7B, Method Variant=GSPO2026.0435.66
EGRSDBackbone=Qwen3-8B2026.0535.48
Qwen3-1.7BModel Name=Qwen3-1.7B, Model Size=1.7B, Method Type=Baseline2026.0435.4
AAPO-7BZero-shot=true, Model Category=Qwen 7B Models, Training Samples=8,5232025.0535.3
LPPOBackbone=Qwen2.5-7B, Category=Scheduling Methods2025.1035.3
Qwen2.5-7B + SimpleRLEvaluation Approach=Symbolic (Baseline), Model Size=7B, Training Strategy=SimpleRL2026.0435.1
OPSDBackbone=Qwen3-8B2026.0534.94
Qwen2.5-7B w. KL-CovBackbone=Qwen2.5-7B, Method Variant=KL-Cov2026.0434.92
TEPOBackbone=Qwen2.5-7B, Method Variant=TEPO2026.0434.92
Oat-Zero-7BZero-shot=true, Model Category=Qwen 7B Models, Training Samples=8,5232025.0534.9
GRPO w/ SFT LossBase Model=Qwen2.5-Math-7B2025.0734.9
PMPOModel Scale=7B, Base Architecture=Qwen2.5-Math, Training Phase/Objective=RL Post-Trained2026.0534.9
HölderPOModel Scale=7B, Base Architecture=Qwen2.5-Math, Training Phase/Objective=RL Post-Trained, p-Scheduling Strategy=Linear Des: 2 → -22026.0534.9
CL-EGRSDBackbone=Qwen3-8B2026.0534.83
SCRLBase Model=Qwen3-14B-Base2026.0534.7
GRPOBackbone=Qwen3-8B2026.0534.65
OatBase Model=Qwen2.5-Math-7B2025.0734.6
Oat-ZeroModel Category=On-Policy Methods2026.0534.6
Self-Instruct + RLMTBackbone=Qwen3-8B-Base, # Train=71282025.1134.56
Qwen2.5-7B w. GPGBackbone=Qwen2.5-7B, Method Variant=GPG2026.0434.55
CRISPBackbone=Qwen3-8B2026.0534.47
Baseline (no-train)Backbone=Qwen3-8B2026.0534.32
ACC_sigmoidBackbone=Qwen2.5-7B, Category=Scheduling Methods2025.1034.2
GPG-7BModel Scale=7B, Base Architecture=Qwen2.5-Math, Training Phase/Objective=RL Post-Trained2026.0534.2
QuestABase Model=Qwen3-14B-Base2026.0534