Mathematical Reasoning on AIME 24 (Pass@1, Pass@K)
3,000Pass@1DoPR
Evaluation results
| Method | Links | ||||||
|---|---|---|---|---|---|---|---|
| DoPRBackbone=Qwen, Model Size=7B2026.01 | 3,000 | — | — | — | — | — | |
| UFOBackbone=Qwen, Model Size=7B2026.01 | 2,790 | — | — | — | — | — | |
| GRPOBackbone=Qwen, Model Size=7B2026.01 | 2,670 | — | — | — | — | — | |
| GRPOBackbone=Qwen, Model Size=1.5B2026.01 | 2,000 | — | — | — | — | — | |
| DoPRBackbone=Qwen, Model Size=1.5B2026.01 | 1,970 | — | — | — | — | — | |
| UFOBackbone=Qwen, Model Size=1.5B2026.01 | 1,940 | — | — | — | — | — | |
| One-Shot RLBackbone=Qwen, Model Size=7B2026.01 | 1,670 | — | — | — | — | — | |
| Qwen2.5-baseModel Size=7B, RL Strategy=Base2026.01 | 1,330 | — | — | — | — | — | |
| One-Shot RLBackbone=Qwen, Model Size=1.5B2026.01 | 1,330 | — | — | — | — | — | |
| Qwen2.5-Math-baseModel Size=7B, RL Strategy=Base2026.01 | 1,000 | — | — | — | — | — | |
| Qwen2.5-Math-baseModel Size=1.5B, RL Strategy=Base2026.01 | 330 | — | — | — | — | — | |
| GRPOBackbone=LLaMA, Model Size=8B2026.01 | 330 | — | — | — | — | — | |
| DoPRBackbone=LLaMA, Model Size=8B2026.01 | 330 | — | — | — | — | — | |
| UFOBackbone=LLaMA, Model Size=8B2026.01 | 310 | — | — | — | — | — | |
| APOBackbone=Qwen2.5-Math-7B, K=2562026.02 | 33.4 | 73.33 | — | — | — | — | |
| GRPO (Baseline)Backbone=Qwen2.5-Math-7B, K=2562026.02 | 32.63 | 70 | — | — | — | — | |
| NSRBackbone=Qwen2.5-Math-7B, K=2562026.02 | 32.1 | 73.33 | — | — | — | — | |
| P-ALIGNBackbone=Qwen3-8B2026.01 | 30 | — | 36.67 | — | — | — | |
| GRPO-KL (Error-Only)Backbone=Qwen2.5-Math-7B, K=2562026.02 | 29.87 | 73.33 | — | — | — | — | |
| PACED-RLModel=Qwen2.5-Math-7B, Avg. Rollouts=1.0x, Avg@32=true2026.02 | 28.7 | — | — | — | 40.1 | — | |
| GRPO-KLBackbone=Qwen2.5-Math-7B, K=2562026.02 | 28.59 | 70 | — | — | — | — | |
| LILOModel=Qwen2.5-Math-7B, Avg. Rollouts=4.0x, Avg@32=true2026.02 | 28 | — | — | — | 40.1 | — | |
| Zero-ShotBackbone=Qwen3-8B2026.01 | 26.67 | — | 36.67 | — | — | — | |
| SFT (Long-CoT)Backbone=Qwen3-8B2026.01 | 26.67 | — | 40 | — | — | — | |
| DSModel=Qwen2.5-Math-7B, Avg. Rollouts=2.5x, Avg@32=true2026.02 | 26.6 | — | — | — | 39.4 | — | |
| SetPO+DAPOBase Model=Qwen2.5-Math-7B, Optimization Algorithm=DAPO2026.02 | 25.3 | — | — | — | — | — | |
| FlowRLModel=Qwen2.5-Math-7B, Avg. Rollouts=1.0x, Avg@32=true2026.02 | 24.9 | — | — | — | 36.5 | — | |
| MoPPSModel=Qwen2.5-Math-7B, Avg. Rollouts=1.0x, Avg@32=true2026.02 | 24 | — | — | — | 38.6 | — | |
| GRPOModel=Qwen2.5-Math-7B, Avg. Rollouts=1.0x, Avg@32=true2026.02 | 23.9 | — | — | — | 37.2 | — | |
| UPFT (2025)Backbone=Qwen3-8B2026.01 | 23.33 | — | 36.67 | — | — | — | |
| DAPOBase Model=Qwen2.5-Math-7B2026.02 | 21.7 | — | — | — | — | — | |
| SetPO+GRPOBase Model=Qwen2.5-Math-7B, Optimization Algorithm=GRPO2026.02 | 21.6 | — | — | — | — | — | |
| SetPO+GSPOBase Model=Qwen2.5-Math-7B, Optimization Algorithm=GSPO2026.02 | 21.1 | — | — | — | — | — | |
| GSPOBase Model=Qwen2.5-Math-7B2026.02 | 17.4 | — | — | — | — | — | |
| P-ALIGNBackbone=Qwen2.5-7B-Instruct2026.01 | 16.67 | — | 26.67 | — | — | — | |
| APOBackbone=Qwen2.5-7B, K=2562026.02 | 15.85 | 60 | — | — | — | — | |
| GRPOBase Model=Qwen2.5-Math-7B2026.02 | 15.4 | — | — | — | — | — | |
| GRPO (Baseline)Backbone=Qwen2.5-7B, K=2562026.02 | 14.31 | 50 | — | — | — | — | |
| GRPO-KLBackbone=Qwen2.5-7B, K=2562026.02 | 13.72 | 56.67 | — | — | — | — | |
| Base ModelBackbone=Qwen2.5-Math-7B, K=2562026.02 | 13.66 | 73.33 | — | — | — | — | |
| UPFT (2025)Backbone=Qwen2.5-7B-Instruct2026.01 | 13.33 | — | 23.33 | — | — | — | |
| PACED-RLModel=Qwen2.5-Math-1.5B, Avg. Rollouts=1.0x, Avg@32=true2026.02 | 13.3 | — | — | — | 32.1 | — | |
| LILOModel=Qwen2.5-Math-1.5B, Avg. Rollouts=4.0x, Avg@32=true2026.02 | 12 | — | — | — | 31.2 | — | |
| DSModel=Qwen2.5-Math-1.5B, Avg. Rollouts=2.0x, Avg@32=true2026.02 | 11.8 | — | — | — | 31.2 | — | |
| MoPPSModel=Qwen2.5-Math-1.5B, Avg. Rollouts=1.0x, Avg@32=true2026.02 | 11.4 | — | — | — | 30.4 | — | |
| APOBackbone=Llama-3.2-3B-Instruct, K=2562026.02 | 11.12 | 26.67 | — | — | — | — | |
| GRPO (Baseline)Backbone=Llama-3.2-3B-Instruct, K=2562026.02 | 10.85 | 26.67 | — | — | — | — | |
| GRPOModel=Qwen2.5-Math-1.5B, Avg. Rollouts=1.0x, Avg@32=true2026.02 | 10.3 | — | — | — | 29.1 | — | |
| Zero-ShotBackbone=Qwen2.5-7B-Instruct2026.01 | 10 | — | 20 | — | — | — | |
| SFT (Long-CoT)Backbone=Qwen2.5-7B-Instruct2026.01 | 10 | — | 26.67 | — | — | — | |
| SFT (Label)Backbone=Qwen3-8B2026.01 | 10 | — | 10 | — | — | — | |
| Qwen2.5-Math-7BModel Type=Base Model2026.02 | 9.9 | — | — | — | — | — | |
| FlowRLModel=Qwen2.5-Math-1.5B, Avg. Rollouts=1.0x, Avg@32=true2026.02 | 9.5 | — | — | — | 27.1 | — | |
| GRPO-KLBackbone=Llama-3.2-3B-Instruct, K=2562026.02 | 8.09 | 26.67 | — | — | — | — | |
| Base ModelBackbone=Llama-3.2-3B-Instruct, K=2562026.02 | 6.81 | 36.67 | — | — | — | — | |
| Base ModelBackbone=Qwen2.5-7B, K=2562026.02 | 6.67 | 60 | — | — | — | — | |
| SFT (Label)Backbone=Qwen2.5-7B-Instruct2026.01 | 3.33 | — | 10 | — | — | — | |
| Qwen2.5-baseModel Size=1.5B, RL Strategy=Base2026.01 | 0 | — | — | — | — | — | |
| One-Shot RLBackbone=LLaMA, Model Size=8B2026.01 | 0 | — | — | — | — | — | |
| BAPOBackbone=DeepSeek-R1-Distill-Qwen-1.5B2026.02 | — | — | — | 38.3 | — | 72.3 | |
| BAPOBackbone=DeepSeek-R1-Distill-Qwen-7B2026.02 | — | — | — | 47.1 | — | 80.3 | |
| Base LLMBackbone=Qwen2.5-Math-1.5B2025.11 | — | — | — | 6.2 | — | — | |
| Base LLMBackbone=Qwen2.5-Math-7B2025.11 | — | — | — | 6 | — | — | |
| Base LLMBackbone=Qwen2.5-Base-7B2025.11 | — | — | — | 3.2 | — | — | |
| Clip HigherBackbone=DeepSeek-R1-Distill-Qwen-1.5B2026.02 | — | — | — | 36.6 | — | 70.1 | |
| Clip HigherBackbone=DeepSeek-R1-Distill-Qwen-7B2026.02 | — | — | — | 47.4 | — | 82.4 | |
| DACBackbone=DeepSeek-R1-Distill-Qwen-1.5B2026.02 | — | — | — | 40 | — | 73.6 | |
| DACBackbone=DeepSeek-R1-Distill-Qwen-7B2026.02 | — | — | — | 50.2 | — | 81.2 | |
| Entropy Adv.Backbone=DeepSeek-R1-Distill-Qwen-1.5B2026.02 | — | — | — | 29.6 | — | 67.8 | |
| Entropy Adv.Backbone=DeepSeek-R1-Distill-Qwen-7B2026.02 | — | — | — | 49.1 | — | 81.5 | |
| Forking TokensBackbone=Qwen2.5-Math-1.5B2025.11 | — | — | — | 21.6 | — | — | |
| Forking TokensBackbone=Qwen2.5-Math-7B2025.11 | — | — | — | 36.6 | — | — | |
| Forking TokensBackbone=Qwen2.5-Base-7B2025.11 | — | — | — | 20.2 | — | — | |
| GRPOBackbone=Qwen2.5-Math-1.5B2025.11 | — | — | — | 21.6 | — | — | |
| GRPOBackbone=Qwen2.5-Math-7B2025.11 | — | — | — | 33.3 | — | — | |
| GRPOBackbone=Qwen2.5-Base-7B2025.11 | — | — | — | 18.9 | — | — | |
| GRPOBackbone=DeepSeek-R1-Distill-Qwen-1.5B2026.02 | — | — | — | 33.2 | — | 71.8 | |
| GRPOBackbone=DeepSeek-R1-Distill-Qwen-7B2026.02 | — | — | — | 48.2 | — | 82.5 | |
| KL-CovBackbone=Qwen2.5-Math-1.5B2025.11 | — | — | — | 22 | — | — | |
| KL-CovBackbone=Qwen2.5-Math-7B2025.11 | — | — | — | 35.2 | — | — | |
| KL-CovBackbone=Qwen2.5-Base-7B2025.11 | — | — | — | 18.7 | — | — | |
| LESSBackbone=Qwen2.5-Math-1.5B2025.11 | — | — | — | 26.2 | — | — | |
| LESSBackbone=Qwen2.5-Math-7B2025.11 | — | — | — | 36 | — | — | |
| LESSBackbone=Qwen2.5-Base-7B2025.11 | — | — | — | 20.5 | — | — | |
| MASPOBackbone=DeepSeek-R1-Distill-Qwen-1.5B2026.02 | — | — | — | 41 | — | 74.8 | |
| MASPOBackbone=DeepSeek-R1-Distill-Qwen-7B2026.02 | — | — | — | 53.2 | — | 82.4 | |
| SAPOBackbone=DeepSeek-R1-Distill-Qwen-1.5B2026.02 | — | — | — | 39.3 | — | 73.7 | |
| SAPOBackbone=DeepSeek-R1-Distill-Qwen-7B2026.02 | — | — | — | 47.5 | — | 79.2 | |
| SDAR-1.7B-Chat-b16Method=Original Checkpoint, Block size=b162026.01 | — | — | 3.33 | — | — | — | |
| SDAR-1.7B-Chat-b32Method=Original Checkpoint, Block size=b322026.01 | — | — | 2.22 | — | — | — | |
| SDAR-1.7B-Chat-b4Method=Original Checkpoint, Block size=b42026.01 | — | — | 4.44 | — | — | — | |
| SDAR-1.7B-Chat-b8Method=Original Checkpoint, Block size=b82026.01 | — | — | 5.56 | — | — | — | |
| SDAR-4B-Chat-b16Method=Original Checkpoint, Block size=b162026.01 | — | — | 6.67 | — | — | — | |
| SDAR-4B-Chat-b4Method=Original Checkpoint, Block size=b42026.01 | — | — | 5.56 | — | — | — | |
| SDAR-4B-Chat-b8Method=Original Checkpoint, Block size=b82026.01 | — | — | 5.56 | — | — | — | |
| T*Base model=SDAR-1.7B-Chat-b8, Block size=b82026.01 | — | — | 7.78 | — | — | — | |
| T*Base model=SDAR-1.7B-Chat-b16, Block size=b162026.01 | — | — | 6.66 | — | — | — | |
| T*Base model=SDAR-1.7B-Chat-b32, Block size=b322026.01 | — | — | 4.44 | — | — | — | |
| T*Base model=SDAR-4B-Chat-b8, Block size=b82026.01 | — | — | 8.89 | — | — | — | |
| T*Base model=SDAR-4B-Chat-b16, Block size=b162026.01 | — | — | 8.89 | — | — | — |