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Mathematical Reasoning on GSM8K

97.1AccuracyGHG-TDA
91.58893.01994.4595.881Jul 18, 2023Jan 1, 2024Jun 17, 2024Dec 2, 2024May 18, 2025Nov 2, 2025Apr 19, 2026

Evaluation results

MethodLinks
GHG-TDABase Model=Claude 3.5 Sonnet2026.0297.1——
GPT-4-0613Base model=-, Model size=-, Answer format=code, Eval method=pass@12024.0297——
GPT-4Protocol=PAL, Setting=Tool manipulation2024.0597——
GHG-TDABase Model=GPT-4o2026.0296.9——
AoTBase Model=Claude 3.5 Sonnet2026.0296.8——
GPT-4o + QuaSARBackbone=GPT-4o, Prompting Strategy=QuaSAR2025.0296.5——
AoTBase Model=GPT-4o2026.0296.5——
VATPModel=Qwen3-8B, Budget=32002026.0396.43——
H2OModel=Qwen3-8B, Budget=32002026.0396.36——
R-KVModel=Qwen3-8B, Budget=32002026.0396.36——
LongFlowModel=Qwen3-8B, Budget=32002026.0396.36——
VATPModel=Qwen3-8B, Budget=24002026.0396.29——
ToTBase Model=Claude 3.5 Sonnet2026.0296.2——
MCTS with Const-o-TBackbone=GPT-4.12025.1096.2——
R-KVModel=Qwen3-8B, Budget=24002026.0396.13——
Const-o-TBackbone=GPT-4.12025.1096.1——
ToTBase Model=GPT-4o2026.0296——
H2OModel=Qwen3-8B, Budget=24002026.0395.98——
LongFlowModel=Qwen3-8B, Budget=24002026.0395.83——
VanillaModel=Qwen3-8B, Budget=24002026.0395.68——
VanillaModel=Qwen3-8B, Budget=32002026.0395.68——
C-MOP (Ours)Task Model=Q30BA3B-Inst, Optimizer Model=Q30BA3B-Think2026.0295.5382.08—
GoTBase Model=Claude 3.5 Sonnet2026.0295.4——
PromptWizardTask Model=GPT-4, Optimizer Model=GPT-42026.0295.4——
GoTBase Model=GPT-4o2026.0295.2——
Llama3.1-70B-InstructLength=128k2024.0895.1——
CoTBackbone=GPT-4.12025.1095.1——
MCTS with CoTBackbone=GPT-4.12025.1095.1——
ProTeGi*Task Model=Q30BA3B-Inst, Optimizer Model=Q30BA3B-Think2026.0295.0778.72—
GPO*Task Model=Q30BA3B-Inst, Optimizer Model=Q30BA3B-Think2026.0295.0478.5—
GPT-4o + FCoTBackbone=GPT-4o, Prompting Strategy=FCoT2025.0295——
MCTSBackbone=GPT-4.12025.1095——
PromptWizard*Task Model=Q30BA3B-Inst, Optimizer Model=Q30BA3B-Think2026.0294.5480.5—
GPT-4o + CoTBackbone=GPT-4o, Prompting Strategy=CoT2025.0294.5——
Gemini UltraBase model=-, Model size=-, Answer format=nlp, Eval method=maj1@322024.0294.4——
PROMPTEDPrompting Technique=PROMPTED2023.1094.4——
ePF2025.1094.3——
BiRouterDyn.=true, Dis.=true2025.1194.09——
Jupiter-NReasoning mode=on, Temperature=1.0, top-p=0.952026.0494.01——
GPT-4oBackbone=GPT-4o, Prompting Strategy=Zero-shot2025.0294——
Output RefinementPrompting Technique=Output Refinement2023.1094——
CTPBackbone=GPT-4.12025.1094——
G-DesignerDyn.=false, Dis.=false2025.1193.97——
SPICEBackbone=Qwen3-8B-Base2026.0393.9——
GPT-4o + CoMATBackbone=GPT-4o, Prompting Strategy=CoMAT2025.0293.7——
ToTBackbone=GPT-4.12025.1093.7——
Zero-Shot CoTPrompting Technique=Zero-Shot Chain-of-Thought2023.1093.6——
GPT-4Decoding Strategy=Greedy decoding2025.0293.6——
CoVBackbone=GPT-4.12025.1093.6——
NemotronReasoning mode=on, Temperature=1.0, top-p=0.952026.0493.56——
CoTBase Model=Claude 3.5 Sonnet2026.0293.5——
DenserModel=GPT-4o2025.1293.5——
DenserBackbone=Qwen3-32B-think2025.1293.4——
WISTBackbone=Qwen3-8B-Base2026.0393.4——
MCTS with Const-o-TBackbone=LLaMA-32025.1093.4——
ERMTask Model=Doubao-Pro, Optimizer Model=GPT-4o2026.0293.3——
Process SupervisionModel=GPT-4o2025.1293.3——
Process SupervisionBackbone=Qwen3-32B-think2025.1293.2——
CoT + RSBackbone=GPT-4.12025.1093.1——
GPT-4Length=128k2024.0893——
Llama-3-70B-InstructDecoding Strategy=Greedy decoding2025.0293——
MegaAgentBackbone=GPT-4o API2024.0893——
SPO*Task Model=Q30BA3B-Inst, Optimizer Model=Q30BA3B-Think2026.029378.84—
Qwen3-14BPrecision=BF162026.0292.95——
GPT-4o2025.0292.9——
Reflection-CoTModel=GPT-4o2025.1292.9——
WISTBackbone=Qwen3-4B-Base2026.0392.9——
R-ZeroBackbone=Qwen3-8B-Base2026.0392.9——
MCTSBackbone=LLaMA-32025.1092.9——
Reflection-CoTBackbone=Qwen3-32B-think2025.1292.8——
Qwen2.5-7B + GRPOBase Model=Qwen2.5-7B, Algorithm=GRPO2025.1292.8——
CoTBase Model=GPT-4o2026.0292.7——
Qwen2.5-Math-RM-72BSamples=128, Parameter Size=72B2025.0392.7——
Qwen2.5-Math-RM-72BSamples=64, Parameter Size=72B2025.0392.6——
ToTBackbone=LLaMA-32025.1092.6——
SPICEBackbone=Qwen3-4B-Base2026.0392.5——
Const-o-TBackbone=LLaMA-32025.1092.5——
Zero-ShotPrompting Technique=Zero-Shot2023.1092.4——
Tree-of-ThoughtModel=GPT-4o2025.1292.4——
CoT + RSBackbone=LLaMA-32025.1092.4——
Self-VerificationModel=GPT-4o2025.1292.3——
MaASDyn.=true, Dis.=false2025.1192.3——
Qwen2.5-Math-RM-72BSamples=32, Parameter Size=72B2025.0392.3——
GPT-42024.0592.2——
Qwen2.5-7B + Reinforce ++Base Model=Qwen2.5-7B, Algorithm=Reinforce ++2025.1292.2——
Qwen2.5-7B + ARPOBase Model=Qwen2.5-7B, Algorithm=ARPO2025.1292.2——
DenserModel=DeepSeek-V32025.1292.1——
EDU-72BSamples=32, Parameter Size=72B2025.0392.1——
GPT-4shots=8-shot2023.0792——
GPT-4Prompt=CoT2023.1092——
GPT-42024.0792——
Tree-of-ThoughtBackbone=Qwen3-32B-think2025.1292——
Self-VerificationBackbone=Qwen3-32B-think2025.1292——
EDU-72BSamples=64, Parameter Size=72B2025.0392——
Qwen2.5-Math-RM-72BSamples=16, Parameter Size=72B2025.0391.9——
CoTBackbone=LLaMA-32025.1091.9——
Self-ConsistencyModel=GPT-4o2025.1291.8——
Process SupervisionModel=DeepSeek-V32025.1291.8——
EDU-72BSamples=16, Parameter Size=72B2025.0391.8——
MCTS with CoTBackbone=LLaMA-32025.1091.8——