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Hallucination Detection on MATH 500

88.89AUROCEigenWD M1
21.269238.824656.3873.9354Jan 24, 2026Feb 17, 2026Mar 13, 2026Apr 6, 2026Apr 30, 2026May 24, 2026Jun 17, 2026

Evaluation results

MethodLinks
EigenWD M1Target Model=DeepSeek-Chat, Teacher Model=Llama-2-7B, Detection Setting=Black-box case study2026.0388.89
ARS (CCS)Model=DeepSeek-R1-Distill-Llama-8B, Judge Method=ROUGE2026.0188
ERTarget Model=DeepSeek-Chat, Teacher Model=Llama-2-7B, Detection Setting=Black-box case study2026.0387.6
ARS (CCS)Model=DeepSeek-R1-Distill-Llama-8B, Single Sampling=true, Supervision=false2026.0186.38
ARS (CCS)Model=DeepSeek-R1-Distill-Llama-8B, Judge Method=DeepSeek-R1-Distill-Qwen-32B2026.0186.24
TSVModel=DeepSeek-R1-Distill-Llama-8B, Judge Method=ROUGE2026.0184.71
LSTarget Model=DeepSeek-Chat, Teacher Model=Llama-2-7B, Detection Setting=Black-box case study2026.0383.35
TSVModel=DeepSeek-R1-Distill-Llama-8B, Judge Method=BLEURT2026.0181.36
ARS (CCS)Model=DeepSeek-R1-Distill-Llama-8B, Judge Method=BLEURT2026.0181
ARS (Probing)Model=DeepSeek-R1-Distill-Llama-8B, Single Sampling=true, Supervision=true2026.0179.95
ARS (CCS)Model=Qwen3-8B, Single Sampling=true, Supervision=false2026.0178.66
TSVModel=DeepSeek-R1-Distill-Llama-8B, Judge Method=DeepSeek-R1-Distill-Qwen-32B2026.0178.64
ARS (Probing)Model=Qwen3-8B, Single Sampling=true, Supervision=true2026.0178.17
G-DetectorModel=DeepSeek-R1-Distill-Llama-8B, Judge Method=ROUGE2026.0171.48
FESSignal=Free-energy + SFF2026.0668.3
Best spec.Description=Strongest non-FES in-tree attention-spectral baseline2026.0667.4
G-DetectorModel=DeepSeek-R1-Distill-Llama-8B, Single Sampling=true, Supervision=true2026.0164.45
TSVModel=DeepSeek-R1-Distill-Llama-8B, Single Sampling=true, Supervision=true2026.0163.24
TSVModel=Qwen3-8B, Single Sampling=true, Supervision=true2026.0163.12
RACEModel=Qwen3-8B, Single Sampling=false, Supervision=false2026.0163.02
G-DetectorModel=DeepSeek-R1-Distill-Llama-8B, Judge Method=BLEURT2026.0161.44
DSETarget Model=DeepSeek-Chat, Teacher Model=Llama-2-7B, Detection Setting=Black-box case study2026.0359.97
Best LMDescription=Best language-model probability baseline among MSP and PPL−12026.0659.6
SelfCKGPTModel=DeepSeek-R1-Distill-Llama-8B, Single Sampling=false, Supervision=false2026.0159.15
Best rep.Description=Strongest reported reference hidden-state or sampling baseline2026.0658
G-DetectorModel=Qwen3-8B, Single Sampling=true, Supervision=true2026.0157.67
RHDModel=DeepSeek-R1-Distill-Llama-8B, Single Sampling=true, Supervision=false2026.0156.5
Semantic EntropyModel=Qwen3-8B, Single Sampling=false, Supervision=false2026.0156.13
ESTarget Model=DeepSeek-Chat, Teacher Model=Llama-2-7B, Detection Setting=Black-box case study2026.0355.87
SelfCKGPTModel=Qwen3-8B, Single Sampling=false, Supervision=false2026.0155.47
RACEModel=DeepSeek-R1-Distill-Llama-8B, Single Sampling=false, Supervision=false2026.0153.55
LNETarget Model=DeepSeek-Chat, Teacher Model=Llama-2-7B, Detection Setting=Black-box case study2026.0353.44
PerplexityModel=Qwen3-8B, Single Sampling=true, Supervision=false2026.0151.62
RHDModel=Qwen3-8B, Single Sampling=true, Supervision=false2026.0150.51
Lexical SimilarityModel=DeepSeek-R1-Distill-Llama-8B, Single Sampling=false, Supervision=false2026.0149.92
Verbalized CertaintyModel=DeepSeek-R1-Distill-Llama-8B, Single Sampling=true, Supervision=false2026.0148.98
Lexical SimilarityModel=Qwen3-8B, Single Sampling=false, Supervision=false2026.0144.13
Semantic EntropyModel=DeepSeek-R1-Distill-Llama-8B, Single Sampling=false, Supervision=false2026.0143.6
PerplexityModel=DeepSeek-R1-Distill-Llama-8B, Single Sampling=true, Supervision=false2026.0140.96
G-DetectorModel=DeepSeek-R1-Distill-Llama-8B, Judge Method=DeepSeek-R1-Distill-Qwen-32B2026.0138.06
Verbalized CertaintyModel=Qwen3-8B, Single Sampling=true, Supervision=false2026.0123.87