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Hallucination Detection on Math500

88.89EigenWD M1EigenWD M1
67.195672.827878.4684.0922Mar 17, 2026

Evaluation results

MethodLinks
EigenWD M1Black model=deepseek-chat, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.0388.89—————
EigenWD M1Black model=deepseek-chat, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.0387.38—————
EigenWD M1Black model=chatgpt-4o-mini, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.0383.29—————
EigenWD M1Black model=chatgpt-4o-mini, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.0378.76—————
EigenWD M1Black model=deepseek-chat, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.0374.65—————
EigenWD M1Black model=chatgpt-4o-mini, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.0368.03—————
DSEBlack model=chatgpt-4o-mini, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03—————56.86
DSEBlack model=chatgpt-4o-mini, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03—————56.86
DSEBlack model=chatgpt-4o-mini, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03—————56.86
DSEBlack model=deepseek-chat, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03—————59.97
DSEBlack model=deepseek-chat, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03—————59.97
DSEBlack model=deepseek-chat, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03—————59.97
ERBlack model=chatgpt-4o-mini, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03—80.99————
ERBlack model=chatgpt-4o-mini, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03—75.56————
ERBlack model=chatgpt-4o-mini, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03—78.09————
ERBlack model=deepseek-chat, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03—87.6————
ERBlack model=deepseek-chat, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03—81.74————
ERBlack model=deepseek-chat, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03—80.14————
ESBlack model=chatgpt-4o-mini, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03——63.07———
ESBlack model=chatgpt-4o-mini, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03——67.94———
ESBlack model=chatgpt-4o-mini, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03——62.07———
ESBlack model=deepseek-chat, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03——55.87———
ESBlack model=deepseek-chat, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03——63.81———
ESBlack model=deepseek-chat, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03——58.03———
LNEBlack model=chatgpt-4o-mini, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03———64.49——
LNEBlack model=chatgpt-4o-mini, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03———61.76——
LNEBlack model=chatgpt-4o-mini, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03———65.95——
LNEBlack model=deepseek-chat, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03———53.44——
LNEBlack model=deepseek-chat, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03———54.7——
LNEBlack model=deepseek-chat, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03———49.52——
LSBlack model=chatgpt-4o-mini, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03————77.95—
LSBlack model=chatgpt-4o-mini, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03————77.95—
LSBlack model=chatgpt-4o-mini, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03————77.95—
LSBlack model=deepseek-chat, Teacher model=Llama-2-7b, Number of samples=10, Teacher forcing=true2026.03————83.35—
LSBlack model=deepseek-chat, Teacher model=Llama-3.1-8b, Number of samples=10, Teacher forcing=true2026.03————83.35—
LSBlack model=deepseek-chat, Teacher model=Qwen3-8B, Number of samples=10, Teacher forcing=true2026.03————83.35—