Are Hallucinations Bad Estimations?

2025/09/25 by Liu, Hude, Hu, Jerry Yao-Chieh, Zhang, Jennifer Yuntong +2
#Artificial Intelligence (cs.AI) #Computation and Language (cs.CL) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.2509.21473

Abstract

We formalize hallucinations in generative models as failures to link an estimate to any plausible cause. Under this interpretation, we show that even loss-minimizing optimal estimators still hallucinate. We confirm this with a general high probability lower bound on hallucinate rate for generic data distributions. This reframes hallucination as structural misalignment between loss minimization and human-acceptable outputs, and hence estimation errors induced by miscalibration. Experiments on coin aggregation, open-ended QA, and text-to-image support our theory.

Citations

• Layer-0 Suppressors Ground Hallucination Inevitability: A Mechanistic Account of How Transformers Trade Factuality for Hedging
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