Hallucination, Monofacts, and Miscalibration: An Empirical Investigation

Recent theoretical work by [Kalai and Vempala 2024] proves that a particular notion of hallucination rate in LLMs must be lower bounded by the training data monofact rate (related to the classical Good-Turing missing mass estimator) minus model miscalibration. Through systematic experiments with n-gram models and in-context learning with LLMs, we empirically investigate and validate this theory by examining how different underlying data distributions affect the monofact rate and a model's tendency to hallucinate. We then vary model miscalibration through controlled upweighting of training samples while holding monofact rates constant, allowing us to isolate miscalibration's reduction effect on hallucination. These findings suggest that both the distribution of fact frequencies in training data and the calibration-hallucination trade-off are inherent to probabilistic language generation. Our results also suggest that current practices of aggressive deduplication in training data may need to be reconsidered, as selective duplication could serve as a principled mechanism for reducing hallucination.