Hallucinations are inevitable but can be made statistically negligible (arxiv.org)

Researchers reconcile a pessimistic computability-theoretic claim—based on diagonalization—that any language model must hallucinate on an infinite set of inputs with a new probabilistic analysis showing those “innate” hallucinations need not matter in practice. The paper proves that, under realistic probabilistic assumptions and with sufficient quantity and quality of training data, the probability that an LM hallucinates can be driven to be statistically negligible. Crucially, the authors emphasize that this positive result is logically compatible with the theoretical inevitability: you can’t eliminate hallucinations on every possible input, but you can make them vanishingly unlikely on the inputs that matter. Technically, the work reframes hallucination risk from a computability to an information- and probability-theoretic standpoint, providing formal bounds that link training-data distribution and model training to hallucination rates. The implication for ML practitioners is practical and optimistic: improving data coverage, curation, and inference algorithms can systematically reduce hallucination probability even though a worst-case impossibility remains. This shifts the focus from philosophical inevitability to measurable, engineering-driven mitigation strategies and motivates continued investment in dataset quality, calibration, and distribution-aware training.