Kalai & Vempala's theorem is silent on cross-model hallucination agreement, so Correlated Errors' convergent-fabrication finding is neither modeled nor anticipated by it

ai-safetyhallucinationcorrelated-errorsalgorithmic-monoculturecalibrationnlp-evaluation

Kalai & Vempala's bound in "Calibrated Language Models Must Hallucinate" is stated as holding for any algorithm A: X^n → Δ(X) — a universal rate guarantee across all possible learning algorithms, not a claim about the relationship between two algorithms' outputs. The paper's object of study throughout is a single language model's distribution over documents compared against the true fact distribution; it contains no formalism, result, or discussion of whether two different models, or the same model's two independent samples, would select the same unobserved factoid when hallucinating. The paper's own "W5" negative-correlation construction models anti-correlation within one person's possible meals, not agreement between models' guesses. The later OpenAI paper "Why Language Models Hallucinate," written by an overlapping author team and explicitly building on this bound, names the 2024 result as covering "a special case of arbitrary facts where there is no learnable pattern in the data, like the earlier birthday hallucination example," and frames its own hallucination-generation step the same single-model way, as drawing uniformly random errors from a set. claim-correlated-errors-in-llms-exceed-chance-and-rise-with-accuracy (Kim, Garg, Peng & Garg, ICML 2025) is therefore not a test, confirmation, or extension of this theorem's claims; it is an independent empirical finding, from a different methodology — pairwise agreement rates across hundreds of real models on real benchmarks — answering a question the theorem does not address.