kalai-2023-hallucination-inevitable-under-perfect-conditions

IN premise — summaries/2026/08/24/kalai-2023-hallucination-inevitable-s9-conclusions-limitations-and-future-work.md

Created 2026-08-24T17:10:59+00:00

Kalai & Vempala (2023) prove that a calibrated LM must hallucinate even when training data is perfectly factual, documents contain at most one fact, and no prompt encourages fabrication — the hallucination is a statistical consequence of calibration, not a data-quality or prompting problem.

Summary

Hallucination in language models is not a fixable bug caused by messy data or bad prompts; it is a mathematical necessity that follows from the model being well-calibrated. This means no amount of data cleaning, single-fact curation, or prompt engineering can eliminate it, so the system should treat hallucination as an irreducible cost of the architecture rather than a defect to be patched.