Reading list: the formal proofs that LLM hallucination is mathematically inevitable
2C_ornot2C · x · 2026-11-15
alexverem curates the research backing the claim that hallucination is architectural, not a bug:
- "Hallucination is Inevitable" (arXiv:2401.11817, Xu, Jain & Kankanhalli): formalizes a computable world and uses learning theory to prove LLMs cannot learn all computable functions, so they must hallucinate as general problem solvers; also characterizes hallucination-prone tasks under time-complexity constraints
- "LLMs Will Always Hallucinate": draws on undecidability and Gödel's First Incompleteness Theorem to argue every LLM stage produces hallucinations with non-zero probability — "structural hallucinations"
- Plus alternative-architecture pointers: the generalization-hallucination trade-off paper, Mamba, LeCun's JEPA, and "Speed Always Wins"
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