In plain words: Using results from logic about problems no computer can always solve, the analysis argues every step of a language model — from gathering training text to writing an answer — can make things up. Better data, designs, or fact-checking can reduce this but never remove it.
Abstract · LLMs Will Always Hallucinate, and We Need to Live With This
As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.
Sourav Banerjee, Ayushi Agarwal, Saloni Singla
arXiv:2409.05746 · stat.ML, cs.LG · submitted Sep 9, 2024
abstract · pdf · html
Having a mathematical proof is nice, but honestly this whole misunderstanding could have been avoided if we'd just picked a different name for the concept of "producing false information in the course of generating probabilistic text".
"Hallucination" makes it sound like something is going awry in the normal functioning of the model, which subtly suggests that if we could just identify what went awry we could get rid of the problem and restore normal cognitive function to the LLM. The trouble is that the normal functioning of the model is simply to produce plausible-sounding text.
A "hallucination" is not a malfunction of the model, it's a value judgement we assign to the resulting text. All it says is that the text produced is not fit for purpose. Seen through that lens it's obvious that mitigating hallucinations and creating "alignment" are actually identical problems, and we won't solve one without the other.