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LLMs Will Always Hallucinate, and We Need to Live With This
arxiv.orgAs 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.
The word “hallucination” itself is a marketing term. It’s not because it’s been frequently used in the technical literature that it is free of any problem. It’s used because it highlights a problem (namely that some of the output of LLM are not factually correct) but the very name is wrong. Hallucination implies there is someone, perceiving and with a world model, who typically via heuristics (for efficient interfaces like Donald Hoffman suggests) do so incorrectly leading to bad decision regarding the current problem to solve.
So… sure, “it” (trying not to use the term) is structural but it is simply because LLM have no notion of veracity or truth (or anything else, to be clear). They have no simulation to verify from if the output they propose (the tokens out, the sentence the user gets) is correct or not, it is solely highly probably based on their training data.
Brand new example : “Skills” by Anthropic https://www.anthropic.com/news/skills even though here the audience is technical it is still a marketing term. Why? Because the entire phrasing implies agency. There is no “one” getting new skills here. It’s as if I was adding bash scripts to my
~/bindirectory but instead of saying “The first script will use regex to start the appropriate script” I named my process “Theodore” and that I was “teaching” it new “abilities”. It would be literally the same thing, it would be functionally equivalent and the implement would be actually identical… but users, specifically non technical users, would assume that there is more than just branching options. They would also assume errors are just “it” in the process of “learning”.It’s really a brilliant marketing trick, but it’s nothing more.
Also your scripts will always do what they were meant to do.
LLMs will do whatever.
To be clear, I’m not saying the word itself shouldn’t be used but I bet that 99% of the time if it’s not used by someone with a degree in AI or CS it’s going to be used incorrectly.