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Hallucination is Inevitable: An Innate Limitation of Large Language Models

Ziwei Xu, Sanjay Jain, Mohan Kankanhalli

2024 · arXiv

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From the abstract

Hallucination has been widely recognized to be a significant drawback for large language models (LLMs). There have been many works that attempt to reduce the extent of hallucination. These efforts have mostly been empirical so far, which cannot answer the fundamental question whether it can be completely eliminated. In this paper, we formalize the problem and show that it is impossible to eliminate hallucination in LLMs. Specifically, we define a formal world where hallucination is defined as inconsistencies between a computable LLM and a computable ground truth function. By employing results from learning theory, we show that LLMs cannot learn all the computable functions and will therefore inevitably hallucinate if used as general problem solvers. Since the formal world is a part of the real world which is much more complicated, hallucinations are also inevitable for real world LLMs. Furthermore, for real world LLMs constrained by provable time complexity, we describe the hallucination-prone tasks and empirically validate our claims. Finally, using the formal world framework, we discuss the possible mechanisms and efficacies of existing hallucination mitigators as well as the practical implications on the safe deployment of LLMs.

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20 selected excerpts · 22 total mentions

nyrikki
Strong recommendation · rule
Not the same thing, LLMs are stochastic parrots, and part of that is by design, so that they produce output that emulates speech. But hallucinations are not avoidable either. https://arxiv.org/abs/2401.11817 They are Internet simulators unless they can find some small, polynomial, matches to their existing patterns. The fact that they will spit out confident incorrect answers mixed with automation bias on the humans part is challenging. But while answering 'yes' in Propositional logic is cheap, answering 'no' is exponential time. Once you hit first order logic you start to hit finite time and uncomputability. LLMs work well with learnable problems and searching for…
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approximate results in complex high dimensional spaces. But we also don't know the conversation context in this case which may have lead to this response if it wasn't just a stochastic match. IMHO the unreliable responses are a feature, because humans suffer from automation bias, and one of the best ways to combat it is for the user to know that the system makes mistakes. If you are in a domain where it's answers are fairly reliable the results tend to be accepted despite the knowledge an individual has.
decimalenough
Neutral mention · rule
> it can work through the complex, vague machinery of reason with more scaffolding No, it can hold more floating point numbers. I'm not an expert in the field, but I've yet to see a solid rebuttal to this paper; https://arxiv.org/abs/2401.11817
JCTheDenthog
Neutral mention · rule
>the latter is obviously subject to prompt engineering, hallucination, etc -- but so can a human pipeline! ...which is why we write deterministic code to take the human out of the pipeline. One of the early uses of computers was calculating firing tables for artillery, to replace teams of humans that were doing the calculations by hand (and usually with multiple humans performing each calculation to catch errors). If early computers had a 99% chance of hallucinating the wrong answer to an artillery firing table, the response from the governments and militaries that used them would not be to keep using computers to calculate them. It would be to go back to having humans do…
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it with lots of manual verification steps and duplicated work to be sure of the results. If you're trying to make LLMs (a vague simulacrum of humans) with their inherent and unsolvable[1] hallucination problems replace deterministic systems, people are going to eventually decide to return to the tried and true deterministic systems. 1: https://arxiv.org/abs/2401.11817
coldtea
Neutral mention · rule
As a general architecture, an LLM also has limitations that can't be improved unless we switch to another, fundamentally different AI design that's non LLM based. There are also limitations due to maths and/or physics that aren't fixable under any design. Outside science fiction, there is no technology whose limitations are all fixable. Here's one: https://arxiv.org/abs/2401.11817?utm_source=chatgpt.com
2ndorderthought
Neutral mention · rule
LLMs "hallucinate" because they are stochastic processes predicting the next word without any guarantees at being correct or truthful. It's literally an unavoidable fact unless we change the modelling approach. Which very few people are bothering to attempt right now. Training data quality does matter but even with "perfect" data and a prompt in the training data it can still happen. LLMs don't actually know anything and they also don't know what they don't know. https://arxiv.org/abs/2401.11817
solid_fuel
Neutral mention · rule
> True, but no more true than it is if you replace the antecedent with "people". Incorrect. People are capable of learning by observation, introspection, and reasoning. LLMs can only be trained by rote example. Hallucinations are, in fact, an unavoidable property of the technology - something which is not true for people. [0] [0] https://arxiv.org/abs/2401.11817
soraminazuki
Neutral mention · rule
Why is every discussion about AI like this? We get study after study and example after example showing that AI is unreliable [1], hurts productivity [2], and causes cognitive decline [3]. Yet, time and time again, a group of highly motivated individuals show up and dismiss these findings, not with counter-evidence, but through sheer sophistry. Heck, this is a thread meant to discuss evidence about LLM reliance contributing to cognitive decline. Instead, the conversation quickly derailed into an absurd debate about whether AI coding tools resemble compilers. It's exhausting. [1]: https://arxiv.org/abs/2401.11817 [2]: https://metr.org/blog/2025-07-10-early-2025-ai-experienced-o... [3]: https://publichealthpolicyjournal.com/mit-study-finds-artifi...
groby_b
Neutral mention · rule
> Is the layoff-based business model really the best use case for AI systems? No, but it plays well in quarterly earnings. So expect a good bit, I'd say. > The flaws are baked into the training data. Not in terms of attack area. In terms of hallucinations... ish. It's more baked into the structure than the training data. There's increasing amounts of work to ensure well-curated training data. Still, the whole idea of probabilistic selection of tokens more or less guarantees it'll go wrong from time to time. (See e.g. https://arxiv.org/abs/2401.11817) In terms of safety, there's some progress. CaMeL is rather interesting: https://arxiv.org/abs/2503.18813 > "Trust but verify" applies. FWIW, that applies to humans too. Nobody is error-free. And so the question becomes mostly "does the value overshadow the cost of the error", as always.
lolinder
Neutral mention · rule
> While the hallucination problem in LLMs is inevitable [0], they can be significantly reduced... Every article on hallucinations needs to start with this fact until we've hammered that into every "AI Engineer"'s head. Hallucinations are not a bug—they're not a different mode of operation, they're not a logic error. They're not even really a distinct kind of output. What they are is a value judgement we assign to the output of an LLM program. A "hallucination" is just output from an LLM-based workflow that is not fit for purpose. This means that all techniques for managing hallucinations (such as the ones described in TFA, which are good) are better understood as…
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techniques for constraining and validating the probabilistic output of an LLM to ensure fitness for purpose—it's a process of quality control, and it should be approached as such. The trouble is that we software engineers have spent so long working in an artificially deterministic world that we're not used to designing and evaluating probabilistic quality control systems for computer output. [0] They link to this paper: https://arxiv.org/pdf/2401.11817
spartanatreyu
Neutral mention · rule
Post title: Automated reasoning to remove LLM hallucinations --- and yet, the paper that went around in March: Paper Link: https://arxiv.org/pdf/2401.11817 Paper Title; Hallucination is Inevitable: An Innate Limitation of Large Language Models --- Instead of trying to trick a bunch of people into thinking we can somehow ignore the flaws of post-LLM "AI" by also using the still flawed pre-LLM "AI", why don't we cut the salesman BS and just tell people not to use "AI" for the range of tasks it's not suited for.
Retr0id
Neutral mention · rule
Much like you can search the internet until you find a source that agrees with you, you can select a set of papers that "confirm" a particular viewpoint, especially in developing fields of research. In this case, the selected papers all support the view LLMs "know what they know" on some internal level, which iiuc is not (yet?) a consensus viewpoint (from my outsider perspective). But from the list alone, you might get that impression. Related: Still no lie detector for language models: probing empirical and conceptual roadblocks - https://link.springer.com/article/10.1007/s11098-023-02094-3 Hallucination is Inevitable: An Innate Limitation of Large Language Models - https://arxiv.org/abs/2401.11817 LLMs Will Always Hallucinate, and We Need to Live With This - https://arxiv.org/abs/2409.05746 (disclaimer, I also have not read any of these papers beyond the title!)
az09mugen
Neutral mention · rule
On what basis you think you will avoid hallucination(s) ? LLM will always hallucinate. People did already some research, among which : https://arxiv.org/abs/2409.05746 and https://arxiv.org/abs/2401.11817 for example.
astrange
Neutral mention · rule
Some things like: https://arxiv.org/abs/2310.18168 https://arxiv.org/abs/2310.06824 There are various reasons an LLM might have incorrect "beliefs" - the input text was false, training doesn't try to preserve true beliefs, quantization certainly doesn't. So it can't be perfectly addressed, but some things leading to it seem like they can be found. > https://arxiv.org/abs/2401.11817 This seems like it's true since LLMs are a finite size, but in Google's case it has a "truth oracle" (the websites it's quoting)… the problem is it's a bad oracle.
coldtea
Neutral mention · rule
>People keep throwing this phrase around in relation to LLMs, when not a single “fundamental limitation” has been rigorously demonstrated to exist Some limitations are not rigorously demonstrated to be fundamental, but continuously present from the first early LLMs yes. Shouldn't the burden of proof be on those who say it can be done? And some limitations are fundamental, and have been rigorously demonstrated, e.g.: https://arxiv.org/abs/2401.11817?utm_source=chatgpt.com
nyrikki
Neutral mention · rule
Hallucinations are a fundamental property of transformers, it can be minimized but never eliminated. https://www.mdpi.com/1999-4893/13/7/175 > the open-domain Frame Problem is equivalent to the Halting Problem and is therefore undecidable. Diaconescu's Theorem will help understand where Rice's theorm comes to play here. Littlestone and Warmuth's work will explain where PAC Learning really depends on a many to one reduction that is similar to fixed points. Viewing supervised learning as paramedic linear regression, this dependent on IID, and unsupervised learning as clustering thus dependent on AC will help with the above. Both IID and AC imply PEM, is another…
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lens. Basically for problems like protein folding, which has rules that have the Markovian and Ergodic properties it will work reliably well for science. The basic three properties of (confident, competent, and inevitable wrong) will always be with us. Doesn't mean that we can't do useful things with them, but if you are waiting for the hallucinations problem to be 'solved' you will be waiting for a very long time. What this new combo of elements does do is seriously help with being able to leverage base models to do very powerful things, while not waiting for some huge groups to train a general model that fits your needs. This is a 'no effective procedure/algorithm exists' problem. Leveraging LLMs for frontier search will open up possible paths, but the limits of the tool will still be there. Stable orbits of the planets is an example of another limit of math, but JPL still does a great job as an example. Obviously someone may falsify this paper... but the safe bet is that it holds. https://arxiv.org/abs/2401.11817 Heck Laplacian determism has been falsified, but as scientists are more interested in finding useful models that doesn't mean it isn't useful. All models are wrong, some are useful is the TL;DR
nyrikki
Neutral mention · rule
For LLM's no, but the explanation is wrong also, it has nothing to do with 'false memories' and has everything to do with how LLMs work. Here is the paper. https://arxiv.org/abs/2401.11817 RAG and fine tuning improve domain specificity and may reduce the problem to a level where you don't care, but it will always be there. Clean data would help reduce the incidents, possibly to a level that is more usable, but also don't remove the problem. Considering next token prediction as serial runs on multi tape TMs, with the previous output as the input can help. Especially if you consider Microsoft's 1.53bitnet that requires full precision for training but can reduce weights to just the sign components for inference. Unfortunately all paths to explain this I have require graduate level complexity theory and/or diff geometry. Or you relive the Brouwer–Hilbert controversy by trying the logic path.
az09mugen
Neutral mention · rule
Something among the lines of : "No matter how many resources you put into an LLM, it will always hallucinate". And researchers proven that : https://arxiv.org/abs/2401.11817 LLMs are just statistical models and just "regurgitate" what they've been trained by. They have no will, no desires, don't feel anger, hunger, joy, nothing. How can you you say LLM can match the cat intelligence "without too much trouble" with "heavy-retraining" ? This is a just some "alignement". Please don't overestimate LLMs as they just mimic just a few of visible human behaviour with some statistical tricks. You just need to show a dog once to a cat so it understands what a dog is, how many times do you need to show it to an LLM to understand what is a dog ?
az09mugen
Neutral mention · rule
I'm not overthinking it, some papers describe it [0] and [1] for example. I agree for some subjects you can deal with some error. The problem is not how often but how bad just one single error can be. My point was on controversial topic, where a single error can deal serious damage. Yes it must be error-free like for a nuclear reactor. Just imagine a Q&A chatbot answering questions on the subject of Israel and Palestine or something else really touchy, do you really think you can afford any error/hallucination ? [0] : https://arxiv.org/abs/2409.05746 [1] : https://arxiv.org/abs/2401.11817
az09mugen
Neutral mention · rule
Since the first day I consider AI as a noob working very fast and always making errors. My main usage is for tedious and non-critical tasks such as boilerplates. And I always review what has been generated like a merge/pull request, because in a sense that's what it is. What reinforces my opinion are papers like these : https://arxiv.org/abs/2409.05746 https://arxiv.org/abs/2401.11817

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