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 hallucina- tion 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 of the computable functions and will therefore always hal- lucinate. 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.
For those of you who didn’t read the paper, the argument they’re making is similar to Godel’s Incompleteness Theorem: no matter how you build your LLM, there will be a significant number of prompts that make that LLM hallucinate. If the proof holds up then hallucinations aren’t a limitation of the training data or the structure of your particular model, they’re a limitation of the very concept of an LLM. That doesn’t make LLMs useless, but it does mean you shouldn’t ever use one as a source of truth.
It seems weird to describe it as a “limitation.” Isn’t it just the main thing they do? Hallucinations guided by whatever we all typed on reddit, untouched by any lived experience. If this approach occasionally gets near the truth I’ve seen nothing to suggest that it’s by design.
