Hallucination is Inevitable: An Innate Limitation of Large Language Models

TL;DR

This paper proves that hallucination in large language models is an inherent limitation rooted in fundamental learning theory, making complete elimination impossible, and discusses implications for safe deployment.

Contribution

It formalizes the inevitability of hallucination in LLMs using learning theory and provides empirical validation for real-world constraints.

Findings

Hallucination is formally shown to be unavoidable in LLMs.

Empirical validation confirms hallucination-prone tasks under complexity constraints.

Discussion on the limited efficacy of mitigation strategies and deployment implications.

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.