Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

LLMs Will Always Hallucinate, and We Need to Live With This

Sourav Banerjee, Ayushi Agarwal, Saloni Singla

TL;DR

This work argues that hallucinations are not mere errors but an intrinsic Structural Hallucination arising from the mathematical and logical structure of large language models. It grounds this claim in undecidability results (Gödelian incompleteness, Halting/Acceptance problems) and provides a multi-faceted justification spanning training data incompleteness, retrieval limits, intent classification, and generation. The authors illustrate the inevitability with theoretical proofs and an illustrative prompt, and they assess existing mitigation strategies (CoT, self-consistency, uncertainty, faithful explanations) as insufficient to fully eliminate hallucinations. The paper emphasizes responsible use, risk awareness, and future directions for benchmarks and targeted mitigation, while acknowledging the creative potential of LLMs when used judiciously. Overall, it reframes hallucinations as a fundamental trait to be managed rather than eliminated, with broad implications for evaluation, safety, and policy in AI systems.

Abstract

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.

LLMs Will Always Hallucinate, and We Need to Live With This

TL;DR

This work argues that hallucinations are not mere errors but an intrinsic Structural Hallucination arising from the mathematical and logical structure of large language models. It grounds this claim in undecidability results (Gödelian incompleteness, Halting/Acceptance problems) and provides a multi-faceted justification spanning training data incompleteness, retrieval limits, intent classification, and generation. The authors illustrate the inevitability with theoretical proofs and an illustrative prompt, and they assess existing mitigation strategies (CoT, self-consistency, uncertainty, faithful explanations) as insufficient to fully eliminate hallucinations. The paper emphasizes responsible use, risk awareness, and future directions for benchmarks and targeted mitigation, while acknowledging the creative potential of LLMs when used judiciously. Overall, it reframes hallucinations as a fundamental trait to be managed rather than eliminated, with broad implications for evaluation, safety, and policy in AI systems.

Abstract

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.
Paper Structure (60 sections, 32 equations, 9 figures, 1 table)

This paper contains 60 sections, 32 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. The Essence of Large Language Models
  4. Architectures of Large Language Model Generation
  5. How language model generations work
  6. Linear RNNs
  7. Mamba (Linear-Time Sequence Modeling with Selective State Spaces)
  8. Kolmogorov-Arnold Networks (KANs)
  9. Transfer Learning
  10. Parameter-Efficient Fine-Tuning (PEFT): Streamlined Approaches
  11. Combining PEFT Techniques
  12. Retrieval-Augmented Generation (RAG): Bridging Knowledge Gaps
  13. Hallucinations in LLMs: What They Are and How They Happen
  14. Types of Hallucinations in LLMs
  15. Fabrications
  16. ...and 45 more sections

Figures (9)

  • Figure 1: Performance Comparison of Mamba and Other Language Models on The Pile Benchmark Dataset. Mamba exhibits comparable or slightly superior performance to other language models across various metrics on The Pile, a comprehensive dataset designed to evaluate the generalization capabilities of language models. Data reproduced from 55.
  • Figure 2: A comparison between multilayer perceptrons and KANs. Reproduced from 53.
  • Figure 3: Improvement in accuracy as a function of the number of trainable parameters. Reproduced from 65.
  • Figure 4: Stages of LLM Generation and Strategies to Mitigate Hallucination in Each of Them
  • Figure 5: There are limitations associated with every stage of the LLM generation process. This leads to an inevitable non-zero probability of hallucination in LLMs
  • ...and 4 more figures