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Valuable Hallucinations: Realizable Non-realistic Propositions

Qiucheng Chen, Bo Wang

TL;DR

This work reframes hallucinations in large language models as not solely detrimental but potentially valuable when they constitute realizable yet non-realistic propositions. It formally defines valuable hallucinations, classifies them within existing taxonomies, and validates the concept experimentally using HalluQA and the Qwen2.5 model with ReAct prompting, showing a $5.12%$ reduction in overall hallucinations and an increase in valuable hallucinations from $6.45%$ to $7.92%$. The paper also discusses how prompting, reflection, retrieval-augmented generation, and meta-learning can further control and utilize hallucinations. The findings suggest practical implications for creative and scientific contexts, offering a roadmap for leveraging the productive aspects of LLM-generated content while monitoring reliability.

Abstract

This paper introduces the first formal definition of valuable hallucinations in large language models (LLMs), addressing a gap in the existing literature. We provide a systematic definition and analysis of hallucination value, proposing methods for enhancing the value of hallucinations. In contrast to previous works, which often treat hallucinations as a broad flaw, we focus on the potential value that certain types of hallucinations can offer in specific contexts. Hallucinations in LLMs generally refer to the generation of unfaithful, fabricated, inconsistent, or nonsensical content. Rather than viewing all hallucinations negatively, this paper gives formal representations and manual judgments of "valuable hallucinations" and explores how realizable non-realistic propositions--ideas that are not currently true but could be achievable under certain conditions--can have constructive value. We present experiments using the Qwen2.5 model and HalluQA dataset, employing ReAct prompting (which involves reasoning, confidence assessment, and answer verification) to control and optimize hallucinations. Our findings show that ReAct prompting results in a 5.12\% reduction in overall hallucinations and an increase in the proportion of valuable hallucinations from 6.45\% to 7.92\%. These results demonstrate that systematically controlling hallucinations can improve their usefulness without compromising factual reliability.

Valuable Hallucinations: Realizable Non-realistic Propositions

TL;DR

This work reframes hallucinations in large language models as not solely detrimental but potentially valuable when they constitute realizable yet non-realistic propositions. It formally defines valuable hallucinations, classifies them within existing taxonomies, and validates the concept experimentally using HalluQA and the Qwen2.5 model with ReAct prompting, showing a reduction in overall hallucinations and an increase in valuable hallucinations from to . The paper also discusses how prompting, reflection, retrieval-augmented generation, and meta-learning can further control and utilize hallucinations. The findings suggest practical implications for creative and scientific contexts, offering a roadmap for leveraging the productive aspects of LLM-generated content while monitoring reliability.

Abstract

This paper introduces the first formal definition of valuable hallucinations in large language models (LLMs), addressing a gap in the existing literature. We provide a systematic definition and analysis of hallucination value, proposing methods for enhancing the value of hallucinations. In contrast to previous works, which often treat hallucinations as a broad flaw, we focus on the potential value that certain types of hallucinations can offer in specific contexts. Hallucinations in LLMs generally refer to the generation of unfaithful, fabricated, inconsistent, or nonsensical content. Rather than viewing all hallucinations negatively, this paper gives formal representations and manual judgments of "valuable hallucinations" and explores how realizable non-realistic propositions--ideas that are not currently true but could be achievable under certain conditions--can have constructive value. We present experiments using the Qwen2.5 model and HalluQA dataset, employing ReAct prompting (which involves reasoning, confidence assessment, and answer verification) to control and optimize hallucinations. Our findings show that ReAct prompting results in a 5.12\% reduction in overall hallucinations and an increase in the proportion of valuable hallucinations from 6.45\% to 7.92\%. These results demonstrate that systematically controlling hallucinations can improve their usefulness without compromising factual reliability.

Paper Structure

This paper contains 27 sections, 6 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background and Problem Statement
  3. Research Motivation and Limitations of Existing Work
  4. Core Contributions of This Work
  5. Definitions
  6. Hallucinations
  7. Valuable Hallucinations
  8. Definition of Valuable Hallucinations
  9. Classification of Valuable Hallucinations
  10. Examples of Valuable Hallucinations
  11. Formal Definitions
  12. Methodology
  13. Prompts and Reflections
  14. Background Knowledge
  15. Experiments
  16. ...and 12 more sections

Figures (2)

  • Figure 1: A figure with a comparison of the number of content types before and after ReAct prompts.
  • Figure 2: The number and percentage of responses in the class and category to which the question belongs that originally manifested as a non-valuable hallucination and manifested as a non-hallucinatory response after prompting.