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A Mathematical Investigation of Hallucination and Creativity in GPT Models

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  • Minhyeok Lee

    (School of Electrical and Electronics Engineering, Chung-Ang University, Seoul 06974, Republic of Korea)

Abstract

In this paper, we present a comprehensive mathematical analysis of the hallucination phenomenon in generative pretrained transformer (GPT) models. We rigorously define and measure hallucination and creativity using concepts from probability theory and information theory. By introducing a parametric family of GPT models, we characterize the trade-off between hallucination and creativity and identify an optimal balance that maximizes model performance across various tasks. Our work offers a novel mathematical framework for understanding the origins and implications of hallucination in GPT models and paves the way for future research and development in the field of large language models (LLMs).

Suggested Citation

  • Minhyeok Lee, 2023. "A Mathematical Investigation of Hallucination and Creativity in GPT Models," Mathematics, MDPI, vol. 11(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2320-:d:1148235
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    References listed on IDEAS

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    1. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
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    Cited by:

    1. Yujie Sun & Dongfang Sheng & Zihan Zhou & Yifei Wu, 2024. "AI hallucination: towards a comprehensive classification of distorted information in artificial intelligence-generated content," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-14, December.
    2. Janik Ole Wecks & Johannes Voshaar & Benedikt Jost Plate & Jochen Zimmermann, 2024. "Generative AI Usage and Exam Performance," Papers 2404.19699, arXiv.org, revised Nov 2024.

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