CoChat
Sign Up
Cited by 105Topic ModelingNatural Language Processing TechniquesAdversarial Robustness in Machine Learning

A Mathematical Investigation of Hallucination and Creativity in GPT Models

Open access
Lee, Minhyeok·2023·Mathematics
DOI 10.3390/math11102320
Open this paper in CoChat — free accountOpen PDF

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).

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.3390/math11102320

Cites

4 of 4 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Increasing the temperature of an LLM is one way to potentially increase its hallucination frequency.

    “increasing the temperature of an LLM is one way to potentially increase its hallucination frequency (Lee 2023)”

    From Large Legal Fictions: Profiling Legal Hallucinations in Large Language Models (2024) · cites this paper as Lee 2023

    Our copy discusses hallucination risk in ambiguous contexts (Remark 4) and a creativity–hallucination trade-off parameter α (Example 2), but neither establishes an effect of sampling temperature. Searches for “temperature hallucination” and “temperature” found no passage addressing whether raising temperature increases hallucination frequency. (LLM, conf=0.74)

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 27

  1. Wei, J.; Wang, X.; Schuurmans, D.; Bosma, M.; Xia, F.; Chi, E.H.; Le, Q.V.; Zhou, D. Chain-of-Thought Prompting Elicits Reasoning in Large Language Models. In Proceedings of the Advances in Neural Information Processing Systems, New Orleans, LA, USA, 28 November-9 December 2022.
  2. Carlini, N.; Tramer, F.; Wallace, E.; Jagielski, M.; Herbert-Voss, A.; Lee, K.; Roberts, A.; Brown, T.B.; Song, D.; Erlingsson, U.; et al. Extracting Training Data from Large Language Models. In Proceedings of the USENIX Security Symposium, San Diego, CA, USA, 11-13 August 2021; Volume 6.
  3. Shoeybi, M.; Patwary, M.; Puri, R.; LeGresley, P.; Casper, J.; Catanzaro, B. Megatron-lm: Training multi-billion parameter language models using model parallelism. arXiv 2019, arXiv:1909.08053. · arXiv
  4. Hu, E.J.; Shen, Y.; Wallis, P.; Allen-Zhu, Z.; Li, Y.; Wang, S.; Wang, L.; Chen, W. Lora: Low-rank adaptation of large language models. arXiv 2021, arXiv:2106.09685. · arXiv
  5. Kung, T.H.; Cheatham, M.; Medenilla, A.; Sillos, C.; De Leon, L.; Elepaño, C.; Madriaga, M.; Aggabao, R.; Diaz-Candido, G.; Maningo, J.; et al. Performance of ChatGPT on USMLE: Potential for AI-assisted medical education using large language models. PLoS Digit. Health 2023, 2, e0000198. [CrossRef] [PubMed] · DOI · Paper page
  6. Siino, M.; Di Nuovo, E.; Tinnirello, I.; La Cascia, M. Fake News Spreaders Detection: Sometimes Attention Is Not All You Need. Information 2022, 13, 426. [CrossRef] · DOI
  7. Siino, M.; Tinnirello, I.; La Cascia, M. T100: A modern classic ensemble to profile irony and stereotype spreaders. In Proceedings of the CEUR Workshop Proc, Leipzig, Germany, 9-10 November 2022; Volume 3180, pp. 2666-2674.
  8. Liu, Y.; Ott, M.; Goyal, N.; Du, J.; Joshi, M.; Chen, D.; Levy, O.; Lewis, M.; Zettlemoyer, L.; Stoyanov, V. Roberta: A robustly optimized bert pretraining approach. arXiv 2019, arXiv:1907.11692. · arXiv
  9. Liu, G.; Guo, J. Bidirectional LSTM with attention mechanism and convolutional layer for text classification. Neurocomputing 2019, 337, 325-338. [CrossRef] · DOI
  10. Kaiser, Ł.; Sutskever, I. Neural gpus learn algorithms. arXiv 2015, arXiv:1511.08228. · arXiv
  11. Zhu, Q.; Zhang, X.; Luo, J. Biologically Inspired Design Concept Generation Using Generative Pre-Trained Transformers. J. Mech. Des. 2023, 145, 041409. [CrossRef] · DOI
  12. Luo, R.; Sun, L.; Xia, Y.; Qin, T.; Zhang, S.; Poon, H.; Liu, T.Y. BioGPT: Generative pre-trained transformer for biomedical text generation and mining. Brief. Bioinform. 2022, 23, bbac409. [CrossRef] · DOI · Paper page
  13. Brown, T.; Mann, B.; Ryder, N.; Subbiah, M.; Kaplan, J.D.; Dhariwal, P.; Neelakantan, A.; Shyam, P.; Sastry, G.; Askell, A.; et al. Language models are few-shot learners. Adv. Neural Inf. Process. Syst. 2020, 33, 1877-1901.
  14. Radford, A.; Wu, J.; Child, R.; Luan, D.; Amodei, D.; Sutskever, I. Language Models are Unsupervised Multitask Learners. OpenAI Blog 2019, 1, 9.
  15. Liu, X.; Zhang, F.; Hou, Z.; Mian, L.; Wang, Z.; Zhang, J.; Tang, J. Self-supervised learning: Generative or contrastive. IEEE Trans. Knowl. Data Eng. 2021, 35, 857-876. [CrossRef] · DOI
  16. Albelwi, S. Survey on self-supervised learning: Auxiliary pretext tasks and contrastive learning methods in imaging. Entropy 2022, 24, 551. [CrossRef] · DOI · Paper page
  17. Jaiswal, A.; Babu, A.R.; Zadeh, M.Z.; Banerjee, D.; Makedon, F. A survey on contrastive self-supervised learning. Technologies 2020, 9, 2. [CrossRef] · DOI · Paper page
  18. Borgeaud, S.; Mensch, A.; Hoffmann, J.; Cai, T.; Rutherford, E.; Millican, K.; Van Den Driessche, G.B.; Lespiau, J.B.; Damoc, B.; Clark, A.; et al. Improving language models by retrieving from trillions of tokens. In Proceedings of the International Conference on Machine Learning, PMLR, Baltimore, MD, USA, 17-23 July 2022; pp. 2206-2240.
  19. Andrews, D.W. Generic uniform convergence. Econom. Theory 1992, 8, 241-257. [CrossRef] · DOI
  20. Donini, M.; Oneto, L.; Ben-David, S.; Shawe-Taylor, J.S.; Pontil, M. Empirical risk minimization under fairness constraints. Adv. Neural Inf. Process. Syst. 2018, 31, 2796-2806.
  21. Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A.N.; Kaiser, Ł.; Polosukhin, I. Attention is all you need. Adv. Neural Inf. Process. Syst. 2017, 30, 6000-6010.
  22. Shaw, P.; Uszkoreit, J.; Vaswani, A. Self-attention with relative position representations. arXiv 2018, arXiv:1803.02155. · arXiv
  23. Zhao, H.; Jia, J.; Koltun, V. Exploring self-attention for image recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA, 13-19 June 2020; pp. 10076-10085.
  24. Ramachandran, P.; Parmar, N.; Vaswani, A.; Bello, I.; Levskaya, A.; Shlens, J. Stand-alone self-attention in vision models. Adv. Neural Inf. Process. Syst. 2019, 32, 68-80.
  25. Kingma, D.P.; Ba, J. Adam: A method for stochastic optimization. arXiv 2014, arXiv:1412.6980. · arXiv
  26. Mukkamala, M.C.; Hein, M. Variants of rmsprop and adagrad with logarithmic regret bounds. In Proceedings of the International Conference on Machine Learning, PMLR, Sydney, Australia, 6-11 August 2017; pp. 2545-2553.
  27. Ba, J.L.; Kiros, J.R.; Hinton, G.E. Layer normalization. arXiv 2016, arXiv:1607.06450. · arXiv

Cited by

Sorted by citations

Authors
Lee, M.
Affiliations
Chung-Ang University (KR)
Corresponding author
Lee, Minhyeok
ORCID
Lee, Minhyeok
Venue
Mathematics
Publisher
MDPI AG
Published
2023-05-16
Volume
11
Issue
10
Pages
2320
ISSN
2227-7390 (ISSN-L)
DOI
10.3390/math11102320
OpenAlex
W4376874793
Cited by
105
References
4
Citations by year
2026: 22 · 2025: 33 · 2024: 35 · 2023: 15
FWCI
9.87
Type
journal article
Language
en
Open access
Licence
Locations
  • Mathematics (publishedVersion, cc-by)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
Generative Artificial Intelligence System Inc. (GAIS)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Topic Modeling
  • Physical Sciences › Computer Science › Artificial Intelligence › Natural Language Processing Techniques
  • Physical Sciences › Computer Science › Artificial Intelligence › Adversarial Robustness in Machine Learning
Keywords
hallucinations, creativity, GPT models, generative pre-trained transformer, large language models, information theory, probability theory

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review