Academic Journal
Possible Entropic Limits of Iterative Computation in Generative AI: Model Collapse Explained by the Data Processing Inequality and the AI Theorem.
| Τίτλος: | Possible Entropic Limits of Iterative Computation in Generative AI: Model Collapse Explained by the Data Processing Inequality and the AI Theorem. |
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| Συγγραφείς: | Straňák, Pavel |
| Πηγή: | Symmetry (20738994); May2026, Vol. 18 Issue 5, p764, 12p |
| Θεματικοί όροι: | Generative artificial intelligence, Information theory, Electronic data processing, Iterative methods (Mathematics) |
| People: | Shannon, Claude Elwood, 1916-2001 |
| Περίληψη: | Generative AI systems trained on synthetic data exhibit progressive degradation known as model collapse. This paper provides a theoretical explanation of this phenomenon using Shannon's Data Processing Inequality (DPI), modeling iterative synthetic-data training as a Markov chain of lossy transformations. We show that mutual information with respect to the original data distribution must decrease monotonically, yielding qualitative predictions for exponential decay tendencies and indicating that information loss arises from general finite-precision and capacity constraints rather than from any specific architectural mechanism. Building on this analysis, we introduce the AI conceptual theorem, a generalized stability limit for computable systems. The theorem states that any purely computational system that generates outputs iteratively under finite precision, bounded capacity, and without external low-entropy input must experience cumulative information degradation after a finite number of steps. DPI-based collapse emerges as a special case of this broader principle. The framework is intended as a conceptual information-theoretic perspective rather than a fully formalized theory, with several assumptions intentionally simplified to highlight the underlying entropic mechanism. The results should therefore be interpreted as principled limits that motivate further empirical and mathematical investigation rather than as definitive closed-form predictions. Together, DPI and the AI Theorem provide a unified information-theoretic framework for understanding degradation in synthetic training, long-horizon inference, and other iterative computational processes. The resulting predictions are quantitatively falsifiable and offer guidance for designing more stable and information-preserving AI systems. [ABSTRACT FROM AUTHOR] |
| Copyright of Symmetry (20738994) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
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| Items | – Name: Title Label: Title Group: Ti Data: Possible Entropic Limits of Iterative Computation in Generative AI: Model Collapse Explained by the Data Processing Inequality and the AI Theorem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Straňák%2C+Pavel%22">Straňák, Pavel</searchLink> – Name: TitleSource Label: Source Group: Src Data: Symmetry (20738994); May2026, Vol. 18 Issue 5, p764, 12p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Generative+artificial+intelligence%22">Generative artificial intelligence</searchLink><br /><searchLink fieldCode="DE" term="%22Information+theory%22">Information theory</searchLink><br /><searchLink fieldCode="DE" term="%22Electronic+data+processing%22">Electronic data processing</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink> – Name: SubjectPerson Label: People Group: Su Data: <searchLink fieldCode="PE" term="%22Shannon%2C+Claude+Elwood%2C+1916-2001%22">Shannon, Claude Elwood, 1916-2001</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Generative AI systems trained on synthetic data exhibit progressive degradation known as model collapse. This paper provides a theoretical explanation of this phenomenon using Shannon's Data Processing Inequality (DPI), modeling iterative synthetic-data training as a Markov chain of lossy transformations. We show that mutual information with respect to the original data distribution must decrease monotonically, yielding qualitative predictions for exponential decay tendencies and indicating that information loss arises from general finite-precision and capacity constraints rather than from any specific architectural mechanism. Building on this analysis, we introduce the AI conceptual theorem, a generalized stability limit for computable systems. The theorem states that any purely computational system that generates outputs iteratively under finite precision, bounded capacity, and without external low-entropy input must experience cumulative information degradation after a finite number of steps. DPI-based collapse emerges as a special case of this broader principle. The framework is intended as a conceptual information-theoretic perspective rather than a fully formalized theory, with several assumptions intentionally simplified to highlight the underlying entropic mechanism. The results should therefore be interpreted as principled limits that motivate further empirical and mathematical investigation rather than as definitive closed-form predictions. Together, DPI and the AI Theorem provide a unified information-theoretic framework for understanding degradation in synthetic training, long-horizon inference, and other iterative computational processes. The resulting predictions are quantitatively falsifiable and offer guidance for designing more stable and information-preserving AI systems. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Symmetry (20738994) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3390/sym18050764 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 764 Subjects: – SubjectFull: Shannon, Claude Elwood, 1916-2001 Type: general – SubjectFull: Generative artificial intelligence Type: general – SubjectFull: Information theory Type: general – SubjectFull: Electronic data processing Type: general – SubjectFull: Iterative methods (Mathematics) Type: general Titles: – TitleFull: Possible Entropic Limits of Iterative Computation in Generative AI: Model Collapse Explained by the Data Processing Inequality and the AI Theorem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Straňák, Pavel IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 20738994 Numbering: – Type: volume Value: 18 – Type: issue Value: 5 Titles: – TitleFull: Symmetry (20738994) Type: main |
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