Applications of Symmetry/Asymmetry and Machine Learning

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (28 February 2026) | Viewed by 967

Special Issue Editor


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Guest Editor
School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China
Interests: sparse representation; subspace learning; graph learning; medical biometrics

Special Issue Information

Dear Colleagues,

Symmetry and asymmetry are fundamental concepts that underpin a wide range of natural and artificial systems. In the era of data-driven discovery, the integration of these principles with machine learning has opened new avenues for both theoretical exploration and practical innovation. This Special Issue aims to bring together recent advances at the intersection of symmetry/asymmetry and machine learning, demonstrating how structural regularities and irregularities can be harnessed to improve generalization, robustness, and interpretability. Topics of interest include, but are not limited to, symmetric model architecture design/application, asymmetry-aware feature learning, group-equivariant neural networks and variants, partial multilabel learning, symmetry breaking in optimization, and applications across computer vision, bioinformatics, biometrics, signal processing, and beyond. By highlighting diverse methodologies and applications, this issue seeks to provide a comprehensive perspective on how symmetry-related insights can inspire novel machine learning solutions and deepen our understanding of complex systems.

Dr. Jianhang Zhou
Guest Editor

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Keywords

  • symmetry in machine learning
  • asymmetry-aware learning
  • group-equivariant neural networks
  • partial multi-label learning
  • interpretable machine learning
  • robust machine learning
  • applications with symmetric model

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Published Papers (1 paper)

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Research

12 pages, 983 KB  
Article
Possible Entropic Limits of Iterative Computation in Generative AI: Model Collapse Explained by the Data Processing Inequality and the AI Theorem
by Pavel Straňák
Symmetry 2026, 18(5), 764; https://doi.org/10.3390/sym18050764 - 29 Apr 2026
Viewed by 603
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Applications of Symmetry/Asymmetry and Machine Learning)
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