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Symmetry
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Symmetry/Asymmetry and Its Applications in Deep Learning and Artificial Intelligence...
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Symmetry/Asymmetry and Its Applications in Deep Learning and Artificial Intelligence Methods

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

Deadline for manuscript submissions: 31 March 2026 | Viewed by 1034

Special Issue Editors

Prof. Dr. Eréndira Rendón-Lara

E-Mail Website
Guest Editor
Tecnológico Nacional de México, Instituto Tecnológico de Toluca, Avenida Tecnológico s/n, Colonia Agrícola Bellavista, Metepec 52149, Mexico
Interests: big data; multi-class imbalance problem; sampling methods; hyper-spectral remote sensing images; clustering
Prof. Dr. Rosa María Valdovinos-Rosas

E-Mail Website
Guest Editor
Facultad de Ingeniería, Universidad Autónoma del Estado de México, Cerro de Coatepec S/N, Ciudad Universitaria, Universitaria, 50110 Toluca de Lerdo, Mexico
Interests: pattern recognition; data mining; data science; machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The large amount and complexity of information generated around the world have given rise to new research capable of modeling complex real-life problems. Recently, symmetry has been a fundamental tool in the study and analysis of complex systems. In machine learning and artificial intelligence, symmetry/asymmetry has been used in both models and data. This Special Issue, titled “Symmetry/Asymmetry and Its Applications in Deep Learning and Artificial Intelligence Methods”, aims to focus on all aspects of symmetry/asymmetry, including its applications in deep learning and artificial intelligence.

Authors are invited to submit outstanding, original, and unpublished research manuscripts focused on the latest findings in this field. This issue will help technicians in this field exchange the latest technical developments. The topics of interest include but are not limited to the following:

  • Deep learning for symmetry;
  • New deep learning algorithms and architectures;
  • Deep learning for image/video recognition;
  • Deep learning for style transfer and generative adversarial networks;
  • Deep learning for intelligent human–computer interactions.

Prof. Dr. Eréndira Rendón-Lara
Prof. Dr. Rosa María Valdovinos-Rosas
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • deep learning
  • multimedia
  • generative adversarial network
  • pattern recognition
  • intelligent human–computer interaction
  • convolutional neural networks
  • recurrent neural networks
  • graph neural network
  • long short-term memory
  • extreme learning machine
  • generative adversarial networks
  • reinforcement learning
  • clustering analysis
  • natural language processing
  • time series analysis
  • model-based clustering high-dimensional modeling

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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18 pages, 400 KiB  
Article
Symmetry in the Algebra of Learning: Dual Numbers and the Jacobian in K-Nets
by Agustin Solis-Winkler, J. Raymundo Marcial-Romero and J. A. Hernández-Servín
Symmetry 2025, 17(8), 1293; https://doi.org/10.3390/sym17081293 - 11 Aug 2025
Viewed by 241
Abstract
The black-box nature of deep machine learning hinders the extraction of knowledge in science. To address this issue, a proposal for a neural network (k-net) based on the Kolmogorov–Arnold Representation Theorem is presented, pursuing to be an alternative to the traditional Multilayer Perceptron. [...] Read more.
The black-box nature of deep machine learning hinders the extraction of knowledge in science. To address this issue, a proposal for a neural network (k-net) based on the Kolmogorov–Arnold Representation Theorem is presented, pursuing to be an alternative to the traditional Multilayer Perceptron. In its core, the algorithmic nature of neural networks lies in the fundamental symmetry between forward-mode and reverse-mode accumulation techniques, both of which rely on the chain rule of partial derivatives. These methods are essential for computing gradients of functions, an operation that is at the core of the training process of neural networks. Automatic differentiation addresses the need for accurate and efficient calculation of derivative values in scientific computing; procedural programs are thus transformed into the computation of the required derivatives at the same numerical arguments. This work formalizes the algebraic structure of neural network computations by framing the training process within the domain of hyperdual numbers. Specifically, it defines a Kolmogorov–Arnold-inspired neural network (k-net) using dual numbers by extending the univariate functions and their compositions that appear in the representation theorem. This approach focuses on computation of the Jacobian and the ability to implement such procedures algorithmically, without sacrificing accuracy and mathematical rigor, while exploiting the inherent symmetry of the dual number formalism. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Its Applications in Deep Learning and Artificial Intelligence Methods)
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20 pages, 6359 KiB  
Article
Symmetry in Explainable AI: A Morphometric Deep Learning Analysis for Skin Lesion Classification
by Rafael Fernandez, Angélica Guzmán-Ponce, Ruben Fernandez-Beltran and Ginés García-Mateos
Symmetry 2025, 17(8), 1264; https://doi.org/10.3390/sym17081264 - 7 Aug 2025
Viewed by 217
Abstract
Deep learning has achieved remarkable performance in skin lesion classification, but its lack of interpretability often remains a critical barrier to clinical adoption. In this study, we investigate the spatial properties of saliency-based model explanations, focusing on symmetry and other morphometric features. We [...] Read more.
Deep learning has achieved remarkable performance in skin lesion classification, but its lack of interpretability often remains a critical barrier to clinical adoption. In this study, we investigate the spatial properties of saliency-based model explanations, focusing on symmetry and other morphometric features. We benchmark five deep learning architectures (ResNet-50, EfficientNetV2-S, ConvNeXt-Tiny, Swin-Tiny, and MaxViT-Tiny) on a nine-class skin lesion dataset from the International Skin Imaging Collaboration (ISIC) archive, generating saliency maps with Grad-CAM++ and LayerCAM. The best-performing model, Swin-Tiny, achieved an accuracy of 78.2% and a macro-F1 score of 71.2%. Our morphometric analysis reveals statistically significant differences in the explanation maps between correct and incorrect predictions. Notably, the transformer-based models exhibit highly significant differences (p<0.001) in metrics related to attentional focus (Entropy and Gini), indicating that their correct predictions are associated with more concentrated saliency maps. In contrast, convolutional models show less consistent differences, and only at a standard significance level (p<0.05). These findings suggest that the quantitative morphometric properties of saliency maps could serve as valuable indicators of predictive reliability in medical AI. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Its Applications in Deep Learning and Artificial Intelligence Methods)
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