Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.3
2.2
Journals
Symmetry
Special Issues
Symmetry in Deep Learning Networks and Its Applications in the...
share announcement

Symmetry in Deep Learning Networks and Its Applications in the Real World

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

Deadline for manuscript submissions: 31 July 2026 | Viewed by 6096

Special Issue Editors

Dr. Bin Li

E-Mail Website
Guest Editor
School of Computer Science, Northeast Electric Power University, Jilin 132012, China
Interests: traffic classification; support vector machine; feature selection; parameters optimization
Special Issues, Collections and Topics in MDPI journals
Dr. Zhuang Li

E-Mail Website
Guest Editor
School of Computer Science, Northeast Electric Power University, Jilin 132012, China
Interests: artificial intelligence; deep learning; computer vision
Dr. Jiankang Zhang

E-Mail Website
Guest Editor
Department of Computing & Informatics, Bournemouth University, Poole BH12 5BB, UK
Interests: artificial intelligence algorithms; ad-hoc networks; aeronautical communications; wireless communications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Deep learning networks have been widely applied in real-world engineering problems. Some effective deep learning networks have typical symmetric structures. For example, the encoder and decoder in U-Net networks have symmetry, as well as the generator and discriminator in GANs. Actual engineering problems are usually based on nonlinear data or models. Nonlinear models typically exhibit symmetry, nonconvexity, and multiple equivalent solutions. Symmetry problems involve the deep integration and clever application of mathematical principles, physical laws, and engineering design. By conducting in-depth research and utilizing the symmetry of deep learning networks, more efficient and powerful deep learning models can be designed to achieve better application results in practical engineering applications.

Dr. Bin Li
Dr. Zhuang Li
Dr. Jiankang Zhang
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 250 words) can be sent to the Editorial Office for assessment.

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
  • symmetry in engineering problems
  • deep learning networks with symmetrical structure
  • optimization of deep neural networks
  • optimization methods in engineering
  • design of deep neural networks
  • the application of deep learning in engineering

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (6 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

27 pages, 4733 KB  
Article
MDD Detection Based on Time-Spatial Features from EEG Symmetrical Microstate–Brain Networks
by Yang Xi, Bingjie Shi, Ting Lu, Pengfei Tian and Lu Zhang
Symmetry 2026, 18(1), 59; https://doi.org/10.3390/sym18010059 - 29 Dec 2025
Viewed by 610
Abstract
Major depressive disorder (MDD), identified by the World Health Organization as the leading cause of disability worldwide, remains underdiagnosed due to the lack of objective diagnostic tools. Electroencephalogram (EEG) signals offer potential biomarkers, yet conventional analyses often overlook the brain’s nonlinear dynamics. In [...] Read more.
Major depressive disorder (MDD), identified by the World Health Organization as the leading cause of disability worldwide, remains underdiagnosed due to the lack of objective diagnostic tools. Electroencephalogram (EEG) signals offer potential biomarkers, yet conventional analyses often overlook the brain’s nonlinear dynamics. In this study, we analyzed resting-stage EEG data to identify four microstate types in MDD patients. Symmetrical microstate–brain networks were then constructed for each microstate by using time series of four types of microstates as dynamic windows. Then, we compared microstate features (duration, occurrence, coverage, transition probability) and brain network parameters (clustering coefficient, characteristic path length, local and global efficiency) between MDD patients and healthy controls to analyze the characteristics of the changes in the brain activities of the patients with MDD and the topological patterns of the functional connectivity. The comparative analysis showed that MDD patients showed more frequent microstate transitions and reduced network efficiency, suggesting elevated energy consumption and impaired neural integration, which may imply a cognitive shift in MDD patients toward internal focus and psychological withdrawal from external stimuli. By integrating microstate and brain network features, we captured the temporal and spatial characteristics of MDD-related brain activity and validated their diagnostic utility using our previously proposed multiscale spatiotemporal convolutional attention network (MSCAN). Our MSCAN achieved an accuracy of 98.64% for MDD detection, outperforming existing approaches. Our study can offer promising implications for the intelligent diagnosis of MDD and a deeper understanding of its neurophysiological underpinnings. Full article
(This article belongs to the Special Issue Symmetry in Deep Learning Networks and Its Applications in the Real World)
►▼ Show Figures

Figure 1

25 pages, 6176 KB  
Article
Audiovisual Brain Activity Recognition Based on Symmetric Spatio-Temporal–Frequency Feature Association Vectors
by Yang Xi, Lu Zhang, Chenxue Wu, Bingjie Shi and Cunzhen Li
Symmetry 2025, 17(12), 2175; https://doi.org/10.3390/sym17122175 - 17 Dec 2025
Viewed by 468
Abstract
The neural mechanisms of auditory and visual processing are not only a core research focus in cognitive neuroscience but also hold critical importance for the development of brain–computer interfaces, neurological disease diagnosis, and human–computer interaction technologies. However, EEG-based studies on classifying auditory and [...] Read more.
The neural mechanisms of auditory and visual processing are not only a core research focus in cognitive neuroscience but also hold critical importance for the development of brain–computer interfaces, neurological disease diagnosis, and human–computer interaction technologies. However, EEG-based studies on classifying auditory and visual brain activities largely overlook the in-depth utilization of spatial distribution patterns and frequency-specific characteristics inherent in such activities. This paper proposes an analytical framework that constructs symmetrical spatio-temporal–frequency feature association vectors to represent brain activities by computing EEG microstates across multiple frequency bands and brain functional connectivity networks. Then we construct an Adaptive Tensor Fusion Network (ATFN) that leverages feature association vectors to recognize brain activities related to auditory, visual, and audiovisual processing. The ATFN includes a feature fusion and selection module based on differential feature enhancement, a feature encoding module enhanced with attention mechanisms, and a classifier based on a multilayer perceptron to achieve the efficient recognition of audiovisual brain activities. The feature association vectors are then processed by the Adaptive Tensor Fusion Network (ATFN) to efficiently recognize different types of audiovisual brain activities. The results show that the classification accuracy for auditory, visual, and audiovisual brain activity reaches 96.97% using the ATFN, demonstrating that the proposed symmetric spatio-temporal–frequency feature association vectors effectively characterize visual, auditory, and audiovisual brain activities. The symmetrical spatio-temporal–frequency feature association vectors establish a computable mapping that captures the intrinsic correlations among temporal, spatial, and frequency features, offering a more interpretable method to represent brain activities. The proposed ATFN provides an effective recognition framework for brain activity, with a potential application for brain–computer interfaces and neurological disease diagnosis. Full article
(This article belongs to the Special Issue Symmetry in Deep Learning Networks and Its Applications in the Real World)
►▼ Show Figures

Figure 1

20 pages, 1908 KB  
Article
Triple-Flow Dynamic Graph Convolutional Network for Wind Power Forecasting
by Bin Li, Bo Ding, Wei Pang and Hongyin Ni
Symmetry 2025, 17(12), 2026; https://doi.org/10.3390/sym17122026 - 26 Nov 2025
Cited by 1 | Viewed by 842
Abstract
Wind energy is a clean but intermittent and volatile energy source, and its large-scale integration into power systems poses great challenges to ensuring safe and stable operation and achieving scheduling optimization and effective energy planning of the power systems. Accurate wind power forecasting [...] Read more.
Wind energy is a clean but intermittent and volatile energy source, and its large-scale integration into power systems poses great challenges to ensuring safe and stable operation and achieving scheduling optimization and effective energy planning of the power systems. Accurate wind power forecasting is an effective way to mitigate the impact of wind power instability on power systems. However, wind power data are often in the form of multivariate time series. Existing wind power forecasting research often directly models the temporal and spatial characteristics of coupled wind power time-series data, ignoring the heterogeneity of time and space, thereby limiting the model’s expressive power. To address the above problems, we propose a triple-flow dynamic graph convolutional network (TFDGCN) for short-term wind power forecasting. The proposed TFDGCN is a symmetric dynamic graph neural network with three branches. It decouples and learns features of three different dimensions: within a wind power variable sequence, between sequences, and between wind turbines. The proposed TFDGCN constructs dynamic sparse graphs based on cosine similarities within variable sequences, between variable sequences, and between wind turbine nodes, and feeds them into their respective dynamic graph convolution modules. Afterwards, TFDGCN utilizes linear attention encoders which fuse local position encoding (LePE) and rotational position encoding (RoPE) to learn global dependencies within variable sequences, between sequences, and between wind turbines, and provide prediction results. Extensive experimental results on two real-world datasets demonstrate that the proposed TFDGCN outperforms other state-of-the-art methods. On the SDWPF and SD23 datasets, the proposed TFDGCN achieved mean absolute error values of 37.16 and 14.63, respectively, as well as root mean square error values of 44.84 and 17.56, respectively. Full article
(This article belongs to the Special Issue Symmetry in Deep Learning Networks and Its Applications in the Real World)
►▼ Show Figures

Figure 1

19 pages, 5901 KB  
Article
GAN Ownership Verification via Model Watermarking: Protecting Image Generators from Surrogate Model Attacks
by Shuai Cao and Sheng-Chun Yang
Symmetry 2025, 17(11), 1864; https://doi.org/10.3390/sym17111864 - 4 Nov 2025
Cited by 1 | Viewed by 848
Abstract
With the widespread application of generative adversarial networks (GANs) in image generation and content creation, their model architectures and training outcomes have become valuable intellectual property assets. However, in practical deployment, image generative models are vulnerable to surrogate model attacks, posing significant risks [...] Read more.
With the widespread application of generative adversarial networks (GANs) in image generation and content creation, their model architectures and training outcomes have become valuable intellectual property assets. However, in practical deployment, image generative models are vulnerable to surrogate model attacks, posing significant risks to copyright ownership and commercial interests. To address this issue, this paper proposes a novel copyright protection scheme for image generative models with a symmetric embedding–retrieval watermark architecture in GANs focused on defending against surrogate model attacks. Unlike traditional model encryption or architectural constraint strategies, the proposed approach integrates a watermark embedding module directly into the image generative network, enabling generated images to implicitly carry copyright identifiers. Leveraging a symmetric design between the embedding and retrieval processes, the system ensures that, under surrogate model attacks, the original model’s identity can be reliably verified by extracting the embedded watermark from the generated outputs. The implementation comprises three key modules—feature extraction, watermark embedding, and watermark retrieval—forming an end-to-end, balanced embedding–retrieval pipeline. Experimental results demonstrate that this approach achieves efficient and stable watermark embedding and retrieval without compromising generation quality, exhibiting high robustness, traceability, and practical applicability, thereby offering a viable and symmetric solution for intellectual property protection in image generative networks. Full article
(This article belongs to the Special Issue Symmetry in Deep Learning Networks and Its Applications in the Real World)
►▼ Show Figures

Figure 1

17 pages, 3049 KB  
Article
PECNet: A Lightweight Single-Image Super-Resolution Network with Periodic Boundary Padding Shift and Multi-Scale Adaptive Feature Aggregation
by Tianyu Gao and Yuhao Liu
Symmetry 2025, 17(11), 1833; https://doi.org/10.3390/sym17111833 - 1 Nov 2025
Cited by 1 | Viewed by 865
Abstract
Lightweight Single-Image Super-Resolution (SISR) faces the core challenge of balancing computational efficiency with reconstruction quality, particularly in preserving both high-frequency details and global structures under constrained resources. To address this, we propose the Periodically Enhanced Cascade Network (PECNet). Our main contributions are as [...] Read more.
Lightweight Single-Image Super-Resolution (SISR) faces the core challenge of balancing computational efficiency with reconstruction quality, particularly in preserving both high-frequency details and global structures under constrained resources. To address this, we propose the Periodically Enhanced Cascade Network (PECNet). Our main contributions are as follows: 1. Its core component, a novel Multi-scale Adaptive Feature Aggregation (MAFA) module, which employs three functionally complementary branches that work synergistically: one dedicated to extracting local high-frequency details, another to efficiently modeling long-range dependencies and a third to capturing structured contextual information within windows. 2. To seamlessly integrate these branches and enable cross-window information interaction, we introduce the Periodic Boundary Padding Shift (PBPS) mechanism. This mechanism serves as a symmetric preprocessing step that achieves implicit window shifting without introducing any additional computational overhead. Extensive benchmarking shows PECNet achieves better reconstruction quality without a complexity increase. Taking the representative shift-window-based lightweight model, NGswin, as an example, for ×4 SR on the Manga109 dataset, PECNet achieves an average PSNR 0.25 dB higher, while its computational cost (in FLOPs) constitutes merely 40% of NGswin’s. Full article
(This article belongs to the Special Issue Symmetry in Deep Learning Networks and Its Applications in the Real World)
►▼ Show Figures

Figure 1

18 pages, 4601 KB  
Article
An Intrusion Detection Method Based on Symmetric Federated Deep Learning in Complex Networks
by Lei Wang, Xuanrui Ren and Chunyi Wu
Symmetry 2025, 17(6), 952; https://doi.org/10.3390/sym17060952 - 15 Jun 2025
Cited by 1 | Viewed by 1524
Abstract
The rapid development of the current 5G/6G network has added tremendous pressure to traditional security detection in the scenario of dealing with large-scale network attacks, resulting in high time complexity and low efficiency of attack identification. According to the deep network and its [...] Read more.
The rapid development of the current 5G/6G network has added tremendous pressure to traditional security detection in the scenario of dealing with large-scale network attacks, resulting in high time complexity and low efficiency of attack identification. According to the deep network and its symmetry principle, this paper proposes a complex network intrusion detection and recognition method based on symmetric federation optimization, named IDS, which aims to reduce the time complexity and improve the accuracy and efficiency of attack identification. By using a symmetric network UNet-based deep feature learning to reconstruct data and construct the input matrix, we optimize the federated deep learning algorithm with a symmetric auto-encoder to make it more suitable for a complex network environment. The experimental results demonstrate that the technology based on the symmetric network proposed in this paper possesses significant advantages in terms of intrusion detection accuracy and effectiveness, which can effectively identify network intrusion and improve the accuracy of current complex network intrusion detection. The proposed symmetric intrusion detection method not only solves the bottleneck of traditional detection methods and improves the training efficiency of the model, but it also provides a new idea and solution for network security research. Full article
(This article belongs to the Special Issue Symmetry in Deep Learning Networks and Its Applications in the Real World)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-6
Back to TopTop