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Mathematics
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Dynamics in Neural Networks
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Dynamics in Neural Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 31 October 2024 | Viewed by 10580

Special Issue Editors

Prof. Dr. Zheng Tang

E-Mail Website
Guest Editor
Faculty of Engineering, University of Toyama, Toyama-shi 930-8555, Japan
Interests: artificial intelligence; neural networks; engineering; informatics
Special Issues, Collections and Topics in MDPI journals
Dr. Yuki Todo

E-Mail Website
Guest Editor
Faculty of Electrical and Computer Engineering, Kanazawa University, Kanazawa-shi 920-1192, Japan
Interests: multiple-valued logic; neural networks; optimization

Special Issue Information

Dear Colleagues,

As a method of computational intelligence, artificial neural networks and other methods of computational intelligence have intertwined to develop a variety of new neural networks, such as convolutional neural networks, BP neural networks, and evolutionary neural networks, which have both practical value and developmental promise. Despite the remarkable development and application of neural networks, the uncertainty of the network itself makes it a time-consuming process to find a suitable network in the process of design and use; the design of artificial neural networks is an extremely complex dynamic optimization work for a specific problem, and there is still no systematic rule to follow. Although neural networks have a relatively sound theoretical foundation, computational intelligence techniques like evolutionary computation and other important dynamic optimization techniques do not yet have a sound mathematical foundation. The analysis and proof of the stability and convergence of computational intelligence algorithms are still in the research stage. Testing their effectiveness and efficiency through numerical experimental methods and specific applications is still the main method for the study of computational intelligence algorithms.

This Special Issue hopes to serve as a good international exchange platform for researchers in various fields to summarize the latest progress and ideas in neural computing and other fields related to neural networks.

Prof. Dr. Zheng Tang
Dr. Yuki Todo
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • artificial intelligence
  • neural networks
  • computational intelligence
  • big data
  • computational neural models
  • brain-like systems
  • optimization problems

Published Papers (7 papers)

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Research

13 pages, 4950 KiB  
Article
The Mechanism of Orientation Detection Based on Artificial Visual System for Greyscale Images
by Xiliang Zhang, Sichen Tao, Zheng Tang, Shuxin Zheng and Yoki Todo
Mathematics 2023, 11(12), 2715; https://doi.org/10.3390/math11122715 - 15 Jun 2023
Viewed by 917
Abstract
Human visual system is a crucial component of the nervous system, enabling us to perceive and understand the surrounding world. Advancements in research on the visual system have profound implications for our understanding of both biological and computer vision. Orientation detection, a fundamental [...] Read more.
Human visual system is a crucial component of the nervous system, enabling us to perceive and understand the surrounding world. Advancements in research on the visual system have profound implications for our understanding of both biological and computer vision. Orientation detection, a fundamental process in the visual cortex where neurons respond to linear stimuli in specific orientations, plays a pivotal role in both fields. In this study, we propose a novel orientation detection mechanism for local neurons based on dendrite computation, specifically designed for grayscale images. Our model comprises eight neurons capable of detecting local orientation information, with inter-neuronal interactions facilitated through nonlinear dendrites. Through the extraction of local orientation information, this mechanism effectively derives global orientation information, as confirmed by successful computer simulations. Experimental results demonstrate that our mechanism exhibits remarkable orientation detection capabilities irrespective of variations in size, shape, or position, which aligns with previous physiological research findings. These findings contribute to our understanding of the human visual system and provide valuable insights into both biological and computer vision. The proposed orientation detection mechanism, with its nonlinear dendritic computations, offers a promising approach for improving orientation detection in grayscale images. Full article
(This article belongs to the Special Issue Dynamics in Neural Networks)
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23 pages, 7289 KiB  
Article
Yet Another Effective Dendritic Neuron Model Based on the Activity of Excitation and Inhibition
by Yifei Yang, Xiaosi Li, Haotian Li, Chaofeng Zhang, Yuki Todo and Haichuan Yang
Mathematics 2023, 11(7), 1701; https://doi.org/10.3390/math11071701 - 02 Apr 2023
Cited by 3 | Viewed by 1402
Abstract
Neuronal models have remained an important area of research in computer science. The dendritic neuron model (DNM) is a novel neuronal model in recent years. Previous studies have focused on training DNM using more appropriate algorithms. This paper proposes an improvement to DNM [...] Read more.
Neuronal models have remained an important area of research in computer science. The dendritic neuron model (DNM) is a novel neuronal model in recent years. Previous studies have focused on training DNM using more appropriate algorithms. This paper proposes an improvement to DNM based on the activity of excitation and proposes three new models. Each of the three improved models are designed to mimic the excitation and inhibition activity of neurons. The improved model proposed in this paper is shown to be effective in the experimental part. All three models and original DNM have their own strengths, so it can be considered that the new model proposed in this paper well enriches the diversity of neuronal models and contributes to future research on networks models. Full article
(This article belongs to the Special Issue Dynamics in Neural Networks)
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23 pages, 3813 KiB  
Article
OFPI: Optical Flow Pose Image for Action Recognition
by Dong Chen, Tao Zhang, Peng Zhou, Chenyang Yan and Chuanqi Li
Mathematics 2023, 11(6), 1451; https://doi.org/10.3390/math11061451 - 17 Mar 2023
Cited by 3 | Viewed by 1381
Abstract
Most approaches to action recognition based on pseudo-images involve encoding skeletal data into RGB-like image representations. This approach cannot fully exploit the kinematic features and structural information of human poses, and convolutional neural network (CNN) models that process pseudo-images lack a global field [...] Read more.
Most approaches to action recognition based on pseudo-images involve encoding skeletal data into RGB-like image representations. This approach cannot fully exploit the kinematic features and structural information of human poses, and convolutional neural network (CNN) models that process pseudo-images lack a global field of view and cannot completely extract action features from pseudo-images. In this paper, we propose a novel pose-based action representation method called Optical Flow Pose Image (OFPI) in order to fully capitalize on the spatial and temporal information of skeletal data. Specifically, in the proposed method, an advanced pose estimator collects skeletal data before locating the target person and then extracts skeletal data utilizing a human tracking algorithm. The OFPI representation is obtained by aggregating these skeletal data over time. To test the superiority of OFPI and investigate the significance of the model having a global field of view, we trained a simple CNN model and a transformer-based model, respectively. Both models achieved superior outcomes. Because of the global field of view, especially in the transformer-based model, the OFPI-based representation achieved 98.3% and 94.2% accuracy on the KTH and JHMDB datasets, respectively. Compared with other advanced pose representation methods and multi-stream methods, OFPI achieved state-of-the-art performance on the JHMDB dataset, indicating the utility and potential of this algorithm for skeleton-based action recognition research. Full article
(This article belongs to the Special Issue Dynamics in Neural Networks)
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20 pages, 1343 KiB  
Article
A Dendritic Neuron Model Optimized by Meta-Heuristics with a Power-Law-Distributed Population Interaction Network for Financial Time-Series Forecasting
by Yuxin Zhang, Yifei Yang, Xiaosi Li, Zijing Yuan, Yuki Todo and Haichuan Yang
Mathematics 2023, 11(5), 1251; https://doi.org/10.3390/math11051251 - 04 Mar 2023
Cited by 4 | Viewed by 1694
Abstract
The famous McCulloch–Pitts neuron model has been criticized for being overly simplistic in the long term. At the same time, the dendritic neuron model (DNM) has been shown to be effective in prediction problems, and it accounts for the nonlinear information-processing capacity of [...] Read more.
The famous McCulloch–Pitts neuron model has been criticized for being overly simplistic in the long term. At the same time, the dendritic neuron model (DNM) has been shown to be effective in prediction problems, and it accounts for the nonlinear information-processing capacity of synapses and dendrites. Furthermore, since the classical error back-propagation (BP) algorithm typically experiences problems caused by the overabundance of saddle points and local minima traps, an efficient learning approach for DNMs remains desirable but difficult to implement. In addition to BP, the mainstream DNM-optimization methods include meta-heuristic algorithms (MHAs). However, over the decades, MHAs have developed a large number of different algorithms. How to screen suitable MHAs for optimizing DNMs has become a hot and challenging area of research. In this study, we classify MHAs into different clusters with different population interaction networks (PINs). The performance of DNMs optimized by different clusters of MHAs is tested in the financial time-series-forecasting task. According to the experimental results, the DNM optimized by MHAs with power-law-distributed PINs outperforms the DNM trained based on the BP algorithm. Full article
(This article belongs to the Special Issue Dynamics in Neural Networks)
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16 pages, 1373 KiB  
Article
A Novel Bio-Inspired Motion Direction Detection Mechanism in Binary and Grayscale Background
by Yuxiao Hua, Yuki Todo, Zheng Tang, Sichen Tao, Bin Li and Riku Inoue
Mathematics 2022, 10(20), 3767; https://doi.org/10.3390/math10203767 - 13 Oct 2022
Cited by 1 | Viewed by 1599
Abstract
The visual system plays a vital role in the daily life of humans, as more than 90 percent of the external information received by the human brain throughout the day comes from the visual system. However, how the human brain processes the received [...] Read more.
The visual system plays a vital role in the daily life of humans, as more than 90 percent of the external information received by the human brain throughout the day comes from the visual system. However, how the human brain processes the received visual information remains a mystery. The information received from the external through the visual system can be divided into three main categories, namely, shape features, color features, and motion features. Of these, motion features are considered the key to deciphering the secrets of the visual system due to their independence and importance. In this paper, we propose a novel bio-inspired motion direction detection mechanism using direction-selective ganglion cells to explore the mystery of motion information extraction and analysis. The mechanism proposed in this paper is divided into two parts: local motion direction detection neurons and global motion direction detection neurons; the former is used to extract motion direction information from the local area, while the latter infers global motion direction from the local motion direction information. This mechanism is more consistent with the biological perception of the human natural visual system than the previously proposed model and has a higher biological plausibility and greater versatility. It is worth mentioning that we have overcome the problem in which the previous motion direction detection model could only be applied in the binary background by introducing the horizontal cells. Through the association formed by horizontal cells and bipolar cells, this model can be applied to recognizing problems of motion direction detection on a grayscale background. To further validate the effectiveness of the proposed model, a series of experiments with objects of different sizes, shapes, and positions are conducted by computer simulation. According to the simulation results, this model has been proven to have high accuracy rates regardless of objects’ sizes, shapes, and positions in all experiments. Furthermore, the proposed model is verified to own more stable accuracy rates and stronger noise immunity by comparing it with the recognized superior classical convolutional neural network in a background of different percentage noise. Full article
(This article belongs to the Special Issue Dynamics in Neural Networks)
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24 pages, 7564 KiB  
Article
Novel Synchronization Conditions for the Unified System of Multi-Dimension-Valued Neural Networks
by Jianying Xiao and Yongtao Li
Mathematics 2022, 10(17), 3031; https://doi.org/10.3390/math10173031 - 23 Aug 2022
Cited by 4 | Viewed by 1047
Abstract
This paper discusses the novel synchronization conditions about the unified system of multi-dimension-valued neural networks (USOMDVNN). First of all, the general model of USOMDVNN is successfully set up, mainly on the basis of multidimensional algebra, Kirchhoff current law, and neuronal property. Then, the [...] Read more.
This paper discusses the novel synchronization conditions about the unified system of multi-dimension-valued neural networks (USOMDVNN). First of all, the general model of USOMDVNN is successfully set up, mainly on the basis of multidimensional algebra, Kirchhoff current law, and neuronal property. Then, the concise Lyapunov–Krasovskii functional (LKF) and switching controllers are constructed for the USOMDVNN. Moreover, the new inequalities, whose variables, together with some parameters, are employed in a concise and unified form whose variables can be translated into special ones, such as real, complex, and quaternion. It is worth mentioning that the useful parameters really make some contributions to the construction of the concise LKF, the design of the general controllers, and the acquisition of flexible criteria. Further, we acquire the newer criteria mainly by employing Lyapunov analysis, constructing new LKF, applying two unified inequalities, and designing nonlinear controllers. Particularly, the value of the fixed time is less than the other ones in some existing results, owing to the adjustable parameters. Finally, three multidimensional simulations are presented, to demonstrate the availability and progress of the achieved acquisitions. Full article
(This article belongs to the Special Issue Dynamics in Neural Networks)
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32 pages, 2404 KiB  
Article
A Novel Artificial Visual System for Motion Direction Detection in Grayscale Images
by Sichen Tao, Yuki Todo, Zheng Tang, Bin Li, Zhiming Zhang and Riku Inoue
Mathematics 2022, 10(16), 2975; https://doi.org/10.3390/math10162975 - 17 Aug 2022
Cited by 4 | Viewed by 1427
Abstract
How specific features of the environment are represented in the mammalian brain is an important unexplained mystery in neuroscience. Visual information is considered to be captured most preferentially by the brain. As one of the visual information elements, motion direction in the receptive [...] Read more.
How specific features of the environment are represented in the mammalian brain is an important unexplained mystery in neuroscience. Visual information is considered to be captured most preferentially by the brain. As one of the visual information elements, motion direction in the receptive field is thought to be collected already at the retinal direction-selective ganglion cell (DSGC) layer. However, knowledge of direction-selective (DS) mechanisms in the retina has remained only at a cellular level, and there is a lack of complete direction-sensitivity understanding in the visual system. Previous studies of DS models have been limited to the stage of one-dimensional black-and-white (binary) images or still lack biological rationality. In this paper, we innovatively propose a two-dimensional, eight-directional motion direction detection mechanism for grayscale images called the artificial visual system (AVS). The structure and neuronal functions of this mechanism are highly faithful to neuroscientific perceptions of the mammalian retinal DS pathway, and thus highly biologically reasonable. In particular, by introducing the horizontal contact pathway provided by horizontal cells (HCs) in the retinal inner nuclear layer and forming a functional collaboration with bipolar cells (BCs), the limitation that previous DS models can only recognize object motion directions in binary images is overcome; the proposed model can solve the recognizing problem of object motion directions in grayscale images. Through computer simulation experiments, we verified that AVS is effective and has high detection accuracy, and it is not affected by the shape, size, and location of objects in the receptive field. Its excellent noise immunity was also verified by adding multiple types of noise to the experimental data set. Compared to a classical convolutional neural network (CNN), it was verified that AVS is completely significantly better in terms of effectiveness and noise immunity, and has various advantages such as high interpretability, no need for learning, and easy hardware implementation. In addition, activation characteristics of neurons in AVS are highly consistent with those real in the retinal DS pathway, with strong neurofunctional similarity and brain-like superiority. Moreover, AVS will also provide a novel perspective and approach to understanding and analyzing mechanisms as well as principles of mammalian retinal direction-sensitivity in face of a cognitive bottleneck on the DS pathway that has persisted for nearly 60 years. Full article
(This article belongs to the Special Issue Dynamics in Neural Networks)
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