scholarly journals Stability Analysis Based on Caputo-Type Fractional-Order Quantum Neural Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yumin Dong ◽  
Xiang Li ◽  
Wei Liao ◽  
Dong Hou
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Learning Algorithm ◽  
Activation Function ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Sigmoid Function ◽  
Matrix Inequality ◽  
Fractional Quantum ◽  
Quantum Neural Network

In this paper, a quantum neural network with multilayer activation function is proposed by using multilayer Sigmoid function superposition and learning algorithm to adjust quantum interval. On this basis, the quasiuniform stability of fractional quantum neural networks with mixed delays is studied. According to the order of two different cases, the conditions of quasi uniform stability of networks are given by using the techniques of linear matrix inequality analysis, and the sufficiency of the conditions is proved. Finally, the feasibility of the conclusion is verified by experiments.

Relating the Slope of the Activation Function and the Learning Rate Within a Recurrent Neural Network

1999 ◽  
Vol 11 (5) ◽  
pp. 1069-1077 ◽  
Author(s):  
Danilo P. Mandic ◽  
Jonathon A. Chambers
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Recurrent Neural Network ◽  
Recurrent Neural Networks ◽  
Degrees Of Freedom ◽  
Learning Algorithm ◽  
Activation Function ◽  
Learning Rate ◽  
Optimization Task ◽  
Nonlinear Activation Function

A relationship between the learning rate η in the learning algorithm, and the slope β in the nonlinear activation function, for a class of recurrent neural networks (RNNs) trained by the real-time recurrent learning algorithm is provided. It is shown that an arbitrary RNN can be obtained via the referent RNN, with some deterministic rules imposed on its weights and the learning rate. Such relationships reduce the number of degrees of freedom when solving the nonlinear optimization task of finding the optimal RNN parameters.

EXPONENTIAL STABILITY FOR STOCHASTIC NEURAL NETWORKS OF NEUTRAL TYPE WITH IMPULSIVE EFFECTS

2010 ◽  
Vol 24 (11) ◽  
pp. 1099-1110 ◽  
Author(s):  
RATHINASAMY SAKTHIVEL ◽  
R. SAMIDURAI ◽  
S. MARSHAL ANTHONI
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Stochastic Analysis ◽  
Lyapunov Functional ◽  
Neutral Type ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Matrix Inequality

This paper is concerned with the exponential stability of stochastic neural networks of neutral type with impulsive effects. By employing the Lyapunov functional and stochastic analysis, a new stability criterion for the stochastic neural network is derived in terms of linear matrix inequality. A numerical example is provided to show the effectiveness and applicability of the obtained result.

scholarly journals Neutrosophic Compound Orthogonal Neural Network and Its Applications in Neutrosophic Function Approximation

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 147 ◽  
Author(s):  
Jun Ye ◽  
Wenhua Cui
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Learning Algorithm ◽  
Learning Performance ◽  
Uncertain Information ◽  
Sigmoid Function ◽  
Nonlinear Functions ◽  
Single Output ◽  
Classification Pattern ◽  
Hidden Layer

Neural networks are powerful universal approximation tools. They have been utilized for functions/data approximation, classification, pattern recognition, as well as their various applications. Uncertain or interval values result from the incompleteness of measurements, human observation and estimations in the real world. Thus, a neutrosophic number (NsN) can represent both certain and uncertain information in an indeterminate setting and imply a changeable interval depending on its indeterminate ranges. In NsN settings, however, existing interval neural networks cannot deal with uncertain problems with NsNs. Therefore, this original study proposes a neutrosophic compound orthogonal neural network (NCONN) for the first time, containing the NsN weight values, NsN input and output, and hidden layer neutrosophic neuron functions, to approximate neutrosophic functions/NsN data. In the proposed NCONN model, single input and single output neurons are the transmission notes of NsN data and hidden layer neutrosophic neurons are constructed by the compound functions of both the Chebyshev neutrosophic orthogonal polynomial and the neutrosophic sigmoid function. In addition, illustrative and actual examples are provided to verify the effectiveness and learning performance of the proposed NCONN model for approximating neutrosophic nonlinear functions and NsN data. The contribution of this study is that the proposed NCONN can handle the approximation problems of neutrosophic nonlinear functions and NsN data. However, the main advantage is that the proposed NCONN implies a simple learning algorithm, higher speed learning convergence, and higher learning accuracy in indeterminate/NsN environments.

Use of Binary Sigmoid Function And Linear Identity In Artificial Neural Networks For Forecasting Population Density

2017 ◽  
Vol 1 (1) ◽  
pp. 43 ◽  
Author(s):  
Anjar Wanto ◽  
Agus Perdana Windarto ◽  
Dedy Hartama ◽  
Iin Parlina
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Network ◽  
Population Density ◽  
Network Architecture ◽  
Activation Function ◽  
Sigmoid Function ◽  
Backpropagation Algorithm ◽  
Architecture Model ◽  
Artificial Neural

Artificial Neural Network (ANN) is often used to solve forecasting cases. As in this study. The artificial neural network used is with backpropagation algorithm. The study focused on cases concerning overcrowding forecasting based District in Simalungun in Indonesia in 2010-2015. The data source comes from the Central Bureau of Statistics of Simalungun Regency. The population density forecasting its future will be processed using backpropagation algorithm focused on binary sigmoid function (logsig) and a linear function of identity (purelin) with 5 network architecture model used the 3-5-1, 3-10-1, 3-5 -10-1, 3-5-15-1 and 3-10-15-1. Results from 5 to architectural models using Neural Networks Backpropagation with binary sigmoid function and identity functions vary greatly, but the best is 3-5-1 models with an accuracy of 94%, MSE, and the epoch 0.0025448 6843 iterations. Thus, the use of binary sigmoid activation function (logsig) and the identity function (purelin) on Backpropagation Neural Networks for forecasting the population density is very good, as evidenced by the high accuracy results achieved.

Exponential Stability of Periodic Solution for Impulsive Memristor-Based Cohen–Grossberg Neural Networks with Mixed Delays

2017 ◽  
Vol 31 (07) ◽  
pp. 1750022 ◽  
Author(s):  
Jiqiang Feng ◽  
Qiang Ma ◽  
Sitian Qin
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Sensor Arrays ◽  
Activation Function ◽  
Contraction Mapping Principle ◽  
Mixed Delays ◽  
The Neural Network ◽  
Inequality Technique

Memristor, as the future of artificial intelligence, has been widely used in pattern recognition or signal processing from sensor arrays. Memristor-based recurrent neural network (MRNN) is an ideal model to mimic the functionalities of the human brain due to the physical properties of memristor. In this paper, the periodicity for memristor-based Cohen–Grossberg neural networks (MCGNNs) is studied. The neural network (NN) considered in this paper is based on the memristor and involves time-varying delays, distributed delays and impulsive effects. The boundedness and monotonicity of the activation function are not assumed. By some inequality technique and contraction mapping principle, we prove the existence, uniqueness and exponential stability of periodic solution for MCGNNs. Finally, some numeral examples and comparisons are provided to illustrate the validation of our results.

scholarly journals Synchronization of Switched Complex Bipartite Neural Networks with Infinite Distributed Delays and Derivative Coupling

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
Qiuxiang Bian ◽  
Jinde Cao ◽  
Jie Wu ◽  
Hongxing Yao ◽  
Tingfang Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lmi Approach ◽  
Derivative Coupling ◽  
Infinite Distributed Delays ◽  
Theoretical Results

A new model of switched complex bipartite neural network (SCBNN) with infinite distributed delays and derivative coupling is established. Using linear matrix inequality (LMI) approach, some synchronization criteria are proposed to ensure the synchronization between two SCBNNs by constructing effective controllers. Some numerical simulations are provided to illustrate the effectiveness of the theoretical results obtained in this paper.

SYNCHRONIZATION OF NEURAL NETWORKS OF NEUTRAL TYPE WITH STOCHASTIC PERTURBATION

2009 ◽  
Vol 23 (14) ◽  
pp. 1743-1751 ◽  
Author(s):  
JU H. PARK ◽  
O. M. KWON
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Lyapunov Method ◽  
Controller Design ◽  
Neutral Type ◽  
Stochastic Perturbation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Existence Criterion

In this letter, the problem of feedback controller design to achieve synchronization for neural network of neutral type with stochastic perturbation is considered. Based on Lyapunov method and LMI (linear matrix inequality) framework, the goal of this letter is to derive an existence criterion of the controller for the synchronization between master and response networks.

SCORING MODELING BASED ON NEURAL NETWORKS FOR DETERMINING A BANK BORROWER'S RATING

2020 ◽  
Vol 2020 (10) ◽  
pp. 54-62
Author(s):  
Oleksii VASYLIEV ◽  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Statistical Data ◽  
Activation Function ◽  
Decision Making Process ◽  
Neural Network Architecture ◽  
Acceptable Accuracy ◽  
The Neural Network ◽  
Sigmoid Activation Function

The problem of applying neural networks to calculate ratings used in banking in the decision-making process on granting or not granting loans to borrowers is considered. The task is to determine the rating function of the borrower based on a set of statistical data on the effectiveness of loans provided by the bank. When constructing a regression model to calculate the rating function, it is necessary to know its general form. If so, the task is to calculate the parameters that are included in the expression for the rating function. In contrast to this approach, in the case of using neural networks, there is no need to specify the general form for the rating function. Instead, certain neural network architecture is chosen and parameters are calculated for it on the basis of statistical data. Importantly, the same neural network architecture can be used to process different sets of statistical data. The disadvantages of using neural networks include the need to calculate a large number of parameters. There is also no universal algorithm that would determine the optimal neural network architecture. As an example of the use of neural networks to determine the borrower's rating, a model system is considered, in which the borrower's rating is determined by a known non-analytical rating function. A neural network with two inner layers, which contain, respectively, three and two neurons and have a sigmoid activation function, is used for modeling. It is shown that the use of the neural network allows restoring the borrower's rating function with quite acceptable accuracy.

scholarly journals An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chuangxia Huang ◽  
Hanfeng Kuang ◽  
Xiaohong Chen ◽  
Fenghua Wen
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Ultimate Boundedness ◽  
Globally Exponential Stability ◽  
Average Dwell Time Method ◽  
Uniformly Ultimate Boundedness

This paper considers the dynamics of switched cellular neural networks (CNNs) with mixed delays. With the help of the Lyapnnov function combined with the average dwell time method and linear matrix inequalities (LMIs) technique, some novel sufficient conditions on the issue of the uniformly ultimate boundedness, the existence of an attractor, and the globally exponential stability for CNN are given. The provided conditions are expressed in terms of LMI, which can be easily checked by the effective LMI toolbox in Matlab in practice.

scholarly journals A New Robust Training Law for Dynamic Neural Networks with External Disturbance: An LMI Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Choon Ki Ahn
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Exponential Stability ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Lmi Approach ◽  
Dynamic Neural Networks ◽  
Numerical Examples

A new robust training law, which is called an input/output-to-state stable training law (IOSSTL), is proposed for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the IOSSTL is presented to not only guarantee exponential stability but also reduce the effect of an external disturbance. It is shown that the IOSSTL can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. Numerical examples are presented to demonstrate the validity of the proposed IOSSTL.

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