Correlation Between Eigenvalue Spectra and Dynamics of Neural Networks

2009 ◽  
Vol 21 (10) ◽  
pp. 2931-2941 ◽  
Author(s):  
Qingguo Zhou ◽  
Tao Jin ◽  
Hong Zhao
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fixed Point ◽  
The Other ◽  
Associative Memories ◽  
Eigenvalue Spectrum ◽  
Memory Phase ◽  
Dynamical Properties ◽  
Almost All ◽  
Random Background

This letter presents a study of the correlation between the eigenvalue spectra of synaptic matrices and the dynamical properties of asymmetric neural networks with associative memories. For this type of neural network, it was found that there are essentially two different dynamical phases: the chaos phase, with almost all trajectories converging to a single chaotic attractor, and the memory phase, with almost all trajectories being attracted toward fixed-point attractors acting as memories. We found that if a neural network is designed in the chaos phase, the eigenvalue spectrum of its synaptic matrix behaves like that of a random matrix (i.e., all eigenvalues lie uniformly distributed within a circle in the complex plan), and if it is designed in the memory phase, the eigenvalue spectrum will split into two parts: one part corresponds to a random background, the other part equal in number to the memory attractors. The mechanism for these phenomena is discussed in this letter.

N. Belknap's Four-Valued Logic, Belknap Computer and New Proximity Functions for Comparing Discrete Objects

2021 ◽  
Vol 1 (2 (6)) ◽  
Author(s):  
Valerii Dmitrienko ◽  
Sergey Leonov ◽  
Mykola Mezentsev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
The Other ◽  
Proximity Function ◽  
Input Information ◽  
Proximity Measures ◽  
The One ◽  
True Values

The idea of ​​Belknap's four-valued logic is that modern computers should function normally not only with the true values ​​of the input information, but also under the conditions of inconsistency and incompleteness of true failures. Belknap's logic introduces four true values: T (true - true), F (false - false), N (none - nobody, nothing, none), B (both - the two, not only the one but also the other).  For ease of work with these true values, the following designations are introduced: (1, 0, n, b). Belknap's logic can be used to obtain estimates of proximity measures for discrete objects, for which the functions Jaccard and Needhem, Russel and Rao, Sokal and Michener, Hamming, etc. are used. In this case, it becomes possible to assess the proximity, recognition and classification of objects in conditions of uncertainty when the true values ​​are taken from the set (1, 0, n, b). Based on the architecture of the Hamming neural network, neural networks have been developed that allow calculating the distances between objects described using true values ​​(1, 0, n, b). Keywords: four-valued Belknap logic, Belknap computer, proximity assessment, recognition and classification, proximity function, neural network.

A Neural Networks Pruning and Data Fusion Based Intrusion Detection Model

2014 ◽  
Vol 651-653 ◽  
pp. 1772-1775
Author(s):  
Wei Gong
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Intrusion Detection ◽  
Data Fusion ◽  
Input Data ◽  
The Other ◽  
Pruning Algorithm ◽  
Detection Model ◽  
Process Ability

The abilities of summarization, learning and self-fitting and inner-parallel computing make artificial neural networks suitable for intrusion detection. On the other hand, data fusion based IDS has been used to solve the problem of distorting rate and failing-to-report rate and improve its performance. However, multi-sensor input-data makes the IDS lose its efficiency. The research of neural network based data fusion IDS tries to combine the strong process ability of neural network with the advantages of data fusion IDS. A neural network is designed to realize the data fusion and intrusion analysis and Pruning algorithm of neural networks is used for filtering information from multi-sensors. In the process of intrusion analysis pruning algorithm of neural networks is used for filtering information from multi-sensors so as to increase its performance and save the bandwidth of networks.

Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria

2011 ◽  
pp. 331-357 ◽  
Author(s):  
Daniela Danciu
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
Time Delay ◽  
Dynamical Systems ◽  
Qualitative Properties ◽  
The Neural Network ◽  
The Neural Networks ◽  
Global Asymptotics ◽  
Dynamical Properties

Neural networks—both natural and artificial, are characterized by two kinds of dynamics. The first one is concerned with what we would call “learning dynamics”. The second one is the intrinsic dynamics of the neural network viewed as a dynamical system after the weights have been established via learning. The chapter deals with the second kind of dynamics. More precisely, since the emergent computational capabilities of a recurrent neural network can be achieved provided it has suitable dynamical properties when viewed as a system with several equilibria, the chapter deals with those qualitative properties connected to the achievement of such dynamical properties as global asymptotics and gradient-like behavior. In the case of the neural networks with delays, these aspects are reformulated in accordance with the state of the art of the theory of time delay dynamical systems.

Structured Pyramidal Neural Networks

2018 ◽  
Vol 28 (05) ◽  
pp. 1750021 ◽  
Author(s):  
Alessandra M. Soares ◽  
Bruno J. T. Fernandes ◽  
Carmelo J. A. Bastos-Filho
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Processing Time ◽  
Receptive Fields ◽  
Memory Capacity ◽  
The Other ◽  
Support Vector ◽  
Proposed Model ◽  
Novel Method ◽  
Original Approach

The Pyramidal Neural Networks (PNN) are an example of a successful recently proposed model inspired by the human visual system and deep learning theory. PNNs are applied to computer vision and based on the concept of receptive fields. This paper proposes a variation of PNN, named here as Structured Pyramidal Neural Network (SPNN). SPNN has self-adaptive variable receptive fields, while the original PNNs rely on the same size for the fields of all neurons, which limits the model since it is not possible to put more computing resources in a particular region of the image. Another limitation of the original approach is the need to define values for a reasonable number of parameters, which can turn difficult the application of PNNs in contexts in which the user does not have experience. On the other hand, SPNN has a fewer number of parameters. Its structure is determined using a novel method with Delaunay Triangulation and k-means clustering. SPNN achieved better results than PNNs and similar performance when compared to Convolutional Neural Network (CNN) and Support Vector Machine (SVM), but using lower memory capacity and processing time.

MEMRISTOR CELLULAR AUTOMATA AND MEMRISTOR DISCRETE-TIME CELLULAR NEURAL NETWORKS

2009 ◽  
Vol 19 (11) ◽  
pp. 3605-3656 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Cellular Automaton ◽  
Discrete Time ◽  
Cellular Neural Network ◽  
Brain Functions ◽  
Rsa Algorithm ◽  
Logical Operations ◽  
Almost All ◽  
Higher Brain Functions

In this paper, we design a cellular automaton and a discrete-time cellular neural network (DTCNN) using nonlinear passive memristors. They can perform a number of applications, such as logical operations, image processing operations, complex behaviors, higher brain functions, RSA algorithm, etc. By modifying the characteristics of nonlinear memristors, the memristor DTCNN can perform almost all functions of memristor cellular automaton. Furthermore, it can perform more than one function at the same time, that is, it allows multitasking.

scholarly journals Dynamical Properties of Discrete-Time Background Neural Networks with Uniform Firing Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Min Wan ◽  
Jianping Gou ◽  
Desong Wang ◽  
Xiaoming Wang
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Firing Rate ◽  
Lyapunov Exponents ◽  
Discrete Time ◽  
Invariant Set ◽  
Bifurcation And Chaos ◽  
Dynamical Properties ◽  
Background Input

The dynamics of a discrete-time background network with uniform firing rate and background input is investigated. The conditions for stability are firstly derived. An invariant set is then obtained so that the nondivergence of the network can be guaranteed. In the invariant set, it is proved that all trajectories of the network starting from any nonnegative value will converge to a fixed point under some conditions. In addition, bifurcation and chaos are discussed. It is shown that the network can engender bifurcation and chaos with the increase of background input. The computations of Lyapunov exponents confirm the chaotic behaviors.

AUTOASSOCIATIVE MEMORY DESIGN USING INTERCONNECTED GENERALIZED BRAIN-STATE-IN-A-BOX NEURAL NETWORKS

2005 ◽  
Vol 15 (03) ◽  
pp. 181-196 ◽  
Author(s):  
CHEOLHWAN OH ◽  
STANISLAW H. ŻAK ◽  
GUISHENG ZHAI
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Brain State ◽  
Stability Conditions ◽  
Network Architectures ◽  
Associative Memories ◽  
Matrix Inequalities ◽  
Memory Design

A class of interconnected neural networks composed of generalized Brain-State-in-a-Box (gBSB) neural subnetworks is considered. Interconnected gBSB neural network architectures are proposed along with their stability conditions. The design of the interconnected neural networks is reduced to the problem of solving linear matrix inequalities (LMIs) to determine the interconnection parameters. A method for solving LMIs is devised generating the solutions that, in general, are further away from zero than the corresponding solutions obtained using MATLAB's LMI toolbox, thus resulting in stronger interconnections between the subnetworks. The proposed architectures are then used to construct neural associative memories. Simulations are performed to illustrate the results obtained.

Weight to Vision Neural Network Information Processing Influence Research

2012 ◽  
Vol 605-607 ◽  
pp. 2131-2136
Author(s):  
Chun Hua Yin ◽  
Jia Wei Chen ◽  
Lei Chen
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Information Processing ◽  
The Other ◽  
Chinese Characters ◽  
Initial Weight ◽  
Initial Value ◽  
Network Information ◽  
The Neural Network ◽  
Weight Distributions

Many factors influence vision neural network information processing process, for example: Signal initial value, weight, time and number of learning. This paper discussed the importance of weight in vision neural network information processing process. Different weight values can cause different results in neural networks learning. We structure a vision neural network model with three layers based on synapse dynamics at first. Then we change the weights of the vision neural network model’s to make the three layers a neural network of learning Chinese characters. At last we change the initial weight distribution to simulate the neural network of process of the learning Chinese words. Two results are produced. One is that weight plays a very important role in vision neural networks learning, the other is that different initial weight distributions have different results in vision neural networks learning.

scholarly journals Fuzzy Clustering Neural Networks for Real-Time Odor Recognition System

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Bekir Karlık ◽  
Kemal Yüksek
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Real Time ◽  
Fuzzy Clustering ◽  
Input Data ◽  
Recognition System ◽  
Neural System ◽  
The Other ◽  
Odor Recognition ◽  
Recognition Probability

The aim of this study is to develop a novel fuzzy clustering neural network (FCNN) algorithm as pattern classifiers for real-time odor recognition system. In this type of FCNN, the input neurons activations are derived through fuzzy c mean clustering of the input data, so that the neural system could deal with the statistics of the measurement error directly. Then the performance of FCNN network is compared with the other network which is well-known algorithm, named multilayer perceptron (MLP), for the same odor recognition system. Experimental results show that both FCNN and MLP provided high recognition probability in determining various learn categories of odors, however, the FCNN neural system has better ability to recognize odors more than the MLP network.

scholarly journals Exploiting Manipulated Region in an Image using Integrated Convolution Neural Network and LRW Segmentation Features

2019 ◽  
Vol 8 (3) ◽  
pp. 5488-5495
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Random Walk ◽  
Digital Images ◽  
Convolution Neural Network ◽  
The Other ◽  
Final Decision ◽  
Convolution Neural Networks ◽  
Other Hand

To locate the manipulated region in digital images, we suggest to use Convolution Neural Networks and the segmentation based analysis. A unified CNN architecture is designed with set of training procedures for sampled training patches. Tampering map can be generated for the above said Convolution Neural Networks with the help of tampering detectors. In the other hand, a segmentation using lazy random walk based method is second-hand to generate the tampering chance map, finally integrate the maps and generate the final decision map. This can help to locate the manipulated region accurately. Experiments are conducted using the various datasets to prove the efficiency of the suggest method.

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