Neural Networks Theory
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This book, written by a leader in neural network theory in Russia, uses mathematical methods in combination with complexity theory, nonlinear dynamics and optimization. It details more than 40 years of Soviet and Russian neural network research and presents a systematized methodology of neural networks synthesis. The theory is expansive: covering not just traditional topics such as network architecture but also neural continua in function spaces as well.
Three-layer perceptron with the arbitrary connections in the first layer. An excessive number of elements in the first layer were taken. In this case, a function implemented by the neural network is quasi-distributed along the structure. Neural computers are the first example of an analytically calculated computer structure rather than an empirically designed structure based on some subjective views about the problem and the elemental base. The neural computer implementation methods are mainly.
Parallelism. 3 4 I · Introduction The first type of parallelism is efficient for the program that is executed many times with different parameters. It is desirable in this case to represent this program with a set of independent sub-problems (each neuron with its own parameters) and to perform the sub-problems in parallel on different processors. The array processor for floating-point multiplication is an example of algorithmic parallelism implementation. Organization of parallel processing.
Layers is selected to be sufficient for the provision of the required problem solving quality. The number of layers is desired to be minimal in order to decrease the problem solving time. This book is dedicated to the description of neural networks with different structures. The objective conditions for the transfer from Boolean to the threshold basis in computer engineering are given. The main types of the threshold elements such as neuron analogues are described. The reasons for investigations.
Dimensionality N can be divided by H1 hyperplanes. The maximum number of regions ΨNH1 is determined according to the following recurrent Eq. (3.1): (3.1) or in the non-recurrent form It is implied that Cts = 0 if t < s. The following expressions can be derived from (3.1): (3.2) and (3.3) 3.3 Calculation of Upper and Lower Estimation of the Number of Regions Let us consider a multidimensional variant (i = 1,…,N) of the neural network with the structure shown in Fig. 3.3. The number of areas.
Of the Second Order Derivatives The multilayer neural network adjustment procedure (8.1) provides only the local extremum of the optimization functional. The initial values of the adjustable parameters must be given randomly in the interval determined by some physical arguments. In this case, the full adjustment algorithm of the multilayer neural network must consist of the η0-volume set of injection stages of random initial conditions, the following stages of adjustment (8.1) and the stage of.