Neural Networks Theory

Neural Networks Theory

Language: English

Pages: 396

ISBN: 3642080065

Format: PDF / Kindle (mobi) / ePub


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.

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equivalent capacity increase in the process of problem solving. Type 3. This type of computer includes single-processor computers (large-scale computers, mini computers or personal computers) equipped with array processors. Computers of DAP, IBM with FPS, STARAN, etc. -types can serve as examples. Type 4. Neural computers with hardware/software emulation of neural algorithms on the basis of type-3-computers. Type 5. Computers of different classes, beginning with super-computers up to

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neurons with Continuum Input Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuum of Neurons in the Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuum Neurons in the Layer and Discrete Feature Set . . . . . . . . . . . . . . . . . . . . . . . . . Classification of

where gives the following equation for the neural network optimal model: (6.17) The Langrangian multiplier λ is determined by (6.16), (6.17). The limitation in the form of a given average risk function component has the form (6.18) If one were to denote then the expression for the neural network optimal model is or in the other form, The multiplier λ is determined by (6.14), (6.18). Neural network of type 6. The pattern recognition system for K pattern classes and a continuum of solution

arbitrary open-loop neural network structure (arbitrary divisional surface) according to p. 7.1 for b1 = b2 = 1 and c1 = c2 = 1, one obtains where 7.3 · About Selection of the Secondary Optimization Functional in the “Adalin” System Here functional α 2g is proportional to the average risk function under the arbitrary neural network structure (two pattern classes, two solutions) and aforementioned limitations upon matrix L. 9. The consideration of the aforementioned functionals of secondary

. . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 13 Synthesis of Multilayer Neural Networks with Flexible Structure . . . . . . . . . . . . . . 13.1 Sequential Learning Algorithm for the First Neuron Layer of the Multilayer Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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