Neural Networks: An Introduction by Professor Dr. Berndt Müller, Dr. Joachim Reinhardt, Michael

By Professor Dr. Berndt Müller, Dr. Joachim Reinhardt, Michael T. Strickland (auth.)

Neural Networks The ideas of neural-network versions and methods of parallel disbursed processing are comprehensively offered in a three-step process: - After a short evaluation of the neural constitution of the mind and the historical past of neural-network modeling, the reader is brought to associative reminiscence, preceptrons, feature-sensitive networks, studying suggestions, and useful functions. - the second one half covers extra complicated topics corresponding to the statistical physics of spin glasses, the mean-field conception of the Hopfield version, and the "space of interactions" method of the garage means of neural networks. - within the self-contained ultimate half, seven courses that offer functional demonstrations of neural-network versions and their studying recommendations are mentioned. The software program is incorporated on a three 1/2-inch MS-DOS diskette. The resource code will be transformed utilizing Borland's TURBO-C 2.0 compiler, the Microsoft C compiler (5.0), or appropriate compilers.

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Here we shall not pursue this line of research further, since it is primarily of biological interest. 3 General Literature on Neural Network Models For further reading we have listed several monographs which contain a more comprehensive presentation of the subject or emphasize different aspects of this rapidly developing research field. Two classic monographs are the book of Kohonen [K084] , and the two volumes by the PDP research group on parallel distributed processing [PDP86] . The textbooks of Hertz, Krogh, and Palmer [He91] and Haykin [Ha94b] provide excellent overviews of the subject material, and the more hands-on programming books of Masters [Ma94c] and Freeman [Fr94] give practical advice most other texts lack.

3. Solutions of the equation x = tanh(jJx) for jJ < 1 (left) and jJ > 1 (right). In order to find out which solution is realized, we must check for stability against small fluctuations. The condition for a stable solution is that the reaction of the mean orientation of the spin against a small deviation 8(s) from the solution be smaller than the deviation itself: 8[tanh(fJ(s))] = ota~~~(s)) 8(s) < 8(s) . 11) From the graphical representation (Fig. 12) We have thus found the following important result: at high temperatures T > 1 the fluctuations dominate and the network does not have a preferred configuration; at low temperatures T < 1 the network spontaneously settles either into a preferentially active (So > 0) or into a preferentially resting (So < 0) state.

The energy of the configuration rises in proportion to the extent of its deviation from the stored pattern: 1 2 (P - 1) =E[O""J+2n- 2n2 N . 22) The memorized patterns are therefore (at least local) minima of the energy functional E[sJ. A more detailed investigation shows that the energy functional has, in addition, infinitely many other local minima. However, all these spurious minima are less pronounced than those given by the stored patterns O"r; hence these correspond to global minima of the energy surface E[s], at least for moderate values of the parameter a = piN, which indicates the degree of utilization of storage capacity.

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