On the training of neural networks using neurons McCulloch - Pitts, by selective Monte Carlo

Mazurov M.E.

REU named after G.V. Plekhanov

Education multilayer neural network using neurons McCulloch - Pitts, reduces to the calculation of weight coefficients using the recursive transformation, where - the input signal for subsequent -th layer () -th layer; - the matrix of weighting factors; - function characterizing the non-linear transformation threshold; - the threshold value for the i-th layer. The matrices are computed for each th layer network using iterative procedures:, where - the increment weights for the iteration number t; - computation error. When. Numerous iterative procedures of different authors: Rosenbluth procedures Widrow, Hebb, back-propagation method errors and others. Instead, an iterative method for determining weighting coefficients in this study suggested their presence by selective Monte Carlo method. According to the proposed method produced a selective determination of random numbers - weighting coefficients in accordance with the codewords of the input signals. The zero value codeword is assigned a random number in the range around zero, unity in the codeword is assigned a weighting value in the range of random numbers near the center of 1. 7. Matlab software was used to generate random numbers to obtain random numbers from an arbitrary range [a, b] has been used as operator + (ba) * rand. Formation of selective characteristics of random numbers produced by the sensor code combinations of input signals, as described above. As an example, detection of numbers 0 10 were considered, 1, ..., 9 for 4x6 screen. Each of the 10 digits corresponding to a sequence of 24 zeros and ones, discrimination is implemented with a single-layer neural network neurons ten registering McCulloch - Pitts. The total number of weighting factors equal to 240. In calculating the number of realizations of random numbers with uniform distribution varied within (1-200000). When using an iterative procedure for calculating weighting coefficients duration calculation order of magnitude greater.

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