Orthogonal considerations in the design of neural networks for function approximation
Résumé
Two problems occur in the design of feedforward neural networks: the choice of the optimal architecture and the initialization. Generally, input and output data of a system (or a function) are measured and recorded. Then, experimenters wish to design a neural network to map exactly these output values. By formulating this problem as a continuous approximation problem, this paper shows that the use of orthogonal functions is a partial optimization in the choice of hidden functions. Parameters initialization is obtained by using the knowledge of input and output data in the calculation of a discrete approximation. The hidden weights are found by constructing orthogonal directions on which the input values are represented. The pseudo inverse is used to determine output weights such that the Euclidean distances between neural responses and output values are minimized.
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