On the Interpolation Properties of Feedforward Layered Neural Networks.
Final rept. Oct 1988-Jun 1989,
NAVAL WEAPONS CENTER CHINA LAKE CA
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The characterization of the interconnection weights of an L layered feedforward neural net that interpolates through a set of points is considered. A closed form expression for the last layer of weights of a net that interpolates through m sub L - 1 1 points is derived in terms of the points of interpolation. These weights are a function of all the weights in the preceding layers which may be chosen at random, and m sub L -1 is the number of neurons in the layer preceding the output layer. Another method for determining all the weights of a net with only two layers of weights is also presented. This method produces a transfer function that interpolates through m sub o 1 points or less, where m sub o is the number of inputs to the net. The norm of the Jacobian matrix of the transfer function at the interpolation points is introduced as a measure of the sensitivity of the transfer function to perturbations in the inputs of the interpolation points. The points suggest that small weights are required for low sensitivity.
- Numerical Mathematics