Accession Number:

ADA238035

Title:

On the Interpolation Properties of Feedforward Layered Neural Networks.

Descriptive Note:

Final rept. Oct 1988-Jun 1989,

Corporate Author:

NAVAL WEAPONS CENTER CHINA LAKE CA

Personal Author(s):

Report Date:

1990-10-01

Pagination or Media Count:

34.0

Abstract:

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.

Subject Categories:

  • Numerical Mathematics
  • Cybernetics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE