Abstract
It is well known that artificial neural nets can be used as approximators of any continuous functions to any desired degree and therefore be used, e.g., in high-speed, real-time process control. Nevertheless, for a given application and a given network architecture, the nontrivial task remains to determine the necessary number of neurons and the necessary accuracy (number of bits) per weight for a satisfactory operation which are critical issues in VLSI and computer implementations of nontrivial tasks. In this paper the accuracy of the weights and the number of neurons are seen as general system parameters which determine the maximal approximation error by the absolute amount and the relative distribution of information contained in the network. We define as the “error-bounded network descriptional complexity” the minimal number of bits for a class of approximation networks which show a certain approximation error and achieve the conditions for this goal by the new principle of “optimal information distribution.” For two examples, a simple linear approximation of a nonlinear, quadratic function and a nonlinear approximation of the inverse kinematic transformation used in robot manipulator control, the principle of optimal information distribution gives the optimal number of neurons and the resolutions of the variables, i.e., the minimal amount of storage for the neural net.
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