Optimization with Artificial Neural Network Systems: A Mapping Principle and a Comparison to Gradient Based Methods

Part of Neural Information Processing Systems 0 (NIPS 1987)

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Harrison Leong


General formulae for mapping optimization problems into systems of ordinary differential

equations associated with artificial neural networks are presented. A comparison is made to optim(cid:173) ization using gradient-search methods. The perfonnance measure is the settling time from an initial state to a target state. A simple analytical example illustrates a situation where dynamical systems representing artificial neural network methods would settle faster than those representing gradient(cid:173) search. Settling time was investigated for a more complicated optimization problem using com(cid:173) puter simulations. The problem was a simplified version of a problem in medical imaging: deter(cid:173) mining loci of cerebral activity from electromagnetic measurements at the scalp. The simulations showed that gradient based systems typically settled 50 to 100 times faster than systems based on current neural network optimization methods.