Depth efficient neural networks for division and related problems

An artificial neural network (ANN) is commonly modeled by a threshold circuit, a network of interconnected processing units called linear threshold gates. It is shown that ANNs can be much more powerful than traditional logic circuits, assuming that each threshold gate can be built with a cost that is comparable to that of AND/OR logic gates. In particular, the main results indicate that powering and division can be computed by polynomial-size ANNs of depth 4, and multiple product can be computed by polynomial-size ANNs of depth 5. Moreover, using the techniques developed, a previous result can be improved by showing that the sorting of n n-bit numbers can be carried out in a depth-3 polynomial-size ANN. Furthermore, it is shown that the sorting network is optimal in depth