<title>Studies on using the higher order neural network for pattern recognition and optimization</title>

Abstract

The higher order neural network using for pattern recognition and optimization is studied in this paper and the results in two different aspects have been obtained. < 1 > Theoretically , the capacity formula of the Hopfield Neural Network with the second order weights has been obtained. Compared with the first order network, the capacity of the second order network is about three times greater than that of the first order one and the cost to reach such a efficiency is to add higher order weights . The simulated experiments according to the theory by digital computer are satisfied. < 2 > Theoretically , the method of how to solve the optimization problems, whose energy functions are more general than Lyapunov function , has been put forward at the end of this paper. ABSTRACTThe higher order neural network using for pattern recognition and optimization is studied in this paper and the results in two different aspects have been obtained. < 1 > Theoretically, the capacity formula of the Hopfield Neural Network with the second order weights has been obtained. Compared with the first order network, the capacity of the second order network is about three times greater than that of the first order one and the cost to reach such a efficiency is to add higher order weights .The simulated experiments according to the theory by digital computer are satisfied. < 2 > Theoretically , the method of how to solve the optimization problems , whose energy functions are more general than Lyapunov function , has been put forward at the end of this paper.

Near-optimal parallel distributed data detection for page-oriented optical memories

“…11 depicts a locally connected network of subnets. Each subnet can be thought of as a two-layer nonlinear (8th order) network [57]- [59]. Alternately, each subnet may be considered to be a single piecewise linear perceptron operating on 2 socalled Phi-functions, each of which is one of the 2 possible products of 8 neighboring likelihoods [60].…”