A weighting method for hopfield neural networks with discrete weights

Abstract

AbstractThe Hopfield neural network is expected to act as the engine to solve the association problem or the optimization problem. In the associative processing using the Hopfield neural network, it is necessary that the precalculated weights should be memorized in the neural network. In the Hopfield neural network, however, there must be m2 weights, where m is the number of neurons. In other words, a tremendous memory capacity is required when m is increased. the weight can be stored either by an analog memory or a digital memory. the analog meomory, however, has problems of error and the decay of the memorized content. Then, digital memory must be used. In this case, the required number of memory elements is m2 × (data bits) and the hardware complexity increases in proportion to the number of data bits.Another point is that the hardware, such as the multiplier of the synapse, becomes more complicated with the increase of the number of bits. A remedy for those problems may be to reduce the number of bits for the weight. When a digital code of some 2 bits is used to represent the weight, for example, the memory capacity for storage can be reduced and the multiplication at the synapse can be simplified. One of the important issues then is how to determine the weight when the number of bits for the wieght is reduced. Since it is difficult to approximate the weight by a continuous variable, it is desirable to realize an efficint method which is differrent from the existing method of weight determination.With the foregoing as background, this paper discusses the weight determination method for the case where the weight determination method for the case where the weight can take only a few number of discrete values. In the proposed method, the evaluation function for the weight is examined and the weights are determined by optimization using an algorithm, which is an application of the branch‐and‐bound method. It is shown by simulation that a high associative ability is realized by the association processing using the weights obtained by the proposed method. Future applications can be expected.