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The 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 the the pre-calculated 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 memory, 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 numbner 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 simplified. One of the important issues then is how to determine the weight when the number of bits for the weight is reduced. Since it is difficult to approximate the weight by a continuous variable, it is desirable to realize an efficient method which is different from the existing method of weight determination. With the foregoing as backgroun, this paper discusses 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 weighs obtained by the proposed method. Future applications can be expected. [ABSTRACT FROM AUTHOR]

Neural networks have attracted attention due to their capability to perform nonlinear function approximation. In this paper, in order to better understand this capability, a new theorem on an integral transform was derived by applying ridge functions to neural networks. From the theorem, it is possible to obtain approximation bounds which clarify the quantitative relationship between the function approximation accuracy and the number of nodes in the hidden layer. The theorem indicates that the approximation accuracy depends on the smoothness of the target function. Furthermore, the theorem also shows that this type of approximation method differs from usual methods and is able to escape the so-called ‘curse of dimensionality,’ in which the approximation accuracy depends strongly of the input dimension of the function and deteriorates exponentially. [ABSTRACT FROM AUTHOR]