Abstract

An optical implementation of the Hopfield model of neural nets may offer advantages over a microelectronic implementation because of the parallelism and massive interconnectivity of optical systems. As the number of stored patterns increases, the elements of the memory or the synaptic matrix will assume values spread over a wider range. This means wider range of grey levels in the optical mask required. For ease of optical implementation, quantization into a bipolar binary (BB) mask or even into a unipolar binary (UB) mask would be desirable. We examine the use of UB masks with adaptive thresholding and a smooth or graded neuron response. For the UB mask a nonzero thresholding value must be adopted. Since the given information is contained in bits of zeros and ones, one-half of the input energy serves quite well as an adaptive sharp thresholding level. As each iteration proceeds, the weighted projection of the current iterate is applied to an adaptive sharp thresholding unit. The result is multiplied by a relaxation parameter, of value < 1, and is combined with previous iterate and is finally limited to [0,1]. In this way we realize a smooth transition of states of the neural net effectively. The smooth transition method is also related to relaxation techniques used in solving systems of linear equations. Results of digital simulation and experiment are presented for a 32 neuron system. These are shown, as far as storage capacity and error correction are concerned, to compare favorably to the performance of a multivalued mask where merely sharp thresholding is used.

© 1985 Optical Society of America