Optical Modular Architectures for Multi-Layer Bam with 2-Dimensional Patterns

After the first demonstration of optically-implemented Hopfield model [1] many neural network models have been investigated for large-scale optical implementation [2-8]. The 1-dimensional Hopfield model had been extended for 2-dimensional patterns [2], and optical implementation of bidirectional associative memory (BAM) [3-5] and quadratic associative memory [6,7] had been investigated. Adaptive neural network models such as multi-layer perceptron [8] had also been demonstrated. However performance of the simple Hopfield model and BAM is very limited, and many adaptive learning algorithms are too complicated to be implemented efficiently by optics. Also, when a new pattern need be added to the existing system, the correlation matrix learning rule of both the Hopfield model and BAM requires simple addition to existing interconnection weights, while error back-propagation learning rule for multi-layer perceptron requires to bring over all the previously stored patterns. Recently we had extended the BAM into multi-layer architecture, of which performance is quite comparable to that of multi-layer perceptron [9]. This multi-layer BAM (MBAM) still utilizes correlation matrices for easy optical implementation with outer-product matrix formation or inner-product recall. In this paper optical system architectures for the MBAM are presented for 2-dimensional patterns, and several implementation issues are discussed.