Optical information processing based on an associative-memory model of neural nets with thresholding and feedback

Abstract

The remarkable collective computational properties of the Hopfield model for neural networks [Proc. Nat. Acad. Sci. USA 79, 2554(1982] are reviewed. These include recognition from partial input, robustness, and error-correction capability. Features of the model that make its optical implementation attractive are discussed, and specific optical implementation schemes are given.Optical information-processing systems can have high processing power because of the large degree of parallelism as well as the interconnection capability that is achievable. Typically, more than 106 parallel processing channels are available in the optical system, and furthermore each of these channels can be optically interconnected (broadcasted) to 106 other channels. The majority of optical processors are analog systems, designed to perform linear operations. The accuracy of an analog processor is limited by the linear dynamic range of the devices used (detectors, light modulators).In principle, the accuracy and the repertoire of achievable operations can be improved with systems that perform nonlinear operations on binary encoded data using bistable optical devices. Optical bistability is a subject that has received considerable attention recently as a means of achieving efficient high-speed logic, and it has been demonstrated with several nonlinear optical materials and devices. If we are to use such bistable devices to realize powerful, nonlinear optical computers, it is important to find algorithms that are well matched to the characteristics of the optical processor and utilize effectively its parallelism and interconnection capability. In this Letter we examine a method for synthesizing optical processing systems, based on optical associative memory and threshold logic, that appears to meet these requirements well.Associative (or content-addressable) memories are of interest in computer science, and it is theorized that information is stored in the human brain in this manner.Holographic associative memories have been described by Gabor,' who also commented on the similarity of the holographic memory to the way information may be stored in the human brain. More recently, Hopfield 2 introduced an associative-memory model to describe the collective behavior of neural networks. Hopfield's model consists basically of an associative memory similar to the holographic, with the addition of threshold and feedback. The incorporation of nonlinear feedback enhances dramatically the error-correcting capability of the holographic memory. Let where the last term accounts for Tij = 0 and No is the number of l's in vUi(O). We assume that for m # mo the binary words vi (m) are statistically described in the following simple manner:where vim) are independent for all i and m. Then If N is sufficiently larger than M, then with high prob-

Probabilistic and Stochastic Methods in Analysis, with Applications

“…Learning dynamics are used to evolve the interconnection strength pattern as a succession of small perturbations. Because degenerate fourwavelet-mixing wavefront conjugate mirrors, as described above, provide retroreflection and optical tracking novelty filters, Theorem 7.1 is at tile basis of neural network models implemented by local neural networks of reconfigurable holographic optical interconnect patterns in optical neurocomputer architectures [2,3,4,5,7,79,81,82,83,124,126,127,129,128,130,131,142,145,144,143,146]. In the long term, real-time holography in PRCs appears to be the most appealing reconfigurable optical iph-rconnection technique.…”

“…On the simplest level, the information is recorded and retrieved from an erasable magnetooptic disk by optical techniques. Higher-level building-blocks are twodimensional arrays of coherent optical processors [2,3,4,5,7,126,127,129,128,142,145,144,143,146] for the analog implementation of neural network models by holographic optical interconnects, and neural network analog VLSI chips. For instance, the analog silicon models of the orientationselective retina for pattern recognition [1,115,117], and the analog electronic cochlea for auditory localization [92, 115,116] belong to this category.…”

Applicability Of The Liquid Crystal Television For Optical Data Processing

“…The research described in this Letter was sponsored riling pattern on the LCTV screen addressed by (a) 10 In the linear operating mode, the incremental Shown In Fig. 3 is a plot of T vs + as given by Eq.…”

Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression

“…tion [3], separation of signals from noise [4], cooperative and fault-tolerant processing [ 5 ] , estimation and prediction [6], and data compression. The last of these is perhaps both the simplest and the most generic example because it most directly depends upon the exploitation of redundancy.…”