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We present an investigation of the architecture of an optoelectronic cache that can integrate terabit optical memories with the electronic caches associated with high-performance uniprocessors and multiprocessors. The use of optoelectronic-cache memories enables these terabit technologies to provide transparently low-latency secondary memory with frame sizes comparable with disk pages but with latencies that approach those of electronic secondary-cache memories. This enables the implementation of terabit memories with effective access times comparable with the cycle times of current microprocessors. The cache design is based on the use of a smart-pixel array and combines parallel free-space optical input–output to-and-from optical memory with conventional electronic communication to the processor caches. This cache and the optical memory system to which it will interface provide a large random-access memory space that has a lower overall latency than that of magnetic disks and disk arrays. In addition, as a consequence of the high-bandwidth parallel input–output capabilities of optical memories, fault service times for the optoelectronic cache are substantially less than those currently achievable with any rotational media.

A 16-state Hamilton neural-network model is discussed. The storage capacity of the model is analyzed through theory and through a computer numerical simulation. The storage-capacity ratio of the presented model equals that of the Hopfield model. This 16-state neural network can be applied to the recognition of 16-level color patterns, and some examples are discussed.

The optical implementation of the Hopfield algorithm in shift-invariant holographic associative memories is based on the use of correlators with matched filters. However, it is well known that such correlators have poor discrimination. We propose nearly optimal correlation designs for associative memories based on correlation filters that have maximum discrimination ability. These new designs avoid large cross-correlation-peak terms caused by a mismatch between partial input and the fully stored information in the filter. These solutions rely on whitened spectra of the stored and the recalled information.Computer simulations are made of eight different combinations.

A learning and recall algorithm for optical associative memory based on the conventional correlation-learning method with three effective improvements (sparse-encoding method, constant-total-activity method, and binary memory) is proposed from a viewpoint of practical implementation. It is shown that the algorithm is suitable for implementation with a bistable spatial light modulator such as a ferroelectric liquid-crystal spatial light modulator, which has high resolution and a fast response time. The results of theoretical analysis and simulations indicate that the algorithm permits an associative-memory system with a large memory capacity to be realized. An example of an optical system for executing this algorithm is proposed. To determine the performance specifications that are required for the various optical components within the system, we simulate and evaluate the effect of noise (which is caused by nonideal components) on system performance. These results show that the system is robust in the presence of predicted noise levels.

A new polarization-encoding scheme for a bipolar kth-order neural network based on inner-product representation is proposed. Bipolar data multiplication is achieved as the rotation of linearly polarized light. A compact architecture of the bipolar kth-order neural network is suggested. In the architecture, no subtractions are needed, and the threshold levels for the neurons are fixed. Also, we show that a liquid-crystal device such as a liquid-crystal television is acceptable as a polarization modulator in the proposed architecture by computer simulation.

Addition is the most primitive arithmetic operation in digital computation. Other arithmetic operations such as subtraction, multiplication, and division can all be performed by addition together with some logic operations. With the binary number system, addition speed is inevitably limited by the carry-propagation schemes. On the other hand, carry-free addition is possible when the modified signed-digit (MSD) number representation is used. We propose a novel optoelectronic scheme to handle the parallel MSD addition and subtraction operations. An optoelectronic shared content-addressable memroy is introduced. The shared content-addressable memory uses free-space optical processing to handle the large amount of parallel memory access operations and uses electronics to postprocess and derive logic decisions. We analyze the accuracy that the required optical hardware can deliver by using a statistical cross-talk-rate model that we propose. We also evaluate other important device and system performance parameters, such as the memory capacity or the maximum number of parallel bits the adder can handle in terms of a given cross-talk rate at a certain repetition rate, the corresponding diffraction-limited memory density, and the system’s power efficiency. To confirm the underlining operational principles of the proposed optoelectronic shared content-addressable-memory MSD adder, we design and perform initial experiments for handling 8-bit MSD number addition and subtraction and present the results.

An architecture for a novel adaptive optical processing system using optical associative memory with learning capability is proposed. The optical system consists of an optical preprocessor for feature extraction and optical associative memory. The feature-extraction ability can give excellent processing capability to the optical associative memory. In order to demonstrate this system, an optical Fourier transform is used as the preprocessor, and the system can achieve shift invariance. An all-optical configuration of the system is proposed, and the experimental results applied to handwritten-character recognition by using an hybrid opto-electronic system are shown and discussed.

For the purpose of reducing the spurious states in a Hopfield neural net for associative memory, we invoke terminal attractors. In achieving the optical implementation of the terminal-attractor-based associative memory (TABAM) as described in this paper, we first prove the existence of the terminal-attractor model with binary neuron representation. We then present several one- and two-dimensional optical architectures for the TABAM. Finally, as an example, we experimentally demonstrate an inner-product optical neural model using liquid-crystal spatial light modulators with engineering approximations and discuss how to apply the inner-product model to build a two-dimensional parallel processing TABAM.

A modified neural network model suitable for patterns with unequally distributed neuron states is proposed. The storage capacity and content addressability are greatly improved by adding a linear modification term to the interconnection weights of the Hopfield model. Computer simulations were performed to demonstrate the robustness of the modified model compared to the original. A grating-modulated holographic hybrid system was employed for an optical demonstration. Experimental results are shown.

We present an optical implementation of the Hamming net that can be used as an optimum image classifier or an associative memory. We introduce a modified Hamming net, in which the dynamic range requirement of the spatial light modulator can be relaxed and the number of iteration cycles in the second layer (or maxnet) can be reduced. Experimental demonstrations of the optical implementation of the Hamming net are also given.

A heteroassociative memory is proposed that allows a key word in a dictionary of key words to be used to recall an associated holographic image in a database of images. A novel bit-slice search approach finds the word sought in a dictionary of key words and generates a beam that selects the corresponding holographic image from a directory of images. Spatial light rebroadcasters are proposed for the key-word database. Optical experimental results demonstrate that spatial light rebroadcasters may be used in loops with image intensifiers and optically addressable liquid-crystal light valves and that the approach can be used to select holograms based on key-word matching. In the case considered, a holographic image having more than 40,000 bits is selected from 8 by using a key word from a dictionary of 8 words.

A drastic improvement in the performance of the associative memory was achieved using an optical neurochip. The experimental recognition rate agreed well with computer simulation for the associative memory.

An optical neural network using two tightly cascaded liquid crystal televisions is presented. This new optical architecture offers compactness in size, ease of alignment, higher light efficiency, better image quality, and low cost. The implementation of the autoassociative and heteroassociative memories is given.

A new device, a spatial light rebroadcaster, is described that can have optical disk resolution and high speed. Experimental results demonstrate resolution, speed, linearity, logic operation, and arithmetic computation. The device is suitable for optical computing, in particular for memory systems. Optical masking for controlling memory recall and 100 x 100 matrix-vector multiplication are demonstrated. A one pass optical heteroassociative memory system was assembled that uses an optical outer product formulation to store associated 32-bit vectors. Recall is achieved by optical matrix-vector multiplication. The results show the suitability of these devices for memory systems in optical computers.

A Ho-Kashyap (H-K) associative processor (AP) is shown to have a larger storage capacity than the pseudoinverse and correlation APs and to accurately store linearly dependent key vectors. Prior APs have not demonstrated good performance on linearly dependent key vectors. The AP is attractive for optical implementation. A new robust H-K AP is proposed to improve noise performance. These results are demonstrated both theoretically and by Monte Carlo simulation. The H-K AP is also shown to outperform the pseudoinverse AP in an aircraft recognition case study. A technique is developed to indicate the least reliable output vector elements and a new AP error correcting synthesis technique is advanced.

An efficient algorithm for designing a multiprocessor logic unit using a polarization-encoded optical shadow casting system is presented. Both efficient minterm pairing and associative memory mapping with dual addresses are exploited for the design. For illustration, the algorithm is used to design a parallel adder-subtracter unit.

We propose a method for the implementation of the Hopfield algorithm using inner products of unipolar data. This approach is particularly useful for image recognition.

An optical associative neural network with a stochastic thresholding procedure has been demonstrated. The use of stochastic processing drastically improved the convergence rate into the correct global minima (recognition rate). The properties of undesirable spurious minima were also investigated. It was found that the spurious minima were represented as the mixed states of the stored vectors. A useful method to estimate the required noise level to vanish the spurious minima is described.

We describe here a holographic adaptive resonance theory system which self searches through the data store in a highly logical means.

The learning capabilities of optical associative memory called the optical associatron are experimentally shown. The experimental system has a simple architecture for optical associative memory; in particular, the system has versatile adaptive learning capabilities implemented with microchannel spatial light modulators. In this paper, various experimental results of learning and recalling processes on the system are shown. Based on the results, the behavior of learning on the optical associative memory is discussed. In addition, a modified method of learning is proposed and verified on the system. A method for implementation of error backpropagation is also proposed.

We report the optical implementation of a neural network based on a nearest matched filter algorithm and extensive lateral inhibition. Extremely rapid learning is demonstrated in pattern recognition and autonomous control applications, without introducing processing artifacts such as spurious states and ambiguous solutions. The optical implementation is achieved with a reconfigurable, bipolar mask-type crossbar switch based on an inexpensive liquid crystal spatial light modulator.

Using an optical disk as a large capacity associative memory in an optical neural network is described. The proposed architecture is capable of data processing at high speed.

This paper presents a comparison between the field of artificial neural network and the field of image processing and pattern recognition. It shows that some of the adaptive processing algorithms for pattern recognition and image processing, in terms of neural networks, can be seen as adaptive heteroassociative and autoassociative memories, respectively. The similarities and differences between these two fields are addressed.

A new neural network architecture for optical computing is proposed. This architecture can be used for implementing a simple system based on a modified theory of the associative memories. It is shown that the memorized patterns can be recalled perfectly by an experimental system using two microchannel spatial light modulators. The modified theory and principle of operation of the optical associatron system are discussed, and the system itself and basic experimental results are also described.

The feature in the 15 Jan. 1989 issue of Applied Optics includes papers dealing with the problem of pattern recognition including triple correlation, preprocessing, differentiating spatial light modulators, synthetic discriminant functions, circular harmonics for space-invariant pattern recognition, and adaptive associative memory techniques. The feature issue concludes with a paper comparing conventional digital–optical image processing to artificial neural networks.

A new holographic associative memory (HAM) using optical polarization is proposed. Picture elements (pixels) of binary objects are encoded with two mutually perpendicular states of linear polarization, and they are stored in the HAM using a lensless diffuser system. Experimental results of recognizing various inputs are presented. Analytical expressions about the present HAM are derived, and results of computer simulation are also presented.

A matched filter-based architecture for associative memories (MFAMs) has been proposed by many researchers. The correlation from a leg of a matched filter bank, after being altered nonlinearly, weights its corresponding library vector. The weighted vectors are summed and clipped to give an estimate of the library vector closest to the input. We analyze the performance of such architectures for binary and/or bipolar inputs and libraries. Sufficient conditions are derived for the correlation nonlinearity so that the MFAM outputs the correct result. If, for example, N bipolar library vectors are stored, theicorrelation nonlinearity Z(x) = N(x/2) will always result in that library vector closest to the input in the Hamming sense.

Electronic neural networks can perform the function of associative memory. Given an input pattern, the network searches through its stored memories to find which of them best matches the input. Thus the network does a combination of content-addressable search and error correction. The number of random memories that a network can store is limited to a fraction of the number of electronic neurons in the circuit. We propose a method for building a hierarchy of networks that allows the fast parallel search through a list of memories that is too large to store in a single network. We have demonstrated the principle of this approach by an example in image vector quantization.

The bidirectional associative memory (BAM) is a powerful neural network paradigm that is well suited to optical implementation. The BAM is heteroassociative (of which autoassociative operation is a special case) and is guaranteed to converge to a stable final state regardless of the connection weight matrix used. The BAM is placed in a conceptual framework that facilitates comparison with other neural network models. Variations on the BAM such as the bidirectional optimal memory (BOM), the competitive BAM (CBAM), and the adaptive BAM (ABAM) indicate some of the interesting directions this simple structure may evolve, leading in a natural progression toward the power of a model such as the Carpenter-Grossberg ART. The simplicity of the BAM invites uncomplicated optical implementations. BAM designs based on optical matrix—vector multipliers (MVMs) and on volume holographic connections are presented. Spatial light modulator (SLM) device designs currently under development to support the MVM BAMs are given.

An associative memory is described which utilizes a hologram in a hybrid optoelectronic resonator. The nonlinear end mirrors of the resonator are two sets of video detectors and spatial light modulators which act as pseudoconjugators. The transformation properties of the end mirrors are programmable which allows the real-time selection of various associative pathways. An extension of the system to multilayer neural network models, in particular a backpropagation network, is also described.

The discrete-valued neural network proposed by Hopfield requires zero-diagonal terms in the memory matrix so that the net evolves toward a local minimum of an energy function. For a version of this model with bipolar nodes and positive terms along the diagonal, the net evolves so that only updates that lower the energy by a sufficient amount are accepted. For a net programmed as an outer-product associative content-addressable memory, the version with nonzero-diagonal elements performs nearly identically to one with zero-diagonal terms, and the dropping of the zero-diagonal requirement is advantageous for optical implementation.

Optical associative, parallel-processing architectures are being developed using a multimodule approach, where a number of smaller, adaptive, associative modules are nonlinearly interconnected and cascaded under the guidance of a variety of organizational principles to structure larger architectures for solving specific problems. A number of novel optical implementations with versatile adaptive learning capabilities are presented for the individual associative modules, including holographic configurations and five specific electrooptic configurations. The practical issues involved in real optical architectures are analyzed, and actual laboratory optical implementations of associative modules based on Hebbian and Widrow-Hoff learning rules are discussed, including successful experimental demonstrations of their operation.

The property inheritance network (PIN) is a dynamically controlled machine that accesses information stored in a hierarchical content addressable memory. The associative memory is implemented using adaptive resonance circuits. These circuits are monitored by a set of control neurons that become active when certain system states occur and generate signals that control a sequential search through a taxonomy of stored information. This paper reviews pertinent knowledge representation concepts and summarizes the adaptive resonance theory of Carpenter and Grossberg as it applies to the PIN. The PIN architecture and control implementation are presented and simulation results are discussed.

Bidirectionality, forward and backward information flow, is introduced in neural networks to produce two-way associative search for stored stimulus-response associations (A(i),B(i)). Two fields of neurons, F(A) and F(B), are connected by an n x p synaptic marix M. Passing information through M gives one direction, passing information through its transpose M(T) gives the other. Every matrix is bidirectionally stable for bivalent and for continuous neurons. Paired data (A(i),B(i)) are encoded in M by summing bipolar correlation matrices. The bidirectional associative memory (BAM) behaves as a two-layer hierarchy of symmetrically connected neurons. When the neurons in F(A) and F(B) are activated, the network quickly evolves to a stable state of twopattern reverberation, or pseudoadaptive resonance, for every connection topology M. The stable reverberation corresponds to a system energy local minimum. An adaptive BAM allows M to rapidly learn associations without supervision. Stable short-term memory reverberations across F(A) and F(B) gradually seep pattern information into the long-term memory connections M, allowing input associations (A(i),B(i)) to dig their own energy wells in the network state space. The BAM correlation encoding scheme is extended to a general Hebbian learning law. Then every BAM adaptively resonates in the sense that all nodes and edges quickly equilibrate in a system energy local minimum. A sampling adaptive BAM results when many more training samples are presented than there are neurons in F(B) and F(B), but presented for brief pulses of learning, not allowing learning to fully or nearly converge. Learning tends to improve with sample size. Sampling adaptive BAMs can learn some simple continuous mappings and can rapidly abstract bivalent associations from several noisy gray-scale samples.

The application of symbolic processing and rule-based methods for target recognition using correlation filters is considered. The concept of partitioning images is introduced, and its advantages are described. Techniques for rule development, symbolic substitution, error correction via associative processing, and on-line filter adaptation are advanced. Initial simulation results are also presented and discussed.

A new technique for the realization of general linear transformations using associative memories is described. An optical architecture for its implementation is also presented. A low-level feature space processor using this architecture is proposed. The processor is capable of recognizing and locating objects of various shapes and uses certain linear transformations in the feature space for distortion invariance.

Approaches are advanced for pattern recognition when a large number of classes must be identified. Multilevel encoded multiple-iconic filters are considered for this problem. Hierarchical arrangements of iconic filters and/or preprocessing stages are described. A theoretical basis for the sidelobe level and noise effects of filters designed for large class problems is advanced. Experimental data are provided for an optical character recognition case study.

A new model is proposed for a content-addressable memory (CAM) based on neural networks. Like the previous Hopfield model, the information is stored in the structure of the network and the read-out procedure may be implemented in the form of an optical vector–matrix multiplier. This model introduces intermediate layers of interneurons between the neuron layers and a dependence of the interconnection weights to a given neuron on the previous history of the neuron. The storage prescription allows each matrix element to have three values instead of only two as in the previous Hopfield model. This more complex model gives better results than the Hopfield model.

The long-standing problem of the superresolving reconstruction (restoration) of an object of known finite spatial extent from a noisy linearly degraded image is considered. The resolution of two-point sources (objects) spaced less than one Rayleigh distance apart is an ill-posed problem. To determine a superresolving inverse of an ill-conditioned linear degradation operator with a known set of input/output training signals, a linear associative memory (LAM) technique is employed. By limiting the set of reconstructable signals, an exceptionally robust inverse filter has been obtained. This filter is based on a new constrained LAM matrix operator technique. Superresolving restoration of 1-D and 2-D two-point sources as well as some typical edge-type signals in the presence of considerable measurement noise is demonstrated.

A technique for encoding binary outputs from optical filters or matrix memories used in an associative processor for object recognition is discussed. Binary coded output vectors (rather than unit vectors) are used and considerably improve storage capacity. The output codes or matrix memories are chosen from coding theory to enable error correction and detection. The error classification rate for the coded scheme is compared to the noncoded version for different amounts of noise in the input and output planes. Discussion of extensions to more classes, more errors, and multilevel coding are included.

There are many pattern recognition problems where the pattern's structural information is important. In these problems, a syntactic method of pattern recognition is of value. In this paper, both parallel syntactic pattern recognition algorithm and optical architecture implementation approaches are described. In particular, the applications of syntactic pattern recognition algorithm to shape classification are illustrated. A number of parallel optical syntactic pattern coding methods, a structural matched filter and associative memory filter, and an optical symbolic substitution syntactic parser are discussed.

Dennis Gabor is well-known as the inventor of holography. Less well-known, perhaps, are his contributions to other areas. Yet they are important and, like holography, characteristic of his foresight. In the field of communications, Gabor investigated the classic dichotomy of time and frequency. Guided by analogies to quantum mechanics, he postulated a set of elementary signals and made brilliant use of time-frequency diagrams to analyze communication systems. Applying his theories to acoustics, he researched the mechanism of hearing, defining acoustical quanta in the process and inventing early prototype frequency compressors and expanders. In a completely different field, Gabor, inspired by some early work of Longuet-Higgins on models for holographic temporal recall in the brain, suggested novel approaches which contributed significantly to the understanding of associative memories. In this paper we describe Gabor's pioneering work in these areas and trace the subsequent development by himself and others.

Defocusing the recording material away from the Fourier plane is necessary to reduce the strong dc component and produce a more homogeneous object beam distribution in the hologram plane in volume holographic digital data-storage systems with amplitude-modulated data pages. However, content-addressable searching with defocused recording results in higher cross-correlation peak intensities. We present a method for performing a faithful content-addressable search in a defocused volume holographic data-storage system. A new dc-filtered content-addressable search method for defocused volume holographic data-storage systems with binary data pages is demonstrated. Both simulation and experimental results are presented. The experimental results show good discrimination capability and confirm the feasibility of the proposed technique.

We present a new technique for the design of diffractive optical elements (DOE’s) that is based on previous nonlinear least squares (NLS) and phase-shifting quantization methods [Appl. Opt.36, 7297–7306 (1997)]. The technique uses a memory-matrix-based identification (MMBI) optimization procedure. We compare results from the MMBI method with those from iterative Fourier transform and NLS methods. In comparison, the MMBI DOE designs produce better-quality reconstructions for DOE’s with eight or more fabrication phase levels and generally have a higher signal-to-noise ratio and better uniformity.

A method for improving the generalization capability for optical pattern recognition by use of a Gaussian-synapse neuron model is discussed. By the dispersive effect of the Gaussian function the input images are blurred and then fed into a multilayer neural network for learning and recognition. The effectiveness of this method is demonstrated in two-dimensional shift- and scale-invariant optical pattern recognition.

A compact two-step modified-signed-digit arithmetic-logic array processor is proposed. When the reference digits are programmed, both addition and subtraction can be performed by the same binary logic operations regardless of the sign of the input digits. The optical implementation and experimental demonstration with an electron-trapping device are shown. Each digit is encoded by a single pixel, and no polarization is included. Any combinational logic can be easily performed without optoelectronic and electro-optic conversions of the intermediate results. The system is compact, general purpose, simple to align, and has a high signal-to-noise ratio.

An algorithm for optimizing a bipolar interconnection weight matrix with the Hopfield network is proposed. The effectiveness of this algorithm is demonstrated by computer simulation and optical implementation. In the optical implementation of the neural network the interconnection weights are biased to yield a nonnegative weight matrix. Moreover, a threshold subchannel is added so that the system can realize, in real time, the bipolar weighted summation in a single channel. Preliminary experimental results obtained from the applications in associative memories and multitarget classification with rotation invariance are shown.