Abstract

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.

© 1987 Optical Society of America

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1987

A. D. Fisher, “On Applying Associative Networks: an Approach for Representation and Goal-Directed Learning,” in Proceedings, IEEE First Annual International Conference on Neural Networks (1987).

B. Kosko, C. C. Guest, “Optical Bidirectional Associative Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 758, 11 (1987).

E. G. Paek, D. Psaltis, “Optical Associative Memory Using Fourier Transform Holograms,” Opt. Eng. 26, 428 (1987).
[CrossRef]

A. J. Ticknor, H. H. Barrett, “Optical Implementations in Boltzmann Machines,” Opt. Eng. 26, 16 (1987).
[CrossRef]

1986

D. Z. Anderson, “Coherent Optical Eigenstate Memory,” Opt. Lett. 11, 56 (1986).
[CrossRef] [PubMed]

B. H. Soffer, G. J. Dunning, Y. Owechko, E. Marom, “Associative Holographic Memory with Feedback Using Phase-Conjugate Mirrors,” Opt. Lett. 11, 118 (1986).
[CrossRef] [PubMed]

A. Yariv, S. K. Kwong, “Associative Memories Based on Message-Bearing Optical Modes in Phase-Conjugate Resonators,” Opt. Lett. 11, 186 (1986).
[CrossRef] [PubMed]

R. A. Athale, “Attentive Associative Architectures and Their Implications to Optical Computing,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 179 (1986).

M. S. Cohen, “Self-Organization, Association, and Categorization in a Phase Conjugating Resonator,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 214 (1986).

M. S. Kim, C. C. Guest, “Adaptive 2-D Holographic Associative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 174 (1986).

T. Jannson, H. M. Stoll, C. Karaguleff, “The Interconnectability of Neuro-Optic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 15 (1986).

A. Yariv, S. K. Kwong, “Demonstration of All-Optical Associative Holographic Memory,” Appl. Phys. Lett. 48, 1114 (1986).
[CrossRef]

G. J. Dunning, E. Maron, Y. Owechko, B. H. Soffer, “Optical Holographic Associative Memory Using a Phase Conjugate Resonator,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 205 (1986).

A. D. Fisher, R. C. Fukuda, J. N. Lee, “Implementations of Adaptive Associative Optical Computing Elements,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

K. H. Brenner, A. Huang, N. Streibel, “Digital Optical Computing with Symbolic Substitution,” Appl. Opt. 25, 3054 (1986).
[CrossRef] [PubMed]

1985

1984

A. D. Fisher, C. L. Giles, J. N. Lee, “Associative Processor Architectures for Optical Computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

1983

A. C. Sanderson, Y. Y. Zeevi, Eds., Special issue on Neural and Sensory Information Processing, IEEE Trans. Syst. Man Cybern. SMC-13 (1983).
[CrossRef]

A. W. Lohmann, C. Thum, “Two-Way Code Translation by Computer-Generated Holographic Filters,” Opt. Commun. 46, 74 (1983).
[CrossRef]

K. Fukushima, S. Miyake, T. Ito, “Neocognitron: a Neural Network Model for a Mechanism of Visual Pattern Recognition,” IEEE Trans. Syst. Man Cybern. SMC-13, 826 (1983).
[CrossRef]

A. G. Barto, R. S. Sutton, C. W. Anderson, “Neuronlike Adaptive Elements that Can Solve Difficult Learning and Control Problems,” IEEE Trans. Syst. Man Cybern. SMC-13, 834 (1983).
[CrossRef]

C. Warde, J. I. Thackara, “Operating Modes of the Micro-channel Spatial Light Modulator,” Opt. Eng. 22, 695 (1983).
[CrossRef]

1982

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982).
[CrossRef] [PubMed]

R. A. Athale, W. C. Collins, “Optical Matrix–Matrix Multiplier Based on Outer Product Decomposition,” Appl. Opt. 21, 2089 (1982).
[CrossRef] [PubMed]

1981

1978

1977

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, “Distinctive Features, Categorical Perception, and Probability Learning: Some Applications of a Neural Model,” Psychol. Rev. 84, 413 (1977).
[CrossRef]

1976

P. N. Tamura, J. C. Wyant, “Matrix Multiplication Using Coherent Optical Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 83, 97 (1976).

1974

1972

1970

D. J. Willshaw, H. C. Longuet-Higgins, “Associative Memory Models,” Mach. Intell. 5, 351 (1970).

1969

D. Gabor, “Associative Holographic Memories,” IBM J. Res. Dev. 13, 156 (1969).
[CrossRef]

D. J. Willshaw, O. P. Buneman, H. C. Longuet-Higgins, “Non-Holographic Associative Memory,” Nature London 222, 960 (1969).
[CrossRef] [PubMed]

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2209 (1969).

1967

A. W. Lohmann, H. W. Werlich, “Holographic Production of Spatial Filters for Code Translation and Image Restoration,” Phys. Lett. A 25, 570 (1967).
[CrossRef]

1966

R. J. Collier, K. S. Pennington, “Ghost Imaging by Holograms Formed in the Near Field,” Appl. Phys. Lett. 8, 44 (1966).
[CrossRef]

1965

D. Gabor, “Character Recognition by Holography,” Nature London 206, 422 (1965).
[CrossRef]

1960

B. Widrow, M. E. Hoff, “Adaptive Switching Circuits,” IRE WESCON Conv. Rec. Part 4, 96 (1960).

Akahori, H.

Anderson, C. W.

A. G. Barto, R. S. Sutton, C. W. Anderson, “Neuronlike Adaptive Elements that Can Solve Difficult Learning and Control Problems,” IEEE Trans. Syst. Man Cybern. SMC-13, 834 (1983).
[CrossRef]

Anderson, D. Z.

D. Z. Anderson, “Coherent Optical Eigenstate Memory,” Opt. Lett. 11, 56 (1986).
[CrossRef] [PubMed]

D. Z. Anderson, D. M. Lininger, M. J. O'Callahan, “Competitive Learning, Unlearning, and Forgetting in Optical Resonators,” in Proceedings, IEEE Conference on Neural Information Processing Systems—Natural and Synthetic (1987), to be published.

Anderson, J. A.

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, “Distinctive Features, Categorical Perception, and Probability Learning: Some Applications of a Neural Model,” Psychol. Rev. 84, 413 (1977).
[CrossRef]

G. E. Hinton, J. A. Anderson, Parallel Models of Associative Memory (Erlbaum, Hillsdale, NJ, 1981).

Athale, R. A.

R. A. Athale, “Attentive Associative Architectures and Their Implications to Optical Computing,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 179 (1986).

R. A. Athale, W. C. Collins, “Optical Matrix–Matrix Multiplier Based on Outer Product Decomposition,” Appl. Opt. 21, 2089 (1982).
[CrossRef] [PubMed]

Babcock, T. R.

T. R. Babcock, R. C. Friend, P. Hegges, “Linear Discrimination Optical-Electronic Implementation,” in Optical Processing in Information, C. K. Pollock, C. J. Koester, J. T. Tippet, Eds. (Spartan, Baltimore, MD, 1963), p. 145.

Barrett, H. H.

A. J. Ticknor, H. H. Barrett, “Optical Implementations in Boltzmann Machines,” Opt. Eng. 26, 16 (1987).
[CrossRef]

Barto, A. G.

A. G. Barto, R. S. Sutton, C. W. Anderson, “Neuronlike Adaptive Elements that Can Solve Difficult Learning and Control Problems,” IEEE Trans. Syst. Man Cybern. SMC-13, 834 (1983).
[CrossRef]

Brenner, K. H.

Buneman, O. P.

D. J. Willshaw, O. P. Buneman, H. C. Longuet-Higgins, “Non-Holographic Associative Memory,” Nature London 222, 960 (1969).
[CrossRef] [PubMed]

Carlson, A. B.

A. B. Carlson, Communication Systems (McGraw-Hill, New York, 1968).

Chen, H. H.

T. Maxwell, C. L. Giles, Y. C. Lee, H. H. Chen, “Nonlinear Dynamics of Artificial Neural Systems,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 299.

Clifton, C.

C. Clifton, Chairman, Digest of Papers of the Eighth Annual Conference of the Cognitive Science Society (Erlbaum, Hillsdale, NJ, 1986).

Cohen, M. S.

M. S. Cohen, “Self-Organization, Association, and Categorization in a Phase Conjugating Resonator,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 214 (1986).

Collier, R. J.

R. J. Collier, K. S. Pennington, “Ghost Imaging by Holograms Formed in the Near Field,” Appl. Phys. Lett. 8, 44 (1966).
[CrossRef]

Collins, W. C.

Condon, D. J.

D. J. Condon, M. C. Reichenbach, A. Tarasevich, W. T. Rhodes, “Optical Window Addressable Memory Processing,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), postdeadline paper PD2.

Dias, A. R.

Dunning, G. J.

B. H. Soffer, G. J. Dunning, Y. Owechko, E. Marom, “Associative Holographic Memory with Feedback Using Phase-Conjugate Mirrors,” Opt. Lett. 11, 118 (1986).
[CrossRef] [PubMed]

G. J. Dunning, E. Maron, Y. Owechko, B. H. Soffer, “Optical Holographic Associative Memory Using a Phase Conjugate Resonator,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 205 (1986).

Farhat, N.

D. Psaltis, N. Farhat, “Optical Information Processing Models Based on an Associative-Memory Model of Neural Nets with Thresholding and Feedback,” Opt. Lett. 10, 98 (1985).
[CrossRef] [PubMed]

D. Psaltis, N. Farhat, “A New Approach to Optical Information Processing Based on the Hopfield Model,” in Technical Digest, Thirteenth Congress of the ICO, Sapporo, Japan (1984), p. 24.

Fisher, A. D.

A. D. Fisher, “On Applying Associative Networks: an Approach for Representation and Goal-Directed Learning,” in Proceedings, IEEE First Annual International Conference on Neural Networks (1987).

A. D. Fisher, R. C. Fukuda, J. N. Lee, “Implementations of Adaptive Associative Optical Computing Elements,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

A. D. Fisher, C. L. Giles, J. N. Lee, “Associative Processor Architectures for Optical Computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

C. Warde, A. M. Weiss, A. D. Fisher, J. I. Thackara, “Optical Information Processing Characteristics of the MicroChannel Spatial Light Modulator,” Appl. Opt. 20, 2066 (1981).
[CrossRef] [PubMed]

J. A. McEwan, A. D. Fisher, J. N. Lee, “Four Special Functions of a MicroChannel Spatial Light Modulator,” in Technical Digest, Conference onLasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), postdeadline paper PD1.

A. D. Fisher, C. L. Giles, “Optical Adaptive Associative Computer Architectures,” in Proceedings, IEEE 1985 COMP-CON Spring Meeting, Catalog No. CH2135-2/85 (1985), p. 342.

A. D. Fisher, J. N. Lee, “Optical Associative Processing Elements with Versatile Adaptive Learning Capabilities,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 137.

Friend, R. C.

T. R. Babcock, R. C. Friend, P. Hegges, “Linear Discrimination Optical-Electronic Implementation,” in Optical Processing in Information, C. K. Pollock, C. J. Koester, J. T. Tippet, Eds. (Spartan, Baltimore, MD, 1963), p. 145.

Fukuda, R. C.

A. D. Fisher, R. C. Fukuda, J. N. Lee, “Implementations of Adaptive Associative Optical Computing Elements,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

Fukushima, K.

K. Fukushima, S. Miyake, T. Ito, “Neocognitron: a Neural Network Model for a Mechanism of Visual Pattern Recognition,” IEEE Trans. Syst. Man Cybern. SMC-13, 826 (1983).
[CrossRef]

Gabor, D.

D. Gabor, “Associative Holographic Memories,” IBM J. Res. Dev. 13, 156 (1969).
[CrossRef]

D. Gabor, “Character Recognition by Holography,” Nature London 206, 422 (1965).
[CrossRef]

Giles, C. L.

A. D. Fisher, C. L. Giles, J. N. Lee, “Associative Processor Architectures for Optical Computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

T. Maxwell, C. L. Giles, Y. C. Lee, H. H. Chen, “Nonlinear Dynamics of Artificial Neural Systems,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 299.

A. D. Fisher, C. L. Giles, “Optical Adaptive Associative Computer Architectures,” in Proceedings, IEEE 1985 COMP-CON Spring Meeting, Catalog No. CH2135-2/85 (1985), p. 342.

Goodman, J. W.

Grossberg, S.

S. Grossberg, Studies of Mind and Brain (Reidel, Boston, 1982).
[CrossRef]

Gu, X. G.

D. Psaltis, J. Yu, X. G. Gu, H. Lee, “Optical Neural Nets Implemented with Volume Holograms,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 129.

Guest, C. C.

B. Kosko, C. C. Guest, “Optical Bidirectional Associative Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 758, 11 (1987).

M. S. Kim, C. C. Guest, “Adaptive 2-D Holographic Associative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 174 (1986).

Hawkins, J. K.

J. K. Hawkins, C. J. Munsey, “A Natural Image Computer,” in Optical Processing of Information, C. K. Pollock, C. J. Koester, J. T. Tippet, Eds. (Spartan, Baltimore, MD, 1963), p. 233.

Hebb, D.

D. Hebb, Organization of Behavior (Wiley, New York, 1949).

Hegges, P.

T. R. Babcock, R. C. Friend, P. Hegges, “Linear Discrimination Optical-Electronic Implementation,” in Optical Processing in Information, C. K. Pollock, C. J. Koester, J. T. Tippet, Eds. (Spartan, Baltimore, MD, 1963), p. 145.

Hinton, G. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning Internal Representations by Error Propagation,” in Parallel Distributed Processing, J. J. McClelland et al., Eds. (MIT Press, Cambridge, MA, 1986), 318.

G. E. Hinton, J. A. Anderson, Parallel Models of Associative Memory (Erlbaum, Hillsdale, NJ, 1981).

G. E. Hinton, T. J. Sejknowski, “Optimal Perceptual Inference,” in Proceedings, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Catalog No. CH1891-1/83 (1983).

Hoff, M. E.

B. Widrow, M. E. Hoff, “Adaptive Switching Circuits,” IRE WESCON Conv. Rec. Part 4, 96 (1960).

Hopfield, J. J.

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. U.S.A. 79, 2554 (1982).
[CrossRef] [PubMed]

Huang, A.

Ito, T.

K. Fukushima, S. Miyake, T. Ito, “Neocognitron: a Neural Network Model for a Mechanism of Visual Pattern Recognition,” IEEE Trans. Syst. Man Cybern. SMC-13, 826 (1983).
[CrossRef]

Jannson, T.

T. Jannson, H. M. Stoll, C. Karaguleff, “The Interconnectability of Neuro-Optic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 15 (1986).

Jones, R. S.

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, “Distinctive Features, Categorical Perception, and Probability Learning: Some Applications of a Neural Model,” Psychol. Rev. 84, 413 (1977).
[CrossRef]

Kanerva, P.

P. Kanerva, “Parallel Structures in Human and Computer Memory,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 247.

Karaguleff, C.

T. Jannson, H. M. Stoll, C. Karaguleff, “The Interconnectability of Neuro-Optic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 15 (1986).

Kim, M. S.

M. S. Kim, C. C. Guest, “Adaptive 2-D Holographic Associative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 174 (1986).

Klopf, A. H.

A. H. Klopf, “A Drive Reinforcement Model of Single Neuron Functioning: an Alternative to the Hebbian Neuronal Model,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 265.

Knight, G. R.

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2209 (1969).

Kohonen, T.

T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, New York, 1984).

Kosko, B.

B. Kosko, C. C. Guest, “Optical Bidirectional Associative Memories,” Proc. Soc. Photo-Opt. Instrum. Eng. 758, 11 (1987).

B. Kosko, “Differential Hebbian Learning,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 277.

Kwong, S. K.

A. Yariv, S. K. Kwong, “Associative Memories Based on Message-Bearing Optical Modes in Phase-Conjugate Resonators,” Opt. Lett. 11, 186 (1986).
[CrossRef] [PubMed]

A. Yariv, S. K. Kwong, “Demonstration of All-Optical Associative Holographic Memory,” Appl. Phys. Lett. 48, 1114 (1986).
[CrossRef]

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K. S. Narendra, S. Lakshimivarahan, “Learning Automata—a Critique,” J. Cybern. Inf. Sci. 1, 53 (1978).

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D. Psaltis, J. Yu, X. G. Gu, H. Lee, “Optical Neural Nets Implemented with Volume Holograms,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 129.

Lee, J. N.

A. D. Fisher, R. C. Fukuda, J. N. Lee, “Implementations of Adaptive Associative Optical Computing Elements,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

A. D. Fisher, C. L. Giles, J. N. Lee, “Associative Processor Architectures for Optical Computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

A. D. Fisher, J. N. Lee, “Optical Associative Processing Elements with Versatile Adaptive Learning Capabilities,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 137.

J. A. McEwan, A. D. Fisher, J. N. Lee, “Four Special Functions of a MicroChannel Spatial Light Modulator,” in Technical Digest, Conference onLasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), postdeadline paper PD1.

Lee, Y. C.

T. Maxwell, C. L. Giles, Y. C. Lee, H. H. Chen, “Nonlinear Dynamics of Artificial Neural Systems,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 299.

Lininger, D. M.

D. Z. Anderson, D. M. Lininger, M. J. O'Callahan, “Competitive Learning, Unlearning, and Forgetting in Optical Resonators,” in Proceedings, IEEE Conference on Neural Information Processing Systems—Natural and Synthetic (1987), to be published.

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A. W. Lohmann, C. Thum, “Two-Way Code Translation by Computer-Generated Holographic Filters,” Opt. Commun. 46, 74 (1983).
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Marom, E.

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G. J. Dunning, E. Maron, Y. Owechko, B. H. Soffer, “Optical Holographic Associative Memory Using a Phase Conjugate Resonator,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 205 (1986).

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T. Maxwell, C. L. Giles, Y. C. Lee, H. H. Chen, “Nonlinear Dynamics of Artificial Neural Systems,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 299.

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J. L. McClelland et al., Parallel Distributed Processing (MIT Press, Cambridge, MA, 1986), Vols. 1 and 2.

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J. A. McEwan, A. D. Fisher, J. N. Lee, “Four Special Functions of a MicroChannel Spatial Light Modulator,” in Technical Digest, Conference onLasers and Electro-Optics (Optical Society of America, Washington, DC, 1985), postdeadline paper PD1.

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K. Fukushima, S. Miyake, T. Ito, “Neocognitron: a Neural Network Model for a Mechanism of Visual Pattern Recognition,” IEEE Trans. Syst. Man Cybern. SMC-13, 826 (1983).
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J. K. Hawkins, C. J. Munsey, “A Natural Image Computer,” in Optical Processing of Information, C. K. Pollock, C. J. Koester, J. T. Tippet, Eds. (Spartan, Baltimore, MD, 1963), p. 233.

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D. Z. Anderson, D. M. Lininger, M. J. O'Callahan, “Competitive Learning, Unlearning, and Forgetting in Optical Resonators,” in Proceedings, IEEE Conference on Neural Information Processing Systems—Natural and Synthetic (1987), to be published.

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G. J. Dunning, E. Maron, Y. Owechko, B. H. Soffer, “Optical Holographic Associative Memory Using a Phase Conjugate Resonator,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 205 (1986).

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D. B. Parker, “A Comparison of Algorithms for Neuron-Like Cells,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 327.

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E. G. Paek, D. Psaltis, “Optical Associative Memory Using Fourier Transform Holograms,” Opt. Eng. 26, 428 (1987).
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D. Psaltis, N. Farhat, “A New Approach to Optical Information Processing Based on the Hopfield Model,” in Technical Digest, Thirteenth Congress of the ICO, Sapporo, Japan (1984), p. 24.

K. Wagner, D. Psaltis, “Multilayer Optical Learning Networks,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 133.

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D. J. Condon, M. C. Reichenbach, A. Tarasevich, W. T. Rhodes, “Optical Window Addressable Memory Processing,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), postdeadline paper PD2.

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D. J. Condon, M. C. Reichenbach, A. Tarasevich, W. T. Rhodes, “Optical Window Addressable Memory Processing,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), postdeadline paper PD2.

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J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, “Distinctive Features, Categorical Perception, and Probability Learning: Some Applications of a Neural Model,” Psychol. Rev. 84, 413 (1977).
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Sakurai, K.

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G. E. Hinton, T. J. Sejknowski, “Optimal Perceptual Inference,” in Proceedings, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Catalog No. CH1891-1/83 (1983).

Silverstein, J. W.

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, “Distinctive Features, Categorical Perception, and Probability Learning: Some Applications of a Neural Model,” Psychol. Rev. 84, 413 (1977).
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B. H. Soffer, G. J. Dunning, Y. Owechko, E. Marom, “Associative Holographic Memory with Feedback Using Phase-Conjugate Mirrors,” Opt. Lett. 11, 118 (1986).
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T. Jannson, H. M. Stoll, C. Karaguleff, “The Interconnectability of Neuro-Optic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 15 (1986).

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Sutton, R. S.

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H. Szu, “Fast Simulated Annealing,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 420.

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P. N. Tamura, J. C. Wyant, “Matrix Multiplication Using Coherent Optical Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 83, 97 (1976).

Tarasevich, A.

D. J. Condon, M. C. Reichenbach, A. Tarasevich, W. T. Rhodes, “Optical Window Addressable Memory Processing,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1985), postdeadline paper PD2.

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Thum, C.

A. W. Lohmann, C. Thum, “Two-Way Code Translation by Computer-Generated Holographic Filters,” Opt. Commun. 46, 74 (1983).
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A. J. Ticknor, H. H. Barrett, “Optical Implementations in Boltzmann Machines,” Opt. Eng. 26, 16 (1987).
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K. Wagner, D. Psaltis, “Multilayer Optical Learning Networks,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 133.

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Weiss, A. M.

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A. W. Lohmann, H. W. Werlich, “Holographic Production of Spatial Filters for Code Translation and Image Restoration,” Phys. Lett. A 25, 570 (1967).
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B. Widrow, M. E. Hoff, “Adaptive Switching Circuits,” IRE WESCON Conv. Rec. Part 4, 96 (1960).

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D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning Internal Representations by Error Propagation,” in Parallel Distributed Processing, J. J. McClelland et al., Eds. (MIT Press, Cambridge, MA, 1986), 318.

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D. J. Willshaw, H. C. Longuet-Higgins, “Associative Memory Models,” Mach. Intell. 5, 351 (1970).

D. J. Willshaw, O. P. Buneman, H. C. Longuet-Higgins, “Non-Holographic Associative Memory,” Nature London 222, 960 (1969).
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Wyant, J. C.

P. N. Tamura, J. C. Wyant, “Matrix Multiplication Using Coherent Optical Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 83, 97 (1976).

Yariv, A.

A. Yariv, S. K. Kwong, “Demonstration of All-Optical Associative Holographic Memory,” Appl. Phys. Lett. 48, 1114 (1986).
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A. Yariv, S. K. Kwong, “Associative Memories Based on Message-Bearing Optical Modes in Phase-Conjugate Resonators,” Opt. Lett. 11, 186 (1986).
[CrossRef] [PubMed]

Yu, J.

D. Psaltis, J. Yu, X. G. Gu, H. Lee, “Optical Neural Nets Implemented with Volume Holograms,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 129.

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K. Fukushima, S. Miyake, T. Ito, “Neocognitron: a Neural Network Model for a Mechanism of Visual Pattern Recognition,” IEEE Trans. Syst. Man Cybern. SMC-13, 826 (1983).
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B. Widrow, M. E. Hoff, “Adaptive Switching Circuits,” IRE WESCON Conv. Rec. Part 4, 96 (1960).

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K. S. Narendra, S. Lakshimivarahan, “Learning Automata—a Critique,” J. Cybern. Inf. Sci. 1, 53 (1978).

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A. D. Fisher, C. L. Giles, J. N. Lee, “Associative Processor Architectures for Optical Computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

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D. J. Willshaw, H. C. Longuet-Higgins, “Associative Memory Models,” Mach. Intell. 5, 351 (1970).

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A. W. Lohmann, C. Thum, “Two-Way Code Translation by Computer-Generated Holographic Filters,” Opt. Commun. 46, 74 (1983).
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E. G. Paek, D. Psaltis, “Optical Associative Memory Using Fourier Transform Holograms,” Opt. Eng. 26, 428 (1987).
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A. D. Fisher, R. C. Fukuda, J. N. Lee, “Implementations of Adaptive Associative Optical Computing Elements,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

G. J. Dunning, E. Maron, Y. Owechko, B. H. Soffer, “Optical Holographic Associative Memory Using a Phase Conjugate Resonator,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 205 (1986).

R. A. Athale, “Attentive Associative Architectures and Their Implications to Optical Computing,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 179 (1986).

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M. S. Kim, C. C. Guest, “Adaptive 2-D Holographic Associative Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 625, 174 (1986).

T. Jannson, H. M. Stoll, C. Karaguleff, “The Interconnectability of Neuro-Optic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 15 (1986).

P. N. Tamura, J. C. Wyant, “Matrix Multiplication Using Coherent Optical Techniques,” Proc. Soc. Photo-Opt. Instrum. Eng. 83, 97 (1976).

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[CrossRef]

Other

Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987).

P. Kanerva, “Parallel Structures in Human and Computer Memory,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 247.

T. Maxwell, C. L. Giles, Y. C. Lee, H. H. Chen, “Nonlinear Dynamics of Artificial Neural Systems,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 299.

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F. Rosenblatt, Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanism (Spartan, Washington, DC, 1961).

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D. Psaltis, J. Yu, X. G. Gu, H. Lee, “Optical Neural Nets Implemented with Volume Holograms,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 129.

K. Wagner, D. Psaltis, “Multilayer Optical Learning Networks,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 133.

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A. D. Fisher, C. L. Giles, “Optical Adaptive Associative Computer Architectures,” in Proceedings, IEEE 1985 COMP-CON Spring Meeting, Catalog No. CH2135-2/85 (1985), p. 342.

A. D. Fisher, J. N. Lee, “Optical Associative Processing Elements with Versatile Adaptive Learning Capabilities,” in Technical Digest of Topical Meeting on Optical Computing (Optical Society of America, Washington, DC, 1987), p. 137.

T. R. Babcock, R. C. Friend, P. Hegges, “Linear Discrimination Optical-Electronic Implementation,” in Optical Processing in Information, C. K. Pollock, C. J. Koester, J. T. Tippet, Eds. (Spartan, Baltimore, MD, 1963), p. 145.

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D. Z. Anderson, D. M. Lininger, M. J. O'Callahan, “Competitive Learning, Unlearning, and Forgetting in Optical Resonators,” in Proceedings, IEEE Conference on Neural Information Processing Systems—Natural and Synthetic (1987), to be published.

G. E. Hinton, T. J. Sejknowski, “Optimal Perceptual Inference,” in Proceedings, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Catalog No. CH1891-1/83 (1983).

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning Internal Representations by Error Propagation,” in Parallel Distributed Processing, J. J. McClelland et al., Eds. (MIT Press, Cambridge, MA, 1986), 318.

D. B. Parker, “A Comparison of Algorithms for Neuron-Like Cells,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 327.

B. Kosko, “Differential Hebbian Learning,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 277.

A. H. Klopf, “A Drive Reinforcement Model of Single Neuron Functioning: an Alternative to the Hebbian Neuronal Model,” in Neural Nets for Computing, J. S. Denker, Ed. (American Institute of Physics, New York, 1986), p. 265.

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Figures (12)

Fig. 1
Fig. 1

Optical associative module implementing Hebbian conjunction-of-activity learning rule using a microchannel plate spatial light modulator (MSLM) and two 1-D acoustooptic Bragg modulators (B1 and B2). D is the input side and M is the output reflective modulator side of the MSLM, the mn are mirrors and the BSn are beam splitters.

Fig. 2
Fig. 2

Cascadable optical associative module implementing Hebbian conjunction-of-activity learning rule (top view) using two microchannel spatial light modulators (MSLM1 and MSLM2).

Fig. 3
Fig. 3

Optical associative module implementing the Widrow-Hoff learning rule using a microchannel spatial light modulator (MSLM) and two 1-D acoustooptic Bragg modulators (B1 and B2).

Fig. 4
Fig. 4

Cascadable optical associative module implementing the Widrow-Hoff learning rule (top view) using two microchannel spatial light modulators (MSLM1 and MSLM2).

Fig. 5
Fig. 5

Cascadable optical associative module implementing differential learning rules of the form dM/dt = g′(dv/dt)(du/dt)T (top view). D is the input detector side, M is the output reflective modulator side of the MSLMs, and S is a uniform 2-D light source.

Fig. 6
Fig. 6

Simulation example of an optical associative module based on the Widrow-Hoff learning rule (Bragg-MSLM configuration of Fig. 3). The final M matrix is equal to V↑1/2U−1 and (Muk)↑2 (corresponds to detected intensity) then equals the stored vk vectors.

Fig. 7
Fig. 7

Experimental configuration for the Widrow-Hoff architecture of Fig. 3.

Fig. 8
Fig. 8

Actual experimental apparatus for implementation of the Widrow-Hoff architecture of Fig. 3.

Fig. 9
Fig. 9

Experimental results from the open-loop Hebbian configuration.

Fig. 10
Fig. 10

Experimental results from the full closed-loop Widrow-Hoff architecture.

Fig. 11
Fig. 11

Holographic adaptive, associative module. H is a realtime reusable holographic medium and R implements encoding operations to increase information capacity.

Fig. 12
Fig. 12

Holographic adaptive, associative module employing 1-D encoding to recall and adaptively learn the 1-D patterns uk(y) and υk(x). His a real-time reusable holographic medium.

Equations (30)

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υ ( x ) = M ( x , y ) u k ( y ) d y .
d M / d t = g υ k ( x ) u k ( y ) .
M ( x , y ) = g k = 1 m υ k ( x ) u k ( y ) ,
v = Mu .
d M / d t = g ( v k u k T ) .
U = ( u 1 , u 2 , u 3 , , u m ) ,
V = ( v 1 , v 2 , v 3 , , v m ) ,
V = MU .
M = VU 1 .
M = VU T .
M = VU + ,
d M / d t = g ( v k v ) u k T ,
M n + 1 = M n + g v k u k T g vu k T ,
M n + 1 = M n + g ( v k u k T ) ,
d M / d t = g ( d v / d t ) ( d u / d t ) T .
F ( y , w 0 ) = M ( y , z ) u ( z ) exp ( jwz ) d z w 0 = j m i j u j .
I i = | F ( i , 0 ) | 2 = | j m i j u j | 2 ,
I = ( Mu ) 2 = v 2 .
I i = | F ( i , w ) | 2 d w = | f ( i , z ) | 2 d z .
I i = | M ( y , z ) u ( z ) | 2 d z = j | m i j u j | 2 ,
I = M 2 u 2 .
M n + 1 = M n + g + v k u kT g ( M n u kT ) u k T = M n + g [ ( g + / g v kT ) u k T ( M n u k T ) u k T ] .
M n + 1 = M n + g [ ( v k u k T ) 2 ( M n u k u k T ) 2 ] .
M n + 1 = M n + g [ v k u k T ( M n u k u k T ) 2 ] .
M n + 1 = M n + g { ( v k 2 u k T ) 2 [ ( M n u k ) 2 u k T ] 2 }
( a ) M = 1 1 0.41 ( b ) M = 0.41 1 1 1 0.73 0.73 1 1.41 1.41 0.59
imaging : d H / d t = g υ k u k * ,
Fourier : d H / d t = g V k U k * .
imaging : υ = H u p = k ( u p u k * ) υ k = | u p | 2 υ p + k p ( u p u k * ) υ k ,
Fourier : υ = H ( x , y ) * u p ( x , y ) = k ( u k u p ) * υ k .

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