Abstract

A continuous-time optical neural network capable of executing a broad class of energy-minimizing neural net algorithms has been built. The network is a ring resonator comprising a saturable, two-beam amplifier that acts as an optical neuron array, two volume holograms that provide global network interconnectivity, and a linear, two-beam amplifier that provides sufficient gain to permit network oscillation. The network has been used as an associative memory to store and recall multiple, nonorthogonal visual images.

© 1989 Optical Society of America

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  1. J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, Psychol. Rev. 84, 413 (1977).
    [CrossRef]
  2. J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
    [CrossRef] [PubMed]
  3. S. Grossberg, J. Math. Anal. Appl. 66, 470 (1978).
    [CrossRef]
  4. J. J. Hopfield, D. W. Tank, Biol. Cybern. 52, 141 (1985).
    [PubMed]
  5. D. Psaltis, N. Farhat, Opt. Lett. 10, 98 (1985).
    [CrossRef] [PubMed]
  6. A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).
  7. R. A. Athale, H. H. Szu, C. B. Friedlander, Opt. Lett. 11, 482(1986).
    [CrossRef] [PubMed]
  8. B. Kosko, C. Guest, Proc. Soc. Photo-Opt. Instrum. Eng. 758, 11 (1987).
  9. H.-H. Liu, S. Y. kung, J. A. Davis, Opt. Eng. 25, 853 (1986).
  10. E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).
  11. H. M. Stoll, L.-S. Lee, in Proceedings of the 1888 IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. II-373.
  12. M. S. Cohen, Appl. Opt. 25, 2288 (1986).
    [CrossRef] [PubMed]
  13. D. Z. Anderson, Opt. Lett. 11, 56 (1986).
    [CrossRef] [PubMed]
  14. Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).
  15. D. O. Hebb, The Organization of Behavior ( Wiley, New York, 1949).
  16. C. N. Kurtz, J. Opt. Soc. Am. 62, 982 (1972).
    [CrossRef]
  17. In view of the resolution evidenced by Figs. 3 and 4, the cross-talk criterion may be too restrictive.
  18. The influence of device noise on memory capacity is currently under investigation.

1987 (2)

B. Kosko, C. Guest, Proc. Soc. Photo-Opt. Instrum. Eng. 758, 11 (1987).

E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).

1986 (6)

M. S. Cohen, Appl. Opt. 25, 2288 (1986).
[CrossRef] [PubMed]

D. Z. Anderson, Opt. Lett. 11, 56 (1986).
[CrossRef] [PubMed]

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

H.-H. Liu, S. Y. kung, J. A. Davis, Opt. Eng. 25, 853 (1986).

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

R. A. Athale, H. H. Szu, C. B. Friedlander, Opt. Lett. 11, 482(1986).
[CrossRef] [PubMed]

1985 (2)

J. J. Hopfield, D. W. Tank, Biol. Cybern. 52, 141 (1985).
[PubMed]

D. Psaltis, N. Farhat, Opt. Lett. 10, 98 (1985).
[CrossRef] [PubMed]

1982 (1)

J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[CrossRef] [PubMed]

1978 (1)

S. Grossberg, J. Math. Anal. Appl. 66, 470 (1978).
[CrossRef]

1977 (1)

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, Psychol. Rev. 84, 413 (1977).
[CrossRef]

1972 (1)

Anderson, D. Z.

Anderson, J. A.

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, Psychol. Rev. 84, 413 (1977).
[CrossRef]

Athale, R. A.

Cohen, M. S.

Davis, J. A.

H.-H. Liu, S. Y. kung, J. A. Davis, Opt. Eng. 25, 853 (1986).

Fainman, Y.

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Farhat, N.

Fisher, A. D.

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

Friedlander, C. B.

Fukuda, R. C.

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

Grossberg, S.

S. Grossberg, J. Math. Anal. Appl. 66, 470 (1978).
[CrossRef]

Guest, C.

B. Kosko, C. Guest, Proc. Soc. Photo-Opt. Instrum. Eng. 758, 11 (1987).

Hebb, D. O.

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

Hopfield, J. J.

J. J. Hopfield, D. W. Tank, Biol. Cybern. 52, 141 (1985).
[PubMed]

J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[CrossRef] [PubMed]

Jones, R. S.

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, Psychol. Rev. 84, 413 (1977).
[CrossRef]

Klancnik, E.

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Kosko, B.

B. Kosko, C. Guest, Proc. Soc. Photo-Opt. Instrum. Eng. 758, 11 (1987).

kung, S. Y.

H.-H. Liu, S. Y. kung, J. A. Davis, Opt. Eng. 25, 853 (1986).

Kurtz, C. N.

Lee, J. N.

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

Lee, L.-S.

H. M. Stoll, L.-S. Lee, in Proceedings of the 1888 IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. II-373.

Lee, S. H.

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Liu, H.-H.

H.-H. Liu, S. Y. kung, J. A. Davis, Opt. Eng. 25, 853 (1986).

Paek, E. G.

E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).

Psaltis, D.

E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).

D. Psaltis, N. Farhat, Opt. Lett. 10, 98 (1985).
[CrossRef] [PubMed]

Ritz, S. A.

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, Psychol. Rev. 84, 413 (1977).
[CrossRef]

Silverstein, J. W.

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, Psychol. Rev. 84, 413 (1977).
[CrossRef]

Stoll, H. M.

H. M. Stoll, L.-S. Lee, in Proceedings of the 1888 IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. II-373.

Szu, H. H.

Tank, D. W.

J. J. Hopfield, D. W. Tank, Biol. Cybern. 52, 141 (1985).
[PubMed]

Appl. Opt. (1)

Biol. Cybern. (1)

J. J. Hopfield, D. W. Tank, Biol. Cybern. 52, 141 (1985).
[PubMed]

J. Math. Anal. Appl. (1)

S. Grossberg, J. Math. Anal. Appl. 66, 470 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (3)

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

H.-H. Liu, S. Y. kung, J. A. Davis, Opt. Eng. 25, 853 (1986).

E. G. Paek, D. Psaltis, Opt. Eng. 26, 428 (1987).

Opt. Lett. (3)

Proc. Natl. Acad. Sci. USA (1)

J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

B. Kosko, C. Guest, Proc. Soc. Photo-Opt. Instrum. Eng. 758, 11 (1987).

A. D. Fisher, R. C. Fukuda, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 625, 196 (1986).

Psychol. Rev. (1)

J. A. Anderson, J. W. Silverstein, S. A. Ritz, R. S. Jones, Psychol. Rev. 84, 413 (1977).
[CrossRef]

Other (4)

H. M. Stoll, L.-S. Lee, in Proceedings of the 1888 IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. II-373.

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

In view of the resolution evidenced by Figs. 3 and 4, the cross-talk criterion may be too restrictive.

The influence of device noise on memory capacity is currently under investigation.

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Figures (3)

Fig. 1
Fig. 1

Diagram of continuous-time optical neural network. Optical neurons are generated within the saturable, two-beam amplifier, and a global neural interconnect is realized by using Fourier- and object-space holograms to implement an inner-product, matrix–vector multiplication algorithm. L4–L10, imaging lenses; P1–P4, imagery planes; P5, Fourier plane. 2-D, two-dimensional.

Fig. 2
Fig. 2

Demonstration of network used as associative memory: (a), (b) stored images of an M-1 tank; (c) incestuous input; (d) partial recall.

Fig. 3
Fig. 3

Demonstration of network used as associative memory: (a), (b) stored images of a T-62 tank; (c), (d) simultaneous displays of nonincestuous inputs (right-hand sides of images) and latched outputs (left-hand sides of images).

Equations (1)

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( t ) = k v k ( v k ) T σ ( t ) = k [ σ ( t ) , v k ] v k ,

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