Abstract

Optical-processor architectures for various forms of the alternating-projection neural network are considered. Required iteration is performed by passive optical feedback. No electronics or slow optics (e.g., phase conjugators) are used in the feedback path. The processor can be taught a new training vector by viewing it only once. If the desired outputs are trained to be either ±1, then the network can be configured to converge in one iteration.

© 1988 Optical Society of America

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References

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  1. N. Farhat, D. Psaltis, A. Prata, E. Paek, Appl. Opt. 24, 1469 (1985).
    [CrossRef] [PubMed]
  2. D. Psaltis, N. Farhat, Opt. Lett. 10, 98 (1985).
    [CrossRef] [PubMed]
  3. B. Macukow, H. H. Arsenault, Appl. Opt. 26, 924 (1987).
    [CrossRef] [PubMed]
  4. N. Farhat, Opt. Lett. 12, 448 (1987).
    [CrossRef] [PubMed]
  5. Special issues on optical artificial intelligence and neural networks, Appl. Opt. 26, 1827–1958 (1987).Special issues on optical artificial intelligence and neural networks, Appl. Opt. 26, 4909–5111 (1987).Special issues on optical artificial intelligence and neural networks, Appl. Opt. 26, 5189–5190 (1987).
    [PubMed]
  6. R. J. Marks, Appl. Opt. 26, 2005 (1987).
    [CrossRef]
  7. K. F. Cheung, S. Oh, R. J. Marks, L. E. Atlas, in Proceedings of the IEEE First International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-245.
  8. R. J. Marks, L. E. Atlas, K. F. Cheung, in Proceedings of the Fourteenth Congress of the International Commission for Optics (International Commission for Optics Secretariat, Quebec City, Quebec, 1987), pp. 29–30.
  9. R. J. Marks, L. E. Atlas, S. Oh, J. A. Ritcey, “The performance of convex set projection based neural networks,” presented at the IEEE Conference on Neural Information Processing Systems, Denver, Colo., 1987.
  10. T. Maxwell, C. L. Giles, Y. C. Lee, in Proceedings of the 1986 IEEE International Conference on Systems, Man, and Cybernetics (Institute of Electrical and Electronics Engineers, New York, 1986), p. 627.
  11. J. W. Goodman, A. R. Dias, L. M. Woody, Opt. Lett. 2, 1 (1978).
    [CrossRef] [PubMed]
  12. R. J. Marks, Appl. Opt. 19, 1670 (1980).
    [CrossRef]
  13. See, e.g., H. Haga, IEEE J. Quantum Electron. QE-22, 902 (1986).
    [CrossRef]

1987

Special issues on optical artificial intelligence and neural networks, Appl. Opt. 26, 1827–1958 (1987).Special issues on optical artificial intelligence and neural networks, Appl. Opt. 26, 4909–5111 (1987).Special issues on optical artificial intelligence and neural networks, Appl. Opt. 26, 5189–5190 (1987).
[PubMed]

N. Farhat, Opt. Lett. 12, 448 (1987).
[CrossRef] [PubMed]

B. Macukow, H. H. Arsenault, Appl. Opt. 26, 924 (1987).
[CrossRef] [PubMed]

R. J. Marks, Appl. Opt. 26, 2005 (1987).
[CrossRef]

1986

See, e.g., H. Haga, IEEE J. Quantum Electron. QE-22, 902 (1986).
[CrossRef]

1985

1980

1978

Arsenault, H. H.

Atlas, L. E.

R. J. Marks, L. E. Atlas, K. F. Cheung, in Proceedings of the Fourteenth Congress of the International Commission for Optics (International Commission for Optics Secretariat, Quebec City, Quebec, 1987), pp. 29–30.

K. F. Cheung, S. Oh, R. J. Marks, L. E. Atlas, in Proceedings of the IEEE First International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-245.

R. J. Marks, L. E. Atlas, S. Oh, J. A. Ritcey, “The performance of convex set projection based neural networks,” presented at the IEEE Conference on Neural Information Processing Systems, Denver, Colo., 1987.

Cheung, K. F.

K. F. Cheung, S. Oh, R. J. Marks, L. E. Atlas, in Proceedings of the IEEE First International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-245.

R. J. Marks, L. E. Atlas, K. F. Cheung, in Proceedings of the Fourteenth Congress of the International Commission for Optics (International Commission for Optics Secretariat, Quebec City, Quebec, 1987), pp. 29–30.

Dias, A. R.

Farhat, N.

Giles, C. L.

T. Maxwell, C. L. Giles, Y. C. Lee, in Proceedings of the 1986 IEEE International Conference on Systems, Man, and Cybernetics (Institute of Electrical and Electronics Engineers, New York, 1986), p. 627.

Goodman, J. W.

Haga, H.

See, e.g., H. Haga, IEEE J. Quantum Electron. QE-22, 902 (1986).
[CrossRef]

Lee, Y. C.

T. Maxwell, C. L. Giles, Y. C. Lee, in Proceedings of the 1986 IEEE International Conference on Systems, Man, and Cybernetics (Institute of Electrical and Electronics Engineers, New York, 1986), p. 627.

Macukow, B.

Marks, R. J.

R. J. Marks, Appl. Opt. 26, 2005 (1987).
[CrossRef]

R. J. Marks, Appl. Opt. 19, 1670 (1980).
[CrossRef]

R. J. Marks, L. E. Atlas, K. F. Cheung, in Proceedings of the Fourteenth Congress of the International Commission for Optics (International Commission for Optics Secretariat, Quebec City, Quebec, 1987), pp. 29–30.

K. F. Cheung, S. Oh, R. J. Marks, L. E. Atlas, in Proceedings of the IEEE First International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-245.

R. J. Marks, L. E. Atlas, S. Oh, J. A. Ritcey, “The performance of convex set projection based neural networks,” presented at the IEEE Conference on Neural Information Processing Systems, Denver, Colo., 1987.

Maxwell, T.

T. Maxwell, C. L. Giles, Y. C. Lee, in Proceedings of the 1986 IEEE International Conference on Systems, Man, and Cybernetics (Institute of Electrical and Electronics Engineers, New York, 1986), p. 627.

Oh, S.

K. F. Cheung, S. Oh, R. J. Marks, L. E. Atlas, in Proceedings of the IEEE First International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-245.

R. J. Marks, L. E. Atlas, S. Oh, J. A. Ritcey, “The performance of convex set projection based neural networks,” presented at the IEEE Conference on Neural Information Processing Systems, Denver, Colo., 1987.

Paek, E.

Prata, A.

Psaltis, D.

Ritcey, J. A.

R. J. Marks, L. E. Atlas, S. Oh, J. A. Ritcey, “The performance of convex set projection based neural networks,” presented at the IEEE Conference on Neural Information Processing Systems, Denver, Colo., 1987.

Woody, L. M.

Appl. Opt.

Special issues on optical artificial intelligence and neural networks, Appl. Opt. 26, 1827–1958 (1987).Special issues on optical artificial intelligence and neural networks, Appl. Opt. 26, 4909–5111 (1987).Special issues on optical artificial intelligence and neural networks, Appl. Opt. 26, 5189–5190 (1987).
[PubMed]

Appl. Opt.

IEEE J. Quantum Electron.

See, e.g., H. Haga, IEEE J. Quantum Electron. QE-22, 902 (1986).
[CrossRef]

Opt. Lett.

Other

K. F. Cheung, S. Oh, R. J. Marks, L. E. Atlas, in Proceedings of the IEEE First International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1987), p. III-245.

R. J. Marks, L. E. Atlas, K. F. Cheung, in Proceedings of the Fourteenth Congress of the International Commission for Optics (International Commission for Optics Secretariat, Quebec City, Quebec, 1987), pp. 29–30.

R. J. Marks, L. E. Atlas, S. Oh, J. A. Ritcey, “The performance of convex set projection based neural networks,” presented at the IEEE Conference on Neural Information Processing Systems, Denver, Colo., 1987.

T. Maxwell, C. L. Giles, Y. C. Lee, in Proceedings of the 1986 IEEE International Conference on Systems, Man, and Cybernetics (Institute of Electrical and Electronics Engineers, New York, 1986), p. 627.

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Figures (2)

Fig. 1
Fig. 1

An architecture for performing a layered APNN. In practice, the architecture requires augmentation as in Ref. 11 to allow for the required bipolar operations. The states of the hidden layers are nonlinear functions of the clamped layers and are generated electronically.

Fig. 2
Fig. 2

An architecture for performing a homogeneous APNN.

Equations (3)

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η i = η ( i 1 , i 2 , i P | i P + 1 i L ) T = ( f 1 , f 2 , f P | i P + 1 i L ) T ,
S ( m + 1 ) = η TS ( m ) ,
T + = T + e e T / ( e T e ) ,

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