Abstract

The effect of discretizing interconnection weight strengths in an optoelectronic learning neural network based on the backpropagation algorithm is investigated. We discuss how discretization arises in such an implementation. Using computer simulations we find that learning performance, as tested on the two-input XOR problem, is poor but that the addition of noise to the system results in substantial improvement.

© 1989 Optical Society of America

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References

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  1. A. D. Fisher, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 20 (1987).
  2. D. E. Rumelhart, G. E. Hinton, J. L. McClelland, in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, Chaps. 2 and 8.
  3. J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79, 2554 (1982).
    [CrossRef] [PubMed]
  4. J. W. Goodman, A. R. Dias, L. M. Woody, Opt. Lett. 2, 1 (1978).
    [CrossRef] [PubMed]
  5. N. Farhat, Opt. Lett. 12, 448 (1987).
    [CrossRef] [PubMed]
  6. N. Farhat, Appl. Opt. 26, 5093 (1987).
    [CrossRef] [PubMed]
  7. S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, Opt. Eng. 26, 406 (1987).
  8. R. A. Athale, W. C. Collins, Appl. Opt. 21, 2089 (1982).
    [CrossRef] [PubMed]
  9. A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrakchi, J. S. Patel, J. Opt. Soc. Am. A 4(13), P128 (1987).
  10. N. A. Clark, S. T. Lagerwall, Appl. Phys. Lett. 36, 899 (1980).
    [CrossRef]
  11. W. Ross, Opt. Eng. 22, 485 (1983).
  12. A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrackchi, J. S. Patel, in Proceedings of IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. 335.
    [CrossRef]

1987

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

N. Farhat, Appl. Opt. 26, 5093 (1987).
[CrossRef] [PubMed]

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, Opt. Eng. 26, 406 (1987).

A. D. Fisher, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 20 (1987).

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrakchi, J. S. Patel, J. Opt. Soc. Am. A 4(13), P128 (1987).

1983

W. Ross, Opt. Eng. 22, 485 (1983).

1982

1980

N. A. Clark, S. T. Lagerwall, Appl. Phys. Lett. 36, 899 (1980).
[CrossRef]

1978

Athale, R. A.

Clark, N. A.

N. A. Clark, S. T. Lagerwall, Appl. Phys. Lett. 36, 899 (1980).
[CrossRef]

Collins, W. C.

Dias, A. R.

Drabik, T. J.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, Opt. Eng. 26, 406 (1987).

Esener, S. C.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, Opt. Eng. 26, 406 (1987).

Farhat, N.

Fisher, A. D.

A. D. Fisher, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 20 (1987).

Goodman, J. W.

Hinton, G. E.

D. E. Rumelhart, G. E. Hinton, J. L. McClelland, in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, Chaps. 2 and 8.

Hopfield, J. J.

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

Lagerwall, S. T.

N. A. Clark, S. T. Lagerwall, Appl. Phys. Lett. 36, 899 (1980).
[CrossRef]

Lee, J. N.

A. D. Fisher, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 20 (1987).

Lee, S. H.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, Opt. Eng. 26, 406 (1987).

Liao, P. F.

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrakchi, J. S. Patel, J. Opt. Soc. Am. A 4(13), P128 (1987).

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrackchi, J. S. Patel, in Proceedings of IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. 335.
[CrossRef]

Marrackchi, A.

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrackchi, J. S. Patel, in Proceedings of IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. 335.
[CrossRef]

Marrakchi, A.

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrakchi, J. S. Patel, J. Opt. Soc. Am. A 4(13), P128 (1987).

McClelland, J. L.

D. E. Rumelhart, G. E. Hinton, J. L. McClelland, in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, Chaps. 2 and 8.

Paek, E. G.

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrakchi, J. S. Patel, J. Opt. Soc. Am. A 4(13), P128 (1987).

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrackchi, J. S. Patel, in Proceedings of IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. 335.
[CrossRef]

Patel, J. S.

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrakchi, J. S. Patel, J. Opt. Soc. Am. A 4(13), P128 (1987).

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrackchi, J. S. Patel, in Proceedings of IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. 335.
[CrossRef]

Ross, W.

W. Ross, Opt. Eng. 22, 485 (1983).

Rumelhart, D. E.

D. E. Rumelhart, G. E. Hinton, J. L. McClelland, in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, Chaps. 2 and 8.

Title, M. A.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, Opt. Eng. 26, 406 (1987).

Von Lehmen, A.

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrakchi, J. S. Patel, J. Opt. Soc. Am. A 4(13), P128 (1987).

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrackchi, J. S. Patel, in Proceedings of IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. 335.
[CrossRef]

Wang, J. H.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, Opt. Eng. 26, 406 (1987).

Woody, L. M.

Appl. Opt.

Appl. Phys. Lett.

N. A. Clark, S. T. Lagerwall, Appl. Phys. Lett. 36, 899 (1980).
[CrossRef]

J. Opt. Soc. Am. A

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrakchi, J. S. Patel, J. Opt. Soc. Am. A 4(13), P128 (1987).

Opt. Eng.

S. C. Esener, J. H. Wang, T. J. Drabik, M. A. Title, S. H. Lee, Opt. Eng. 26, 406 (1987).

W. Ross, Opt. Eng. 22, 485 (1983).

Opt. Lett.

Proc. Natl. Acad. Sci. USA

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

Proc. Soc. Photo-Opt. Instrum. Eng.

A. D. Fisher, J. N. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 20 (1987).

Other

D. E. Rumelhart, G. E. Hinton, J. L. McClelland, in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT Press, Cambridge, Mass., 1986), Vol. 1, Chaps. 2 and 8.

A. Von Lehmen, E. G. Paek, P. F. Liao, A. Marrackchi, J. S. Patel, in Proceedings of IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. 335.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Chip design for the matrix–vector multiplier.

Fig. 2
Fig. 2

Results of computer simulations that show the percentage of cases converged as a function of the number of discrete weight levels in the backward propagation algorithm. These results are calculated in the absence of noise.

Fig. 3
Fig. 3

Computer simulation results showing the percentage of cases converged as a function of (a) the maximum noise amplitude and (b) the ratio of maximum noise amplitude to step size. The different curves illustrate the results for different numbers of discrete levels.

Equations (1)

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w ij ( n + 1 ) = w ij ( n ) ηδ w ij ( n + 1 ) + αδ w ij ( n ) .

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