Abstract

The remarkable collective computational properties of the Hopfield model for neural networks [Proc. Nat. Acad. Sci. USA 79, 2554 (1982)] are reviewed. These include recognition from partial input, robustness, and error-correction capability. Features of the model that make its optical implementation attractive are discussed, and specific optical implementation schemes are given.

© 1985 Optical Society of America

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References

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  1. D. Gabor, IBM J. Res. Dev. 13, 156 (1969).
    [CrossRef]
  2. J. J. Hopfield, Proc. Nat. Acad. Sci. USA 79, 2554 (1982).
    [CrossRef] [PubMed]
  3. J. Goodman, A. R. Dias, I. M. Woody, Opt. Lett. 2, 1 (1978).
    [CrossRef] [PubMed]
  4. Z. Porada, Thin Solid Films 109, 213 (1983).
    [CrossRef]
  5. H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Opt. News 5(3), 6 (1979).
    [CrossRef]
  6. D. Psaltis, N. Farhat, presented at the Meeting of the International Commission for Optics, ICO-13, Sapporo, Japan, August 1984.

1983 (1)

Z. Porada, Thin Solid Films 109, 213 (1983).
[CrossRef]

1982 (1)

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

1979 (1)

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Opt. News 5(3), 6 (1979).
[CrossRef]

1978 (1)

1969 (1)

D. Gabor, IBM J. Res. Dev. 13, 156 (1969).
[CrossRef]

Dias, A. R.

Farhat, N.

D. Psaltis, N. Farhat, presented at the Meeting of the International Commission for Optics, ICO-13, Sapporo, Japan, August 1984.

Gabor, D.

D. Gabor, IBM J. Res. Dev. 13, 156 (1969).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Opt. News 5(3), 6 (1979).
[CrossRef]

Goodman, J.

Hopfield, J. J.

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

McCall, S. L.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Opt. News 5(3), 6 (1979).
[CrossRef]

Porada, Z.

Z. Porada, Thin Solid Films 109, 213 (1983).
[CrossRef]

Psaltis, D.

D. Psaltis, N. Farhat, presented at the Meeting of the International Commission for Optics, ICO-13, Sapporo, Japan, August 1984.

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Opt. News 5(3), 6 (1979).
[CrossRef]

Woody, I. M.

IBM J. Res. Dev. (1)

D. Gabor, IBM J. Res. Dev. 13, 156 (1969).
[CrossRef]

Opt. Lett. (1)

Opt. News (1)

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, Opt. News 5(3), 6 (1979).
[CrossRef]

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

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

Thin Solid Films (1)

Z. Porada, Thin Solid Films 109, 213 (1983).
[CrossRef]

Other (1)

D. Psaltis, N. Farhat, presented at the Meeting of the International Commission for Optics, ICO-13, Sapporo, Japan, August 1984.

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Figures (3)

Fig. 1
Fig. 1

Two schemes for adding nonlinear feedback to an optical vector-matrix multiplier utilizing (a) electronic feedback and (b) optical feedback.

Fig. 2
Fig. 2

Scheme for realizing bipolar mask transmittance with incoherent light.

Fig. 3
Fig. 3

Coherent optical implementation for 2-D inputs.

Equations (5)

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T i j = { m M [ 2 υ i ( m ) 1 ] [ 2 υ j ( m ) 1 ] if i j 0 if i = j
υ ̂ i ( m 0 ) = j N T i j υ j ( m 0 ) = N 0 [ 2 υ i ( m 0 ) 1 ] + m m 0 M { j N [ 2 υ j ( m ) 1 ] υ j ( m 0 ) } × [ 2 υ i ( m ) 1 ] M υ i ( m 0 ) ,
P [ υ i ( m ) = 1 ] = ½ , P [ υ i ( m ) = 0 ] = ½ ,
SNR = { | E [ υ ̂ i ( m 0 ) ] | } / { var [ υ ̂ i ( m 0 ) ] } 1 / 2 = [ N / 2 ( M 1 ) ] 1 / 2 .
T ( i , i , j , j ) = m M υ ( m ) ( i , i ) υ ( m ) ( j , j ) .

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