Abstract

We propose a method for the implementation of the Hopfield algorithm using inner products of unipolar data. This approach is particularly useful for image recognition.

© 1990 Optical Society of America

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References

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  1. J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
    [CrossRef] [PubMed]
  2. N. Farhat, D. Psaltis, A. Prata, E. Paek, “Optical Implementation of the Hopfield Model,” Appl. Opt. 24, 1469–1475 (1985).
    [CrossRef] [PubMed]
  3. D. Psaltis, J. Hong, “Shift-Invariant Optical Associative Memories,” Opt. Eng. 26, 10–15 (1987).
    [CrossRef]
  4. E. Paek, D. Psaltis, “Optical Associative Memory Using Fourier Transform Holograms,” Opt. Eng. 26, 428–433 (1987).
    [CrossRef]
  5. B. Stoffer, G. Dunning, Y. Owechko, E. Marrom, “Associative Holographic Memory with Feedback using Phase-Conjugating Mirrors,” Opt. Lett. 11, 118–120 (1986).
    [CrossRef]
  6. R. Athale, H. Szu, C. Friedlander, “Optical Implementation of Associative Memory with Controlled Nonlinearity in the Correlation Domain,” Opt. Lett. 11, 482–484 (1986).
    [CrossRef] [PubMed]
  7. H. J. Caulfield, “Parallel N4 Weighted Optical Interconnections,” Appl. Opt. 26, 4039–4040 (1987).
    [CrossRef] [PubMed]

1987 (3)

D. Psaltis, J. Hong, “Shift-Invariant Optical Associative Memories,” Opt. Eng. 26, 10–15 (1987).
[CrossRef]

E. Paek, D. Psaltis, “Optical Associative Memory Using Fourier Transform Holograms,” Opt. Eng. 26, 428–433 (1987).
[CrossRef]

H. J. Caulfield, “Parallel N4 Weighted Optical Interconnections,” Appl. Opt. 26, 4039–4040 (1987).
[CrossRef] [PubMed]

1986 (2)

1985 (1)

1982 (1)

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Athale, R.

Caulfield, H. J.

Dunning, G.

Farhat, N.

Friedlander, C.

Hong, J.

D. Psaltis, J. Hong, “Shift-Invariant Optical Associative Memories,” Opt. Eng. 26, 10–15 (1987).
[CrossRef]

Hopfield, J. J.

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Marrom, E.

Owechko, Y.

Paek, E.

E. Paek, D. Psaltis, “Optical Associative Memory Using Fourier Transform Holograms,” Opt. Eng. 26, 428–433 (1987).
[CrossRef]

N. Farhat, D. Psaltis, A. Prata, E. Paek, “Optical Implementation of the Hopfield Model,” Appl. Opt. 24, 1469–1475 (1985).
[CrossRef] [PubMed]

Prata, A.

Psaltis, D.

E. Paek, D. Psaltis, “Optical Associative Memory Using Fourier Transform Holograms,” Opt. Eng. 26, 428–433 (1987).
[CrossRef]

D. Psaltis, J. Hong, “Shift-Invariant Optical Associative Memories,” Opt. Eng. 26, 10–15 (1987).
[CrossRef]

N. Farhat, D. Psaltis, A. Prata, E. Paek, “Optical Implementation of the Hopfield Model,” Appl. Opt. 24, 1469–1475 (1985).
[CrossRef] [PubMed]

Stoffer, B.

Szu, H.

Appl. Opt. (2)

Opt. Eng. (2)

D. Psaltis, J. Hong, “Shift-Invariant Optical Associative Memories,” Opt. Eng. 26, 10–15 (1987).
[CrossRef]

E. Paek, D. Psaltis, “Optical Associative Memory Using Fourier Transform Holograms,” Opt. Eng. 26, 428–433 (1987).
[CrossRef]

Opt. Lett. (2)

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

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

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Equations (15)

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T i j = m [ X i ( m ) X j ( m ) - δ i j ]             i , j = 1 , 2 , , N .
V i ( n + 1 ) = Φ [ j T i j V j ( n ) ]             n = 0 , 1 , 2 , 3 , ,
V ( n + 1 ) = Φ [ TV ( n ) ]             n = 0 , 1 , 2 , 3 , ,
V ( n + 1 ) = Φ [ m β ( m ) ( n ) X ( m ) - M V ( n ) ] ,
β ( m ) ( n ) = j X j ( m ) V j ( n ) = X t V .
X = ( 2 x - 1 ) .
v ( n + 1 ) = Ψ [ 4 m β ( m ) ( n ) x ( m ) - M v ( n ) + α ( n ) y - 2 m β ( m ) + z ] ,
β ( m ) ( n ) = j x j ( m ) v j ( n ) ,
α ( n ) = k [ v k ( n ) ] 2
y = M - 2 m x ( m ) ,
z = M ( 1 - N ) / 2 + m x ( m ) [ N - 2 j x j ( m ) ] + m j x j ( m )
α ( n ) = k v k = k v k u k ,
β ( m ) ( n ) = k l x k l ( m ) v k l ( n ) .
v ( n + 1 ) = Φ [ m β ( m ) ( n ) x ( m ) ] .
E = - 1 / 2 i j T i j V j V i ,

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