Abstract

A Hopfield-type neural network with only inhibitory interconnections is shown to perform similarly to networks with both inhibitory and excitatory interconnects. With the use of only inhibitory neurons the need to subtract light intensities is eliminated, so an all-optical neural network can be realized. This realization is achieved with a liquid-crystal light valve for implementing a two-dimensional array of 16 inhibitory neurons and an array of subholograms for the interconnections. Two stable states that can be retrieved from noisy optical inputs are demonstrated.

© 1989 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

1988 (2)

1985 (2)

1982 (1)

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

1973 (1)

T. D. Beard, W. P. Bleha, S.-Y. Wong, Appl. Phys. Lett. 22, 90 (1973).
[CrossRef]

Beard, T. D.

T. D. Beard, W. P. Bleha, S.-Y. Wong, Appl. Phys. Lett. 22, 90 (1973).
[CrossRef]

Bleha, W. P.

T. D. Beard, W. P. Bleha, S.-Y. Wong, Appl. Phys. Lett. 22, 90 (1973).
[CrossRef]

Farhat, N.

Hopfield, J. J.

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

Jang, J.-S.

Jenkins, B. K.

Jung, S.-W.

Lee, S.-Y.

Peak, E.

Prata, A.

Psaltis, D.

Shin, S.-Y.

Wang, C. H.

Wong, S.-Y.

T. D. Beard, W. P. Bleha, S.-Y. Wong, Appl. Phys. Lett. 22, 90 (1973).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. D. Beard, W. P. Bleha, S.-Y. Wong, Appl. Phys. Lett. 22, 90 (1973).
[CrossRef]

Opt. Lett (1)

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

Opt. Lett. (2)

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

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

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Figures (5)

Fig. 1
Fig. 1

Final overlap versus the initial overlap. Solid line, the Hopfield model; dashed line, the negative interconnects only; dotted line, the positive interconnects only.

Fig. 2
Fig. 2

Inhabitory neural response function g(x).

Fig. 3
Fig. 3

Response of the liquid-crystal light valve operating at 3 kHz and 8.8 V peak to peak.

Fig. 4
Fig. 4

All-optical neural network. M’s, mirrors; H, subhologram array; L, imaging lens; PCBS, polarizing cubic beam splitter. Only three representative neurons are shown.

Fig. 5
Fig. 5

Experimental results. (a) The representative inputs and (b) the corresponding outputs, which are the two stored patterns of the numerals 4 and 6.

Equations (7)

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T i j = { μ = 1 C S i μ S j μ for i j 0 for i = j ,
S i = f ( j = 1 N T i j S j ) ,
f ( x ) { 1 for x 0 - 1 otherwise .
T i j = { T i j when     T i j 0 0 otherwise
S i = f ( j = 1 N T i j S j ) .
N i = 1 2 [ 1 - f ( - 2 j T i j N i + j T i j ) ] .
N i = g ( j T i j N j ) ,

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