Abstract

An all-optical error signal based on the generalized delta rule for backpropagation learning in optical multilayer networks is experimentally obtained. Optically addressable microchannel spatial light modulators are used to perform key functional operations for the error signal such as subtraction, soft thresholding, and taking the derivative of the thresholding function. The error signals are readily available to adaptive optical multilayer networks in which photorefractive crystals are used to determine the connection weights between processing units.

© 1989 Optical Society of America

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Corrections

Hisao Yoshinaga, Tsutomu Hara, and Ken-ichi Kitayama, "All-optical error-signal generation for backpropagation learning in optical multilayer neural networks: erratum," Opt. Lett. 14, 901-901 (1989)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-14-16-901

References

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  1. J. L. McClelland, D. E. Rumelhartthe PDP research group, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vol. 1.
  2. A. D. Fisher, W. L. Lippincott, J. N. Lee, Appl. Opt. 26, 5039 (1987).
    [CrossRef] [PubMed]
  3. K. Wagner, D. Psaltis, Appl. Opt. 26, 5061 (1987).
    [CrossRef] [PubMed]
  4. Y. Owechko, Appl. Opt. 26, 5104 (1987).
    [CrossRef] [PubMed]
  5. D. Psaltis, D. Brady, K. Wagner, Appl. Opt. 27, 1752 (1988).
    [CrossRef]
  6. T. Hara, T. Ooi, T. Kao, Y. Suzuki, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 153 (1986).

1988 (1)

1987 (3)

1986 (1)

T. Hara, T. Ooi, T. Kao, Y. Suzuki, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 153 (1986).

Brady, D.

Fisher, A. D.

Hara, T.

T. Hara, T. Ooi, T. Kao, Y. Suzuki, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 153 (1986).

Kao, T.

T. Hara, T. Ooi, T. Kao, Y. Suzuki, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 153 (1986).

Lee, J. N.

Lippincott, W. L.

McClelland, J. L.

J. L. McClelland, D. E. Rumelhartthe PDP research group, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vol. 1.

Ooi, T.

T. Hara, T. Ooi, T. Kao, Y. Suzuki, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 153 (1986).

Owechko, Y.

Psaltis, D.

Rumelhart, D. E.

J. L. McClelland, D. E. Rumelhartthe PDP research group, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vol. 1.

Suzuki, Y.

T. Hara, T. Ooi, T. Kao, Y. Suzuki, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 153 (1986).

Wagner, K.

Appl. Opt. (4)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

T. Hara, T. Ooi, T. Kao, Y. Suzuki, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 153 (1986).

Other (1)

J. L. McClelland, D. E. Rumelhartthe PDP research group, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vol. 1.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the functional operations of Eq. (2). f, Thresholding; f′, derivative of f; SUB, subtraction; MUL, multiplication.

Fig. 2
Fig. 2

Experimental setup. The operations performed by MSLM1, MSLM2, and MSLM3 are soft thresholding of the net input, addressing the target, and taking a derivative of the thresholding function, respectively. M., mirror; H.M.’s, half-mirrors.

Fig. 3
Fig. 3

Photographs of the experimental results. (a) Net input and target patterns, (b) soft thresholding of the net input, (c) negative derivative of the thresholding function, (d) positive derivative of the thresholding function, (e) subtraction of the output from the target, (f) error signal.

Equations (4)

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Δ w k j = δ k o j ,
δ k = ( t k o k ) f k ( net k ) ,
o k = f k ( net k ) ,
δ j = ( k w k j δ k ) f j ( net j ) .

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