Abstract

An optical perceptronlike neural network employing a delta learning rule and consisting of input units and a single output unit is constructed. Photorefractive crystals are used as holographic media for the interconnections between the input and the output layers. The learning rate for interconnection weight changes is optimally determined by setting the exposure time of the hologram. A learning experiment verifies the learning schedule's prediction that a fast, stable convergence of the learning process without oscillatory action can be obtained.

© 1989 Optical Society of America

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References

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  1. B. Irie, S. Miyake, in IEEE Annual International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. I-641.
  2. D. E. Rumelhart, J. L. McClellandthe PDP Research Group, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vol. 1.
  3. A. D. Fisher, W. L. Lippincott, J. N. Lee, Appl. Opt. 26, 5039 (1987).
    [CrossRef] [PubMed]
  4. K. Wagner, D. Psaltis, Appl. Opt. 26, 5061 (1987).
    [CrossRef] [PubMed]
  5. Y. Owechko, Appl. Opt. 26, 5104 (1987).
    [CrossRef] [PubMed]
  6. D. Psaltis, D. Brady, K. Wagner, Appl. Opt. 27, 1752 (1988).
    [CrossRef]
  7. H. Yoshinaga, K. Kitayama, T. Hara, Opt. Lett. 14, 202 (1989).
    [CrossRef] [PubMed]

1989

1988

1987

Brady, D.

Fisher, A. D.

Hara, T.

Irie, B.

B. Irie, S. Miyake, in IEEE Annual International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. I-641.

Kitayama, K.

Lee, J. N.

Lippincott, W. L.

McClelland, J. L.

D. E. Rumelhart, J. L. McClellandthe PDP Research Group, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vol. 1.

Miyake, S.

B. Irie, S. Miyake, in IEEE Annual International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. I-641.

Owechko, Y.

Psaltis, D.

Rumelhart, D. E.

D. E. Rumelhart, J. L. McClellandthe PDP Research Group, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vol. 1.

Wagner, K.

Yoshinaga, H.

Appl. Opt.

Opt. Lett.

Other

B. Irie, S. Miyake, in IEEE Annual International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1988), p. I-641.

D. E. Rumelhart, J. L. McClellandthe PDP Research Group, Parallel Distributed Processing (MIT Press, Cambridge, Mass., 1986), Vol. 1.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. M's, mirrors; MH's, half-mirrors.

Fig. 2
Fig. 2

(a) Response times of recording (circles) and erasing (triangles) versus the laser power. The response time for recording is the time from 10% to 90% of grating saturation; the erasing time is the time from 90% to 10% of grating saturation. Also shown is the temporal behavior of (b) recording and (c) erasing for a beam intensity of 1.0 mW/cm2. The time scale is 0.5 sec/division.

Fig. 3
Fig. 3

Experimental and theoretical outputs at each stage of the learning process. The diffracted beam intensity for holograms illuminated by each pattern at each learning step is plotted versus time. The vertical axis shows the normalized diffracted outputs, and the horizontal axis shows the stage of the hologram learning process. The learning is performed for four letters: Z, U, J, and N. The recording process is performed for letters Z and J, and the erasing process is performed for letters U and N.

Fig. 4
Fig. 4

Diffracted patterns observed by illuminating Z and U during the learning process. The corresponding schematic patterns are also illustrated.

Equations (3)

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Δ ω i = η δ o i ,
δ = t o ,
o = f ( Σ ω i o i )

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