Abstract

We have constructed an optical neural-network system with learning capability by using a Pockels readout optical modulator. The system has a two-dimensional structure that permits easy optical alignment and can handle images without scanning. Learning signals are calculated optically with two liquid-crystal devices by a matrix–matrix outer-product method. The calculated learning signals are added directly to the weights memorized on the Pockels readout optical modulator. A two-layer network is implemented, and the learning and recognition of four alphabetical characters are realized according to the delta rule.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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1996 (1)

S. Gao, J. Yang, Y. Zhang, G. Mu, “Architecture design of an optical neural network with lenslet array,” Optik 101, 127–129 (1996).

1995 (1)

1994 (3)

1992 (1)

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).
[CrossRef]

1991 (1)

1990 (2)

F. Itoh, K. Kitayama, Y. Tanuma, “Optical outer-product learning in a neural network using optically stimulable phosphor,” Opt. Lett. 15, 860–862 (1990).
[CrossRef] [PubMed]

N. Kasama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Experimental demonstration of optical three-layer neural network,” Jpn. J. Appl. Phys. 29, L1565–L1568 (1990).
[CrossRef]

1989 (3)

1985 (2)

1984 (1)

N. H. Farhat, D. Psaltis, “New approach to optical information processing based on the Hopfield model,” (abstract) J. Opt. Soc. Am. A 1, 1296 (1984).

Abe, H.

Y. Osugi, H. Abe, A. Honda, A. Hamajima, S. Toyoda, “A method for making high resolution PROM,” in Technical Digest of International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (Japan Society of Applied Physics, Tokyo, Japan, 1990), pp. 21–22.

Bitoh, Y.

Y. Bitoh, T. Minemoto, “Fast response PROM using GaAs single crystal,” in Spatial Light Modulators, G. Burdge, S. C. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 147–154.

Carpio Perez, E.

Choi, K.

de Bougrenet de la Tocnaye, J. L.

Duvillier, J.

Farhat, N. H.

Gao, S.

S. Gao, J. Yang, Y. Zhang, G. Mu, “Architecture design of an optical neural network with lenslet array,” Optik 101, 127–129 (1996).

S. Gao, Y. Zhang, J. Yang, G. Mu, “Coaxial architecture of an optical neural network with a lenslet array,” Opt. Lett. 19, 2155–2157 (1994).
[CrossRef] [PubMed]

Hamajima, A.

Y. Osugi, H. Abe, A. Honda, A. Hamajima, S. Toyoda, “A method for making high resolution PROM,” in Technical Digest of International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (Japan Society of Applied Physics, Tokyo, Japan, 1990), pp. 21–22.

Hayasaki, Y.

M. Mori, Y. Hayasaki, I. Tohyama, T. Yatagai, “Optical learning neural network using a Selfoc microlens array for pattern recognition,” Opt. Rev. 1, 44–46 (1994).
[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).
[CrossRef]

N. Kasama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Experimental demonstration of optical three-layer neural network,” Jpn. J. Appl. Phys. 29, L1565–L1568 (1990).
[CrossRef]

M. Mori, S. Ishihara, I. Tohyama, Y. Hayasaki, T. Yatagai, “Optical neural networks based on an electron-beam addressed spatial light modulator,” in Optical Computing and Neural Networks, K.-Y. Hsu, H.-K. Liu, eds., Proc. SPIE1812, 57–63 (1992).
[CrossRef]

I. Tohyama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Renewal method of weight matrix in optical neural network,” in Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, S. P. Apanasevich, eds., Proc. SPIE1806, 271–278 (1992).
[CrossRef]

Heggarty, K.

Honda, A.

Y. Osugi, H. Abe, A. Honda, A. Hamajima, S. Toyoda, “A method for making high resolution PROM,” in Technical Digest of International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (Japan Society of Applied Physics, Tokyo, Japan, 1990), pp. 21–22.

Ishihara, S.

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).
[CrossRef]

N. Kasama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Experimental demonstration of optical three-layer neural network,” Jpn. J. Appl. Phys. 29, L1565–L1568 (1990).
[CrossRef]

M. Mori, S. Ishihara, I. Tohyama, Y. Hayasaki, T. Yatagai, “Optical neural networks based on an electron-beam addressed spatial light modulator,” in Optical Computing and Neural Networks, K.-Y. Hsu, H.-K. Liu, eds., Proc. SPIE1812, 57–63 (1992).
[CrossRef]

I. Tohyama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Renewal method of weight matrix in optical neural network,” in Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, S. P. Apanasevich, eds., Proc. SPIE1806, 271–278 (1992).
[CrossRef]

Ishikawa, M.

Itoh, F.

Kasama, N.

N. Kasama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Experimental demonstration of optical three-layer neural network,” Jpn. J. Appl. Phys. 29, L1565–L1568 (1990).
[CrossRef]

Killinger, M.

Kitayama, K.

Kyuma, K.

Lu, T.

Minemoto, T.

Y. Bitoh, T. Minemoto, “Fast response PROM using GaAs single crystal,” in Spatial Light Modulators, G. Burdge, S. C. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 147–154.

Mitsunaga, K.

Mori, M.

M. Mori, Y. Hayasaki, I. Tohyama, T. Yatagai, “Optical learning neural network using a Selfoc microlens array for pattern recognition,” Opt. Rev. 1, 44–46 (1994).
[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).
[CrossRef]

N. Kasama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Experimental demonstration of optical three-layer neural network,” Jpn. J. Appl. Phys. 29, L1565–L1568 (1990).
[CrossRef]

M. Mori, S. Ishihara, I. Tohyama, Y. Hayasaki, T. Yatagai, “Optical neural networks based on an electron-beam addressed spatial light modulator,” in Optical Computing and Neural Networks, K.-Y. Hsu, H.-K. Liu, eds., Proc. SPIE1812, 57–63 (1992).
[CrossRef]

M. Mori, Y. Nagamune, M. Watanabe, T. Noda, H. Sakaki, “Neuron devices based on point contact phototransistors,” in Digest of the IEEE/LEOS 1996 Summer Topical Meeting on Smart Pixels (IEEE, Piscataway, N.J., 1996), pp. 9–10.

I. Tohyama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Renewal method of weight matrix in optical neural network,” in Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, S. P. Apanasevich, eds., Proc. SPIE1806, 271–278 (1992).
[CrossRef]

Mu, G.

S. Gao, J. Yang, Y. Zhang, G. Mu, “Architecture design of an optical neural network with lenslet array,” Optik 101, 127–129 (1996).

S. Gao, Y. Zhang, J. Yang, G. Mu, “Coaxial architecture of an optical neural network with a lenslet array,” Opt. Lett. 19, 2155–2157 (1994).
[CrossRef] [PubMed]

Mukohzaka, N.

Nagamune, Y.

M. Mori, Y. Nagamune, M. Watanabe, T. Noda, H. Sakaki, “Neuron devices based on point contact phototransistors,” in Digest of the IEEE/LEOS 1996 Summer Topical Meeting on Smart Pixels (IEEE, Piscataway, N.J., 1996), pp. 9–10.

Nitta, Y.

Noda, T.

M. Mori, Y. Nagamune, M. Watanabe, T. Noda, H. Sakaki, “Neuron devices based on point contact phototransistors,” in Digest of the IEEE/LEOS 1996 Summer Topical Meeting on Smart Pixels (IEEE, Piscataway, N.J., 1996), pp. 9–10.

Ohta, J.

Osugi, Y.

Y. Osugi, H. Abe, A. Honda, A. Hamajima, S. Toyoda, “A method for making high resolution PROM,” in Technical Digest of International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (Japan Society of Applied Physics, Tokyo, Japan, 1990), pp. 21–22.

Peak, E.

Prata, A.

Psaltis, D.

Sakaki, H.

M. Mori, Y. Nagamune, M. Watanabe, T. Noda, H. Sakaki, “Neuron devices based on point contact phototransistors,” in Digest of the IEEE/LEOS 1996 Summer Topical Meeting on Smart Pixels (IEEE, Piscataway, N.J., 1996), pp. 9–10.

Suzuki, Y.

Tai, S.

Takahashi, M.

Tanuma, Y.

Tohyama, I.

M. Mori, Y. Hayasaki, I. Tohyama, T. Yatagai, “Optical learning neural network using a Selfoc microlens array for pattern recognition,” Opt. Rev. 1, 44–46 (1994).
[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).
[CrossRef]

M. Mori, S. Ishihara, I. Tohyama, Y. Hayasaki, T. Yatagai, “Optical neural networks based on an electron-beam addressed spatial light modulator,” in Optical Computing and Neural Networks, K.-Y. Hsu, H.-K. Liu, eds., Proc. SPIE1812, 57–63 (1992).
[CrossRef]

I. Tohyama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Renewal method of weight matrix in optical neural network,” in Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, S. P. Apanasevich, eds., Proc. SPIE1806, 271–278 (1992).
[CrossRef]

Toyoda, H.

Toyoda, S.

Y. Osugi, H. Abe, A. Honda, A. Hamajima, S. Toyoda, “A method for making high resolution PROM,” in Technical Digest of International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (Japan Society of Applied Physics, Tokyo, Japan, 1990), pp. 21–22.

Watanabe, M.

M. Mori, Y. Nagamune, M. Watanabe, T. Noda, H. Sakaki, “Neuron devices based on point contact phototransistors,” in Digest of the IEEE/LEOS 1996 Summer Topical Meeting on Smart Pixels (IEEE, Piscataway, N.J., 1996), pp. 9–10.

Wu, S.

Xu, X.

Yang, J.

S. Gao, J. Yang, Y. Zhang, G. Mu, “Architecture design of an optical neural network with lenslet array,” Optik 101, 127–129 (1996).

S. Gao, Y. Zhang, J. Yang, G. Mu, “Coaxial architecture of an optical neural network with a lenslet array,” Opt. Lett. 19, 2155–2157 (1994).
[CrossRef] [PubMed]

Yao, K.

Yatagai, T.

M. Mori, Y. Hayasaki, I. Tohyama, T. Yatagai, “Optical learning neural network using a Selfoc microlens array for pattern recognition,” Opt. Rev. 1, 44–46 (1994).
[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).
[CrossRef]

N. Kasama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Experimental demonstration of optical three-layer neural network,” Jpn. J. Appl. Phys. 29, L1565–L1568 (1990).
[CrossRef]

M. Mori, S. Ishihara, I. Tohyama, Y. Hayasaki, T. Yatagai, “Optical neural networks based on an electron-beam addressed spatial light modulator,” in Optical Computing and Neural Networks, K.-Y. Hsu, H.-K. Liu, eds., Proc. SPIE1812, 57–63 (1992).
[CrossRef]

I. Tohyama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Renewal method of weight matrix in optical neural network,” in Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, S. P. Apanasevich, eds., Proc. SPIE1806, 271–278 (1992).
[CrossRef]

Yu, F. T. S.

Zhang, Y.

S. Gao, J. Yang, Y. Zhang, G. Mu, “Architecture design of an optical neural network with lenslet array,” Optik 101, 127–129 (1996).

S. Gao, Y. Zhang, J. Yang, G. Mu, “Coaxial architecture of an optical neural network with a lenslet array,” Opt. Lett. 19, 2155–2157 (1994).
[CrossRef] [PubMed]

Appl. Opt. (5)

J. Opt. Soc. Am. A (1)

N. H. Farhat, D. Psaltis, “New approach to optical information processing based on the Hopfield model,” (abstract) J. Opt. Soc. Am. A 1, 1296 (1984).

Jpn. J. Appl. Phys. (2)

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).
[CrossRef]

N. Kasama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Experimental demonstration of optical three-layer neural network,” Jpn. J. Appl. Phys. 29, L1565–L1568 (1990).
[CrossRef]

Opt. Lett. (5)

Opt. Rev. (1)

M. Mori, Y. Hayasaki, I. Tohyama, T. Yatagai, “Optical learning neural network using a Selfoc microlens array for pattern recognition,” Opt. Rev. 1, 44–46 (1994).
[CrossRef]

Optik (1)

S. Gao, J. Yang, Y. Zhang, G. Mu, “Architecture design of an optical neural network with lenslet array,” Optik 101, 127–129 (1996).

Other (5)

I. Tohyama, Y. Hayasaki, T. Yatagai, M. Mori, S. Ishihara, “Renewal method of weight matrix in optical neural network,” in Optical Computing, A. M. Goncharenko, F. V. Karpushko, G. V. Sinitsyn, S. P. Apanasevich, eds., Proc. SPIE1806, 271–278 (1992).
[CrossRef]

M. Mori, S. Ishihara, I. Tohyama, Y. Hayasaki, T. Yatagai, “Optical neural networks based on an electron-beam addressed spatial light modulator,” in Optical Computing and Neural Networks, K.-Y. Hsu, H.-K. Liu, eds., Proc. SPIE1812, 57–63 (1992).
[CrossRef]

Y. Osugi, H. Abe, A. Honda, A. Hamajima, S. Toyoda, “A method for making high resolution PROM,” in Technical Digest of International Topical Meeting on Optical Computing, J. Tsujiuchi, Y. Ichioka, S. Ishihara, eds. (Japan Society of Applied Physics, Tokyo, Japan, 1990), pp. 21–22.

Y. Bitoh, T. Minemoto, “Fast response PROM using GaAs single crystal,” in Spatial Light Modulators, G. Burdge, S. C. Esener, eds., Vol. 14 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1997), pp. 147–154.

M. Mori, Y. Nagamune, M. Watanabe, T. Noda, H. Sakaki, “Neuron devices based on point contact phototransistors,” in Digest of the IEEE/LEOS 1996 Summer Topical Meeting on Smart Pixels (IEEE, Piscataway, N.J., 1996), pp. 9–10.

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Figures (8)

Fig. 1
Fig. 1

Schematic illustration that explains the principle of the system for optical recall. The multiple images made from the input image are superposed with the weights. The local accumulation of the calculated results and a nonlinear function determine the output of the 2-D neural network.

Fig. 2
Fig. 2

Principle of optical parallel computation of the learning signals. The superposition of the error-signal matrix and the multiple input image produces the outer product. The results are added directly to the weights.

Fig. 3
Fig. 3

Multiple-imaging system with the 10 × 10 SMLA. A photograph of an example multiple image is shown in the lower right-hand region.

Fig. 4
Fig. 4

Learning optical neural-network system that we constructed. The multiple image (input matrix I ijkl ) of an input I ij is displayed on LCD1. The red LED illuminates the input matrix and the weights on the PROM. The calculated results are detected by CCD2 during the recall processes. The outer product is implemented by superposition of the error matrix δ kl from LCD2 and the multiple input from LCD1 by use of the blue LED readout. The outer-product results are then added directly to the weights on the PROM.

Fig. 5
Fig. 5

Output–input characteristic of the PROM when writing with the blue LED and reading out with the red LED. The transmittance saturates at approximately 6.5%.

Fig. 6
Fig. 6

Inputs and the teaching signals used for the experiment. The binarized characters with 64 × 64 bits are input into the system. An output of four bits is produced by the recall processes.

Fig. 7
Fig. 7

Photograph of an outer-product result. The multiple images of M and the error-signal matrix, in which all the elements but three are zero, were overlapped.

Fig. 8
Fig. 8

Learning curve to recognize four alphabetical characters. The total error became zero on completion of six iterations, and the required neural-network performance was obtained.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

O kl = f j i W ijkl × I ij .
W ijkl t + 1 = W ijkl t + Δ W ijkl .
Δ W ijkl = α δ kl × I ij .
δ kl = T kl - O kl .
E total = p k l   | T pkl - O pkl | ,

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