Abstract

The proposed technique for optical neural networks can perform all the neural operations in a positive range. Bipolar weights of the neurons are represented by unipolar weights with a positive constant. By superposing the reversal inputs to the weighted sums, we can perform subtraction in a neuron by the nonlinear output function with a negative offset constant. This means that the number of processing elements needed in the proposed system is the same as that of neurons in the original neural network model. An experimental neural system is demonstrated for verification of this technique. The Hopfield model is adapted as an example of the neural networks implemented in the experimental neural system.

© 1994 Optical Society of America

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References

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1992 (1)

1991 (3)

1990 (6)

1989 (6)

1988 (1)

1987 (2)

1986 (1)

1985 (1)

T. Hara, M. Sugiyama, Y. Suzuki, “A spatial light modulator,” Adv. Electron. Phys. 64B, 637–639 (1985).
[CrossRef]

1984 (2)

A. D. Fisher, C. L. Giles, J. N. Lee, “Associative processor architectures for optical computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

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

1982 (1)

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. U.S.A. 79, 2554–2558 (1982).
[CrossRef] [PubMed]

1972 (1)

Bibner, B. J.

M. Kranzdorf, B. J. Bibner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization-based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

Denker, B. J. S.

H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, B. J. S. Denker, W. Hubbard, D. M. Tennat, D. Schwartz, “VLSI implementation of a neural network memory with several hundreds of neurons,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 182–187.

Emeling, M. R.

M. A. Sivvilotti, M. R. Emeling, C. A. Mead, “VLSI architectures for implementation of neural networks,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 408–413.

Farhat, N.

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

Farhat, N. H.

Feinleib, J.

Fisher, A. D.

A. D. Fisher, C. L. Giles, J. N. Lee, “Associative processor architectures for optical computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

Friesem, A. A.

Gila, O.

Giles, C. L.

A. D. Fisher, C. L. Giles, J. N. Lee, “Associative processor architectures for optical computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

Goodman, J. W.

Graf, H. P.

H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, B. J. S. Denker, W. Hubbard, D. M. Tennat, D. Schwartz, “VLSI implementation of a neural network memory with several hundreds of neurons,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 182–187.

Gregory, D. A.

Hara, T.

T. Hara, M. Sugiyama, Y. Suzuki, “A spatial light modulator,” Adv. Electron. Phys. 64B, 637–639 (1985).
[CrossRef]

Hayasaki, Y.

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]

Hopfield, J. J.

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. U.S.A. 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Howard, R. E.

H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, B. J. S. Denker, W. Hubbard, D. M. Tennat, D. Schwartz, “VLSI implementation of a neural network memory with several hundreds of neurons,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 182–187.

Hubbard, W.

H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, B. J. S. Denker, W. Hubbard, D. M. Tennat, D. Schwartz, “VLSI implementation of a neural network memory with several hundreds of neurons,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 182–187.

Ishihara, S.

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]

Ishikawa, M.

Ito, F.

Ittycheriah, A. P.

Ivanov, V. A.

A. L. Mikaelian, B. S. Kiselyov, N. Y. Kulakov, V. A. Shkitin, V. A. Ivanov, “Optical implementation of high-order associative memory,” Int. Natl. Opt. Comp. 1, 89–92 (1990).

Jackel, L. D.

H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, B. J. S. Denker, W. Hubbard, D. M. Tennat, D. Schwartz, “VLSI implementation of a neural network memory with several hundreds of neurons,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 182–187.

Jang, J. S.

Jenkins, B. K.

Johnson, K.

Johnson, K. M.

M. Kranzdorf, B. J. Bibner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization-based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

Jung, S. M.

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]

Kawakami, W.

Kiselyov, B. S.

A. L. Mikaelian, B. S. Kiselyov, N. Y. Kulakov, V. A. Shkitin, V. A. Ivanov, “Optical implementation of high-order associative memory,” Int. Natl. Opt. Comp. 1, 89–92 (1990).

Kitayama, K.

Kohonen, T.

T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, New York, 1984), Chap. 3, p.67.

Kranzdorf, M.

M. Kranzdorf, B. J. Bibner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization-based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

Krile, T. F.

Kulakov, N. Y.

A. L. Mikaelian, B. S. Kiselyov, N. Y. Kulakov, V. A. Shkitin, V. A. Ivanov, “Optical implementation of high-order associative memory,” Int. Natl. Opt. Comp. 1, 89–92 (1990).

Kyuma, K.

Lee, J. N.

A. D. Fisher, C. L. Giles, J. N. Lee, “Associative processor architectures for optical computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

Lee, S. Y.

Lim, S. L.

Lu, T.

McClelland, J. L.

D. E. Rumelhart, J. L. McClelland, and the PDP Research Group, Parallel Distributed Processing (MIT, Cambridge, Mass., 1986), Chap. 2, p. 45.

Mead, C. A.

M. A. Sivvilotti, M. R. Emeling, C. A. Mead, “VLSI architectures for implementation of neural networks,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 408–413.

Mikaelian, A. L.

A. L. Mikaelian, B. S. Kiselyov, N. Y. Kulakov, V. A. Shkitin, V. A. Ivanov, “Optical implementation of high-order associative memory,” Int. Natl. Opt. Comp. 1, 89–92 (1990).

Miteva, M.

Mitsunaga, K.

Mori, M.

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]

Mukouzaka, N.

Nitta, Y.

Ohta, J.

Oliver, D. S.

Psaltis, D.

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5061–5076 (1987).
[CrossRef] [PubMed]

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

Robinson, M. G.

Rumelhart, D. E.

D. E. Rumelhart, J. L. McClelland, and the PDP Research Group, Parallel Distributed Processing (MIT, Cambridge, Mass., 1986), Chap. 2, p. 45.

Schwartz, D.

H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, B. J. S. Denker, W. Hubbard, D. M. Tennat, D. Schwartz, “VLSI implementation of a neural network memory with several hundreds of neurons,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 182–187.

Shariv, I.

Shin, S. Y.

Shkitin, V. A.

A. L. Mikaelian, B. S. Kiselyov, N. Y. Kulakov, V. A. Shkitin, V. A. Ivanov, “Optical implementation of high-order associative memory,” Int. Natl. Opt. Comp. 1, 89–92 (1990).

Sivvilotti, M. A.

M. A. Sivvilotti, M. R. Emeling, C. A. Mead, “VLSI architectures for implementation of neural networks,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 408–413.

Straughn, B.

H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, B. J. S. Denker, W. Hubbard, D. M. Tennat, D. Schwartz, “VLSI implementation of a neural network memory with several hundreds of neurons,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 182–187.

Sugiyama, M.

T. Hara, M. Sugiyama, Y. Suzuki, “A spatial light modulator,” Adv. Electron. Phys. 64B, 637–639 (1985).
[CrossRef]

Suzuki, Y.

Tai, S.

Takahashi, M.

Takeda, M.

Tennat, D. M.

H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, B. J. S. Denker, W. Hubbard, D. M. Tennat, D. Schwartz, “VLSI implementation of a neural network memory with several hundreds of neurons,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 182–187.

Toyoda, H.

Wagner, K.

Walkup, J. F.

Wang, C. H.

Yang, X.

Yatagai, T.

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]

Yoshinaga, H.

Yu, F. T. S.

Zhang, L.

M. Kranzdorf, B. J. Bibner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization-based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

Zhivkova, S.

Adv. Electron. Phys. (1)

T. Hara, M. Sugiyama, Y. Suzuki, “A spatial light modulator,” Adv. Electron. Phys. 64B, 637–639 (1985).
[CrossRef]

Appl. Opt. (10)

J. Feinleib, D. S. Oliver, “Reusable optical image storage and processing device,” Appl. Opt. 11, 2752–2759 (1972).
[CrossRef] [PubMed]

A. P. Ittycheriah, J. F. Walkup, T. F. Krile, S. L. Lim, “Outer product processor using polarization encoding,” Appl. Opt. 29, 275–283 (1990).
[CrossRef] [PubMed]

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5061–5076 (1987).
[CrossRef] [PubMed]

N. H. Farhat, “Optoelectronic analogs of self-programming neural nets: architecture and methodologies for implementing fast stochastic learning by simulated annealing,” Appl. Opt. 26, 5093–5103 (1987).
[CrossRef] [PubMed]

C. H. Wang, B. K. Jenkins, “Subtracting incoherent optical neural model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990).
[CrossRef] [PubMed]

M. Ishikawa, N. Mukouzaka, H. Toyoda, Y. Suzuki, “Optical association: a simple model for optical associative memory,” Appl. Opt. 28, 291–301 (1989).
[CrossRef] [PubMed]

M. Ishikawa, N. Mukouzaka, H. Toyoda, Y. Suzuki, “Experimental studies on learning capabilities of optical associative memory,” Appl. Opt. 29, 289–295 (1990).
[CrossRef] [PubMed]

M. G. Robinson, K. Johnson, “Noise analysis of polarization-based optoelectronic connectionist machines,” Appl. Opt. 31, 263–272 (1992).
[CrossRef] [PubMed]

M. Takeda, J. W. Goodman, “Neural networks for computation: number representations and programing complexity,” Appl. Opt. 25, 3033–3046 (1986).
[CrossRef] [PubMed]

F. Ito, K. Kitayama, “Optical implementation of the Hopfield neural network using multiple fiber nets,” Appl. Opt. 28, 4176–4181 (1989).
[CrossRef] [PubMed]

Int. Natl. Opt. Comp. (1)

A. L. Mikaelian, B. S. Kiselyov, N. Y. Kulakov, V. A. Shkitin, V. A. Ivanov, “Optical implementation of high-order associative memory,” Int. Natl. Opt. Comp. 1, 89–92 (1990).

J. Opt. Soc. Am. A (2)

A. D. Fisher, C. L. Giles, J. N. Lee, “Associative processor architectures for optical computing,” J. Opt. Soc. Am. A 1, 1337 (1984).

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

Jpn. J. Appl. Phys. (1)

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. Eng. (1)

M. Kranzdorf, B. J. Bibner, L. Zhang, K. M. Johnson, “Optical connectionist machine with polarization-based bipolar weight values,” Opt. Eng. 28, 844–848 (1989).

Opt. Lett. (8)

Proc. Natl. Acad. Sci. U.S.A. (1)

J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities,” Proc. Natl. Acad. Sci. U.S.A. 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Other (4)

T. Kohonen, Self-Organization and Associative Memory (Springer-Verlag, New York, 1984), Chap. 3, p.67.

D. E. Rumelhart, J. L. McClelland, and the PDP Research Group, Parallel Distributed Processing (MIT, Cambridge, Mass., 1986), Chap. 2, p. 45.

M. A. Sivvilotti, M. R. Emeling, C. A. Mead, “VLSI architectures for implementation of neural networks,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 408–413.

H. P. Graf, L. D. Jackel, R. E. Howard, B. Straughn, B. J. S. Denker, W. Hubbard, D. M. Tennat, D. Schwartz, “VLSI implementation of a neural network memory with several hundreds of neurons,” in Proceedings of the AIP Conference on Neural Networks for Computing (American Institute of Physics, New York, 1986), pp. 182–187.

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Figures (8)

Fig. 1
Fig. 1

Block diagram of the RIST in a neural network.

Fig. 2
Fig. 2

Generation of an input pattern and its reversal-input pattern in parallel by the use of a polarization technique.

Fig. 3
Fig. 3

Experimental neural system based on the RIST: (a) schematic diagram, (b) photograph. The light source, which is omitted in (a), is a He–Ne laser. The light of the polarization pattern on the liquid-crystal television (LCTV) is divided in two orthogonally polarized lights by Analyzer1 and Analyzer2, and two divided beams are superposed by the beam splitter. Analyzer1 and Analyzer2 are set to 0° and 90° with respect to the vertical axis, respectively. Analyzer3 adjusts the light intensity ratio between both paths and decides the constant α. ND, neutral density.

Fig. 4
Fig. 4

Measured transmittance of the LCTV for the input signals. The solid curve and the dashed curve show the light transmitted intensities of the input pattern on PATH1 and the reversal input pattern on PATH2, respectively. The light intensities are normalized by the maximum value of the reversal input.

Fig. 5
Fig. 5

Three stored patterns A, B, and C, consisting of 5 × 5 elements. The hamming distances between two patterns are shown.

Fig. 6
Fig. 6

(a) Synaptic weights W calculated from three stored patterns. The weights have 25 × 25 elements. (b) Photographic film memorizing the biased synaptic weights W b .

Fig. 7
Fig. 7

Experimental results of recalling the retrieval of three stored patterns. The solid lines show the experimental recalling of all positive initial inputs whose deviations from the the stored pattern are 3 and less. For comparison, the dashed lines show the results of the computer simulation of recallings the initial inputs whose deviations are 6 and less.

Fig. 8
Fig. 8

Example of the recalling process. The photographs in (b), (d), (f), (h), and (j) are the CCD outputs. The input pattern is displayed by the vertical 1-D vector with horizontal spreading. The CCD outputs are performed for the nonlinear operation g after summing up along vertical direction, and the next recalled pattern is obtained. For simplicity, the input patterns are shown by 2-D rearrangement. The initial input pattern X = {10100 11111 00111 11110 01010} in (a) is the deviation of 8 from the stored pattern C = {01010 11111 01010 11111 01010}. The patterns in (c), (e), (i), (g), (k) are recalled patterns in the retrival process, and the pattern in (k) is the pattern C.

Equations (19)

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

u j = i w j i x i - h j ,
v j = f ( u j ) ,
u j = i ( w j i + α ) x i + α i ( β - x i ) - N α β .
α - min ( w j i ) ,
β max ( x i ) ,
u ¯ j = i w j i b x i + α i x ¯ j .
v j = g ( u ¯ j ) ,
g ( u ) = f ( u - N α β ) .
x j ( t + 1 ) = g [ i w j i b x i ( t ) + α i x ¯ i ( t ) ] ,
u ¯ j = i ( w j i b x i + α x ¯ i ) .
α = - min ( w j i ) = max ( w j i ) ,
max ( x i ) = max ( x ¯ i ) = 1.
max ( w j i b x i ) = max ( w j i b ) = max ( w j i + α ) = 2 α ,
max ( α x ¯ i ) = α .
w j i = p ( 2 x p j - 1 ) ( 2 x p i - 1 ) for i j , = 0 for i = j .
u j = i w j i x i ,
x j = 1 if u j > 0 , = 0 otherwise .
g ( u ) = 1 if u > N P , = 0 otherwise .
A = { 01111 00000 11111 00000 11110 } , B = { 10100 10101 10101 10101 00101 } , C = { 01010 11111 01010 11111 01010 } .

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