Abstract

A learning and recall algorithm for optical associative memory based on the conventional correlation-learning method with three effective improvements (sparse-encoding method, constant-total-activity method, and binary memory) is proposed from a viewpoint of practical implementation. It is shown that the algorithm is suitable for implementation with a bistable spatial light modulator such as a ferroelectric liquid-crystal spatial light modulator, which has high resolution and a fast response time. The results of theoretical analysis and simulations indicate that the algorithm permits an associative-memory system with a large memory capacity to be realized. An example of an optical system for executing this algorithm is proposed. To determine the performance specifications that are required for the various optical components within the system, we simulate and evaluate the effect of noise (which is caused by nonideal components) on system performance. These results show that the system is robust in the presence of predicted noise levels.

© 1995 Optical Society of America

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References

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    [CrossRef]

1993 (2)

1990 (2)

1989 (4)

1987 (1)

1985 (1)

1980 (1)

G. Palm, “On associative memory,” Biol. Cybernet. 36, 19–31 (1980).
[CrossRef]

1972 (1)

T. Kohonen, “Correlation matrix memories,” IEEE Trans. Comput. C-21, 353–359 (1972).
[CrossRef]

Amari, S.

S. Amari, “Characteristics of sparsely encoded associative memory,” Neural Net. 2, 451–457 (1989).
[CrossRef]

Casasent, D. P.

Farhat, N. H.

Fisher, A. D.

Fukushima, S.

Hara, T.

Hinton, G. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClellandthe PDP Research Group, eds. (MIT Press, Cambridge, Mass., 1986), pp. 318–362.

Ishikawa, M.

Johnson, K. M.

Kohonen, T.

T. Kohonen, “Correlation matrix memories,” IEEE Trans. Comput. C-21, 353–359 (1972).
[CrossRef]

Kurokawa, T.

Lee, J. N.

Lippincott, W. L.

Matsuo, S.

Moddel, G.

Mukohzaka, N.

Ooi, Y.

Paek, E.

Palm, G.

G. Palm, “On associative memory,” Biol. Cybernet. 36, 19–31 (1980).
[CrossRef]

Prata, A.

Psaltis, D.

Rumelhart, D. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClellandthe PDP Research Group, eds. (MIT Press, Cambridge, Mass., 1986), pp. 318–362.

Suzuki, Y.

Telfer, B.

Toyoda, H.

Williams, R. J.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClellandthe PDP Research Group, eds. (MIT Press, Cambridge, Mass., 1986), pp. 318–362.

Wu, M. H.

Appl. Opt. (8)

Biol. Cybernet. (1)

G. Palm, “On associative memory,” Biol. Cybernet. 36, 19–31 (1980).
[CrossRef]

IEEE Trans. Comput. (1)

T. Kohonen, “Correlation matrix memories,” IEEE Trans. Comput. C-21, 353–359 (1972).
[CrossRef]

Neural Net. (1)

S. Amari, “Characteristics of sparsely encoded associative memory,” Neural Net. 2, 451–457 (1989).
[CrossRef]

Opt. Lett. (1)

Other (2)

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClellandthe PDP Research Group, eds. (MIT Press, Cambridge, Mass., 1986), pp. 318–362.

H. Toyoda, M. Ishikawa, “Sparse encoding algorithm for optical associative memory using bistable spatial light modulator,” in Japan Display ’92, Proceedings of the Twelfth International Display Research Conference (Society for Information Display, Playa del Rey, Calif., 1992).

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Figures (11)

Fig. 1
Fig. 1

Design consideration presented in this paper. The proposed algorithm improves the performance of the correlation-learning method yet maintains the good optoelectronic realizability of this method. This permits a larger number of neurons to be implemented than is possible for error backpropagation (EBP) and so is better suited to an optical implementation.

Fig. 2
Fig. 2

Memory capacity of the proposed algorithm. Error function Φ(n, m, s) is the error probability for the recall process.

Fig. 3
Fig. 3

Memory capacity for recall from untrained patterns with Hamming distance ±h from one of the trained patterns.

Fig. 4
Fig. 4

Influence of the constant total activity and the binary memory on memory capacity.

Fig. 5
Fig. 5

Conceptual diagram of the proposed system.

Fig. 6
Fig. 6

Optical system.

Fig. 7
Fig. 7

Example of the optical constant-total-activity unit (CAU) utilizing a threshold device.

Fig. 8
Fig. 8

Effect of nonuniformity of the FLC SLM on memory capacity. When α = 0.1, the FLC SLM has a random nonuniformity of 10%.

Fig. 9
Fig. 9

Effect of cross talk of the cylindrical lens on memory capacity. When β = 0.1, a lateral cross-talk level of 10% is introduced at the SLM by the cylindrical lens.

Fig. 10
Fig. 10

Effect of nonuniformity of the PD array on memory capacity. When γ is 0.1, a PD array has a random nonuniformity in sensitivity of 10%.

Fig. 11
Fig. 11

Effect on memory capacity when two effective error sources (nonuniformity of the PD array and cross talk of the cylindrical lens) occur at the same time. The nonuniformity of the PD array, γ, was assumed to be 3% in consideration of practical devices. The parameter β* indicates a lateral cross-talk level on the SLM by the cylindrical lens in the case of γ = 3%.

Equations (14)

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M = p = 1 m ( x p x t p T ) ,
y = ϕ out ( M x ) .
ϕ out ( x ) = ϕ th ( x ) = { 0 ( x < threshold ) 1 ( x threshold ) .
M = ϕ th [ p = 1 m ( x p x p T ) ] ,
y = ϕ th ( M x ) ,
i = 1 n x i = i = 1 n x p i = i = 1 n y i = n s ,
E ( y i ; x i = 1 ) = j = 1 n M x j = j = 1 n { ϕ th ( x 1 i x 1 j + + x i x j + ) } x j = j = 1 n x j = n s .
P [ ( k = 1 , m k p x k i ) = 0 ] = ( 1 s 2 ) m 1 .
μ = n s [ 1 ( 1 s 2 ) m 1 ] ,
σ 2 = n s [ 1 ( 1 s 2 ) m 1 ] ( 1 s 2 ) m 1 .
E ( y i ; x i = 0 ) E ( y i ; x i = 1 ) .
P error = Φ ( n s μ σ ) = Φ ( n s ( 1 s 2 ) m 1 { n s [ 1 ( 1 s 2 ) m 1 ] ( 1 s 2 ) m 1 } 1 / 2 ) ,
Φ ( x ) = 2 π 0 x exp ( x 2 ) d x .
P error ( h ) = Φ ( ( n s h ) ( 1 s 2 ) m 1 { n s [ 1 ( 1 s 2 ) m 1 ] ( 1 s 2 ) m 1 } 1 / 2 )

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