Abstract

A method to achieve bipolar performance in a single-channel optical associative memory is presented. By coding the biased interconnection weights, a distributed background, and an input-dependent dynamic threshold on a single mask, we construct an optical network with both bipolar neural states and bipolar interconnections. Content addressability and other properties are improved by the introduction of a distributed background, as compared with the case in which this background is not used. Computer simulations and optical experiments are performed based on the Hopfield algorithm.

© 1992 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  9. X.-M. Wang, G.-G. Mu, “Holographic associative memory with bipolar features,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadam, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 1558–1565 (1991).
  10. D. J. Amit, H. Gutfreund, “Statistical mechanics of neural networks near saturation,” Ann. Phys. (N.Y.) 173, 30–67 (1987).
    [CrossRef]
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1990 (1)

1989 (2)

1988 (3)

1987 (1)

D. J. Amit, H. Gutfreund, “Statistical mechanics of neural networks near saturation,” Ann. Phys. (N.Y.) 173, 30–67 (1987).
[CrossRef]

1985 (2)

1982 (1)

J. J. Hopfield, “Neural network and physical system with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Amit, D. J.

D. J. Amit, H. Gutfreund, “Statistical mechanics of neural networks near saturation,” Ann. Phys. (N.Y.) 173, 30–67 (1987).
[CrossRef]

Chavel, P.

David, A. J.

Farhat, N.

Farhat, N. H.

Gutfreund, H.

D. J. Amit, H. Gutfreund, “Statistical mechanics of neural networks near saturation,” Ann. Phys. (N.Y.) 173, 30–67 (1987).
[CrossRef]

Hopfield, J. J.

J. J. Hopfield, “Neural network and physical system with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Jang, J.-S.

Jenkins, B. K.

Jung, S.-W.

Kim, J. C.

Kyuma, K.

Lalanne, P.

Lee, S.-Y.

Mitsunaga, K.

Mu, G.-G.

X.-M. Wang, G.-G. Mu, “Holographic associative memory with bipolar features,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadam, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 1558–1565 (1991).

Nitta, Y.

Oh, S.-H.

Ohta, J.

Paek, E.

Prata, A.

Psaltis, D.

Saleh, B. E. A.

Shin, S.-Y.

Taboury, J.

Tai, S.

Takahashi, M.

Wang, C. H.

Wang, X.-M.

X.-M. Wang, G.-G. Mu, “Holographic associative memory with bipolar features,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadam, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 1558–1565 (1991).

Yoon, T.-H.

Ann. Phys. (N.Y.) (1)

D. J. Amit, H. Gutfreund, “Statistical mechanics of neural networks near saturation,” Ann. Phys. (N.Y.) 173, 30–67 (1987).
[CrossRef]

Appl. Opt. (3)

Opt. Lett. (5)

Proc. Natl. Acad. Sci. USA (1)

J. J. Hopfield, “Neural network and physical system with emergent collective computational abilities,” Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982).
[CrossRef] [PubMed]

Other (1)

X.-M. Wang, G.-G. Mu, “Holographic associative memory with bipolar features,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadam, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1558, 1558–1565 (1991).

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Figures (2)

Fig. 1
Fig. 1

Distribution formation of the enlarged matrix: Tij|p, biased interconnection weight; BGDi, background; A, biased level; Max, maximum of DTi.

Fig. 2
Fig. 2

Hybrid optical associative memory. L1 L2, lenses.

Tables (3)

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Table 1 Computer Comparison of Results for a Bipolar System and a Unipolar Systema

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Table 2 Results of Computer Simulations for a Clipped Memory Matrixa

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Table 3 Results of Optical Experiments by Using the Enlarged Matrix Maska

Equations (23)

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T i j = m = 1 M [ 2 V i ( m ) - 1 ] [ 2 V j ( m ) - 1 ] - M δ i j ,             i , j = 1 , 2 , , N ,
U i ( m 0 ) = j = 1 N T i j V j ( m 0 ) .
V i ( m 0 ) = f { U i ( m 0 ) } = { 1 for U i ( m 0 ) > 0 0 otherwise ,
V i ( n + 1 ) = f { U i ( n ) } , U i ( n ) = j = 1 N T i j V j ( n ) ,
2 U i ( n ) b = j = 1 N T i j [ 2 V j ( n ) - 1 ] ,
U i ( n ) b = U i ( n ) - j = 1 N ½ T i j ,
DT i = j = 1 N ½ T i j ,
V i ( n + 1 ) = f { U i ( n ) b } = { 1 for U i ( n ) > DT i 0 otherwise .
DT i = m = 1 M [ 2 V i ( m ) - 1 ] [ N 0 ( m ) - ½ N ] - ½ M ,
T i j p = T i j + A ,
U i ( n ) b = j = 1 N T i j [ V j ( n ) - ½ ] = j = 1 N T i j p V j ( n ) + [ Max - DT i ] - [ N 0 ( n ) A + Max ] = j = 1 N T i j p V j ( n ) + BGD i - TH ( n ) ,
W i j = T i j p , W i , N + 1 = BGD i , W N + 1 , j = A , W N + 1 , N + 1 = Max ,
V N + 1 ( n ) = 1 ;
j = 1 N T i j p V j ( n ) + BGD i - [ N 0 ( n ) A + Max ] = j = 1 N + 1 W i j V j ( n ) - j = 1 N + 1 W N + 1 , j V j ( n ) .
j = 1 N T i j p V j ( n ) - [ A N 0 ( n ) ] = j = 1 N W i j V j ( n ) - j = 1 N W N + 1 , j V j ( n ) .
V ( 1 ) = { 1 , 0 , 0 , 1 , 0 , 0 , 0 , 1 , 0 , 0 , 1 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 1 , 0 } , V ( 2 ) = { 0 , 1 , 0 , 0 , 1 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 1 , 1 , 1 , 0 , 0 , 0 , 0 , 1 } , V ( 3 ) = { 0 , 0 , 1 , 0 , 1 , 0 , 0 , 0 , 1 , 0 , 0 , 1 , 1 , 0 , 1 , 0 , 0 , 0 , 1 , 0 } , V ( 4 ) = { 0 , 1 , 0 , 1 , 0 , 0 , 1 , 0 , 1 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 1 , 1 , 0 , 0 } ,
BGD = { 8 , 12 , 6 , 14 , 12 , 0 , 6 , 14 , 12 , 0 , 14 , 6 , 12 , 14 , 12 , 0 , 6 , 6 , 14 , 6 } ,
4 2 4 6 2 6 4 6 2 6 6 4 2 6 2 6 4 4 6 4 8 2 4 2 4 4 4 6 4 4 4 4 2 4 4 4 4 6 6 0 6 12 4 2 4 2 6 6 4 2 6 6 2 8 6 2 6 6 4 4 6 4 6 6 4 2 4 0 4 6 4 4 4 8 2 0 4 0 4 6 6 4 2 14 2 4 6 0 4 4 2 4 4 4 0 6 8 4 8 4 2 2 4 6 12 6 4 6 4 4 4 6 4 4 8 4 6 4 4 4 8 6 6 4 6 0 4 6 4 6 2 6 4 2 6 6 6 4 2 2 2 6 8 8 2 4 6 6 4 2 4 4 4 2 4 0 4 4 2 4 8 4 4 2 2 4 6 14 2 4 6 4 4 4 6 0 4 4 4 6 4 0 4 4 6 6 4 2 12 6 4 6 4 4 8 6 4 4 4 4 6 4 4 4 8 6 6 4 6 0 6 4 2 8 0 4 6 4 4 4 4 2 0 4 0 4 6 6 4 2 14 4 2 8 2 6 6 4 2 6 6 2 4 6 2 6 6 4 4 6 4 6 2 4 6 0 8 4 2 4 4 4 0 6 4 4 8 4 2 2 4 6 12 6 4 2 4 4 4 2 8 0 4 4 2 4 4 4 4 2 2 4 6 14 2 4 6 0 8 4 2 4 4 4 0 6 8 4 4 4 2 2 4 6 12 6 4 6 4 4 8 6 4 4 8 4 6 4 4 4 4 6 6 4 6 0 4 6 4 6 2 6 8 2 6 6 6 4 2 2 2 6 4 8 2 4 6 4 6 4 6 2 6 8 2 6 6 6 4 2 2 2 6 8 4 2 4 6 6 0 6 4 4 4 2 4 4 4 4 6 4 4 4 4 2 2 4 2 14 4 6 4 2 6 6 4 6 2 6 2 4 6 6 6 6 4 4 2 4 6 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 11
V ( 1 ) = 8 , 10 , 15 , 1 , 6 , 7 , 4 , 9 , 20 , 2 , 12 , 5 , 17 , 13 , 18 , 19 , 3 , 11 , 14 , 16 ; V ( 2 ) = 18 , 17 , 20 , 1 , 9 , 6 , 5 , 19 , 10 , 8 , 15 , 3 , 2 , 4 , 7 , 12 , 13 , 14 , 16 , 11 ; V ( 3 ) = 4 , 7 , 8 , 11 , 16 , 12 , 19 , 10 , 15 , 14 , 6 , 3 , 2 , 1 , 20 , 5 , 17 , 9 , 18 , 13 ; V ( 4 ) = 13 , 11 , 17 , 6 , 1 , 7 , 15 , 16 , 2 , 9 , 10 , 18 , 20 , 19 , 3 , 8 , 4 , 14 , 12 , 5.
SGN ( T i j ) = 1 ( a > 0 ) = 0 ( a = 0 ) = - 1 ( a < 0 ) ,
BGD = { 3 , 4.5 , 2.5 , 5 , 5 , 0 , 3 , 6 , 4 , 0 , 5 , 2.5 , 5 , 6 , 5 , 0 , 3 , 3 , 5.5 , 2 }
TH ( n ) = N 0 ( n ) + 4.5.
1 0 1 2 0 2 1 2 0 2 2 1 0 2 0 2 1 1 2 1 3 . 0 0 1 0 1 1 1 2 1 1 1 1 0 1 1 1 1 2 2 0 2 4 . 5 1 0 1 0 2 2 1 0 2 2 0 2 2 0 2 2 1 1 2 1 2 . 5 2 1 0 1 0 1 2 1 1 1 2 0 0 1 0 1 2 2 1 0 5 . 0 0 1 2 0 1 1 0 1 1 1 0 2 2 1 2 1 0 0 1 2 5 . 0 2 1 2 1 1 1 2 1 1 2 1 2 1 1 1 2 2 2 1 2 0 . 0 1 2 1 2 0 2 1 0 2 2 2 1 0 0 0 2 2 2 0 1 3 . 0 2 1 0 1 1 1 0 1 0 1 1 0 1 2 1 1 0 0 1 2 6 . 0 0 1 2 1 1 1 2 0 1 1 1 2 1 0 1 1 2 2 1 0 4 . 0 2 1 2 1 1 2 2 1 1 1 1 2 1 1 1 2 2 2 1 2 0 . 0 2 1 0 2 0 1 2 1 1 1 1 0 0 1 0 1 2 2 1 0 5 . 0 1 0 2 0 2 2 1 0 2 2 0 1 2 0 2 2 1 1 2 1 2 . 5 0 1 2 0 2 1 0 1 1 1 0 2 1 1 2 1 0 0 1 2 5 . 0 2 1 0 1 1 1 0 2 0 1 1 0 1 1 1 1 0 0 1 2 6 . 0 0 1 2 0 2 1 0 1 1 1 0 2 2 1 1 1 0 0 1 2 5 . 0 2 1 2 1 1 2 2 1 1 2 1 2 1 1 1 1 2 2 1 2 0 . 0 1 2 1 2 0 2 2 0 2 2 2 1 0 0 0 2 1 2 0 1 3 . 0 1 2 1 2 0 2 2 0 2 2 2 1 0 0 0 2 2 1 0 1 3 . 0 2 0 2 1 1 1 0 1 1 1 1 2 1 1 1 1 0 0 1 0 5 . 5 1 2 1 0 2 2 1 2 0 2 0 1 2 2 2 2 1 1 0 1 2 . 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 . 5

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