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.
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Computer Comparison of Results for a Bipolar System and a Unipolar Systema
Hamming Distance of Initializing Vector from Vi(m)
Final Output Vector (Number of Iterations)
Bipolar System
Unipolar System
m = 1
m = 2
m = 3
m = 4
m = 1
m = 2
m = 3
m = 4
0
1 (1)
2 (1)
3 (1)
4 (1)
F (4)
(3)
(4)
F (2)
1
1 (1)
2 (1)
3 (1)
4 (1)
F (4)
(3)
(4)
F (2)
2
1 (1)
2 (1)
3 (1)
4 (1)
F (4)
(5)
(3)
F (2)
3
1 (1)
2 (1)
3 (1)
4 (1)
F (3)
(5)
(4)
F (2)
4
1 (1)
2 (1)
3 (1)
4 (1)
F (3)
(5)
(4)
F (2)
5
1 (1)
2 (1)
3 (1)
4 (1)
F (3)
(2)
(4)
F (2)
6
1 (3)
2 (1)
3 (1)
4 (1)
F (2)
(2)
(4)
F (2)
7
1 (1)
1 (3)
3 (2)
4 (2)
F (2)
(3)
(3)
(5)
8
1 (5)
1 (3)
F (4)
(5)
F (2)
(3)
(3)
(5)
9
O
F (4)
O
O
(4)
(3)
(4)
F (3)
10
F (4)
O
O
O
(4)
(3)
(4)
F (3)
11
O
F (2)
O
O
(3)
F (2)
(4)
F (3)
12
F (4)
(5)
F (4)
F (3)
(3)
F (3)
F (2)
(4)
13
(1)
(4)
F (2)
(2)
(2)
F (3)
F (2)
(4)
14
(3)
(1)
(1)
(1)
(2)
F (5)
F (3)
(4)
15
(1)
(1)
(1)
(1)
(2)
F (2)
F (3)
(4)
16
(1)
(1)
(1)
(1)
(1)
F (5)
F (3)
(4)
17
(1)
(1)
(1)
(1)
(1)
F (5)
F (3)
(1)
18
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
19
(1)
(1)
(1)
(1)
(1)
F (S)
(1)
(1)
20
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
A number indicates a stored vector, a number with an overhead bar depicts the complementary vesion of a stored vector, a number in parentheses shows the number of iterations, an O represents an oscillation, and an F denotes a false vector.
Table 2
Results of Computer Simulations for a Clipped Memory Matrixa
Hamming Distance of Initializing Vector from Vi(m)
Final Output Vector (Number of Iterations)
Bipolar System
Unipolar System
m = 1
m = 2
m = 3
m = 4
m = 1
m = 2
m = 3
m = 4
0
1 (1)
2 (1)
3 (1)
4 (1)
F (3)
(2)
(4)
F (2)
1
1 (1)
2 (1)
3 (1)
4 (1)
F (2)
(2)
(4)
F (2)
2
1 (1)
2 (1)
3 (1)
4 (1)
F (2)
(2)
(4)
F (2)
3
1 (1)
2 (1)
3 (1)
4 (1)
F (2)
(4)
(4)
F (2)
4
1 (1)
1 (3)
3 (1)
4 (1)
F (2)
O
(4)
F (2)
5
1 (1)
1 (3)
3 (1)
4 (1)
F (2)
(4)
(4)
F (2)
6
O
F (3)
3 (1)
4 (3)
F (2)
(3)
(4)
F (2)
7
1 (2)
1 (3)
3 (2)
F (2)
F (2)
F (2)
(2)
F (2)
8
(5)
F (3)
O
F (2)
F (1)
F (4)
(2)
F (2)
9
F (4)
F (5)
(4)
F (2)
F (3)
F (2)
F (3)
F (2)
10
(7)
(6)
(6)
F (4)
F (3)
F (1)
F (3)
F (2)
11
F (3)
F (2)
O
F (2)
(2)
F (1)
F (3)
F (2)
12
(4)
(4)
F (2)
O
(2)
F (2)
F (2)
F (2)
13
(1)
(2)
(3)
(4)
(2)
F (3)
F (2)
(3)
14
(3)
(1)
(3)
F (2)
(2)
F (3)
F (3)
(5)
15
(1)
(2)
(1)
(1)
(2)
F (1)
F (3)
(5)
16
(1)
(1)
(1)
(1)
(1)
F (3)
F (3)
(5)
17
(1)
(1)
(1)
(1)
(1)
F (3)
F (3)
(1)
18
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
19
(1)
(1)
(1)
(1)
(1)
F (3)
(1)
(1)
20
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
The table elements have the same denotations as given in the footnote to Table 1.
Table 3
Results of Optical Experiments by Using the Enlarged Matrix Maska
Hopfield Model
Clipped Model
HD
V(1)
V(2)
V(3)
V(4)
V(1)
V(2)
V(3)
V(4)
0
1
2
3
4
1
2
3
4
1
1
2
3
4
1
2
3
4
2
1
2
3
4
1
2
3
4
3
1
2
3
4
1
2
3
4
4
1
2
3
4
1
1
3
4
5
1
2
4
4
1
·
·
4
6
·
·
4
4
·
·
·
·
7
·
·
·
4
·
·
·
·
8
·
·
·
·
·
·
·
·
9
·
·
·
·
·
·
·
·
10
·
·
·
·
·
·
·
·
11
·
·
·
·
·
·
·
·
12
·
·
·
·
·
·
13
·
·
14
15
16
17
18
19
20
A number indicates a stored vector, a number with an overhead bar represents the complementary version of a stored vector, and a centered dot denotes a nonpredictable output.
Tables (3)
Table 1
Computer Comparison of Results for a Bipolar System and a Unipolar Systema
Hamming Distance of Initializing Vector from Vi(m)
Final Output Vector (Number of Iterations)
Bipolar System
Unipolar System
m = 1
m = 2
m = 3
m = 4
m = 1
m = 2
m = 3
m = 4
0
1 (1)
2 (1)
3 (1)
4 (1)
F (4)
(3)
(4)
F (2)
1
1 (1)
2 (1)
3 (1)
4 (1)
F (4)
(3)
(4)
F (2)
2
1 (1)
2 (1)
3 (1)
4 (1)
F (4)
(5)
(3)
F (2)
3
1 (1)
2 (1)
3 (1)
4 (1)
F (3)
(5)
(4)
F (2)
4
1 (1)
2 (1)
3 (1)
4 (1)
F (3)
(5)
(4)
F (2)
5
1 (1)
2 (1)
3 (1)
4 (1)
F (3)
(2)
(4)
F (2)
6
1 (3)
2 (1)
3 (1)
4 (1)
F (2)
(2)
(4)
F (2)
7
1 (1)
1 (3)
3 (2)
4 (2)
F (2)
(3)
(3)
(5)
8
1 (5)
1 (3)
F (4)
(5)
F (2)
(3)
(3)
(5)
9
O
F (4)
O
O
(4)
(3)
(4)
F (3)
10
F (4)
O
O
O
(4)
(3)
(4)
F (3)
11
O
F (2)
O
O
(3)
F (2)
(4)
F (3)
12
F (4)
(5)
F (4)
F (3)
(3)
F (3)
F (2)
(4)
13
(1)
(4)
F (2)
(2)
(2)
F (3)
F (2)
(4)
14
(3)
(1)
(1)
(1)
(2)
F (5)
F (3)
(4)
15
(1)
(1)
(1)
(1)
(2)
F (2)
F (3)
(4)
16
(1)
(1)
(1)
(1)
(1)
F (5)
F (3)
(4)
17
(1)
(1)
(1)
(1)
(1)
F (5)
F (3)
(1)
18
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
19
(1)
(1)
(1)
(1)
(1)
F (S)
(1)
(1)
20
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
A number indicates a stored vector, a number with an overhead bar depicts the complementary vesion of a stored vector, a number in parentheses shows the number of iterations, an O represents an oscillation, and an F denotes a false vector.
Table 2
Results of Computer Simulations for a Clipped Memory Matrixa
Hamming Distance of Initializing Vector from Vi(m)
Final Output Vector (Number of Iterations)
Bipolar System
Unipolar System
m = 1
m = 2
m = 3
m = 4
m = 1
m = 2
m = 3
m = 4
0
1 (1)
2 (1)
3 (1)
4 (1)
F (3)
(2)
(4)
F (2)
1
1 (1)
2 (1)
3 (1)
4 (1)
F (2)
(2)
(4)
F (2)
2
1 (1)
2 (1)
3 (1)
4 (1)
F (2)
(2)
(4)
F (2)
3
1 (1)
2 (1)
3 (1)
4 (1)
F (2)
(4)
(4)
F (2)
4
1 (1)
1 (3)
3 (1)
4 (1)
F (2)
O
(4)
F (2)
5
1 (1)
1 (3)
3 (1)
4 (1)
F (2)
(4)
(4)
F (2)
6
O
F (3)
3 (1)
4 (3)
F (2)
(3)
(4)
F (2)
7
1 (2)
1 (3)
3 (2)
F (2)
F (2)
F (2)
(2)
F (2)
8
(5)
F (3)
O
F (2)
F (1)
F (4)
(2)
F (2)
9
F (4)
F (5)
(4)
F (2)
F (3)
F (2)
F (3)
F (2)
10
(7)
(6)
(6)
F (4)
F (3)
F (1)
F (3)
F (2)
11
F (3)
F (2)
O
F (2)
(2)
F (1)
F (3)
F (2)
12
(4)
(4)
F (2)
O
(2)
F (2)
F (2)
F (2)
13
(1)
(2)
(3)
(4)
(2)
F (3)
F (2)
(3)
14
(3)
(1)
(3)
F (2)
(2)
F (3)
F (3)
(5)
15
(1)
(2)
(1)
(1)
(2)
F (1)
F (3)
(5)
16
(1)
(1)
(1)
(1)
(1)
F (3)
F (3)
(5)
17
(1)
(1)
(1)
(1)
(1)
F (3)
F (3)
(1)
18
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
19
(1)
(1)
(1)
(1)
(1)
F (3)
(1)
(1)
20
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
The table elements have the same denotations as given in the footnote to Table 1.
Table 3
Results of Optical Experiments by Using the Enlarged Matrix Maska
Hopfield Model
Clipped Model
HD
V(1)
V(2)
V(3)
V(4)
V(1)
V(2)
V(3)
V(4)
0
1
2
3
4
1
2
3
4
1
1
2
3
4
1
2
3
4
2
1
2
3
4
1
2
3
4
3
1
2
3
4
1
2
3
4
4
1
2
3
4
1
1
3
4
5
1
2
4
4
1
·
·
4
6
·
·
4
4
·
·
·
·
7
·
·
·
4
·
·
·
·
8
·
·
·
·
·
·
·
·
9
·
·
·
·
·
·
·
·
10
·
·
·
·
·
·
·
·
11
·
·
·
·
·
·
·
·
12
·
·
·
·
·
·
13
·
·
14
15
16
17
18
19
20
A number indicates a stored vector, a number with an overhead bar represents the complementary version of a stored vector, and a centered dot denotes a nonpredictable output.