Biomedical Engineering Reference
In-Depth Information
subsequent matrix rows with new random numbers from the sequence
U
. In this
case, the entire matrix of
n
n
connections will take in the memory
n
of
k
-bit words
(one
k
-bit word for each row).
Let us consider an example. Let
n
=8,
k
=2,
r
=4,
s
= 2 (Table
5.2
). Let us select
the sequence of random numbers
U
= {10, 10, 01, 00, 01, 00, 11, 01}. Let us
describe the values
p
for the first matrix row,
p
1
= 10 & 10 = 10,
p
2
= 10 & 01 = 00,
p
3
= 01 & 10 = 00,
p
4
= 01 & 01 = 01,
and then enter them in the first matrix row. After performing analogous operations
for all lines, we will obtain the matrix shown in Table
5.2
. Unit elements in the
matrix correspond to permitted interneuronal connections. After training, the
weights of interneuronal connections will appear on the permitted positions as
shown in Table
5.3
. To store these weights in memory, they are collected from
each matrix row into the compact word. The resulting compact array is shown in
Table
5.4
. While the network calculates neural activity, the conversion of the
compact array into the complete matrix is accomplished, as shown in Table
5.3
.
Advantages of this method are the compact presentation of the not fully
connected matrix in the memory of the computer and the uniform distribution of
the permitted connections over the matrix. The disadvantage is the high expenditure
of time for the conversion of a compact array into a complete matrix. This
conversion procedure is comparatively complicated to execute in parallel with the
aid of the hardware; therefore, it is expedient to find a method of constructing not
fully connected networks that would allow compact storage of information about
the connections but that would not require such a complex procedure for restoring
10
00
00
01
Table 5.2
00
01
00
10
00
01
00
10
01
10
00
00
00
10
00
01
01
00
10
00
00
01
00
10
00
10
00
01
Table 5.3
W
11
0
0
0
0
0
0
W
18
0
0
0
W
24
0
0
W
27
0
0
0
0
W
34
0
0
W
37
0
0
W
42
W
43
0
0
0
0
0
0
0
W
53
0
0
0
0
W
58
0
W
62
0
0
W
65
0
0
0
0
0
0
W
73
0
0
W
77
0
0
0
W
83
0
0
0
0
W
88
