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Tabl e 6 . 11 Results for the experiments with the embedded Reber grammar. ANS
stands for Average Number of Sequences necessary to converge.
η
=0
.
3
ANS (std) [
10
3
] % conv. ANS (std) [
10
3
]%conv.
η
=0
.
1
MMSE
44.4(48.4)
8
66.3 (40.1)
6
MEE h=1.3
79.6 (94.5)
7
-
0
MEE h=1.4
13.1 (6.5)
8
-
0
MEE h=1.5
49.9 (53.8)
12
327 (-)
1
MEE h=1.6
65.7 (46.9)
8
62.0 (74.5)
3
MEE h=1.7
41.2 (26.9)
8
183.7 (137.4)
3
MEE h=1.8
60.6 (35.8)
12
102.4 (101.4)
5
MEE h=1.9
124.3 62.4
13
76.9 (125.0)
7
MEE h=2.0
143.2 (111.9)
14
84.6 (87.6)
7
Tabl e 6 . 12 Results for the experiments with the grammar
A
n
B
n
. ANS stands for
Average Number of Sequences necessary to converge.
Test
n
=1
,...,
50
Test
n
=1
,...,
100
10
3
]%conv.Averagen.seq.(std)[
10
3
]%conv.
Average n. seq. (std) [
MMSE
4.93 (2.80)
17
4.90 (2.41)
12
MEE h=1.3
10.31 (7.40)
18
8.75 (6.48)
13
MEE h=1.4
11.67 (8.11)
19
11.90 (7.94)
12
MEE h=1.5
15.31 (8.25)
28
16.08 (7.76)
18
MEE h=1.6
17.06 (8.62)
36
17.51 (8.46)
25
MEE h=1.7
18.77 (8.78)
45
18.33 (8.33)
29
MEE h=1.8
20.74 (8.74)
50
19.69 (7.83)
35
MEE h=1.9
20.80 (8.38)
48
21.09 (7.39)
35
MEE h=2.0
22.19 (8.20)
49
22.50 (7.52)
33
6.2.2.4
Discussion
In the Reber grammar experiments, the MEE approach improved the percent-
age of convergence in all six sets of experiments except for the first topology
with
η
=0
.
3. In one case (first topology and
η
=0
.
2) it not only outperformed
MMSE but there was also a statistical significant average reduction in the
number of sequences necessary for the network to converge from 74
.
9
×
10
3
to 57
.
6
10
3
(
t
-test
p<
0
.
01).
In the case of the experiments with the ERG, and for
η
=0
.
1, two benefits
were found from the application of MEE: in two cases (
h
=1
.
4 and 1.7)
the same percentage of convergence as with MMSE was obtained but with a
smaller number of required training sequences on average, highly significant
for
h
=1
.
4 (
t
-test
p
×
0). In four other cases, the percentage of convergence
increased from 8 to 12, 13 and 14%. In these cases the number of necessary
sequences also increased when compared to the use of MMSE. When
η
was
setat0.3,thereweretwocases(
h
=1
.
3 and 1.4) where MEE was not able
≈
