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8
]
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[
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I
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4D
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s
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8D
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(
1
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w
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d
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n t
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dim
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ns
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n
s
[
1
0
]
.
T
h
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es
[
1
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3,
6]
a
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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SN
:
2
252
-
88
14
IJ
A
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7
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2
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J
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201
8
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177
–
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a
l
ne
t
w
or
k a
n
d l
e
a
d t
o l
owe
r
c
om
pl
e
xi
t
y
.
T
he
q
ua
t
e
r
ni
o
n i
s
one
of
t
he
hy
pe
r
c
o
m
pl
e
x num
be
r
i
nt
r
od
uc
e
d by
I
r
i
s
m
a
t
he
m
a
ti
c
i
a
n H
a
m
i
l
t
on [
11]
w
hi
c
h h
a
s
be
e
n e
xt
e
ns
i
ve
l
y
e
m
pl
oy
e
d i
n
t
he
f
i
e
l
d
o
f
qua
nt
um
m
a
the
m
a
ti
c
s
,
p
hy
s
i
c
s
,
c
om
put
e
r
g
r
a
phi
c
s
,
s
i
gna
l
p
r
o
ces
s
i
n
g
an
d
c
ont
r
ol
[
1
2
-
1
3
,
1
8
-
1
7
]
.
T
hi
s
num
be
r
s
y
s
t
e
m
ha
s
r
e
c
e
nt
l
y
p
op
pe
d
up
i
n
ne
u
r
a
l
ne
t
w
or
k
t
hr
o
ug
h
q
ua
t
e
r
ni
oni
c
ne
u
r
on
s
,
as
co
m
p
l
ex
o
r
r
eal
-
va
l
ue
d
ne
u
r
o
ns
,
t
o
de
ve
l
o
p
e
f
f
i
c
i
e
nt
m
a
c
hi
ne
l
e
a
r
ni
ng
i
n
hi
g
he
r
di
m
e
ns
i
o
ns
.
F
e
w
a
t
t
e
m
pt
s
ha
ve
be
e
n m
a
de
i
n t
hi
s
di
r
e
c
t
i
on,
t
he
or
t
h
og
o
na
l
de
c
i
s
i
o
n b
o
un
da
r
y
of
s
i
ngl
e
q
ua
t
e
r
ni
o
ni
c
ne
u
r
on
ha
s
be
e
n ut
i
l
i
z
e
d
t
o s
ol
ve
4
-
b
i
t
p
a
r
i
t
y
p
r
o
b
l
e
m
i
n
[
1
4
];
q
u
a
t
e
r
ni
o
ni
c
M
L
P
s
p
r
o
pos
e
d
i
n
[
15
]
h
as
t
h
e
p
r
o
b
l
e
m
o
f
e
x
i
s
t
e
n
c
e
o
f
s
i
n
g
u
l
a
r
i
t
i
e
s
;
q
ua
t
e
r
ni
on
-
v
al
u
ed
a
l
g
o
r
i
t
h
m
s
a
r
e
p
r
o
pos
e
d f
or
a
da
pt
i
ve
f
i
l
t
e
r
i
n
g [
1
8
]
.
[
1
7
]
;
a
ba
s
i
c
wor
k f
or
q
u
a
t
e
r
n
i
o
n
i
c
-
va
l
ue
d n
e
ur
a
l
ne
t
wo
r
k
w
i
t
h s
i
gm
oi
da
l
a
c
t
i
va
t
i
on f
u
n
c
t
i
on
i
s
p
r
e
s
e
n
t
e
d
i
n
[
18
,
1
9
].
I
n t
hi
s
pa
pe
r
,
we
pr
e
s
e
nt
n
ot
onl
y
s
im
pl
e
,
s
t
r
a
i
gh
t
f
or
wa
r
d
,
b
ut
p
ot
e
nt
i
a
l
m
a
c
hi
ne
l
e
a
r
ni
ng a
l
g
or
i
t
hm
f
o
r
s
u
f
f
i
ci
en
t
g
en
er
al
s
t
r
u
ct
u
r
e o
f
t
h
e
q
ua
t
e
r
ni
o
ni
c
d
om
a
i
n ne
u
r
a
l
ne
t
w
or
k
(
Q
D
NN
)
but
a
l
s
o d
e
m
ons
t
r
a
t
e
t
he
e
va
l
ua
t
i
o
n ove
r
t
he
wi
de
s
pe
c
t
r
um
of
a
p
pl
i
c
a
t
i
ons
,
l
i
ke
f
unc
t
i
o
n a
p
pr
o
xi
m
a
t
i
on,
m
ot
ion i
nt
e
r
pr
e
t
a
t
i
on
a
n
d
r
eco
g
n
i
t
i
o
n
i
n
s
p
ace.
T
h
e
p
ar
am
et
er
s
i
n
Q
D
N
N
,
l
i
k
e s
y
n
ap
t
i
c w
ei
g
h
t
s
,
b
i
as
es
,
i
n
p
u
t
s
-
ou
tpu
ts
s
igna
ls
a
n
d
i
n
t
er
n
al
p
o
t
en
t
i
al
s
ar
e q
u
at
er
n
i
o
n
s
a
n
d
r
e
p
r
es
en
t
e
d
as
q
u
at
er
n
i
o
n
m
a
t
r
i
x
,
i
n
m
u
l
t
i
l
a
y
e
r
n
e
u
r
a
l
n
e
t
w
o
r
k
.
A
l
t
ho
u
gh
,
H
a
m
i
lt
on pr
o
pos
e
d qua
t
e
r
ni
oni
c
n
um
be
r
s
(
=
0
+
1
+
2
+
3
)
f
or
4
D num
be
r
s
y
s
t
e
m
[
1
1]
,
but
i
t
c
a
n a
l
s
o
br
i
n
g i
n
t
o pl
a
y
a
ny
3
D i
n
f
or
m
a
t
i
on i
n t
he
s
pa
c
e
a
f
t
e
r
e
qu
a
t
i
ng
i
t
s
r
e
a
l
pa
r
t
z
e
r
o
.
T
he
pr
e
s
e
nt
e
d
l
e
a
r
n
i
ng a
l
go
r
i
t
hm
ba
s
e
d o
n t
he
e
r
r
o
r
ba
c
k
pr
o
pa
g
a
t
i
on
f
o
r
Q
D
N
N c
a
n e
f
f
i
c
i
e
nt
l
y
s
ol
ve
a
ny
t
y
pi
c
a
l
c
l
a
s
s
of
pr
o
bl
e
m
s
i
n 3D
a
nd
4D
.
T
he
a
na
l
y
t
i
c
[
1,
8
]
o
r
s
p
l
i
t
t
y
p
e
[
1
]
,
[
5
]
,
[
7
]
a
c
t
i
va
t
i
on f
u
nc
t
i
o
ns
ha
ve
be
e
n
ch
o
s
en
f
o
r
co
m
p
l
ex
-
va
l
ue
d
ne
u
r
on
w
hi
c
h
ha
ve
t
he
i
r
o
w
n i
s
s
ue
s
c
o
nc
e
r
ni
ng
bo
u
nde
d
ne
s
s
a
nd a
na
l
y
t
i
c
it
y
.
T
h
er
e
f
o
r
e,
s
el
e
ct
i
o
n
o
f
s
ui
t
a
bl
e
a
c
t
i
va
t
i
on
f
u
nc
t
i
on
f
o
r
ne
ur
on
de
a
l
i
n
g
wi
t
h
q
ua
t
e
r
ni
o
n
i
s
one
of
t
he
i
m
por
t
a
nt
c
onc
e
r
ns
.
T
he
s
pl
i
t
t
y
pe
f
u
nc
t
i
on
m
a
y
not
be
a
pp
r
op
r
i
a
t
e
w
he
n
a
na
l
y
t
i
c
i
t
y
i
s
c
onc
e
r
ne
d
,
s
im
i
l
a
r
ly
t
he
a
na
l
y
t
i
c
f
u
n
c
t
i
o
n
i
s
n
o
t
s
u
i
t
a
b
l
e
w
h
e
n
t
h
e
s
i
n
g
u
l
a
r
i
t
y
a
r
i
s
e
s
.
T
h
e
p
r
e
s
e
nt
e
d
Q
D
N
N
pr
e
f
e
r
b
o
un
de
d
ne
s
ove
r
a
na
l
y
t
i
c
i
t
y
an
d
u
s
e “s
p
l
i
t
-
t
y
p
e”
act
i
v
at
i
o
n
f
u
n
ct
i
o
n
.
T
h
e
Q
D
N
N
o
u
t
p
er
f
o
r
m
w
i
t
h
l
e
s
s
er
n
u
m
b
er
o
f
n
eu
r
o
n
s
an
d
f
as
t
e
r
l
e
a
r
ni
n
g w
he
r
e
c
on
ve
nt
i
ona
l
r
e
a
l
-
va
l
ue
d
n
e
ur
a
l
ne
t
w
o
r
k
(
R
V
N
N
)
l
a
c
ks
.
T
he
q
ua
t
e
r
ni
oni
c
-
v
al
u
ed
n
eu
r
al
ne
t
w
or
k (
Q
D
N
N
)
ha
s
a
n a
bi
l
i
t
y
t
o l
e
a
r
n a
n
d ge
ne
r
a
l
i
z
e
3
D
m
ot
i
on o
f
o
bje
c
t
s
a
n
d r
e
c
og
ni
t
i
on
o
f
t
he
poi
nt
c
l
ou
d
ob
je
c
t
,
but
R
V
N
N
c
a
nn
ot
,
be
c
a
us
e
Q
D
N
N ha
s
a
b
i
l
i
ty
t
o c
a
pt
u
r
e
a
n
d m
a
i
nt
a
i
n pha
s
e
i
n
f
o
r
m
a
ti
on
of
e
a
c
h
poi
nt
d
u
r
i
ng
t
he
l
e
a
r
ni
ng
a
n
d
ge
ne
r
a
l
i
z
a
t
i
on
.
Th
i
s
p
a
p
e
r
i
n
v
e
s
t
i
g
a
t
e
s
t
h
e
g
e
n
e
r
a
l
s
t
r
u
c
t
u
r
e
o
f
Q
D
N
N
w
i
t
h
l
e
a
r
n
i
n
g
a
l
g
o
r
i
t
h
m
t
h
r
o
u
g
h
s
i
m
u
l
a
t
i
o
n
on
va
r
i
ous
be
n
c
hm
a
r
k pr
o
bl
e
m
s
of
di
f
f
e
r
e
nt
s
phe
r
e
o
f
i
nf
l
ue
nc
e
.
T
he
s
e
c
t
i
ons
a
n
d s
ub
-
s
e
c
t
i
ons
o
f
t
he
pa
pe
r
ar
e o
r
g
a
n
i
zed
as
f
o
l
l
o
w
s
:
T
h
e s
ect
i
o
n
2
,
p
r
es
en
t
s
a co
m
pl
e
t
e
m
a
c
hi
ne
l
e
a
r
ni
ng
f
r
a
m
e
wor
k wi
t
h ps
e
u
d
o c
o
de
of
l
e
a
r
ni
n
g i
n
qua
t
e
r
ni
oni
c
d
om
a
i
n.
S
e
c
t
i
on
3 e
va
l
ua
t
e
s
t
h
e
l
e
a
r
ni
n
g a
n
d
ge
ne
r
a
l
i
z
a
t
i
on
c
a
pa
bi
l
i
t
y
t
hr
ou
g
h
f
u
nc
t
i
o
n a
p
p
r
oxi
m
a
t
i
ons
,
l
i
ne
a
r
t
r
a
ns
f
or
m
a
t
i
ons
a
n
d
3D
f
a
c
e
r
e
c
o
gni
t
i
o
n.
S
e
c
t
i
o
n 4
p
r
e
s
e
nt
s
t
he
f
i
n
a
l
c
onc
l
us
i
o
n
a
n
d
f
ut
ur
e
s
c
ope
o
f
t
he
w
or
k
.
2.
MA
CH
I
N
E
L
E
AR
NI
NG
I
N
Q
U
AT
E
R
N
I
O
NI
C
D
O
MA
I
N
A
q
ua
t
e
r
ni
o
ni
c
num
be
r
s
y
s
t
e
m
i
s
t
he
s
t
r
a
i
ght
f
or
wa
r
d e
xt
e
ns
i
o
n o
f
r
e
a
l
a
nd c
om
pl
e
x n
u
m
be
r
s
y
s
t
e
m
,
w
he
r
e
f
ou
r
c
o
m
pone
nt
s
a
r
e
i
nc
o
r
po
r
a
t
e
d i
n
s
i
ngl
e
n
um
be
r
;
t
he
f
i
r
s
t
c
om
p
o
n
e
n
t
act
s
as
r
eal
an
d
o
t
h
e
r
t
h
r
ee a
s
im
a
gi
na
r
y
wi
t
h uni
t
ve
c
t
or
s
(
,
,
)
.
T
he
s
e
i
m
a
gi
na
r
y
c
om
po
ne
nt
s
o
ve
r
l
i
e
o
n t
he
a
xe
s
i
n t
h
r
e
e
di
m
e
ns
i
ona
l
s
pa
c
e
[
1
1,
1
2]
.
A qua
t
e
r
ni
oni
c
va
r
i
a
bl
e
(
=
0
+
1
+
2
+
3
)
c
o
n
s
i
s
t
s
of
a
r
e
a
l
c
om
pone
nt
(
0
)
a
n
d
t
hr
e
e
i
m
a
gi
na
r
y
c
om
po
ne
nt
s
(
1
,
2
,
3
)
.
It
s
b
as
es
(
,
,
)
a
r
e
or
t
ho
g
ona
l
s
pe
c
i
a
l
ve
c
t
o
r
s
.
T
hus
,
t
he
y
f
ol
l
o
w
t
h
e
p
r
o
p
e
r
t
i
e
s
a
s
2
=
2
=
2
=
−
1
a
n
d
c
r
os
s
pr
o
duc
t
pr
o
pe
r
t
i
e
s
a
s
×
=
−
(
×
)
=
,
×
=
−
(
×
)
=
,
×
=
−
(
×
)
=
.
I
n
a
pr
om
i
ne
nt
r
e
p
r
e
s
e
nt
a
t
i
on
,
a
q
ua
t
e
r
ni
o
n
(
)
can
b
e
e
xp
r
e
s
s
e
d in th
e
f
or
m
o
f
a
m
a
t
r
i
x
(
q
u
a
t
e
r
n
i
o
n
i
c
m
a
t
r
i
x
)
:
=
0
−
1
−
2
−
3
1
0
3
−
2
2
−
3
0
1
3
2
−
1
0
.
(
1)
T
he
b
ol
d t
y
p
e
l
e
t
t
e
r
de
not
e
s
qua
t
e
r
ni
oni
c
va
r
i
a
bl
e
or
qua
t
e
r
ni
oni
c
m
a
t
r
i
x.
T
he
c
on
j
uga
t
e
o
f
qua
t
e
r
ni
oni
c
v
a
r
i
a
bl
e
(
∗
=
0
−
1
−
2
−
3
)
i
s
s
i
m
i
l
ar
t
o
co
m
p
l
ex
co
n
j
u
g
at
e
an
d
t
h
e c
o
n
j
u
g
at
e o
f
qua
t
e
r
ni
oni
c
m
a
t
r
i
x
de
n
ot
e
s
t
he
t
r
a
ns
po
s
e
of
t
he
qua
t
e
r
ni
on
i
c
m
a
t
r
i
x,
de
f
i
n
e
d
a
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
A
S
I
S
S
N
:
225
2
-
88
14
O
n
t
he
H
i
g
h
D
i
m
e
nt
i
o
nal
I
nf
o
r
mat
i
on
P
r
oc
e
s
s
i
ng
i
n
Q
uat
e
r
ni
on
ic
D
om
a
in
…
(
S
u
s
h
i
l
Ku
m
a
r
)
1
79
∗
=
=
0
−
1
−
2
−
3
1
0
3
−
2
2
−
3
0
1
3
2
−
1
0
=
0
1
2
3
−
1
0
−
3
2
−
2
3
0
−
1
−
3
−
2
1
0
.
(
2)
T
h
e
m
ach
i
n
e l
ear
n
i
n
g
o
p
t
i
m
i
zat
i
o
n
t
ech
n
i
q
u
e
i
n
c
o
r
p
o
r
at
es
t
h
e b
as
i
c
o
p
er
at
i
o
n
s
o
f
q
u
at
er
n
i
o
n
a
l
ge
b
r
a
[
11
,
1
2]
.
T
he
a
d
di
t
i
on a
n
d s
ubt
r
a
c
t
i
on
of
t
w
o
q
ua
t
e
r
ni
oni
c
m
a
t
r
ic
e
s
a
nd
c
a
b
be
o
bt
a
i
ne
d s
i
m
ply
a
s
m
a
t
r
i
x
o
p
e
r
a
t
i
o
n
s
.
T
h
e
m
u
l
t
i
p
l
i
c
a
t
i
o
n
o
f
t
w
o
q
u
a
t
e
r
n
i
o
n
i
c
m
a
t
r
i
c
e
s
a
nd
d
o
e
s
not
f
ol
l
ow
t
he
co
m
m
u
t
at
i
v
e
p
r
o
p
er
t
y
(
≠
).
T
he
i
nne
r
pr
o
duc
t
of
t
w
o
qua
t
e
r
ni
oni
c
m
a
t
r
i
c
e
s
a
n
d
i
s
ex
p
r
es
s
ed
b
y
:
⊙
=
0
−
1
−
2
−
3
1
0
3
−
2
2
−
3
0
1
3
2
−
1
0
⊙
0
−
1
−
2
−
3
1
0
3
−
2
2
−
3
0
1
3
2
−
1
0
=
0
0
1
1
2
2
3
3
1
1
0
0
3
3
2
2
2
2
3
3
0
0
1
1
3
3
2
2
1
1
0
0
.
(
3)
T
he
n
or
m
of
q
ua
t
e
r
ni
o
ni
c
m
a
t
r
i
x
i
s
ex
p
r
es
s
ed
a
s:
‖
‖
=
1
2
(
)
=
0
2
+
1
2
+
2
2
+
3
2
(
4)
2.
1.
Le
a
r
n
i
n
g
i
n
Q
u
a
t
ern
i
o
n
i
c
D
o
m
a
i
n
N
eu
r
a
l
N
et
w
o
rk
s
L
et
a t
h
r
ee l
ay
er
(
−
−
)
Q
D
N
N
p
os
s
e
s
s
e
s
L
i
np
ut
s
;
M
a
nd
N
q
ua
t
e
r
ni
o
ni
c
ne
u
r
o
ns
i
n
hi
dde
n
a
nd
out
put
l
a
y
e
r
s
r
e
s
pe
c
t
i
ve
l
y
.
A
l
l
i
nput
s
,
o
ut
p
ut
s
,
we
i
ght
s
a
nd bi
a
s
e
s
s
i
g
na
l
s
a
r
e
c
o
ns
i
d
e
r
e
d a
s
q
ua
t
e
r
ni
o
ni
c
m
a
t
r
i
c
e
s
,
a
s
r
e
pr
e
s
e
nt
e
d
i
n
E
q.
(
1
)
.
T
he
de
r
i
va
t
i
on
of
o
pt
i
m
i
z
a
t
i
on
t
e
c
hn
i
que
i
nc
o
r
p
or
a
t
e
s
t
he
ba
s
i
c
o
p
e
r
a
t
i
on
s
o
f
q
u
at
er
n
i
o
n
al
g
eb
r
a
w
h
i
c
h
p
r
es
en
t
t
h
e c
o
m
p
act
an
d
t
h
e g
e
n
er
a
l
i
zed
d
er
i
v
at
i
o
n
o
f
t
h
e b
ack
p
r
o
p
a
g
at
i
o
n
a
l
g
o
r
i
t
h
m
(
Q
D
BP
)
o
f
t
h
r
e
e
-
l
a
y
e
r
ne
t
w
or
k.
T
he
b
ol
d
l
e
t
t
e
r
s
de
n
ot
e
t
he
qut
e
r
ni
oni
c
m
a
t
r
i
x
or
m
a
t
r
i
x
c
ont
a
i
ni
ng
q
u
at
e
r
n
i
o
n
i
c
m
at
r
i
ces
as
el
em
en
t
s
.
2.
1.
1.
F
or
w
ar
d
P
as
s
L
et
u
s
co
n
s
i
d
er
,
,
,
be
t
he
4
D
qua
t
e
r
ni
oni
c
i
n
put
of
ℎ
(
=
1
…
)
ne
ur
on
i
n
t
he
i
n
p
ut
l
a
y
e
r
o
f
t
h
e
n
et
w
o
r
k
.
T
h
e
q
u
at
er
n
i
o
n
i
c
i
n
p
u
t
c
an
b
e
ex
p
r
es
s
ed
as
a
q
u
at
er
n
i
o
n
i
c
m
at
r
i
x
(
)
:
=
⎣
⎢
⎢
⎢
⎡
−
−
−
−
−
−
⎦
⎥
⎥
⎥
⎤
.
(
5)
T
he
m
a
t
r
i
x
o
f
i
np
ut
s
(
)
a
t
t
he
i
np
ut
l
a
y
e
r
of
t
h
e
ne
t
w
o
r
k
i
s
de
f
i
ne
d
by
:
=
[
1
2
3
⋯
]
(6
)
T
h
e
i
n
i
t
i
a
l
i
z
a
t
i
o
n
o
f
s
y
n
a
p
t
i
c
c
o
n
n
e
c
t
i
o
n
w
e
i
g
h
t
s
a
nd
ar
e
d
ef
i
n
e
d
f
o
r
ℎ
i
n
p
u
t
t
o
ℎ
(
=
1
…
)
hi
dde
n
ne
u
r
on
pa
i
r
a
nd f
or
ℎ
hi
d
de
n
t
o
ℎ
(
=
1
…
)
out
put
ne
ur
o
n
pa
i
r
o
f n
e
t
wo
rk
r
es
p
ect
i
v
el
y
.
T
h
es
e
w
ei
g
h
t
s
ar
e p
r
es
e
n
t
ed
i
n
q
u
at
er
n
i
o
n
i
c m
at
r
i
ces
co
n
t
ai
n
i
n
g
a
r
eal
an
d
o
t
h
er
t
h
r
e
e
im
a
gi
na
r
y
c
om
po
ne
nt
s
a
s
f
ol
l
ow
s
:
=
⎣
⎢
⎢
⎢
⎡
−
−
−
−
−
−
⎦
⎥
⎥
⎥
⎤
.
(
7)
=
⎣
⎢
⎢
⎡
−
−
−
−
−
−
⎦
⎥
⎥
⎤
.
(
8)
S
i
m
i
l
a
r
l
y
,
t
h
e
i
n
i
t
i
a
l
i
z
a
t
i
o
n
o
f
b
i
a
s
e
s
a
nd
ar
e d
ef
i
n
ed
f
o
r
ℎ
hi
d
de
n a
nd
ℎ
ou
tpu
t n
e
ur
o
n of
ne
t
w
or
k:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-
88
14
IJ
A
A
S
V
o
l
.
7
,
N
o
.
2
,
J
un
e
201
8
:
177
–
1
90
1
80
=
⎣
⎢
⎢
⎡
−
−
−
−
−
−
⎦
⎥
⎥
⎤
.
(
9)
=
⎣
⎢
⎢
⎡
−
−
−
−
−
−
⎦
⎥
⎥
⎤
(
10
)
T
h
e
i
n
t
e
r
n
a
l
p
o
t
e
n
t
i
a
l
m
a
t
r
i
x
,
fo
r
n
e
u
r
o
n
s
(
1
.
.
M
)
a
t
h
i
d
d
e
n
la
ye
r
of
th
e
ne
tw
or
k
is
d
e
f
in
e
d
a
s
:
=
+
.
(
11
)
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎡
1
1
2
1
3
1
⋮
1
1
2
2
2
3
2
⋮
2
1
3
2
3
3
3
⋮
3
…
…
…
…
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
+
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
.
(
12
)
w
h
e
r
e,
el
em
en
t
s
o
f
w
ei
g
h
t
m
at
r
i
x
c
o
nt
a
i
ns
c
or
r
e
s
p
o
ndi
ng
we
i
g
ht
s
be
t
w
e
e
n i
n
put
t
o
hi
dde
n
ne
u
r
o
ns
a
n
d
e
l
e
m
e
n
t
s
o
f
b
i
a
s
m
a
t
r
i
x
co
n
t
ai
n
s
b
i
as
es
o
f
hi
d
de
n
ne
ur
o
ns
.
L
e
t
be
a
n
a
c
t
i
va
t
i
on f
u
nc
t
i
on a
nd
′
b
e
i
t
s
de
r
i
va
t
i
ve
.
T
he
o
ut
put
m
a
t
r
i
x (
)
i
s
o
b
t
a
i
n
e
d
b
y
s
p
l
i
t
-
t
y
p
e
a
c
t
i
v
a
t
i
o
n
f
u
n
c
t
i
o
n
o
v
e
r
i
n
t
e
r
n
a
l
p
o
t
e
n
t
i
a
l
m
a
t
r
i
x
(
)
a
t
h
i
d
d
e
n
l
a
y
e
r
:
O
=
f
(U
).
(
13
)
[
1
2
…
⋯
]
=
[
(
1
)
(
2
)
…
(
)
⋯
(
)
]
.
(
14
)
w
h
e
re
,
=
(
)
=
⎣
⎢
⎢
⎡
(
)
(
−
)
(
−
)
(
−
)
(
)
(
)
(
)
(
−
)
(
)
(
−
)
(
)
(
)
(
)
(
)
(
−
)
(
)
⎦
⎥
⎥
⎤
.
(
15
)
T
h
e
i
n
t
e
r
n
a
l
p
o
t
e
n
t
i
a
l
m
a
t
r
i
x
a
t
out
put
l
a
y
e
r
of
t
he
ne
t
w
or
k
i
s
de
f
i
ne
d
a
s
:
=
+
.
(
16
)
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎡
1
1
2
1
3
1
⋮
1
1
2
2
2
3
2
⋮
2
1
3
2
3
3
3
⋮
3
…
…
…
…
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
+
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
.
(
17
)
w
h
e
r
e
,
e
l
e
m
e
n
t
s
o
f
w
e
i
g
h
t
m
a
t
r
i
x
p
os
s
e
s
s
e
s
s
t
r
e
ngt
h of
s
y
na
pt
i
c
c
on
ne
c
t
i
ons
be
t
w
e
e
n
hi
d
de
n
a
nd
ou
t
put
ne
u
r
ons
a
nd
c
ol
um
n ve
c
t
or
p
os
s
e
s
s
e
s
a
l
l
qua
t
e
r
ni
oni
c
b
i
a
s
e
s
o
f
r
e
s
pe
c
t
i
ve
o
ut
p
ut
n
e
ur
o
ns
.
T
he
o
ut
p
ut
m
a
t
r
i
x
(
)
i
s
o
b
t
a
i
n
e
d
b
y
a
p
p
l
y
i
n
g
s
p
l
i
t
-
t
y
p
e
a
c
t
i
v
a
t
i
o
n
f
u
n
c
t
i
o
n
o
v
e
r
i
n
t
e
r
n
a
l
p
o
t
e
n
t
i
a
l
m
a
t
r
i
x
(
)
a
t
t
h
e
out
put
l
a
y
e
r
:
=
(
)
.
(
18
)
[
1
2
3
⋯
]
=
[
(
1
)
(
2
)
(
3
)
⋯
(
)
]
.
(
19
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
A
S
I
S
S
N
:
225
2
-
88
14
O
n
t
he
H
i
g
h
D
i
m
e
nt
i
o
nal
I
nf
o
r
mat
i
on
P
r
oc
e
s
s
i
ng
i
n
Q
uat
e
r
ni
on
ic
D
om
a
in
…
(
S
u
s
h
i
l
Ku
m
a
r
)
1
81
w
h
e
re
,
=
(
)
=
⎣
⎢
⎢
⎡
(
)
(
−
)
(
−
)
(
−
)
(
)
(
)
(
)
(
−
)
(
)
(
−
)
(
)
(
)
(
)
(
)
(
−
)
(
)
⎦
⎥
⎥
⎤
.
(
20
)
2.
1.
2.
Ba
c
k
w
a
r
d
Pa
ss
I
n
or
de
r
t
o d
e
ve
l
o
p a
Q
D
NN
ba
s
e
d l
e
a
r
ni
ng m
a
c
hi
ne
,
w
e
p
r
e
s
e
nt
t
he
de
r
i
va
t
i
o
n
of
t
he
e
r
r
o
r
ba
c
k
p
r
o
pa
ga
t
i
on l
e
a
r
ni
n
g a
l
go
r
i
t
hm
i
n qu
a
t
e
r
ni
o
n d
om
a
i
n (
Q
D
B
P
)
t
hr
ou
g
h
m
i
n
i
m
i
z
at
i
o
n
o
f
av
e
r
a
g
e m
ean
s
q
u
a
re
e
rr
o
r
(
)
of
t
he
ne
t
w
or
k:
=
1
8
(
)
(
∗
)
4
=
1
=
1
8
⎝
⎜
⎜
⎛
⎝
⎜
⎛
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
⎠
⎟
⎞
⎝
⎜
⎛
⎣
⎢
⎢
⎢
⎡
1
∗
2
∗
3
∗
⋮
∗
⎦
⎥
⎥
⎥
⎤
⎠
⎟
⎞
⎠
⎟
⎟
⎞
4
=
1
=
1
8
⎝
⎜
⎛
⎣
⎢
⎢
⎢
⎡
1
0
2
3
⋱
0
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
1
∗
0
2
∗
3
∗
⋱
0
∗
⎦
⎥
⎥
⎥
⎤
⎠
⎟
⎞
4
=
1
.
(
21
)
w
h
e
re
,
∗
de
n
ot
e
s
qua
t
e
r
ni
oni
c
c
on
j
uga
t
e
(
a
s
de
f
i
ne
d
i
n
E
q.
(
2
)
)
a
nd
t
he
o
u
t
put
e
r
r
o
r
m
a
t
r
i
x
(
)
p
r
e
s
e
n
t
s
t
h
e
d
i
f
f
e
r
e
n
ce
b
et
w
een
act
u
al
(
)
a
n
d
d
e
s
ir
e
d
(
)
out
put
a
t
o
ut
p
ut
l
a
y
e
r
,
de
f
i
ne
d
a
s
:
=
−
.
(
22
)
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
−
⎣
⎢
⎢
⎢
⎡
1
2
3
⋮
⎦
⎥
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎡
1
−
1
2
−
2
3
−
3
⋮
−
⎦
⎥
⎥
⎥
⎤
.
(
23
)
T
h
e u
p
d
at
e
e
q
u
at
i
o
n
s
o
f
w
ei
g
h
t
a
n
d
b
i
as
m
at
r
i
ces
ar
e
o
b
t
ai
n
ed
b
y
em
p
l
o
y
i
n
g
a g
r
ad
i
en
t
d
ece
n
t
opt
i
m
i
z
a
ti
on a
pp
r
oa
c
h
o
n M
S
E
,
m
e
a
n s
q
u
ar
e
er
r
o
r
(
)
.
T
h
e
w
e
i
g
h
t
u
p
d
a
t
e
m
a
t
r
i
x
(
∆
)
be
t
w
e
e
n
hi
dde
n
-
out
put
l
a
y
e
r
s
a
nd
bi
a
s
u
p
da
t
e
m
a
t
r
i
x
(
∆
)
a
t
t
he
o
ut
p
ut
l
a
y
e
r
of
t
he
ne
t
w
or
k
a
r
e
p
r
e
s
e
nt
e
d
a
s
f
ol
l
ow
s
:
∆
=
⎣
⎢
⎢
⎢
⎡
∆
1
∆
2
∆
3
⋮
∆
⎦
⎥
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎡
1
⊙
′
(
1
)
2
⊙
′
(
2
)
3
⊙
′
(
3
)
⋮
⊙
′
(
)
⎦
⎥
⎥
⎥
⎤
.
(
24
)
∆
=
⎣
⎢
⎢
⎢
⎡
∆
1
1
∆
2
1
∆
3
1
⋮
∆
1
∆
1
2
∆
2
2
∆
3
2
⋮
∆
2
∆
1
3
∆
2
3
∆
3
3
⋮
∆
3
…
…
…
…
∆
1
∆
2
∆
3
⋮
∆
⎦
⎥
⎥
⎥
⎤
=
⎣
⎢
⎢
⎢
⎡
1
⊙
′
(
1
)
2
⊙
′
(
2
)
3
⊙
′
(
3
)
⋮
⊙
′
(
)
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
1
∗
2
∗
3
∗
⋮
∗
⎦
⎥
⎥
⎥
⎤
.
(
25
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-
88
14
IJ
A
A
S
V
o
l
.
7
,
N
o
.
2
,
J
un
e
201
8
:
177
–
1
90
1
82
w
h
e
re
,
∈
ℝ
+
d
en
o
t
es
a l
ear
n
i
n
g
r
at
e an
d
⊙
d
e
n
o
t
es
el
em
en
t
-
w
i
s
e
m
u
l
t
i
p
l
i
c
a
t
i
o
n
o
f
t
w
o
q
u
a
t
e
r
n
i
o
n
i
c
m
a
t
r
i
c
e
s
(
a
s
d
e
f
i
n
e
d
i
n
E
q
.
(
3
)
)
.
S
i
m
i
l
a
r
l
y
,
w
e
i
g
h
t
u
p
d
a
t
e
m
a
t
r
i
x
(
∆
)
be
t
we
e
n i
n
p
ut
-
h
idd
e
n
l
ay
er
s
an
d
b
i
as
u
p
d
at
e m
at
r
i
x
(
∆
)
at
h
i
d
d
en
l
ay
er
o
f
t
h
e
n
et
w
o
r
k
ar
e
p
r
e
s
en
t
e
d
as
f
o
l
l
o
w
s
:
∆
=
⎣
⎢
⎢
⎢
⎡
∆
1
∆
2
∆
3
⋮
∆
⎦
⎥
⎥
⎥
⎤
=
⎝
⎜
⎜
⎛
⎣
⎢
⎢
⎢
⎡
∆
1
1
∆
2
1
∆
3
1
⋮
∆
1
∆
1
2
∆
2
2
∆
3
2
⋮
∆
2
∆
1
3
∆
2
3
∆
3
3
⋮
∆
3
…
…
…
…
∆
1
∆
2
∆
3
⋮
∆
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
1
⊙
′
(
1
)
2
⊙
′
(
2
)
3
⊙
′
(
3
)
⋮
⊙
′
(
)
⎦
⎥
⎥
⎥
⎤
⎠
⎟
⎟
⎞
⊙
⎣
⎢
⎢
⎢
⎡
′
(
1
)
′
(
2
)
′
(
3
)
⋮
′
(
)
⎦
⎥
⎥
⎥
⎤
.
(
26
)
∆
=
⎣
⎢
⎢
⎢
⎡
∆
1
1
∆
2
1
∆
3
1
⋮
∆
1
∆
1
2
∆
2
2
∆
3
2
⋮
∆
2
∆
1
3
∆
23
∆
3
3
⋮
∆
3
…
…
…
…
∆
1
∆
2
∆
3
⋮
∆
⎦
⎥
⎥
⎥
⎤
=
⎝
⎜
⎜
⎛
⎝
⎜
⎜
⎛
⎣
⎢
⎢
⎢
⎡
∆
1
1
∆
2
1
∆
3
1
⋮
∆
1
∆
1
2
∆
2
2
∆
3
2
⋮
∆
2
∆
1
3
∆
2
3
∆
3
3
⋮
∆
3
…
…
…
…
∆
1
∆
2
∆
3
⋮
∆
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
1
⊙
′
(
1
)
2
⊙
′
(
2
)
3
⊙
′
(
3
)
⋮
⊙
′
(
)
⎦
⎥
⎥
⎥
⎤
⎠
⎟
⎟
⎞
⊙
⎣
⎢
⎢
⎢
⎡
′
(
1
)
′
(
2
)
′
(
3
)
⋮
′
(
)
⎦
⎥
⎥
⎥
⎤
⎠
⎟
⎟
⎞
⎣
⎢
⎢
⎢
⎡
1
∗
2
∗
3
∗
⋮
∗
⎦
⎥
⎥
⎥
⎤
.
(
27
)
2.
2.
Le
a
r
n
i
n
g
a
l
g
o
r
i
t
h
m
i
n
q
u
a
t
e
r
n
i
o
n
i
c
d
o
m
a
i
n
F
or
t
he
s
a
ke
of
s
i
m
pl
i
c
i
ty
a
nd be
t
t
e
r
un
de
r
s
t
a
n
di
n
g,
w
e
f
u
r
t
he
r
pr
e
s
e
nt
a
n
a
l
gor
i
t
hm
Q
D
N
N_
T
R
AI
N(.
)
f
or
t
r
a
i
ni
ng
of
q
ua
t
e
r
ni
oni
c
d
om
a
i
n ne
ur
a
l
ne
t
wo
r
k
(
QD
N
N
)
,
w
h
i
c
h i
s
e
l
a
bor
a
t
e
d by
p
ro
c
e
d
u
r
e
s
Q
D
N
N_
IN
I
T
(
.
)
,
Q
D
N
N
_
F
O
R
WAR
D
(
.
) a
n
d
QD
N
N_
B
AC
K
W
A
R
D(
.
)
.
T
h
e
le
a
r
n
i
ng
a
nd
g
e
n
e
r
a
l
i
z
a
t
i
o
n
a
b
i
l
i
t
y
o
f
a
t
h
r
e
e
-
l
ay
er
ed
n
e
u
r
al
s
t
r
u
ct
u
r
e i
s
o
b
t
ai
n
e
d
t
h
r
o
u
g
h
o
p
t
i
m
i
zat
i
o
n
o
f
m
ean
s
q
u
ar
e
e
r
ro
r.
T
h
e p
r
o
ced
u
r
e
Q
DN
N_
IN
IT
(
.
)
r
a
n
d
o
m
l
y
i
n
i
t
i
a
l
i
z
e
s
t
h
e
w
e
i
g
h
t
a
n
d
b
i
a
s
m
a
t
r
i
c
e
s
i
n
c
o
n
s
i
d
e
r
e
d
ne
t
w
or
k.
I
t
c
a
l
l
s
t
h
e
RA
N
D
O
M
_
Q
M
(
a
,
b
)
p
r
oc
e
d
ur
e
w
hi
c
h r
a
nd
om
l
y ge
ne
r
a
t
e
s
t
he
qu
a
t
e
r
ni
o
ni
c
m
a
tr
i
x o
f
e
a
c
h i
nt
e
r
c
o
nn
e
c
t
i
on w
e
i
ght
a
nd
bi
a
s
o
f
n
e
ur
o
n i
n t
he
r
a
nge
f
r
om
a
to
b
.
T
h
e
QD
N
N
_
F
O
R
W
A
R
D
(.
)
pr
oc
e
du
r
e
i
s
i
nt
e
n
de
d
t
o
i
m
pl
e
m
e
nt
f
or
wa
r
d
pa
s
s
of
Q
D
NN
,
he
nc
e
ge
ne
r
a
t
e
i
nt
e
r
n
a
l
p
o
t
e
n
t
i
a
l
s
(
,
)
a
nd
he
nc
e
o
ut
p
ut
s
(
,
)
m
at
r
i
ces
at
r
es
p
ect
i
v
e l
ay
er
s
.
T
h
e
A
C
T
IV
A
T
I
O
N_
F
U
N
C
T
IO
N(
.
) l
i
m
i
t
s
t
h
e
o
u
t
p
u
t
o
f
c
or
r
e
s
po
n
di
n
g ne
u
r
on
o
f
t
h
e n
et
w
o
r
k
.
F
o
r
u
p
d
at
es
w
ei
g
h
t
an
d
b
i
as
m
at
r
i
ces
,
Q
D
N
N
_
B
AC
K
WAR
D
(.
)
i
s
de
ve
l
ope
d f
or
t
he
ba
c
k
w
a
r
d pa
s
s
of
Q
D
N
N
.
A
l
l
r
e
qu
i
r
e
d
p
r
o
ced
u
r
es
a
r
e p
r
es
e
n
t
ed
i
n
p
s
e
u
d
o
c
o
d
e
ar
e as
f
o
l
l
o
w
s
:
Q
DN
N
_
TR
AI
N
(
,
,
,
)
Q
DN
N
_
IN
IT
(
,
,
)
;
>
←
1
=
ℎ
(
)
,
,
,
←
Q
DN
N
_
F
O
RW
A
RD
(
,
,
,
,
)
;
←
−
;
←
1
8
∑
(
(
)
(
∗
)
)
;
4
=
1
Q
DN
N
_
BAC
KW
AR
D
(
,
,
,
,
,
,
,
,
,
)
←
1
∑
;
=
1
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
A
S
I
S
S
N
:
225
2
-
88
14
O
n
t
he
H
i
g
h
D
i
m
e
nt
i
o
nal
I
nf
o
r
mat
i
on
P
r
oc
e
s
s
i
ng
i
n
Q
uat
e
r
ni
on
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T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
252
-
88
14
IJ
A
A
S
V
o
l
.
7
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2
,
J
un
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201
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1
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a
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d
A
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[
2
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].
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n
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e
r
c
l
a
s
s
of
be
nc
hm
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k pr
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s
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l
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a
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g o
f
l
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e
a
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m
a
t
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s
(
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c
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3
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m
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t
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u
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.
I
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l
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t
s
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t
w
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p
r
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p
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m
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n
t
s
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p
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n
t
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d
f
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3
D
f
a
c
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g
n
i
t
i
o
n
;
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u
r
e
l
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i
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w
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s
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t
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a l
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at
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l
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t
t
w
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nt
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by
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ni
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c
h c
ont
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de
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m
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s
a
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g w
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h p
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s
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i
nf
or
m
a
t
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on e
m
be
d
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d
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hi
n
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n
um
be
r
,
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s
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ot
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t
o
pe
r
f
o
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m
s
uc
h
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xpe
r
i
m
e
nt
s
.
3.
1.
F
unc
t
i
o
n
A
pp
r
o
x
i
m
a
t
i
o
ns
3.
1.
1.
T
h
e
L
or
e
n
z
S
y
s
t
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T
he
dy
na
m
i
c
s
of
t
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L
o
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e
nz
s
y
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t
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m
[
21]
i
s
p
r
e
s
e
nt
e
d
by
t
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s
y
s
t
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m
of
t
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c
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r
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m
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s
.
dx/
dt
=
σ
(
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-
x
)
d
y/d
t=
x(
ρ
-
z)
-
y
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/
dt
=
xy
-
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(
28
)
w
he
r
e
,
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he
s
y
m
bol
s
,
a
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re
p
a
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b
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(
=
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=
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a
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=
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)
,
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(
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q
.
(
2
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g
e
n
e
r
a
t
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s
6
5
3
7
t
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m
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al
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o
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d
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(
=
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7
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=
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1
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=
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1
)
us
i
n
g f
o
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t
h or
de
r
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u
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-
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ut
t
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m
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t
hod.
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a
c
h t
e
r
m
c
a
n be
c
on
s
i
de
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d
i
n t
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f
o
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m
of
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t
e
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ni
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c
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put
a
s
0
+
+
+
.
F
u
r
t
he
r
,
t
he
n
o
r
m
a
li
z
a
t
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on i
s
pe
r
f
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m
e
d i
n t
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r
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f
r
o
m
-
0.
8 t
o
0
.
8.
T
he
f
i
r
s
t
5
00 t
e
r
m
s
of
t
h
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t
im
e
s
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s
ha
ve
be
e
n
us
e
d
f
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r
t
r
a
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n
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nd
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s
t
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t
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of
t
h
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e
e
-
l
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e
re
d
R
VN
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(
3
-
11
-
3
)
a
n
d
Q
DN
N
n
e
t
w
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s
(1
-
3
-
1)
s
e
pa
r
a
t
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l
y
.
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xpe
r
i
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e
nts
de
m
ons
t
r
a
t
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t
ha
t
t
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s
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n
d
n
et
w
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k
r
e
q
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l
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m
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ai
n
i
n
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cl
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o
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i
e
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M
S
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as
p
r
e
s
e
n
t
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d
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n
T
a
b
l
e
1
.
F
i
g
u
r
e
.
1
s
h
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s
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t
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s
t
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s
ul
t
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t
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c
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m
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Qu
ater
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Alg
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3
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4503
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
A
S
I
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S
N
:
225
2
-
88
14
O
n
t
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H
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m
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mat
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on
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s
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n
Q
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r
ni
on
ic
D
om
a
in
…
(
S
u
s
h
i
l
Ku
m
a
r
)
1
85
3.
1.
2.
Th
e
C
hu
a
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s
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r
r
e
s
ul
t
t
h
e
t
r
a
ns
f
or
m
e
d p
oi
n
t
(
′
,
′
,
′
)
o
n
l
i
n
e an
d
t
r
an
s
f
o
r
m
ed
r
ef
e
r
en
ce
p
o
i
n
t
(
′
,
′
,
′
)
r
es
p
ect
i
v
el
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.
T
h
e l
ear
n
i
n
g
o
f
t
h
e
t
r
a
ns
f
o
r
m
a
ti
on
i
s
a
c
hi
e
ve
d b
y
l
e
a
r
ni
n
g t
he
a
l
go
r
i
t
hm
pr
e
s
e
nt
e
d i
n
s
e
c
t
i
o
n 2
.
2
wi
t
h a
s
ui
t
ab
l
e l
ear
n
i
n
g
r
at
e
.
T
h
e t
r
ai
n
e
d
Q
D
N
N
i
s
ab
l
e t
o
g
e
n
er
al
i
ze o
v
er
h
u
g
e n
u
m
b
er
o
f
p
o
i
n
t
s
cl
o
u
d
d
at
a o
f
co
m
p
l
i
cat
ed
g
eo
m
et
r
i
cal
s
t
r
u
c
t
u
r
e
l
i
k
e
s
p
h
e
r
e
,
c
y
l
i
n
d
e
r
,
t
o
r
u
s
a
n
d
t
h
i
s
a
b
i
l
i
t
y
o
f
t
h
e
n
e
t
w
o
r
k
p
r
e
s
e
n
t
s
t
h
e
3
D
m
o
t
i
o
n
i
n
t
e
r
p
r
e
t
a
t
i
o
n
o
f
o
b
j
e
c
t
s
.
I
t
i
s
w
o
r
t
hw
hi
l
e
t
o
m
e
nt
i
on
he
r
e
t
ha
t
l
e
a
r
ni
n
g
o
f
p
ha
s
e
i
nf
or
m
a
t
ion
i
s
not
p
os
s
i
bl
e
by
R
V
N
N
he
nc
e
s
uc
h
t
r
a
ns
f
or
m
a
t
i
on
i
s
not
po
s
s
i
bl
e
t
hr
o
ug
h
R
VN
N
;
t
he
r
e
f
or
e
t
hi
s
s
e
c
t
i
o
n
onl
y
pr
e
s
e
nt
s
t
he
r
e
s
ul
t
o
bt
a
i
ne
d
by
Q
DN
N
.
3
.
2
.
1
.
S
i
m
i
l
a
r
i
t
y
T
r
an
s
f
or
m
at
i
on
T
he
l
e
a
r
ni
n
g of
QD
N
N (2
-
6
-
2 m
ode
l
)
i
s
pe
r
f
o
r
m
e
d f
or
s
im
il
a
r
i
t
y
t
r
a
ns
f
or
m
a
t
i
on,
t
hr
o
ug
h i
n
put
-
out
put
m
a
ppi
n
g f
or
s
c
a
l
i
ng
f
a
c
t
or
½
ove
r
t
he
l
i
ne
c
o
nt
a
i
n
i
ng
21
p
oi
nt
s
,
r
e
f
e
r
e
nc
e
d i
n
(
0
,
0
,
0
)
,
a
s
s
h
o
w
n
i
n
F
ig
ur
e
.
3
(
a)
.
C
o
n
v
er
g
e
n
ce o
f
m
ean
s
q
u
ar
e er
r
o
r
(
F
igur
e
.
3(
b)
)
s
h
ow
s
t
he
s
m
a
r
t
l
e
a
r
n
i
n
g
c
a
p
a
b
i
l
i
t
y
o
f
t
h
e
pr
o
pos
e
d ne
t
w
or
k.
T
he
t
r
a
i
ni
ng
of
Q
D
NN
wi
t
h 0.
0
00
0
5 l
e
a
r
ni
ng r
a
t
e
c
on
ve
r
ge
s
t
o M
S
E
=
1.
0
0
55
6
7e
-
05
a
f
t
e
r
2
0
00
0 i
t
e
r
a
t
i
ons
.
T
he
t
r
a
i
ne
d
ne
t
w
or
k
i
s
a
bl
e
t
o ge
ne
r
a
l
i
z
e
ove
r
m
a
ny
c
om
pl
i
c
a
t
e
d s
t
a
n
da
r
d
ge
o
m
e
t
r
i
c
s
t
r
u
c
t
u
r
e
s
l
i
k
e
s
p
h
e
r
e
(
4
1
41
d
a
t
a
poi
nt
s
)
,
c
y
l
i
nde
r
(
2
92
9
da
t
a
poi
nt
s
)
,
a
n
d
t
or
us
(
1
02
0
1
d
a
t
a
poi
nt
s
)
w
hi
c
h i
s
pr
e
s
e
nt
e
d
i
n
F
ig
ur
e
.
4
(
a)
,
4
(
b
)
,
an
d
4
(
c)
r
es
p
ect
i
v
el
y
.
(
a)
(
b)
F
ig
ur
e
3
.
(
a
)
T
r
a
i
ni
n
g
i
np
ut
-
o
ut
p
ut
m
a
ppi
n
g
f
o
r
s
c
a
l
i
n
g
w
i
t
h
s
c
a
l
i
n
g
f
a
c
t
o
r
½
;
(b
)
C
on
ve
r
ge
n
ce
o
f
m
ean
s
q
u
ar
e
er
r
o
r
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