<s>
A	O
widely	O
used	O
type	O
of	O
composition	O
is	O
the	O
nonlinear	O
weighted	O
sum	O
,	O
where	O
,	O
where	O
(	O
commonly	O
referred	O
to	O
as	O
the	O
activation	B-Algorithm
function	I-Algorithm
)	O
is	O
some	O
predefined	O
function	O
,	O
such	O
as	O
the	O
hyperbolic	O
tangent	O
,	O
sigmoid	B-Algorithm
function	I-Algorithm
,	O
softmax	B-Algorithm
function	I-Algorithm
,	O
or	O
rectifier	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
The	O
important	O
characteristic	O
of	O
the	O
activation	B-Algorithm
function	I-Algorithm
is	O
that	O
it	O
provides	O
a	O
smooth	O
transition	O
as	O
input	O
values	O
change	O
,	O
i.e.	O
</s>
<s>
This	O
view	O
is	O
most	O
commonly	O
encountered	O
in	O
the	O
context	O
of	O
graphical	B-Algorithm
models	I-Algorithm
.	O
</s>
<s>
Networks	O
such	O
as	O
the	O
previous	O
one	O
are	O
commonly	O
called	O
feedforward	B-Algorithm
,	O
because	O
their	O
graph	O
is	O
a	O
directed	O
acyclic	O
graph	O
.	O
</s>
<s>
Networks	O
with	O
cycles	O
are	O
commonly	O
called	O
recurrent	B-Algorithm
.	O
</s>
<s>
steepest	B-Algorithm
descent	I-Algorithm
(	O
with	O
variable	O
learning	B-General_Concept
rate	I-General_Concept
and	O
momentum	O
,	O
resilient	B-Algorithm
backpropagation	I-Algorithm
)	O
;	O
</s>
<s>
quasi-Newton	O
(	O
Broyden	B-Algorithm
–	I-Algorithm
Fletcher	I-Algorithm
–	I-Algorithm
Goldfarb	I-Algorithm
–	I-Algorithm
Shanno	I-Algorithm
,	O
one	O
step	O
secant	O
)	O
;	O
</s>
<s>
Levenberg	B-Algorithm
–	I-Algorithm
Marquardt	I-Algorithm
and	O
conjugate	B-Algorithm
gradient	I-Algorithm
(	O
Fletcher	O
–	O
Reeves	O
update	O
,	O
Polak	O
–	O
Ribiére	O
update	O
,	O
Powell	O
–	O
Beale	O
restart	O
,	O
scaled	O
conjugate	B-Algorithm
gradient	I-Algorithm
)	O
.	O
</s>
<s>
is	O
calculated	O
from	O
by	O
considering	O
a	O
variable	O
weight	O
and	O
applying	O
gradient	B-Algorithm
descent	I-Algorithm
to	O
the	O
function	O
to	O
find	O
a	O
local	O
minimum	O
,	O
starting	O
at	O
.	O
</s>
<s>
This	O
makes	O
the	O
minimizing	O
weight	O
found	O
by	O
gradient	B-Algorithm
descent	I-Algorithm
.	O
</s>
<s>
The	O
learning	B-General_Concept
rate	I-General_Concept
is	O
the	O
ratio	O
(	O
percentage	O
)	O
that	O
influences	O
the	O
speed	O
and	O
quality	O
of	O
learning	O
.	O
</s>
<s>
Pseudocode	B-Language
for	O
a	O
stochastic	B-Algorithm
gradient	I-Algorithm
descent	I-Algorithm
algorithm	O
for	O
training	O
a	O
three-layer	O
network	O
(	O
one	O
hidden	O
layer	O
)	O
:	O
</s>
