<s>
A	O
multilayer	B-Algorithm
perceptron	I-Algorithm
(	O
MLP	O
)	O
is	O
a	O
fully	O
connected	O
class	O
of	O
feedforward	B-Algorithm
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
(	O
ANN	O
)	O
.	O
</s>
<s>
The	O
term	O
MLP	O
is	O
used	O
ambiguously	O
,	O
sometimes	O
loosely	O
to	O
mean	O
any	O
feedforward	B-Algorithm
ANN	O
,	O
sometimes	O
strictly	O
to	O
refer	O
to	O
networks	O
composed	O
of	O
multiple	O
layers	B-Algorithm
of	O
perceptrons	B-Algorithm
(	O
with	O
threshold	O
activation	O
)	O
;	O
see	O
.	O
</s>
<s>
Multilayer	B-Algorithm
perceptrons	I-Algorithm
are	O
sometimes	O
colloquially	O
referred	O
to	O
as	O
"	O
vanilla	O
"	O
neural	B-Architecture
networks	I-Architecture
,	O
especially	O
when	O
they	O
have	O
a	O
single	O
hidden	O
layer	O
.	O
</s>
<s>
An	O
MLP	O
consists	O
of	O
at	O
least	O
three	O
layers	B-Algorithm
of	O
nodes	O
:	O
an	O
input	O
layer	O
,	O
a	O
hidden	O
layer	O
and	O
an	O
output	O
layer	O
.	O
</s>
<s>
Except	O
for	O
the	O
input	O
nodes	O
,	O
each	O
node	O
is	O
a	O
neuron	O
that	O
uses	O
a	O
nonlinear	O
activation	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
MLP	O
utilizes	O
a	O
chain	O
rule	O
based	O
supervised	B-General_Concept
learning	I-General_Concept
technique	O
called	O
backpropagation	B-Algorithm
or	O
reverse	O
mode	O
of	O
automatic	B-Algorithm
differentiation	I-Algorithm
for	O
training	O
.	O
</s>
<s>
Its	O
multiple	O
layers	B-Algorithm
and	O
non-linear	O
activation	O
distinguish	O
MLP	O
from	O
a	O
linear	B-Algorithm
perceptron	I-Algorithm
.	O
</s>
<s>
If	O
a	O
multilayer	B-Algorithm
perceptron	I-Algorithm
has	O
a	O
linear	O
activation	B-Algorithm
function	I-Algorithm
in	O
all	O
neurons	O
,	O
that	O
is	O
,	O
a	O
linear	O
function	O
that	O
maps	O
the	O
weighted	B-Algorithm
inputs	I-Algorithm
to	O
the	O
output	O
of	O
each	O
neuron	O
,	O
then	O
linear	B-Language
algebra	I-Language
shows	O
that	O
any	O
number	O
of	O
layers	B-Algorithm
can	O
be	O
reduced	O
to	O
a	O
two-layer	O
input-output	O
model	O
.	O
</s>
<s>
In	O
MLPs	O
some	O
neurons	O
use	O
a	O
nonlinear	O
activation	B-Algorithm
function	I-Algorithm
that	O
was	O
developed	O
to	O
model	O
the	O
frequency	O
of	O
action	B-Algorithm
potentials	I-Algorithm
,	O
or	O
firing	O
,	O
of	O
biological	O
neurons	O
.	O
</s>
<s>
Alternative	O
activation	B-Algorithm
functions	I-Algorithm
have	O
been	O
proposed	O
,	O
including	O
the	O
rectifier	B-Algorithm
and	I-Algorithm
softplus	I-Algorithm
functions	O
.	O
</s>
<s>
More	O
specialized	O
activation	B-Algorithm
functions	I-Algorithm
include	O
radial	B-Algorithm
basis	I-Algorithm
functions	I-Algorithm
(	O
used	O
in	O
radial	B-Algorithm
basis	I-Algorithm
networks	I-Algorithm
,	O
another	O
class	O
of	O
supervised	O
neural	B-Architecture
network	I-Architecture
models	I-Architecture
)	O
.	O
</s>
<s>
In	O
recent	O
developments	O
of	O
deep	B-Algorithm
learning	I-Algorithm
the	O
rectified	B-Algorithm
linear	I-Algorithm
unit	I-Algorithm
(	O
ReLU	B-Algorithm
)	O
is	O
more	O
frequently	O
used	O
as	O
one	O
of	O
the	O
possible	O
ways	O
to	O
overcome	O
the	O
numerical	O
problems	B-Algorithm
related	O
to	O
the	O
sigmoids	B-Algorithm
.	O
</s>
<s>
The	O
MLP	O
consists	O
of	O
three	O
or	O
more	O
layers	B-Algorithm
(	O
an	O
input	O
and	O
an	O
output	O
layer	O
with	O
one	O
or	O
more	O
hidden	O
layers	B-Algorithm
)	O
of	O
nonlinearly-activating	O
nodes	O
.	O
</s>
<s>
Learning	O
occurs	O
in	O
the	O
perceptron	B-Algorithm
by	O
changing	O
connection	O
weights	O
after	O
each	O
piece	O
of	O
data	O
is	O
processed	O
,	O
based	O
on	O
the	O
amount	O
of	O
error	O
in	O
the	O
output	O
compared	O
to	O
the	O
expected	O
result	O
.	O
</s>
<s>
This	O
is	O
an	O
example	O
of	O
supervised	B-General_Concept
learning	I-General_Concept
,	O
and	O
is	O
carried	O
out	O
through	O
backpropagation	B-Algorithm
,	O
a	O
generalization	O
of	O
the	O
least	O
mean	O
squares	O
algorithm	O
in	O
the	O
linear	B-Algorithm
perceptron	I-Algorithm
.	O
</s>
<s>
We	O
can	O
represent	O
the	O
degree	O
of	O
error	O
in	O
an	O
output	O
node	O
in	O
the	O
th	O
data	O
point	O
(	O
training	O
example	O
)	O
by	O
,	O
where	O
is	O
the	O
desired	O
target	O
value	O
for	O
th	O
data	O
point	O
at	O
node	O
,	O
and	O
is	O
the	O
value	O
produced	O
by	O
the	O
perceptron	B-Algorithm
at	O
node	O
when	O
the	O
th	O
data	O
point	O
is	O
given	O
as	O
an	O
input	O
.	O
</s>
<s>
where	O
is	O
the	O
output	O
of	O
the	O
previous	O
neuron	O
,	O
and	O
is	O
the	O
learning	B-General_Concept
rate	I-General_Concept
,	O
which	O
is	O
selected	O
to	O
ensure	O
that	O
the	O
weights	O
quickly	O
converge	O
to	O
a	O
response	O
,	O
without	O
oscillations	O
.	O
</s>
<s>
where	O
is	O
the	O
derivative	O
of	O
the	O
activation	B-Algorithm
function	I-Algorithm
described	O
above	O
,	O
which	O
itself	O
does	O
not	O
vary	O
.	O
</s>
<s>
So	O
to	O
change	O
the	O
hidden	O
layer	O
weights	O
,	O
the	O
output	O
layer	O
weights	O
change	O
according	O
to	O
the	O
derivative	O
of	O
the	O
activation	B-Algorithm
function	I-Algorithm
,	O
and	O
so	O
this	O
algorithm	O
represents	O
a	O
backpropagation	B-Algorithm
of	O
the	O
activation	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
The	O
term	O
"	O
multilayer	B-Algorithm
perceptron	I-Algorithm
"	O
does	O
not	O
refer	O
to	O
a	O
single	O
perceptron	B-Algorithm
that	O
has	O
multiple	O
layers	B-Algorithm
.	O
</s>
<s>
Rather	O
,	O
it	O
contains	O
many	O
perceptrons	B-Algorithm
that	O
are	O
organized	O
into	O
layers	B-Algorithm
.	O
</s>
<s>
An	O
alternative	O
is	O
"	O
multilayer	B-Algorithm
perceptron	I-Algorithm
network	O
"	O
.	O
</s>
<s>
Moreover	O
,	O
MLP	O
"	O
perceptrons	B-Algorithm
"	O
are	O
not	O
perceptrons	B-Algorithm
in	O
the	O
strictest	O
possible	O
sense	O
.	O
</s>
<s>
True	O
perceptrons	B-Algorithm
are	O
formally	O
a	O
special	O
case	O
of	O
artificial	O
neurons	O
that	O
use	O
a	O
threshold	O
activation	B-Algorithm
function	I-Algorithm
such	O
as	O
the	O
Heaviside	O
step	O
function	O
.	O
</s>
<s>
MLP	O
perceptrons	B-Algorithm
can	O
employ	O
arbitrary	O
activation	B-Algorithm
functions	I-Algorithm
.	O
</s>
<s>
A	O
true	O
perceptron	B-Algorithm
performs	O
binary	O
classification	B-General_Concept
,	O
an	O
MLP	O
neuron	O
is	O
free	O
to	O
either	O
perform	O
classification	B-General_Concept
or	O
regression	O
,	O
depending	O
upon	O
its	O
activation	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
The	O
term	O
"	O
multilayer	B-Algorithm
perceptron	I-Algorithm
"	O
later	O
was	O
applied	O
without	O
respect	O
to	O
nature	O
of	O
the	O
nodes/layers	O
,	O
which	O
can	O
be	O
composed	O
of	O
arbitrarily	O
defined	O
artificial	O
neurons	O
,	O
and	O
not	O
perceptrons	B-Algorithm
specifically	O
.	O
</s>
<s>
This	O
interpretation	O
avoids	O
the	O
loosening	O
of	O
the	O
definition	O
of	O
"	O
perceptron	B-Algorithm
"	O
to	O
mean	O
an	O
artificial	O
neuron	O
in	O
general	O
.	O
</s>
<s>
Frank	O
Rosenblatt	O
,	O
who	O
published	O
the	O
Perceptron	B-Algorithm
in	O
1958	O
,	O
also	O
introduced	O
an	O
MLP	O
with	O
3	O
layers	B-Algorithm
:	O
an	O
input	O
layer	O
,	O
a	O
hidden	O
layer	O
with	O
randomized	O
weights	O
that	O
did	O
not	O
learn	O
,	O
and	O
an	O
output	O
layer	O
.	O
</s>
<s>
Since	O
only	O
the	O
output	O
layer	O
had	O
learning	O
connections	O
,	O
this	O
was	O
not	O
yet	O
deep	B-Algorithm
learning	I-Algorithm
.	O
</s>
<s>
It	O
was	O
what	O
later	O
was	O
called	O
an	O
extreme	B-Algorithm
learning	I-Algorithm
machine	I-Algorithm
.	O
</s>
<s>
The	O
first	O
deep	B-Algorithm
learning	I-Algorithm
MLP	O
was	O
published	O
by	O
Alexey	O
Grigorevich	O
Ivakhnenko	O
and	O
Valentin	O
Lapa	O
in	O
1965	O
,	O
as	O
the	O
Group	B-Algorithm
Method	I-Algorithm
of	I-Algorithm
Data	I-Algorithm
Handling	I-Algorithm
.	O
</s>
<s>
The	O
first	O
deep	B-Algorithm
learning	I-Algorithm
MLP	O
trained	O
by	O
stochastic	B-Algorithm
gradient	I-Algorithm
descent	I-Algorithm
was	O
published	O
in	O
1967	O
by	O
Shun'ichi	O
Amari	O
.	O
</s>
<s>
In	O
computer	O
experiments	O
conducted	O
by	O
Amari	O
's	O
student	O
Saito	O
,	O
a	O
five	O
layer	O
MLP	O
with	O
two	O
modifiable	O
layers	B-Algorithm
learned	O
internal	O
representations	O
required	O
to	O
classify	O
non-linearily	O
separable	O
pattern	O
classes	O
.	O
</s>
<s>
In	O
1970	O
,	O
Seppo	O
Linnainmaa	O
published	O
the	O
general	O
method	O
for	O
automatic	B-Algorithm
differentiation	I-Algorithm
of	O
discrete	O
connected	O
networks	O
of	O
nested	O
differentiable	O
functions	O
.	O
</s>
<s>
This	O
became	O
known	O
as	O
backpropagation	B-Algorithm
or	O
reverse	O
mode	O
of	O
automatic	B-Algorithm
differentiation	I-Algorithm
.	O
</s>
<s>
The	O
terminology	O
"	O
back-propagating	O
errors	O
"	O
was	O
actually	O
introduced	O
in	O
1962	O
by	O
Rosenblatt	O
himself	O
,	O
but	O
he	O
did	O
not	O
know	O
how	O
to	O
implement	O
this	O
,	O
although	O
Henry	O
J	O
.	O
Kelley	O
had	O
a	O
continuous	O
precursor	O
of	O
backpropagation	B-Algorithm
already	O
in	O
1960	O
in	O
the	O
context	O
of	O
control	O
theory	O
.	O
</s>
<s>
In	O
1982	O
,	O
Paul	O
Werbos	O
applied	O
backpropagation	B-Algorithm
to	O
MLPs	O
in	O
the	O
way	O
that	O
has	O
become	O
standard	O
.	O
</s>
<s>
MLPs	O
are	O
useful	O
in	O
research	O
for	O
their	O
ability	O
to	O
solve	O
problems	B-Algorithm
stochastically	O
,	O
which	O
often	O
allows	O
approximate	O
solutions	O
for	O
extremely	O
complex	O
problems	B-Algorithm
like	O
fitness	B-Algorithm
approximation	I-Algorithm
.	O
</s>
<s>
MLPs	O
are	O
universal	O
function	O
approximators	O
as	O
shown	O
by	O
Cybenko	B-Algorithm
's	I-Algorithm
theorem	I-Algorithm
,	O
so	O
they	O
can	O
be	O
used	O
to	O
create	O
mathematical	O
models	O
by	O
regression	O
analysis	O
.	O
</s>
<s>
As	O
classification	B-General_Concept
is	O
a	O
particular	O
case	O
of	O
regression	O
when	O
the	O
response	O
variable	O
is	O
categorical	O
,	O
MLPs	O
make	O
good	O
classifier	B-General_Concept
algorithms	O
.	O
</s>
<s>
MLPs	O
were	O
a	O
popular	O
machine	O
learning	O
solution	O
in	O
the	O
1980s	O
,	O
finding	O
applications	O
in	O
diverse	O
fields	O
such	O
as	O
speech	B-Application
recognition	I-Application
,	O
image	O
recognition	O
,	O
and	O
machine	B-Application
translation	I-Application
software	O
,	O
but	O
thereafter	O
faced	O
strong	O
competition	O
from	O
much	O
simpler	O
(	O
and	O
related	O
)	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
.	O
</s>
<s>
Interest	O
in	O
backpropagation	B-Algorithm
networks	O
returned	O
due	O
to	O
the	O
successes	O
of	O
deep	B-Algorithm
learning	I-Algorithm
.	O
</s>
