<s>
Artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
(	O
ANNs	O
)	O
,	O
usually	O
simply	O
called	O
neural	B-Architecture
networks	I-Architecture
(	O
NNs	O
)	O
or	O
neural	B-Architecture
nets	I-Architecture
,	O
are	O
computing	O
systems	O
inspired	O
by	O
the	O
biological	B-General_Concept
neural	I-General_Concept
networks	I-General_Concept
that	O
constitute	O
animal	O
brains	O
.	O
</s>
<s>
An	O
ANN	O
is	O
based	O
on	O
a	O
collection	O
of	O
connected	O
units	O
or	O
nodes	O
called	O
artificial	B-Algorithm
neurons	I-Algorithm
,	O
which	O
loosely	O
model	O
the	O
neurons	O
in	O
a	O
biological	O
brain	O
.	O
</s>
<s>
Each	O
connection	O
,	O
like	O
the	O
synapses	B-Application
in	O
a	O
biological	O
brain	O
,	O
can	O
transmit	O
a	O
signal	O
to	O
other	O
neurons	O
.	O
</s>
<s>
An	O
artificial	B-Algorithm
neuron	I-Algorithm
receives	O
signals	O
then	O
processes	O
them	O
and	O
can	O
signal	O
neurons	O
connected	O
to	O
it	O
.	O
</s>
<s>
Neurons	O
and	O
edges	O
typically	O
have	O
a	O
weight	B-General_Concept
that	O
adjusts	O
as	O
learning	O
proceeds	O
.	O
</s>
<s>
The	O
weight	B-General_Concept
increases	O
or	O
decreases	O
the	O
strength	O
of	O
the	O
signal	O
at	O
a	O
connection	O
.	O
</s>
<s>
Neural	B-Architecture
networks	I-Architecture
learn	O
(	O
or	O
are	O
trained	O
)	O
by	O
processing	O
examples	O
,	O
each	O
of	O
which	O
contains	O
a	O
known	O
"	O
input	O
"	O
and	O
"	O
result	O
,	O
"	O
forming	O
probability-weighted	O
associations	O
between	O
the	O
two	O
,	O
which	O
are	O
stored	O
within	O
the	O
data	O
structure	O
of	O
the	O
net	O
itself	O
.	O
</s>
<s>
The	O
training	O
of	O
a	O
neural	B-Architecture
network	I-Architecture
from	O
a	O
given	O
example	O
is	O
usually	O
conducted	O
by	O
determining	O
the	O
difference	O
between	O
the	O
processed	O
output	O
of	O
the	O
network	O
(	O
often	O
a	O
prediction	O
)	O
and	O
a	O
target	O
output	O
.	O
</s>
<s>
Successive	O
adjustments	O
will	O
cause	O
the	O
neural	B-Architecture
network	I-Architecture
to	O
produce	O
output	O
that	O
is	O
increasingly	O
similar	O
to	O
the	O
target	O
output	O
.	O
</s>
<s>
This	O
is	O
a	O
form	O
of	O
supervised	B-General_Concept
learning	I-General_Concept
.	O
</s>
<s>
For	O
example	O
,	O
in	O
image	O
recognition	O
,	O
they	O
might	O
learn	O
to	O
identify	O
images	O
that	O
contain	O
cats	O
by	O
analyzing	O
example	O
images	O
that	O
have	O
been	O
manually	O
labeled	B-General_Concept
as	O
"	O
cat	O
"	O
or	O
"	O
no	O
cat	O
"	O
and	O
using	O
the	O
results	O
to	O
identify	O
cats	O
in	O
other	O
images	O
.	O
</s>
<s>
The	O
simplest	O
kind	O
of	O
feedforward	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
(	O
FNN	O
)	O
is	O
a	O
linear	O
network	O
,	O
which	O
consists	O
of	O
a	O
single	O
layer	O
of	O
output	O
nodes	O
;	O
the	O
inputs	O
are	O
fed	O
directly	O
to	O
the	O
outputs	O
via	O
a	O
series	O
of	O
weights	O
.	O
</s>
<s>
The	O
mean	B-Algorithm
squared	I-Algorithm
errors	I-Algorithm
between	O
these	O
calculated	O
outputs	O
and	O
a	O
given	O
target	O
values	O
are	O
minimized	O
by	O
creating	O
an	O
adjustment	O
to	O
the	O
weights	O
.	O
</s>
<s>
This	O
technique	O
has	O
been	O
known	O
for	O
over	O
two	O
centuries	O
as	O
the	O
method	B-Algorithm
of	I-Algorithm
least	I-Algorithm
squares	I-Algorithm
or	O
linear	B-General_Concept
regression	I-General_Concept
.	O
</s>
<s>
It	O
was	O
used	O
as	O
a	O
means	O
of	O
finding	O
a	O
good	O
rough	O
linear	B-General_Concept
fit	I-General_Concept
to	O
a	O
set	O
of	O
points	O
by	O
Legendre	O
(	O
1805	O
)	O
and	O
Gauss	B-Algorithm
(	O
1795	O
)	O
for	O
the	O
prediction	O
of	O
planetary	O
movement	O
.	O
</s>
<s>
Wilhelm	O
Lenz	O
and	O
Ernst	O
Ising	O
created	O
and	O
analyzed	O
the	O
Ising	O
model	O
(	O
1925	O
)	O
which	O
is	O
essentially	O
a	O
non-learning	O
artificial	O
recurrent	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
(	O
RNN	O
)	O
consisting	O
of	O
neuron-like	O
threshold	O
elements	O
.	O
</s>
<s>
Warren	O
McCulloch	O
and	O
Walter	O
Pitts	O
(	O
1943	O
)	O
also	O
considered	O
a	O
non-learning	O
computational	O
model	O
for	O
neural	B-Architecture
networks	I-Architecture
.	O
</s>
<s>
In	O
1958	O
,	O
psychologist	O
Frank	O
Rosenblatt	O
invented	O
the	O
perceptron	B-Algorithm
,	O
the	O
first	O
implemented	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
,	O
funded	O
by	O
the	O
United	O
States	O
Office	O
of	O
Naval	O
Research	O
.	O
</s>
<s>
Some	O
say	O
that	O
research	O
stagnated	O
following	O
Minsky	O
and	O
Papert	O
(	O
1969	O
)	O
,	O
who	O
discovered	O
that	O
basic	O
perceptrons	B-Algorithm
were	O
incapable	O
of	O
processing	O
the	O
exclusive-or	O
circuit	O
and	O
that	O
computers	O
lacked	O
sufficient	O
power	O
to	O
process	O
useful	O
neural	B-Architecture
networks	I-Architecture
.	O
</s>
<s>
However	O
,	O
by	O
the	O
time	O
this	O
book	O
came	O
out	O
,	O
methods	O
for	O
training	O
multilayer	B-Algorithm
perceptrons	I-Algorithm
(	O
MLPs	O
)	O
were	O
already	O
known	O
.	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>
Self-organizing	B-Algorithm
maps	I-Algorithm
(	O
SOMs	O
)	O
were	O
described	O
by	O
Teuvo	O
Kohonen	B-Algorithm
in	O
1982	O
.	O
</s>
<s>
SOMs	O
are	O
neurophysiologically	O
inspired	O
neural	B-Architecture
networks	I-Architecture
that	O
learn	O
low-dimensional	B-Algorithm
representations	O
of	O
high-dimensional	O
data	O
while	O
preserving	O
the	O
topological	B-Architecture
structure	I-Architecture
of	O
the	O
data	O
.	O
</s>
<s>
They	O
are	O
trained	O
using	O
competitive	B-Algorithm
learning	I-Algorithm
.	O
</s>
<s>
The	O
convolutional	B-Architecture
neural	I-Architecture
network	I-Architecture
(	O
CNN	B-Architecture
)	O
architecture	O
with	O
convolutional	O
layers	O
and	O
downsampling	O
layers	O
was	O
introduced	O
by	O
Kunihiko	O
Fukushima	O
in	O
1980	O
.	O
</s>
<s>
He	O
called	O
it	O
the	O
neocognitron	B-Algorithm
.	O
</s>
<s>
In	O
1969	O
,	O
he	O
also	O
introduced	O
the	O
ReLU	B-Algorithm
(	O
rectified	B-Algorithm
linear	I-Algorithm
unit	I-Algorithm
)	O
activation	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
The	O
rectifier	B-Algorithm
has	O
become	O
the	O
most	O
popular	O
activation	B-Algorithm
function	I-Algorithm
for	O
CNNs	B-Architecture
and	O
deep	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
in	O
general	O
.	O
</s>
<s>
CNNs	B-Architecture
have	O
become	O
an	O
essential	O
tool	O
for	O
computer	B-Application
vision	I-Application
.	O
</s>
<s>
The	O
backpropagation	B-Algorithm
algorithm	O
is	O
an	O
efficient	O
application	O
of	O
the	O
Leibniz	O
chain	O
rule	O
(	O
1673	O
)	O
to	O
networks	O
of	O
differentiable	O
nodes	O
.	O
</s>
<s>
the	O
reverse	O
mode	O
of	O
automatic	B-Algorithm
differentiation	I-Algorithm
or	O
reverse	O
accumulation	O
,	O
due	O
to	O
Seppo	O
Linnainmaa	O
(	O
1970	O
)	O
.	O
</s>
<s>
The	O
term	O
"	O
back-propagating	O
errors	O
"	O
was	O
introduced	O
in	O
1962	O
by	O
Frank	O
Rosenblatt	O
,	O
but	O
he	O
did	O
not	O
have	O
an	O
implementation	O
of	O
this	O
procedure	O
,	O
although	O
Henry	O
J	O
.	O
Kelley	O
and	O
Bryson	O
had	O
dynamic	B-Algorithm
programming	I-Algorithm
based	O
continuous	O
precursors	O
of	O
backpropagation	B-Algorithm
already	O
in	O
1960-61	O
in	O
the	O
context	O
of	O
control	O
theory	O
.	O
</s>
<s>
In	O
1973	O
,	O
Dreyfus	O
used	O
backpropagation	B-Algorithm
to	O
adapt	O
parameters	O
of	O
controllers	O
in	O
proportion	O
to	O
error	O
gradients	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>
The	O
time	B-Algorithm
delay	I-Algorithm
neural	I-Algorithm
network	I-Algorithm
(	O
TDNN	B-Algorithm
)	O
of	O
Alex	O
Waibel	O
(	O
1987	O
)	O
combined	O
convolutions	O
and	O
weight	B-General_Concept
sharing	O
and	O
backpropagation.Alexander	O
Waibel	O
et	O
al.	O
,	O
Phoneme	O
Recognition	O
Using	O
Time-Delay	O
Neural	B-Architecture
Networks	I-Architecture
IEEE	O
Transactions	O
on	O
Acoustics	O
,	O
Speech	O
,	O
and	O
Signal	O
Processing	O
,	O
Volume	O
37	O
,	O
No	O
.	O
</s>
<s>
applied	O
backpropagation	B-Algorithm
to	O
a	O
CNN	B-Architecture
(	O
a	O
simplified	O
Neocognitron	B-Algorithm
with	O
convolutional	O
interconnections	O
between	O
the	O
image	O
feature	O
layers	O
and	O
the	O
last	O
fully	O
connected	O
layer	O
)	O
for	O
alphabet	O
recognition	O
.	O
</s>
<s>
trained	O
a	O
CNN	B-Architecture
to	O
recognize	O
handwritten	B-Application
ZIP	O
codes	O
on	O
mail.LeCun	O
et	O
al.	O
,	O
"	O
Backpropagation	B-Algorithm
Applied	O
to	O
Handwritten	B-Application
Zip	O
Code	O
Recognition	O
,	O
"	O
Neural	O
Computation	O
,	O
1	O
,	O
pp	O
.	O
</s>
<s>
In	O
1992	O
,	O
max-pooling	O
for	O
CNNs	B-Architecture
was	O
introduced	O
by	O
Juan	O
Weng	O
et	O
al	O
.	O
</s>
<s>
Weng	O
,	O
N	O
.	O
Ahuja	O
and	O
T	O
.	O
S	O
.	O
Huang	O
,	O
"	O
Cresceptron	O
:	O
a	O
self-organizing	O
neural	B-Architecture
network	I-Architecture
which	O
grows	O
adaptively	O
,	O
"	O
Proc	O
.	O
</s>
<s>
International	O
Joint	O
Conference	O
on	O
Neural	B-Architecture
Networks	I-Architecture
,	O
Baltimore	O
,	O
Maryland	O
,	O
vol	O
I	O
,	O
pp	O
.	O
</s>
<s>
Computer	B-Application
Vision	I-Application
,	O
Berlin	O
,	O
Germany	O
,	O
pp	O
.	O
</s>
<s>
Weng	O
,	O
N	O
.	O
Ahuja	O
and	O
T	O
.	O
S	O
.	O
Huang	O
,	O
"	O
Learning	O
recognition	O
and	O
segmentation	O
using	O
the	O
Cresceptron	O
,	O
"	O
International	O
Journal	O
of	O
Computer	B-Application
Vision	I-Application
,	O
vol	O
.	O
</s>
<s>
LeNet-5	O
(	O
1998	O
)	O
,	O
a	O
7-level	O
CNN	B-Architecture
by	O
Yann	O
LeCun	O
et	O
al.	O
,	O
that	O
classifies	O
digits	O
,	O
was	O
applied	O
by	O
several	O
banks	O
to	O
recognize	O
hand-written	O
numbers	O
on	O
checks	O
digitized	O
in	O
32x32	O
pixel	O
images	O
.	O
</s>
<s>
"	O
Protein	O
secondary	O
structure	O
and	O
homology	O
by	O
neural	B-Architecture
networks	I-Architecture
The	O
α-helices	O
in	O
rhodopsin.	O
"	O
</s>
<s>
FEBS	O
letters	O
241	O
,	O
(	O
1988	O
)	O
:	O
223-228	O
the	O
use	O
of	O
neural	B-Architecture
networks	I-Architecture
transformed	O
the	O
field	O
of	O
protein	O
structure	O
prediction	O
,	O
in	O
particular	O
when	O
the	O
first	O
cascading	O
networks	O
were	O
trained	O
on	O
profiles	O
(	O
matrices	O
)	O
produced	O
by	O
multiple	O
sequence	O
alignments.Rost	O
,	O
Burkhard	O
,	O
and	O
Chris	O
Sander	O
.	O
</s>
<s>
In	O
the	O
1980s	O
,	O
backpropagation	B-Algorithm
did	O
not	O
work	O
well	O
for	O
deep	O
FNNs	O
and	O
RNNs	O
.	O
</s>
<s>
To	O
overcome	O
this	O
problem	O
,	O
Juergen	O
Schmidhuber	O
(	O
1992	O
)	O
proposed	O
a	O
hierarchy	O
of	O
RNNs	O
pre-trained	O
one	O
level	O
at	O
a	O
time	O
by	O
self-supervised	B-General_Concept
learning	I-General_Concept
.	O
</s>
<s>
This	O
can	O
substantially	O
facilitate	O
downstream	O
deep	B-Algorithm
learning	I-Algorithm
.	O
</s>
<s>
The	O
RNN	O
hierarchy	O
can	O
be	O
collapsed	O
into	O
a	O
single	O
RNN	O
,	O
by	O
distilling	B-Algorithm
a	O
higher	O
level	O
chunker	O
network	O
into	O
a	O
lower	O
level	O
automatizer	O
network	O
.	O
</s>
<s>
In	O
1993	O
,	O
a	O
chunker	O
solved	O
a	O
deep	B-Algorithm
learning	I-Algorithm
task	O
whose	O
depth	O
exceeded	O
1000	O
.	O
</s>
<s>
In	O
1992	O
,	O
Juergen	O
Schmidhuber	O
also	O
published	O
an	O
alternative	O
to	O
RNNs	O
which	O
is	O
now	O
called	O
a	O
linear	O
Transformer	B-Algorithm
or	O
a	O
Transformer	B-Algorithm
with	O
linearized	O
self-attention	O
(	O
save	O
for	O
a	O
normalization	O
operator	O
)	O
.	O
</s>
<s>
It	O
learns	O
internal	O
spotlights	O
of	O
attention	O
:	O
a	O
slow	O
feedforward	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
learns	O
by	O
gradient	B-Algorithm
descent	I-Algorithm
to	O
control	O
the	O
fast	O
weights	O
of	O
another	O
neural	B-Architecture
network	I-Architecture
through	O
outer	O
products	O
of	O
self-generated	O
activation	O
patterns	O
FROM	O
and	O
TO	O
(	O
which	O
are	O
now	O
called	O
key	O
and	O
value	O
for	O
self-attention	O
)	O
.	O
</s>
<s>
This	O
fast	O
weight	B-General_Concept
attention	O
mapping	O
is	O
applied	O
to	O
a	O
query	O
pattern	O
.	O
</s>
<s>
The	O
modern	O
Transformer	B-Algorithm
was	O
introduced	O
by	O
Ashish	O
Vaswani	O
et	O
.	O
</s>
<s>
Transformers	B-Algorithm
have	O
increasingly	O
become	O
the	O
model	O
of	O
choice	O
for	O
natural	B-Language
language	I-Language
processing	I-Language
.	O
</s>
<s>
Many	O
modern	O
large	O
language	O
models	O
such	O
as	O
ChatGPT	B-General_Concept
,	O
GPT-4	O
,	O
and	O
BERT	B-General_Concept
use	O
it	O
.	O
</s>
<s>
Transformers	B-Algorithm
are	O
also	O
increasingly	O
being	O
used	O
in	O
computer	B-Application
vision	I-Application
.	O
</s>
<s>
In	O
1991	O
,	O
Juergen	O
Schmidhuber	O
also	O
published	O
adversarial	O
neural	B-Architecture
networks	I-Architecture
that	O
contest	O
with	O
each	O
other	O
in	O
the	O
form	O
of	O
a	O
zero-sum	O
game	O
,	O
where	O
one	O
network	O
's	O
gain	O
is	O
the	O
other	O
network	O
's	O
loss	O
.	O
</s>
<s>
The	O
second	O
network	O
learns	O
by	O
gradient	B-Algorithm
descent	I-Algorithm
to	O
predict	O
the	O
reactions	O
of	O
the	O
environment	O
to	O
these	O
patterns	O
.	O
</s>
<s>
In	O
2014	O
,	O
this	O
principle	O
was	O
used	O
in	O
a	O
generative	B-Algorithm
adversarial	I-Algorithm
network	I-Algorithm
(	O
GAN	O
)	O
by	O
Ian	O
Goodfellow	O
et	O
al	O
.	O
</s>
<s>
This	O
can	O
be	O
used	O
to	O
create	O
realistic	O
deepfakes	B-Application
.	O
</s>
<s>
Excellent	O
image	O
quality	O
is	O
achieved	O
by	O
Nvidia	O
's	O
StyleGAN	B-Application
(	O
2018	O
)	O
based	O
on	O
the	O
Progressive	O
GAN	O
by	O
Tero	O
Karras	O
,	O
Timo	O
Aila	O
,	O
Samuli	O
Laine	O
,	O
and	O
Jaakko	O
Lehtinen	O
.	O
</s>
<s>
Hochreiter	O
identified	O
and	O
analyzed	O
the	O
vanishing	B-Algorithm
gradient	I-Algorithm
problem	I-Algorithm
and	O
proposed	O
recurrent	O
residual	B-Algorithm
connections	O
to	O
solve	O
it	O
.	O
</s>
<s>
This	O
led	O
to	O
the	O
deep	B-Algorithm
learning	I-Algorithm
method	O
called	O
long	B-Algorithm
short-term	I-Algorithm
memory	I-Algorithm
(	O
LSTM	B-Algorithm
)	O
,	O
published	O
in	O
Neural	O
Computation	O
(	O
1997	O
)	O
.	O
</s>
<s>
LSTM	B-Algorithm
recurrent	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
can	O
learn	O
"	O
very	O
deep	B-Algorithm
learning	I-Algorithm
"	O
tasks	O
with	O
long	O
credit	O
assignment	O
paths	O
that	O
require	O
memories	O
of	O
events	O
that	O
happened	O
thousands	O
of	O
discrete	O
time	O
steps	O
before	O
.	O
</s>
<s>
The	O
"	O
vanilla	O
LSTM	B-Algorithm
"	O
with	O
forget	O
gate	O
was	O
introduced	O
in	O
1999	O
by	O
Felix	O
Gers	O
,	O
Schmidhuber	O
and	O
Fred	O
Cummins	O
.	O
</s>
<s>
LSTM	B-Algorithm
has	O
become	O
the	O
most	O
cited	O
neural	B-Architecture
network	I-Architecture
of	O
the	O
20th	O
century	O
.	O
</s>
<s>
In	O
2015	O
,	O
Rupesh	O
Kumar	O
Srivastava	O
,	O
Klaus	O
Greff	O
,	O
and	O
Schmidhuber	O
used	O
the	O
LSTM	B-Algorithm
principle	O
to	O
create	O
the	O
Highway	B-General_Concept
network	I-General_Concept
,	O
a	O
feedforward	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
with	O
hundreds	O
of	O
layers	O
,	O
much	O
deeper	O
than	O
previous	O
networks	O
.	O
</s>
<s>
7	O
months	O
later	O
,	O
Kaiming	O
He	O
,	O
Xiangyu	O
Zhang	O
;	O
Shaoqing	O
Ren	O
,	O
and	O
Jian	O
Sun	O
won	O
the	O
ImageNet	O
2015	O
competition	O
with	O
an	O
open-gated	O
or	O
gateless	O
Highway	B-General_Concept
network	I-General_Concept
variant	O
called	O
Residual	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
.	O
</s>
<s>
This	O
has	O
become	O
the	O
most	O
cited	O
neural	B-Architecture
network	I-Architecture
of	O
the	O
21st	O
century	O
.	O
</s>
<s>
The	O
development	O
of	O
metal	B-Architecture
–	I-Architecture
oxide	I-Architecture
–	I-Architecture
semiconductor	I-Architecture
(	O
MOS	O
)	O
very-large-scale	O
integration	O
(	O
VLSI	O
)	O
,	O
in	O
the	O
form	O
of	O
complementary	O
MOS	O
(	O
CMOS	O
)	O
technology	O
,	O
enabled	O
increasing	O
MOS	B-Architecture
transistor	I-Architecture
counts	O
in	O
digital	O
electronics	O
.	O
</s>
<s>
This	O
provided	O
more	O
processing	O
power	O
for	O
the	O
development	O
of	O
practical	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
in	O
the	O
1980s	O
.	O
</s>
<s>
Neural	B-Architecture
networks	I-Architecture
 '	O
early	O
successes	O
included	O
predicting	O
the	O
stock	O
market	O
and	O
in	O
1995	O
a	O
(	O
mostly	O
)	O
self-driving	O
car	O
.	O
</s>
<s>
(	O
2006	O
)	O
proposed	O
learning	O
a	O
high-level	O
representation	O
using	O
successive	O
layers	O
of	O
binary	O
or	O
real-valued	O
latent	O
variables	O
with	O
a	O
restricted	B-Algorithm
Boltzmann	I-Algorithm
machine	I-Algorithm
to	O
model	O
each	O
layer	O
.	O
</s>
<s>
Unsupervised	O
pre-training	O
and	O
increased	O
computing	O
power	O
from	O
GPUs	B-Architecture
and	O
distributed	B-Architecture
computing	I-Architecture
allowed	O
the	O
use	O
of	O
larger	O
networks	O
,	O
particularly	O
in	O
image	O
and	O
visual	O
recognition	O
problems	O
,	O
which	O
became	O
known	O
as	O
"	O
deep	B-Algorithm
learning	I-Algorithm
"	O
.	O
</s>
<s>
Ciresan	O
and	O
colleagues	O
(	O
2010	O
)	O
showed	O
that	O
despite	O
the	O
vanishing	B-Algorithm
gradient	I-Algorithm
problem	I-Algorithm
,	O
GPUs	B-Architecture
make	O
backpropagation	B-Algorithm
feasible	O
for	O
many-layered	O
feedforward	O
neural	O
networks.Dominik	O
Scherer	O
,	O
Andreas	O
C	O
.	O
Müller	O
,	O
and	O
Sven	O
Behnke	O
:	O
"	O
Evaluation	O
of	O
Pooling	O
Operations	O
in	O
Convolutional	O
Architectures	O
for	O
Object	O
Recognition	O
,	O
"	O
In	O
20th	O
International	O
Conference	O
Artificial	B-Architecture
Neural	I-Architecture
Networks	I-Architecture
(	O
ICANN	O
)	O
,	O
pp	O
.	O
</s>
<s>
Between	O
2009	O
and	O
2012	O
,	O
ANNs	O
began	O
winning	O
prizes	O
in	O
image	O
recognition	O
contests	O
,	O
approaching	O
human	O
level	O
performance	O
on	O
various	O
tasks	O
,	O
initially	O
in	O
pattern	O
recognition	O
and	O
handwriting	O
recognition.2012	O
Kurzweil	O
AI	O
Interview	O
with	O
Jürgen	O
Schmidhuber	O
on	O
the	O
eight	O
competitions	O
won	O
by	O
his	O
Deep	B-Algorithm
Learning	I-Algorithm
team	O
2009	O
–	O
2012	O
For	O
example	O
,	O
the	O
bi-directional	O
and	O
multi-dimensional	O
long	B-Algorithm
short-term	I-Algorithm
memory	I-Algorithm
(	O
LSTM	B-Algorithm
)	O
of	O
Graves	O
et	O
al	O
.	O
</s>
<s>
won	O
three	O
competitions	O
in	O
connected	O
handwriting	B-Application
recognition	I-Application
in	O
2009	O
without	O
any	O
prior	O
knowledge	O
about	O
the	O
three	O
languages	O
to	O
be	O
learned	O
.	O
</s>
<s>
An	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
consists	O
of	O
simulated	O
neurons	O
.	O
</s>
<s>
Each	O
neuron	O
is	O
connected	O
to	O
other	O
nodes	O
via	O
links	O
like	O
a	O
biological	O
axon-synapse-dendrite	O
connection	O
.	O
</s>
<s>
Each	O
link	O
has	O
a	O
weight	B-General_Concept
,	O
determining	O
the	O
strength	O
of	O
one	O
node	O
's	O
influence	O
on	O
another	O
,	O
allowing	O
weights	O
to	O
choose	O
the	O
signal	O
between	O
neurons	O
.	O
</s>
<s>
ANNs	O
are	O
composed	O
of	O
artificial	B-Algorithm
neurons	I-Algorithm
which	O
are	O
conceptually	O
derived	O
from	O
biological	O
neurons	O
.	O
</s>
<s>
Each	O
artificial	B-Algorithm
neuron	I-Algorithm
has	O
inputs	O
and	O
produces	O
a	O
single	O
output	O
which	O
can	O
be	O
sent	O
to	O
multiple	O
other	O
neurons	O
.	O
</s>
<s>
The	O
outputs	O
of	O
the	O
final	O
output	O
neurons	O
of	O
the	O
neural	B-Architecture
net	I-Architecture
accomplish	O
the	O
task	O
,	O
such	O
as	O
recognizing	O
an	O
object	O
in	O
an	O
image	O
.	O
</s>
<s>
This	O
weighted	O
sum	O
is	O
then	O
passed	O
through	O
a	O
(	O
usually	O
nonlinear	O
)	O
activation	B-Algorithm
function	I-Algorithm
to	O
produce	O
the	O
output	O
.	O
</s>
<s>
The	O
neurons	O
are	O
typically	O
organized	O
into	O
multiple	O
layers	O
,	O
especially	O
in	O
deep	B-Algorithm
learning	I-Algorithm
.	O
</s>
<s>
A	O
hyperparameter	B-General_Concept
is	O
a	O
constant	O
parameter	O
whose	O
value	O
is	O
set	O
before	O
the	O
learning	O
process	O
begins	O
.	O
</s>
<s>
Examples	O
of	O
hyperparameters	B-General_Concept
include	O
learning	B-General_Concept
rate	I-General_Concept
,	O
the	O
number	O
of	O
hidden	O
layers	O
and	O
batch	O
size	O
.	O
</s>
<s>
The	O
values	O
of	O
some	O
hyperparameters	B-General_Concept
can	O
be	O
dependent	O
on	O
those	O
of	O
other	O
hyperparameters	B-General_Concept
.	O
</s>
<s>
The	O
learning	B-General_Concept
rate	I-General_Concept
defines	O
the	O
size	O
of	O
the	O
corrective	O
steps	O
that	O
the	O
model	O
takes	O
to	O
adjust	O
for	O
errors	O
in	O
each	O
observation	O
.	O
</s>
<s>
A	O
high	O
learning	B-General_Concept
rate	I-General_Concept
shortens	O
the	O
training	O
time	O
,	O
but	O
with	O
lower	O
ultimate	O
accuracy	O
,	O
while	O
a	O
lower	O
learning	B-General_Concept
rate	I-General_Concept
takes	O
longer	O
,	O
but	O
with	O
the	O
potential	O
for	O
greater	O
accuracy	O
.	O
</s>
<s>
Optimizations	O
such	O
as	O
Quickprop	B-Algorithm
are	O
primarily	O
aimed	O
at	O
speeding	O
up	O
error	O
minimization	O
,	O
while	O
other	O
improvements	O
mainly	O
try	O
to	O
increase	O
reliability	O
.	O
</s>
<s>
In	O
order	O
to	O
avoid	O
oscillation	B-Algorithm
inside	O
the	O
network	O
such	O
as	O
alternating	O
connection	O
weights	O
,	O
and	O
to	O
improve	O
the	O
rate	O
of	O
convergence	O
,	O
refinements	O
use	O
an	O
adaptive	O
learning	B-General_Concept
rate	I-General_Concept
that	O
increases	O
or	O
decreases	O
as	O
appropriate	O
.	O
</s>
<s>
The	O
concept	O
of	O
momentum	O
allows	O
the	O
balance	O
between	O
the	O
gradient	O
and	O
the	O
previous	O
change	O
to	O
be	O
weighted	O
such	O
that	O
the	O
weight	B-General_Concept
adjustment	O
depends	O
to	O
some	O
degree	O
on	O
the	O
previous	O
change	O
.	O
</s>
<s>
Backpropagation	B-Algorithm
is	O
a	O
method	O
used	O
to	O
adjust	O
the	O
connection	O
weights	O
to	O
compensate	O
for	O
each	O
error	O
found	O
during	O
learning	O
.	O
</s>
<s>
Technically	O
,	O
backprop	B-Algorithm
calculates	O
the	O
gradient	O
(	O
the	O
derivative	O
)	O
of	O
the	O
cost	O
function	O
associated	O
with	O
a	O
given	O
state	O
with	O
respect	O
to	O
the	O
weights	O
.	O
</s>
<s>
The	O
weight	B-General_Concept
updates	O
can	O
be	O
done	O
via	O
stochastic	B-Algorithm
gradient	I-Algorithm
descent	I-Algorithm
or	O
other	O
methods	O
,	O
such	O
as	O
extreme	B-Algorithm
learning	I-Algorithm
machines	I-Algorithm
,	O
"	O
no-prop	O
"	O
networks	O
,	O
training	O
without	O
backtracking	O
,	O
"	O
weightless	O
"	O
networks	O
,	O
ESANN	O
.	O
</s>
<s>
2009	O
.	O
and	O
non-connectionist	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
.	O
</s>
<s>
Machine	O
learning	O
is	O
commonly	O
separated	O
into	O
three	O
main	O
learning	O
paradigms	O
,	O
supervised	B-General_Concept
learning	I-General_Concept
,	O
unsupervised	B-General_Concept
learning	I-General_Concept
and	O
reinforcement	O
learning	O
.	O
</s>
<s>
Supervised	B-General_Concept
learning	I-General_Concept
uses	O
a	O
set	O
of	O
paired	O
inputs	O
and	O
desired	O
outputs	O
.	O
</s>
<s>
A	O
commonly	O
used	O
cost	O
is	O
the	O
mean-squared	B-Algorithm
error	I-Algorithm
,	O
which	O
tries	O
to	O
minimize	O
the	O
average	O
squared	O
error	O
between	O
the	O
network	O
's	O
output	O
and	O
the	O
desired	O
output	O
.	O
</s>
<s>
Tasks	O
suited	O
for	O
supervised	B-General_Concept
learning	I-General_Concept
are	O
pattern	O
recognition	O
(	O
also	O
known	O
as	O
classification	B-General_Concept
)	O
and	O
regression	O
(	O
also	O
known	O
as	O
function	O
approximation	O
)	O
.	O
</s>
<s>
Supervised	B-General_Concept
learning	I-General_Concept
is	O
also	O
applicable	O
to	O
sequential	O
data	O
(	O
e.g.	O
,	O
for	O
hand	O
writing	O
,	O
speech	O
and	O
gesture	B-General_Concept
recognition	I-General_Concept
)	O
.	O
</s>
<s>
In	O
unsupervised	B-General_Concept
learning	I-General_Concept
,	O
input	O
data	O
is	O
given	O
along	O
with	O
the	O
cost	O
function	O
,	O
some	O
function	O
of	O
the	O
data	O
and	O
the	O
network	O
's	O
output	O
.	O
</s>
<s>
Its	O
form	O
depends	O
on	O
the	O
application	O
:	O
for	O
example	O
,	O
in	O
compression	B-General_Concept
it	O
could	O
be	O
related	O
to	O
the	O
mutual	O
information	O
between	O
and	O
,	O
whereas	O
in	O
statistical	O
modeling	O
,	O
it	O
could	O
be	O
related	O
to	O
the	O
posterior	O
probability	O
of	O
the	O
model	O
given	O
the	O
data	O
(	O
note	O
that	O
in	O
both	O
of	O
those	O
examples	O
,	O
those	O
quantities	O
would	O
be	O
maximized	O
rather	O
than	O
minimized	O
)	O
.	O
</s>
<s>
Tasks	O
that	O
fall	O
within	O
the	O
paradigm	O
of	O
unsupervised	B-General_Concept
learning	I-General_Concept
are	O
in	O
general	O
estimation	O
problems	O
;	O
the	O
applications	O
include	O
clustering	B-Algorithm
,	O
the	O
estimation	O
of	O
statistical	B-General_Concept
distributions	I-General_Concept
,	O
compression	B-General_Concept
and	O
filtering	B-Application
.	O
</s>
<s>
In	O
reinforcement	O
learning	O
,	O
the	O
aim	O
is	O
to	O
weight	B-General_Concept
the	O
network	O
(	O
devise	O
a	O
policy	O
)	O
to	O
perform	O
actions	O
that	O
minimize	O
long-term	O
(	O
expected	O
cumulative	O
)	O
cost	O
.	O
</s>
<s>
Dynamic	B-Algorithm
programming	I-Algorithm
coupled	O
with	O
ANNs	O
(	O
giving	O
neurodynamic	B-Algorithm
programming	O
)	O
has	O
been	O
applied	O
to	O
problems	O
such	O
as	O
those	O
involved	O
in	O
vehicle	B-Algorithm
routing	I-Algorithm
,	O
video	O
games	O
,	O
natural	O
resource	O
management	O
and	O
medicine	O
because	O
of	O
ANNs	O
ability	O
to	O
mitigate	O
losses	O
of	O
accuracy	O
even	O
when	O
reducing	O
the	O
discretization	B-Algorithm
grid	O
density	O
for	O
numerically	O
approximating	O
the	O
solution	O
of	O
control	O
problems	O
.	O
</s>
<s>
Self-learning	O
in	O
neural	B-Architecture
networks	I-Architecture
was	O
introduced	O
in	O
1982	O
along	O
with	O
a	O
neural	B-Architecture
network	I-Architecture
capable	O
of	O
self-learning	O
named	O
crossbar	O
adaptive	O
array	O
(	O
CAA	O
)	O
.Bozinovski	O
,	O
S	O
.	O
(	O
1982	O
)	O
.	O
</s>
<s>
The	O
system	O
is	O
driven	O
by	O
the	O
interaction	O
between	O
cognition	O
and	O
emotion.Bozinovski	O
,	O
S	O
.	O
(	O
2014	O
)	O
"	O
Modeling	O
mechanisms	O
of	O
cognition-emotion	O
interaction	O
in	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
,	O
since	O
1981	O
.	O
"	O
</s>
<s>
Procedia	O
Computer	O
Science	O
p	O
.	O
255-263	O
Given	O
the	O
memory	B-Architecture
matrix	O
,	O
W	O
=|	O
|	O
w(a,s )	O
||	O
,	O
the	O
crossbar	O
self-learning	O
algorithm	O
in	O
each	O
iteration	O
performs	O
the	O
following	O
computation	O
:	O
</s>
<s>
Update	O
crossbar	O
memory	B-Architecture
w'( a	O
,	O
s	O
)	O
=	O
w(a,s )	O
+	O
v(s' )	O
.	O
</s>
<s>
Neuroevolution	B-Algorithm
can	O
create	O
neural	B-Architecture
network	I-Architecture
topologies	B-Architecture
and	O
weights	O
using	O
evolutionary	O
computation	O
.	O
</s>
<s>
With	O
modern	O
enhancements	O
,	O
neuroevolution	B-Algorithm
is	O
competitive	O
with	O
sophisticated	O
gradient	B-Algorithm
descent	I-Algorithm
approaches	O
.	O
</s>
<s>
One	O
advantage	O
of	O
neuroevolution	B-Algorithm
is	O
that	O
it	O
may	O
be	O
less	O
prone	O
to	O
get	O
caught	O
in	O
"	O
dead	O
ends	O
"	O
.	O
</s>
<s>
Stochastic	B-Algorithm
neural	B-Architecture
networks	I-Architecture
originating	O
from	O
Sherrington	O
–	O
Kirkpatrick	O
models	O
are	O
a	O
type	O
of	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
built	O
by	O
introducing	O
random	O
variations	O
into	O
the	O
network	O
,	O
either	O
by	O
giving	O
the	O
network	O
's	O
artificial	B-Algorithm
neurons	I-Algorithm
stochastic	B-Algorithm
transfer	O
functions	O
,	O
or	O
by	O
giving	O
them	O
stochastic	B-Algorithm
weights	O
.	O
</s>
<s>
Stochastic	B-Algorithm
neural	B-Architecture
networks	I-Architecture
trained	O
using	O
a	O
Bayesian	O
approach	O
are	O
known	O
as	O
Bayesian	O
neural	B-Architecture
networks	I-Architecture
.	O
</s>
<s>
Evolutionary	B-Algorithm
methods	I-Algorithm
,	O
gene	B-Algorithm
expression	I-Algorithm
programming	I-Algorithm
,	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
expectation-maximization	B-Algorithm
,	O
non-parametric	B-General_Concept
methods	I-General_Concept
and	O
particle	B-Algorithm
swarm	I-Algorithm
optimization	I-Algorithm
are	O
other	O
learning	O
algorithms	O
.	O
</s>
<s>
Convergent	O
recursion	O
is	O
a	O
learning	O
algorithm	O
for	O
cerebellar	B-Algorithm
model	I-Algorithm
articulation	I-Algorithm
controller	I-Algorithm
(	O
CMAC	B-Algorithm
)	O
neural	B-Architecture
networks	I-Architecture
.	O
</s>
<s>
Two	O
modes	O
of	O
learning	O
are	O
available	O
:	O
stochastic	B-Algorithm
and	O
batch	O
.	O
</s>
<s>
In	O
stochastic	B-Algorithm
learning	O
,	O
each	O
input	O
creates	O
a	O
weight	B-General_Concept
adjustment	O
.	O
</s>
<s>
Stochastic	B-Algorithm
learning	O
introduces	O
"	O
noise	O
"	O
into	O
the	O
process	O
,	O
using	O
the	O
local	O
gradient	O
calculated	O
from	O
one	O
data	O
point	O
;	O
this	O
reduces	O
the	O
chance	O
of	O
the	O
network	O
getting	O
stuck	O
in	O
local	O
minima	O
.	O
</s>
<s>
The	O
simplest	O
types	O
have	O
one	O
or	O
more	O
static	O
components	O
,	O
including	O
number	O
of	O
units	O
,	O
number	O
of	O
layers	O
,	O
unit	O
weights	O
and	O
topology	B-Architecture
.	O
</s>
<s>
Some	O
of	O
the	O
main	O
breakthroughs	O
include	O
:	O
convolutional	B-Architecture
neural	I-Architecture
networks	I-Architecture
that	O
have	O
proven	O
particularly	O
successful	O
in	O
processing	O
visual	O
and	O
other	O
two-dimensional	O
data	O
;	O
Yann	O
LeCun	O
(	O
2016	O
)	O
.	O
</s>
<s>
Slides	O
on	O
Deep	B-Algorithm
Learning	I-Algorithm
Online	O
long	B-Algorithm
short-term	I-Algorithm
memory	I-Algorithm
avoid	O
the	O
vanishing	B-Algorithm
gradient	I-Algorithm
problem	I-Algorithm
and	O
can	O
handle	O
signals	O
that	O
have	O
a	O
mix	O
of	O
low	O
and	O
high	O
frequency	O
components	O
aiding	O
large-vocabulary	O
speech	O
recognition	O
,	O
text-to-speech	O
synthesis	O
,	O
and	O
photo-real	O
talking	O
heads	O
;	O
competitive	O
networks	O
such	O
as	O
generative	B-Algorithm
adversarial	I-Algorithm
networks	I-Algorithm
in	O
which	O
multiple	O
networks	O
(	O
of	O
varying	O
structure	O
)	O
compete	O
with	O
each	O
other	O
,	O
on	O
tasks	O
such	O
as	O
winning	O
a	O
game	O
or	O
on	O
deceiving	O
the	O
opponent	O
about	O
the	O
authenticity	O
of	O
an	O
input	O
.	O
</s>
<s>
Neural	O
architecture	B-General_Concept
search	I-General_Concept
(	O
NAS	O
)	O
uses	O
machine	O
learning	O
to	O
automate	O
ANN	O
design	O
.	O
</s>
<s>
Available	O
systems	O
include	O
AutoML	B-General_Concept
and	O
AutoKeras	O
.	O
</s>
<s>
Hyperparameters	B-General_Concept
must	O
also	O
be	O
defined	O
as	O
part	O
of	O
the	O
design	O
(	O
they	O
are	O
not	O
learned	O
)	O
,	O
governing	O
matters	O
such	O
as	O
how	O
many	O
neurons	O
are	O
in	O
each	O
layer	O
,	O
learning	B-General_Concept
rate	I-General_Concept
,	O
step	O
,	O
stride	O
,	O
depth	O
,	O
receptive	O
field	O
and	O
padding	O
(	O
for	O
CNNs	B-Architecture
)	O
,	O
etc	O
.	O
</s>
<s>
Using	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
requires	O
an	O
understanding	O
of	O
their	O
characteristics	O
.	O
</s>
<s>
Almost	O
any	O
algorithm	O
will	O
work	O
well	O
with	O
the	O
correct	O
hyperparameters	B-General_Concept
for	O
training	O
on	O
a	O
particular	O
data	O
set	O
.	O
</s>
<s>
Function	O
approximation	O
,	O
or	O
regression	O
analysis	O
,	O
including	O
time	O
series	O
prediction	O
,	O
fitness	B-Algorithm
approximation	I-Algorithm
and	O
modeling	O
.	O
</s>
<s>
Classification	B-General_Concept
,	O
including	O
pattern	O
and	O
sequence	O
recognition	O
,	O
novelty	B-Algorithm
detection	I-Algorithm
and	O
sequential	O
decision	O
making	O
.	O
</s>
<s>
Data	B-General_Concept
processing	I-General_Concept
,	O
including	O
filtering	B-Application
,	O
clustering	B-Algorithm
,	O
blind	B-Application
source	I-Application
separation	I-Application
and	O
compression	B-General_Concept
.	O
</s>
<s>
Because	O
of	O
their	O
ability	O
to	O
reproduce	O
and	O
model	O
nonlinear	O
processes	O
,	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
have	O
found	O
applications	O
in	O
many	O
disciplines	O
.	O
</s>
<s>
Application	O
areas	O
include	O
system	O
identification	O
and	O
control	O
(	O
vehicle	O
control	O
,	O
trajectory	O
prediction	O
,	O
process	O
control	O
,	O
natural	O
resource	O
management	O
)	O
,	O
quantum	O
chemistry	O
,	O
general	B-Algorithm
game	I-Algorithm
playing	I-Algorithm
,	O
pattern	O
recognition	O
(	O
radar	O
systems	O
,	O
face	O
identification	O
,	O
signal	O
classification	B-General_Concept
,	O
3D	B-Algorithm
reconstruction	I-Algorithm
,	O
Choy	O
,	O
Christopher	O
B.	O
,	O
et	O
al	O
.	O
</s>
<s>
"	O
3d-r2n2	O
:	O
A	O
unified	O
approach	O
for	O
single	O
and	O
multi-view	O
3d	B-Algorithm
object	I-Algorithm
reconstruction	I-Algorithm
.	O
"	O
</s>
<s>
European	O
conference	O
on	O
computer	B-Application
vision	I-Application
.	O
</s>
<s>
Springer	O
,	O
Cham	O
,	O
2016	O
.	O
object	O
recognition	O
and	O
more	O
)	O
,	O
sensor	O
data	O
analysis	O
,	O
sequence	O
recognition	O
(	O
gesture	O
,	O
speech	O
,	O
handwritten	B-Application
and	O
printed	O
text	O
recognition	O
)	O
,	O
medical	O
diagnosis	O
,	O
finance	O
(	O
e.g.	O
</s>
<s>
ex-ante	O
models	O
for	O
specific	O
financial	O
long-run	O
forecasts	O
and	O
artificial	O
financial	O
markets	O
)	O
,	O
data	B-Application
mining	I-Application
,	O
visualization	O
,	O
machine	B-Application
translation	I-Application
,	O
social	O
network	O
filtering	B-Application
and	O
e-mail	O
spam	O
filtering	B-Application
.	O
</s>
<s>
In	O
brain	O
research	O
ANNs	O
have	O
studied	O
short-term	O
behavior	O
of	O
individual	O
neurons	O
,	O
the	O
dynamics	O
of	O
neural	B-Architecture
circuitry	I-Architecture
arise	O
from	O
interactions	O
between	O
individual	O
neurons	O
and	O
how	O
behavior	O
can	O
arise	O
from	O
abstract	O
neural	O
modules	O
that	O
represent	O
complete	O
subsystems	O
.	O
</s>
<s>
Studies	O
considered	O
long-and	O
short-term	O
plasticity	O
of	O
neural	O
systems	O
and	O
their	O
relation	O
to	O
learning	O
and	O
memory	B-Architecture
from	O
the	O
individual	O
neuron	O
to	O
the	O
system	O
level	O
.	O
</s>
<s>
The	O
multilayer	B-Algorithm
perceptron	I-Algorithm
is	O
a	O
universal	O
function	O
approximator	O
,	O
as	O
proven	O
by	O
the	O
universal	B-Algorithm
approximation	I-Algorithm
theorem	I-Algorithm
.	O
</s>
<s>
However	O
,	O
the	O
proof	O
is	O
not	O
constructive	O
regarding	O
the	O
number	O
of	O
neurons	O
required	O
,	O
the	O
network	B-Architecture
topology	I-Architecture
,	O
the	O
weights	O
and	O
the	O
learning	O
parameters	O
.	O
</s>
<s>
The	O
information	O
capacity	O
of	O
a	O
perceptron	B-Algorithm
is	O
intensively	O
discussed	O
in	O
Sir	O
David	O
MacKay	O
's	O
book	O
which	O
summarizes	O
work	O
by	O
Thomas	O
Cover	O
.	O
</s>
<s>
The	O
capacity	O
of	O
a	O
network	O
of	O
standard	O
neurons	O
(	O
not	O
convolutional	O
)	O
can	O
be	O
derived	O
by	O
four	O
rules	O
that	O
derive	O
from	O
understanding	O
a	O
neuron	O
as	O
an	O
electrical	B-Algorithm
element	I-Algorithm
.	O
</s>
<s>
As	O
noted	O
in	O
,	O
the	O
VC	O
Dimension	O
for	O
arbitrary	O
inputs	O
is	O
half	O
the	O
information	O
capacity	O
of	O
a	O
Perceptron	B-Algorithm
.	O
</s>
<s>
The	O
VC	O
Dimension	O
for	O
arbitrary	O
points	O
is	O
sometimes	O
referred	O
to	O
as	O
Memory	B-Architecture
Capacity	O
.	O
</s>
<s>
When	O
the	O
width	O
of	O
network	O
approaches	O
to	O
infinity	O
,	O
the	O
ANN	O
is	O
well	O
described	O
by	O
its	O
first	O
order	O
Taylor	O
expansion	O
throughout	O
training	O
,	O
and	O
so	O
inherits	O
the	O
convergence	O
behavior	O
of	O
affine	B-Algorithm
models	I-Algorithm
.	O
</s>
<s>
This	O
behavior	O
is	O
referred	O
to	O
as	O
the	O
spectral	O
bias	O
,	O
or	O
frequency	O
principle	O
,	O
of	O
neural	B-Architecture
networks	I-Architecture
.	O
</s>
<s>
This	O
phenomenon	O
is	O
the	O
opposite	O
to	O
the	O
behavior	O
of	O
some	O
well	O
studied	O
iterative	O
numerical	O
schemes	O
such	O
as	O
Jacobi	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Deeper	O
neural	B-Architecture
networks	I-Architecture
have	O
been	O
observed	O
to	O
be	O
more	O
biased	O
towards	O
low	O
frequency	O
functions	O
.	O
</s>
<s>
The	O
first	O
is	O
to	O
use	O
cross-validation	B-Application
and	O
similar	O
techniques	O
to	O
check	O
for	O
the	O
presence	O
of	O
over-training	O
and	O
to	O
select	O
hyperparameters	B-General_Concept
to	O
minimize	O
the	O
generalization	O
error	O
.	O
</s>
<s>
Supervised	O
neural	B-Architecture
networks	I-Architecture
that	O
use	O
a	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
(	O
MSE	O
)	O
cost	O
function	O
can	O
use	O
formal	O
statistical	O
methods	O
to	O
determine	O
the	O
confidence	O
of	O
the	O
trained	O
model	O
.	O
</s>
<s>
By	O
assigning	O
a	O
softmax	B-Algorithm
activation	I-Algorithm
function	I-Algorithm
,	O
a	O
generalization	O
of	O
the	O
logistic	O
function	O
,	O
on	O
the	O
output	O
layer	O
of	O
the	O
neural	B-Architecture
network	I-Architecture
(	O
or	O
a	O
softmax	O
component	O
in	O
a	O
component-based	O
network	O
)	O
for	O
categorical	O
target	O
variables	O
,	O
the	O
outputs	O
can	O
be	O
interpreted	O
as	O
posterior	O
probabilities	O
.	O
</s>
<s>
This	O
is	O
useful	O
in	O
classification	B-General_Concept
as	O
it	O
gives	O
a	O
certainty	O
measure	O
on	O
classifications	O
.	O
</s>
<s>
The	O
softmax	B-Algorithm
activation	I-Algorithm
function	I-Algorithm
is	O
:	O
</s>
<s>
A	O
common	O
criticism	O
of	O
neural	B-Architecture
networks	I-Architecture
,	O
particularly	O
in	O
robotics	O
,	O
is	O
that	O
they	O
require	O
too	O
much	O
training	O
for	O
real-world	O
operation	O
.	O
</s>
<s>
Potential	O
solutions	O
include	O
randomly	O
shuffling	O
training	O
examples	O
,	O
by	O
using	O
a	O
numerical	O
optimization	O
algorithm	O
that	O
does	O
not	O
take	O
too	O
large	O
steps	O
when	O
changing	O
the	O
network	O
connections	O
following	O
an	O
example	O
,	O
grouping	O
examples	O
in	O
so-called	O
mini-batches	O
and/or	O
introducing	O
a	O
recursive	O
least	B-Algorithm
squares	I-Algorithm
algorithm	O
for	O
CMAC	B-Algorithm
.	O
</s>
<s>
This	O
allows	O
simple	O
statistical	O
association	O
(	O
the	O
basic	O
function	O
of	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
)	O
to	O
be	O
described	O
as	O
learning	O
or	O
recognition	O
.	O
</s>
<s>
In	O
1997	O
,	O
Alexander	O
Dewdney	O
commented	O
that	O
,	O
as	O
a	O
result	O
,	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
have	O
a	O
"	O
something-for-nothing	O
quality	O
,	O
one	O
that	O
imparts	O
a	O
peculiar	O
aura	O
of	O
laziness	O
and	O
a	O
distinct	O
lack	O
of	O
curiosity	O
about	O
just	O
how	O
good	O
these	O
computing	O
systems	O
are	O
.	O
</s>
<s>
One	O
response	O
to	O
Dewdney	O
is	O
that	O
neural	B-Architecture
networks	I-Architecture
handle	O
many	O
complex	O
and	O
diverse	O
tasks	O
,	O
ranging	O
from	O
autonomously	O
flying	O
aircraft	O
to	O
detecting	O
credit	O
card	O
fraud	O
to	O
mastering	O
the	O
game	O
of	O
Go	O
.	O
</s>
<s>
Large	O
and	O
effective	O
neural	B-Architecture
networks	I-Architecture
require	O
considerable	O
computing	O
resources	O
.	O
</s>
<s>
While	O
the	O
brain	O
has	O
hardware	O
tailored	O
to	O
the	O
task	O
of	O
processing	O
signals	O
through	O
a	O
graph	O
of	O
neurons	O
,	O
simulating	O
even	O
a	O
simplified	O
neuron	O
on	O
von	B-Architecture
Neumann	I-Architecture
architecture	I-Architecture
may	O
consume	O
vast	O
amounts	O
of	O
memory	B-Architecture
and	O
storage	O
.	O
</s>
<s>
Furthermore	O
,	O
the	O
designer	O
often	O
needs	O
to	O
transmit	O
signals	O
through	O
many	O
of	O
these	O
connections	O
and	O
their	O
associated	O
neurons	O
which	O
require	O
enormous	O
CPU	B-General_Concept
power	O
and	O
time	O
.	O
</s>
<s>
Schmidhuber	O
noted	O
that	O
the	O
resurgence	O
of	O
neural	B-Architecture
networks	I-Architecture
in	O
the	O
twenty-first	O
century	O
is	O
largely	O
attributable	O
to	O
advances	O
in	O
hardware	O
:	O
from	O
1991	O
to	O
2015	O
,	O
computing	O
power	O
,	O
especially	O
as	O
delivered	O
by	O
GPGPUs	B-Architecture
(	O
on	O
GPUs	B-Architecture
)	O
,	O
has	O
increased	O
around	O
a	O
million-fold	O
,	O
making	O
the	O
standard	O
backpropagation	B-Algorithm
algorithm	O
feasible	O
for	O
training	O
networks	O
that	O
are	O
several	O
layers	O
deeper	O
than	O
before	O
.	O
</s>
<s>
The	O
use	O
of	O
accelerators	O
such	O
as	O
FPGAs	B-Architecture
and	O
GPUs	B-Architecture
can	O
reduce	O
training	O
times	O
from	O
months	O
to	O
days	O
.	O
</s>
<s>
Neuromorphic	O
engineering	O
or	O
a	O
physical	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
addresses	O
the	O
hardware	O
difficulty	O
directly	O
,	O
by	O
constructing	O
non-von-Neumann	O
chips	O
to	O
directly	O
implement	O
neural	B-Architecture
networks	I-Architecture
in	O
circuitry	O
.	O
</s>
<s>
Another	O
type	O
of	O
chip	O
optimized	O
for	O
neural	B-Architecture
network	I-Architecture
processing	O
is	O
called	O
a	O
Tensor	B-Device
Processing	I-Device
Unit	I-Device
,	O
or	O
TPU	O
.	O
</s>
<s>
Analyzing	O
what	O
has	O
been	O
learned	O
by	O
an	O
ANN	O
is	O
much	O
easier	O
than	O
analyzing	O
what	O
has	O
been	O
learned	O
by	O
a	O
biological	B-General_Concept
neural	I-General_Concept
network	I-General_Concept
.	O
</s>
<s>
Furthermore	O
,	O
researchers	O
involved	O
in	O
exploring	O
learning	O
algorithms	O
for	O
neural	B-Architecture
networks	I-Architecture
are	O
gradually	O
uncovering	O
general	O
principles	O
that	O
allow	O
a	O
learning	O
machine	O
to	O
be	O
successful	O
.	O
</s>
<s>
Advocates	O
of	O
hybrid	B-Algorithm
models	O
(	O
combining	O
neural	B-Architecture
networks	I-Architecture
and	O
symbolic	O
approaches	O
)	O
say	O
that	O
such	O
a	O
mixture	O
can	O
better	O
capture	O
the	O
mechanisms	O
of	O
the	O
human	O
mind	O
.	O
</s>
