<s>
Artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
are	O
a	O
class	O
of	O
models	O
used	O
in	O
machine	O
learning	O
,	O
and	O
inspired	O
by	O
biological	B-General_Concept
neural	I-General_Concept
networks	I-General_Concept
.	O
</s>
<s>
They	O
are	O
the	O
core	O
component	O
of	O
modern	O
deep	B-Algorithm
learning	I-Algorithm
algorithms	O
.	O
</s>
<s>
Computation	O
in	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
is	O
usually	O
organized	O
into	O
sequential	O
layers	O
of	O
artificial	B-Algorithm
neurons	I-Algorithm
.	O
</s>
<s>
Theoretical	O
analysis	O
of	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
sometimes	O
considers	O
the	O
limiting	O
case	O
that	O
layer	O
width	O
becomes	O
large	O
or	O
infinite	O
.	O
</s>
<s>
This	O
limit	O
enables	O
simple	O
analytic	O
statements	O
to	O
be	O
made	O
about	O
neural	B-General_Concept
network	I-General_Concept
predictions	O
,	O
training	O
dynamics	O
,	O
generalization	O
,	O
and	O
loss	O
surfaces	O
.	O
</s>
<s>
This	O
wide	O
layer	O
limit	O
is	O
also	O
of	O
practical	O
interest	O
,	O
since	O
finite	O
width	O
neural	B-General_Concept
networks	I-General_Concept
often	O
perform	O
strictly	O
better	O
as	O
layer	O
width	O
is	O
increased	O
.	O
</s>
<s>
The	O
Neural	B-Algorithm
Network	I-Algorithm
Gaussian	I-Algorithm
Process	I-Algorithm
(	O
NNGP	O
)	O
corresponds	O
to	O
the	O
infinite	O
width	O
limit	O
of	O
Bayesian	O
neural	B-General_Concept
networks	I-General_Concept
,	O
and	O
to	O
the	O
distribution	O
over	O
functions	O
realized	O
by	O
non-Bayesian	O
neural	B-General_Concept
networks	I-General_Concept
after	O
random	O
initialization	O
.	O
</s>
<s>
The	O
Neural	B-Algorithm
Tangent	I-Algorithm
Kernel	I-Algorithm
describes	O
the	O
evolution	O
of	O
neural	B-General_Concept
network	I-General_Concept
predictions	O
during	O
gradient	O
descent	O
training	O
.	O
</s>
<s>
In	O
the	O
infinite	O
width	O
limit	O
the	O
NTK	O
usually	O
becomes	O
constant	O
,	O
often	O
allowing	O
closed	O
form	O
expressions	O
for	O
the	O
function	O
computed	O
by	O
a	O
wide	O
neural	B-General_Concept
network	I-General_Concept
throughout	O
gradient	O
descent	O
training	O
.	O
</s>
<s>
The	O
study	O
of	O
infinite	O
width	O
neural	B-General_Concept
networks	I-General_Concept
with	O
a	O
different	O
initial	O
weight	O
scaling	O
and	O
suitably	O
large	O
learning	O
rates	O
leads	O
to	O
qualitatively	O
different	O
nonlinear	O
training	O
dynamics	O
than	O
those	O
described	O
by	O
the	O
fixed	O
neural	B-Algorithm
tangent	I-Algorithm
kernel	I-Algorithm
.	O
</s>
<s>
Catapult	O
dynamics	O
describe	O
neural	B-General_Concept
network	I-General_Concept
training	O
dynamics	O
in	O
the	O
case	O
that	O
logits	O
diverge	O
to	O
infinity	O
as	O
the	O
layer	O
width	O
is	O
taken	O
to	O
infinity	O
,	O
and	O
describe	O
qualitative	O
properties	O
of	O
early	O
training	O
dynamics	O
.	O
</s>
