<s>
Differentiable	B-Application
programming	I-Application
is	O
a	O
programming	O
paradigm	O
in	O
which	O
a	O
numeric	O
computer	O
program	O
can	O
be	O
differentiated	B-Algorithm
throughout	O
via	O
automatic	B-Algorithm
differentiation	I-Algorithm
.	O
</s>
<s>
This	O
allows	O
for	O
gradient-based	B-Algorithm
optimization	I-Algorithm
of	O
parameters	O
in	O
the	O
program	O
,	O
often	O
via	O
gradient	B-Algorithm
descent	I-Algorithm
,	O
as	O
well	O
as	O
other	O
learning	O
approaches	O
that	O
are	O
based	O
on	O
higher	O
order	O
derivative	B-Algorithm
information	O
.	O
</s>
<s>
Differentiable	B-Application
programming	I-Application
has	O
found	O
use	O
in	O
a	O
wide	O
variety	O
of	O
areas	O
,	O
particularly	O
scientific	O
computing	O
and	O
artificial	B-Application
intelligence	I-Application
.	I-Application
</s>
<s>
Most	O
differentiable	B-Application
programming	I-Application
frameworks	O
work	O
by	O
constructing	O
a	O
graph	O
containing	O
the	O
control	O
flow	O
and	O
data	B-General_Concept
structures	I-General_Concept
in	O
the	O
program	O
.	O
</s>
<s>
Static	O
,	O
compiled	B-Language
graph-based	O
approaches	O
such	O
as	O
TensorFlow	B-Language
,	O
Theano	B-Algorithm
,	O
and	O
MXNet	B-Algorithm
.	O
</s>
<s>
They	O
tend	O
to	O
allow	O
for	O
good	O
compiler	B-Application
optimization	I-Application
and	O
easier	O
scaling	O
to	O
large	O
systems	O
,	O
but	O
their	O
static	O
nature	O
limits	O
interactivity	O
and	O
the	O
types	O
of	O
programs	O
that	O
can	O
be	O
created	O
easily	O
(	O
e.g.	O
</s>
<s>
A	O
proof	O
of	O
concept	O
compiler	B-Language
toolchain	O
called	O
Myia	O
uses	O
a	O
subset	O
of	O
Python	O
as	O
a	O
front	O
end	O
and	O
supports	O
higher-order	O
functions	O
,	O
recursion	O
,	O
and	O
higher-order	O
derivatives	B-Algorithm
.	O
</s>
<s>
Operator	O
overloading	O
,	O
dynamic	O
graph	O
based	O
approaches	O
such	O
as	O
PyTorch	B-Algorithm
and	O
AutoGrad	O
.	O
</s>
<s>
However	O
,	O
they	O
lead	O
to	O
interpreter	B-Application
overhead	O
(	O
particularly	O
when	O
composing	O
many	O
small	O
operations	O
)	O
,	O
poorer	O
scalability	O
,	O
and	O
reduced	O
benefit	O
from	O
compiler	B-Application
optimization	I-Application
.	O
</s>
<s>
A	O
package	O
for	O
the	O
Julia	B-Application
programming	I-Application
language	I-Application
works	O
directly	O
on	O
Julia	B-Application
's	O
intermediate	B-Application
representation	I-Application
,	O
allowing	O
it	O
to	O
still	O
be	O
optimized	B-Application
by	O
Julia	B-Application
's	O
just-in-time	O
compiler	B-Language
.	O
</s>
<s>
Newer	O
approaches	O
resolve	O
this	O
issue	O
by	O
constructing	O
the	O
graph	O
from	O
the	O
language	O
's	O
syntax	O
or	O
IR	B-Application
,	O
allowing	O
arbitrary	O
code	O
to	O
be	O
differentiated	B-Algorithm
.	O
</s>
<s>
Differentiable	B-Application
programming	I-Application
has	O
been	O
applied	O
in	O
areas	O
such	O
as	O
combining	O
deep	B-Algorithm
learning	I-Algorithm
with	O
physics	O
engines	O
in	O
robotics	O
,	O
solving	O
electronic	O
structure	O
problems	O
with	O
differentiable	O
density	O
functional	O
theory	O
,	O
differentiable	O
ray	B-Algorithm
tracing	I-Algorithm
,	O
image	B-Algorithm
processing	I-Algorithm
,	O
and	O
probabilistic	O
programming	O
.	O
</s>
