<s>
Symbolic	B-Algorithm
regression	I-Algorithm
(	O
SR	O
)	O
is	O
a	O
type	O
of	O
regression	O
analysis	O
that	O
searches	O
the	O
space	O
of	O
mathematical	O
expressions	O
to	O
find	O
the	O
model	O
that	O
best	O
fits	O
a	O
given	O
dataset	O
,	O
both	O
in	O
terms	O
of	O
accuracy	O
and	O
simplicity	O
.	O
</s>
<s>
No	O
particular	O
model	O
is	O
provided	O
as	O
a	O
starting	O
point	O
for	O
symbolic	B-Algorithm
regression	I-Algorithm
.	O
</s>
<s>
Instead	O
,	O
initial	O
expressions	O
are	O
formed	O
by	O
randomly	O
combining	O
mathematical	O
building	O
blocks	O
such	O
as	O
mathematical	O
operators	O
,	O
analytic	B-Language
functions	I-Language
,	O
constants	O
,	O
and	O
state	O
variables	O
.	O
</s>
<s>
The	O
symbolic	B-Algorithm
regression	I-Algorithm
problem	O
for	O
mathematical	O
functions	O
has	O
been	O
tackled	O
with	O
a	O
variety	O
of	O
methods	O
,	O
including	O
recombining	O
equations	O
most	O
commonly	O
using	O
genetic	B-Algorithm
programming	I-Algorithm
,	O
as	O
well	O
as	O
more	O
recent	O
methods	O
utilizing	O
Bayesian	O
methods	O
and	O
neural	B-Architecture
networks	I-Architecture
.	O
</s>
<s>
By	O
not	O
requiring	O
a	O
priori	O
specification	O
of	O
a	O
model	O
,	O
symbolic	B-Algorithm
regression	I-Algorithm
is	O
n't	O
affected	O
by	O
human	O
bias	O
,	O
or	O
unknown	O
gaps	O
in	O
domain	O
knowledge	O
.	O
</s>
<s>
The	O
fitness	O
function	O
that	O
drives	O
the	O
evolution	O
of	O
the	O
models	O
takes	O
into	O
account	O
not	O
only	O
error	B-Algorithm
metrics	I-Algorithm
(	O
to	O
ensure	O
the	O
models	O
accurately	O
predict	O
the	O
data	O
)	O
,	O
but	O
also	O
special	O
complexity	O
measures	O
,	O
thus	O
ensuring	O
that	O
the	O
resulting	O
models	O
reveal	O
the	O
data	O
's	O
underlying	O
structure	O
in	O
a	O
way	O
that	O
's	O
understandable	O
from	O
a	O
human	O
perspective	O
.	O
</s>
<s>
This	O
facilitates	O
reasoning	O
and	O
favors	O
the	O
odds	O
of	O
getting	O
insights	O
about	O
the	O
data-generating	O
system	O
,	O
as	O
well	O
as	O
improving	O
generalisability	O
and	O
extrapolation	O
behaviour	O
by	O
preventing	O
overfitting	B-Error_Name
.	O
</s>
<s>
It	O
has	O
been	O
proven	O
that	O
symbolic	B-Algorithm
regression	I-Algorithm
is	O
an	O
NP-hard	O
problem	O
,	O
in	O
the	O
sense	O
that	O
one	O
cannot	O
always	O
find	O
the	O
best	O
possible	O
mathematical	O
expression	O
to	O
fit	O
to	O
a	O
given	O
dataset	O
in	O
polynomial	O
time	O
.	O
</s>
<s>
Nevertheless	O
,	O
if	O
the	O
sought-for	O
equation	O
is	O
not	O
too	O
complex	O
it	O
is	O
possible	O
to	O
solve	O
the	O
symbolic	B-Algorithm
regression	I-Algorithm
problem	O
exactly	O
by	O
generating	O
every	O
possible	O
function	O
(	O
built	O
from	O
some	O
predefined	O
set	O
of	O
operators	O
)	O
and	O
evaluating	O
them	O
on	O
the	O
dataset	O
in	O
question	O
.	O
</s>
<s>
While	O
conventional	O
regression	O
techniques	O
seek	O
to	O
optimize	O
the	O
parameters	O
for	O
a	O
pre-specified	O
model	O
structure	O
,	O
symbolic	B-Algorithm
regression	I-Algorithm
avoids	O
imposing	O
prior	O
assumptions	O
,	O
and	O
instead	O
infers	O
the	O
model	O
from	O
the	O
data	O
.	O
</s>
<s>
This	O
approach	O
has	O
the	O
disadvantage	O
of	O
having	O
a	O
much	O
larger	O
space	O
to	O
search	O
,	O
because	O
not	O
only	O
the	O
search	O
space	O
in	O
symbolic	B-Algorithm
regression	I-Algorithm
is	O
infinite	O
,	O
but	O
there	O
are	O
an	O
infinite	O
number	O
of	O
models	O
which	O
will	O
perfectly	O
fit	O
a	O
finite	O
data	O
set	O
(	O
provided	O
that	O
the	O
model	O
complexity	O
is	O
n't	O
artificially	O
limited	O
)	O
.	O
</s>
<s>
This	O
means	O
that	O
it	O
will	O
possibly	O
take	O
a	O
symbolic	B-Algorithm
regression	I-Algorithm
algorithm	O
longer	O
to	O
find	O
an	O
appropriate	O
model	O
and	O
parametrization	O
,	O
than	O
traditional	O
regression	O
techniques	O
.	O
</s>
<s>
This	O
can	O
be	O
attenuated	O
by	O
limiting	O
the	O
set	O
of	O
building	O
blocks	O
provided	O
to	O
the	O
algorithm	O
,	O
based	O
on	O
existing	O
knowledge	O
of	O
the	O
system	O
that	O
produced	O
the	O
data	O
;	O
but	O
in	O
the	O
end	O
,	O
using	O
symbolic	B-Algorithm
regression	I-Algorithm
is	O
a	O
decision	O
that	O
has	O
to	O
be	O
balanced	O
with	O
how	O
much	O
is	O
known	O
about	O
the	O
underlying	O
system	O
.	O
</s>
<s>
Nevertheless	O
,	O
this	O
characteristic	O
of	O
symbolic	B-Algorithm
regression	I-Algorithm
also	O
has	O
advantages	O
:	O
because	O
the	O
evolutionary	B-Algorithm
algorithm	I-Algorithm
requires	O
diversity	O
in	O
order	O
to	O
effectively	O
explore	O
the	O
search	O
space	O
,	O
the	O
result	O
is	O
likely	O
to	O
be	O
a	O
selection	O
of	O
high-scoring	O
models	O
(	O
and	O
their	O
corresponding	O
set	O
of	O
parameters	O
)	O
.	O
</s>
<s>
In	O
2021	O
,	O
was	O
proposed	O
as	O
a	O
large	O
benchmark	O
for	O
symbolic	B-Algorithm
regression	I-Algorithm
.	O
</s>
<s>
In	O
its	O
inception	O
,	O
SRBench	O
featured	O
14	O
symbolic	B-Algorithm
regression	I-Algorithm
methods	O
,	O
7	O
other	O
ML	O
methods	O
,	O
and	O
252	O
datasets	O
from	O
.	O
</s>
<s>
In	O
2022	O
,	O
SRBench	O
announced	O
the	O
competition	O
Interpretable	O
Symbolic	B-Algorithm
Regression	I-Algorithm
for	O
Data	O
Science	O
,	O
which	O
was	O
held	O
at	O
the	O
GECCO	O
conference	O
in	O
Boston	O
,	O
MA	O
.	O
</s>
<s>
The	O
competition	O
pitted	O
nine	O
leading	O
symbolic	B-Algorithm
regression	I-Algorithm
algorithms	O
against	O
each	O
other	O
on	O
a	O
novel	O
set	O
of	O
data	O
problems	O
and	O
considered	O
different	O
evaluation	O
criteria	O
.	O
</s>
<s>
Most	O
symbolic	B-Algorithm
regression	I-Algorithm
algorithms	O
prevent	O
combinatorial	O
explosion	O
by	O
implementing	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
that	O
iteratively	O
improve	O
the	O
best-fit	O
expression	O
over	O
many	O
generations	O
.	O
</s>
<s>
Recently	O
,	O
researchers	O
have	O
proposed	O
algorithms	O
utilizing	O
other	O
tactics	O
in	O
AI	B-Application
.	O
</s>
<s>
Silviu-Marian	O
Udrescu	O
and	O
Max	O
Tegmark	O
developed	O
the	O
"	O
AI	B-Application
Feynman	O
"	O
algorithm	O
,	O
which	O
attempts	O
symbolic	B-Algorithm
regression	I-Algorithm
by	O
training	O
a	O
neural	B-Architecture
network	I-Architecture
to	O
represent	O
the	O
mystery	O
function	O
,	O
then	O
runs	O
tests	O
against	O
the	O
neural	B-Architecture
network	I-Architecture
to	O
attempt	O
to	O
break	O
up	O
the	O
problem	O
into	O
smaller	O
parts	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
,	O
tests	O
against	O
the	O
neural	B-Architecture
network	I-Architecture
can	O
recognize	O
the	O
separation	O
and	O
proceed	O
to	O
solve	O
for	O
and	O
separately	O
and	O
with	O
different	O
variables	O
as	O
inputs	O
.	O
</s>
<s>
This	O
is	O
an	O
example	O
of	O
divide	B-Algorithm
and	I-Algorithm
conquer	I-Algorithm
,	O
which	O
reduces	O
the	O
size	O
of	O
the	O
problem	O
to	O
be	O
more	O
manageable	O
.	O
</s>
<s>
AI	B-Application
Feynman	O
also	O
transforms	O
the	O
inputs	O
and	O
outputs	O
of	O
the	O
mystery	O
function	O
in	O
order	O
to	O
produce	O
a	O
new	O
function	O
which	O
can	O
be	O
solved	O
with	O
other	O
techniques	O
,	O
and	O
performs	O
dimensional	O
analysis	O
to	O
reduce	O
the	O
number	O
of	O
independent	O
variables	O
involved	O
.	O
</s>
<s>
The	O
algorithm	O
was	O
able	O
to	O
"	O
discover	O
"	O
100	O
equations	O
from	O
The	O
Feynman	O
Lectures	O
on	O
Physics	O
,	O
while	O
a	O
leading	O
software	O
using	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
,	O
Eureqa	B-Algorithm
,	O
solved	O
only	O
71	O
.	O
</s>
<s>
AI	B-Application
Feynman	O
,	O
in	O
contrast	O
to	O
classic	O
symbolic	B-Algorithm
regression	I-Algorithm
methods	O
,	O
requires	O
a	O
very	O
large	O
dataset	O
in	O
order	O
to	O
first	O
train	O
the	O
neural	B-Architecture
network	I-Architecture
and	O
is	O
naturally	O
biased	O
towards	O
equations	O
that	O
are	O
common	O
in	O
elementary	O
physics	O
.	O
</s>
<s>
QLattice	B-Algorithm
is	O
a	O
quantum-inspired	O
simulation	O
and	O
machine	O
learning	O
technology	O
that	O
helps	O
search	O
through	O
an	O
infinite	O
list	O
of	O
potential	O
mathematical	O
models	O
to	O
solve	O
a	O
problem	O
.	O
</s>
