<s>
Neural	O
modeling	O
field	O
(	O
NMF	O
)	O
is	O
a	O
mathematical	O
framework	O
for	O
machine	O
learning	O
which	O
combines	O
ideas	O
from	O
neural	B-Architecture
networks	I-Architecture
,	O
fuzzy	O
logic	O
,	O
and	O
model	O
based	O
recognition	O
.	O
</s>
<s>
It	O
has	O
also	O
been	O
referred	O
to	O
as	O
modeling	O
fields	O
,	O
modeling	O
fields	O
theory	O
(	O
MFT	O
)	O
,	O
Maximum	O
likelihood	O
artificial	O
neural	B-Architecture
networks	I-Architecture
(	O
MLANS	O
)	O
.	O
</s>
<s>
This	O
is	O
a	O
well	O
known	O
problem	O
,	O
it	O
is	O
addressed	O
by	O
reducing	O
similarity	O
L	O
using	O
a	O
"	O
skeptic	O
penalty	B-Algorithm
function	I-Algorithm
,	O
"	O
(	O
Penalty	B-Algorithm
method	I-Algorithm
)	O
p(N,M )	O
that	O
grows	O
with	O
the	O
number	O
of	O
models	O
M	O
,	O
and	O
this	O
growth	O
is	O
steeper	O
for	O
a	O
smaller	O
amount	O
of	O
data	O
N	O
.	O
For	O
example	O
,	O
an	O
asymptotically	O
unbiased	O
maximum	O
likelihood	O
estimation	O
leads	O
to	O
multiplicative	O
p(N,M )	O
=	O
exp( 	O
-Npar/2	O
)	O
,	O
where	O
Npar	O
is	O
a	O
total	O
number	O
of	O
adaptive	O
parameters	O
in	O
all	O
models	O
(	O
this	O
penalty	B-Algorithm
function	I-Algorithm
is	O
known	O
as	O
Akaike	O
information	O
criterion	O
,	O
see	O
(	O
Perlovsky	O
2001	O
)	O
for	O
further	O
discussion	O
and	O
references	O
)	O
.	O
</s>
