Many familiar neural network learning algorithms, including
correlational (Hebbian) and back-propagation learning, are
easily transferred to the field computation framework.
For example, Hebbian learning rules can be described in terms
of an outer product of fields, 
:
[ ()_xy = _x _y . ]
(Notice that if 
is a field over 
and 
is a
field over 
, then 
is a field over
.)
For example, simple correlational strengthening of an
interconnection kernel K resulting from pre- and
post-synaptic activity fields 
and 
is given by
,
where r is the rate.
Such a process might occur through long-term potentiation
(LTP).
Recent studies
(surveyed in Singer 1995)
indicate that moderately weak positive correlations cause
synaptic efficacy to be weakened through
long-term depression (LTD),
while very weak connections have no effect on efficacy.
For (biologically realistic) non-negative activity fields,
the change in the interconnection matrix is given by
, where the
upsilon function is defined:
[ (x) =
;(x- 
)
- ;(x-) + 12 .]
When 
, 
and LTP results, but as
x drops below 
, 
becomes negative,
achieving its minimum at 
; further decreases of x
cause 
to approach 0.
(The slopes in the LTP and LTD regions are determined by
and 
.)