In general, if
is some field computational process governed by parameters
(such as synaptic weights), and if
is some performance measure for F on the input fields
, then for fixed 
we may define a potential field
over the parameter space.
If smaller values of M represent better performance,
and if M is bounded below (i.e., there is a best
performance), then we can do gradient descent on the
parameter space,
.
The same analysis can be applied when F is parameterized by
one or more fields (typically, interconnection fields). In
this case, gradient descent occurs by gradual modification
of the parameter fields.
For example, in the case of one parameter field,
,
the descent is given by
.
Of course, more sophisticated hill-descending algorithms can
also be implemented by field computation.