Hopfield nets have units in states 0 or 1 in which the (N) units
are probably fully interconnected.
They attempt to ``memorise'' n different network states - a network
state is an N long binary vector.
If these states are 
, where
we shall set the weights by writing
in the case 
, and 
.
Now load the network with one of the states to be remembered, 
.
implying stability, subject to noise from the 
terms; we assume
enough ``independence'' among the 
to suppose this noise may be
disregarded.
Observe from 6 that we have symmetry in the weights,
, and
define the energy
of the system at a given instant by
If we elect to change the value of processor 
, we can see that the
change in energy 
due to this change 
is
State changes therefore cause E to decrease monotonically, and ``stability'' represents a local minimum of E.
