Hopfield Spurious Stable Points

A Hopfield network with five neurons is designed to have four stable equilibria. However, unavoidably, it has other undesired equilibria.

We would like to obtain a Hopfield network that has the four stable points defined by the two target (column) vectors in T.

T = [+1 +1 -1 +1; ...
      -1 +1 +1 -1; ...
      -1 -1 -1 +1; ...
      +1 +1 +1 +1; ...
      -1 -1 +1 +1];

The function NEWHOP creates Hopfield networks given the stable points T.

net = newhop(T);

Here we define 4 random starting points and simulate the Hopfield network for 50 steps.

Some initial conditions will lead to desired stable points. Others will lead to undesired stable points.

P = {rands(5,4)};
[Y,Pf,Af] = sim(net,{4 50},{},P);
Y{end}

ans =

     1    -1    -1     1
     1    -1     1    -1
     1    -1    -1     1
     1     1     1     1
     1     1     1     1