Question

why there is no self-connection for the feedback in Hopfiled network? what is the advantages ?

Answer 1

In case of the continuous version of the Hopfield neural network, we have to consider neural self-connections wij≠0 and choose as an activation function a sigmoid function. With these new adjustments, the training algorithm operates in the same way.

The convergence property of Hopfield’s network depends on the structure of W (the matrix with elements wij) and the updating mode. An important property of the Hopfield model is that if it operates in a sequential mode and W is symmetric with nonnegative diagonal elements, then the energy function

(7.71)Ehs(t)=12∑i=1n∑j=1nwijxi(t)xj(t)-∑i=1nbixi(t)=-12xT(t)Wx(t)-bTx(t)

is nonincreasing [138]. The network always converges to a fixed point.