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Stability of the network

Given that W is symmetric, Hopfield proved stability for the network by showing that with the abovementioned equations (7 and 8), the network output v evolves so as to minimize the Liapunov function:

 

where denotes the network state. Therefore we have an energy function defined throughout and dynamics which guarantee convergence to minima. Also, for a suitable W, the minima of the first term lie at the hypercube vertices. The second term is minimized at the hypercube center but has negligible impact at low .

In regard to updating the states of the net (or the output of the neurons), it is carried out either asynchronously or synchronously. From a simulation point of view, we found that asynchronous updating is a bit more efficient than synchronous updating since the later gave more limit cycles, hence, worse convergence. From a theoretical point of view, it makes not much of a difference on the operation of the net as to which updating mode is used.



HPF demo web account
Mon Nov 18 19:45:42 EST 1996