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Figure 3.12 A simple Hopfield network containing three processing units. Each pair of units is connected by weighted links in both directions.
the weight to the data flow from i to j (activity in a neurone i is weighted by the amount wji and then passed to neurone j). Hopfield (1984) shows that a set of symmetric weights, i.e. wji=wij, is a sufficient condition to guarantee network convergence to a stable state.
There are two kinds of models, termed discrete and continuous, for characterising the Hopfield network’s dynamics, i.e. the change of network state. In the discrete version, the network output is either 1 or 0. The input to the ith neurone at time n, denoted by , is:
(3.25) |
where Ii is an external input to neurone i. The vi, which is the output of the neurone i, are usually defined in terms of a step function:
(3.26) |
in which si is the predefined threshold for neurone i. In general, si is set to 0.
In the continuous version, the network state for neurone i is described by the differential equation:
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