Network Operation

As indicated above, the initialization of the Hopfield network stores a number of patterns by encoding them in the network weights. An input pattern is fed to the network by setting the states of the units to the levels determined by that pattern. The units are then allowed to interact as described below until the interaction reaches some steady state. This steady state will be one of the exemplar patterns, expressed in terms of the states of the units. (It is possible that the network will not attain a steady state, but will cycle through a sequence of states. We will not consider this case in the discussion to follow.)

The interaction between units is governed by the weights on the network connections. The weights must be set to values that will ensure that the eventual steady states are the ones representing the exemplar patterns. How these values are determined will be described below.

The interaction between the units can be thought of as a sort of competition between the units in which some units excite others, making them more active (that is, increasing the numbers describing their states), and some units inhibit others, making them less active (decreasing the numbers describing their states). The choice of weights ensures that these changes do not continue indefinitely.

An alternative way of considering the network is provided by a very simple model. Consider a billiard table whose surface is not flat, but slopes towards the pockets. The surface of the table can be taken to represent the possible states of a network with two units, and the pockets the positions of exemplar patterns. Supplying the network with an input pattern corresponds to putting a ball down on the table. The interaction between units until a steady state is reached is like the ball rolling down the sloping surface of the table and falling into a pocket.