Hopfield Network is a form of recurrent artificial neural network. Hopfield networks are classical models of memory and collective processing in networks of abstract McCulloch-Pitts neurons, but they have not been widely used in signal processing as they usually have small memory capacity (scaling linearly in the number of neurons) and are challenging to train, especially on noisy data. Hopfield nets serve as content-addressable memory systems with binary threshold nodes. The units in Hopfield nets are binary threshold units, i.e. the units only take on two different values for their states and the value is determined by whether or not the units input exceeds their threshold. Hopfield nets normally have units that take on values of 1 or -1. Every pair of units i and j in a Hopfield network have a connection that is described by the connectivity weight. The constraint that weights must be symmetric guarantees the energy function decreases monotonically while following the activation rules, and the network may exhibit some periodic or chaotic behavior if non-symmetric weights are used. However, it was found that this chaotic behavior is confined to a relatively small space and does not impair the network’s ability to act as a content-addressable associative memory system.
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