Hopfield Networks

A Hopfield autoassociative memory network is able to recover an original stored vector (see Hopfield Network). In the learning process of the Hopfield network, when a single-layer recurrent. When a single-layer recurrent network performs a sequential updating process, an input pattern is first applied to the network, and the output of the network is initialized accordingly. Then, the initialized output becomes the new, updated input through the feedback connections. The first updated output is produced from the first input, and in turn acts as the second updated input through the feedback links to produce the second updated output. The update process of the network is stopped when no new, updated responses are produced and the network has reached its equilibrium.

Each node of the network has an external input (Figure 1). Output of the jth node is connected to each other nodes through a multiplicative weight Wj for i = 1, 2,..., ยป, i = j. There is no self-feedback in a Hopfield network. Additionally, the network weights must be symmetric; Wj = Wfi. The weights of each node in a discrete Hopfield network are updated as follows:

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