Hopfield network — scholarpedia.org

A Hopfield net is a recurrent neural network having synaptic connection pattern such that there is an underlying Lyapunov function for the activity dynamics. Started in any initial state, the state of the system evolves to a final state that is a (local) minimum of the Lyapunov function. There are two popular forms of the model: \[V_j(t+1) = \begin{cases} 1, & \mbox{ if } \ \Sigma_k T_{jk}V_k(t) + I_j>0 \\ 0, & \mbox{ otherwise } \end{cases} \]

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