Gradient Like Behavior and High Gain Design of KWTA Neural Networks

It is considered the static and dynamic analysis of an analog electrical circuit having the structure of the Hopfield neural network, the KWTA (KWinners-Take-All) network. The mathematics of circuit design and operation is discussed via two basic tools: the Liapunov function ensuring the gradient like behavior and the rational choice of the weights that stands for network training to ensure order-preserving trajectories. Dynamics and behavior at equilibria are considered in their natural interaction, and some connections to the ideas in general dynamical systems of convolution type are suggested.