Distribution of winners in local lateral inhibition

The dynamics of an iterative local lateral inhibition system are analyzed. The study of lateral inhibition is generalized in two significant ways. First, the inhibition range from each neuron is limited to a subset of the neurons, called the neighborhood. The only requirement for these neighborhoods in the discussion is that they be symmetric. That is, if a is a neighbor of b, then b is a neighbor of a. Second, a positive feedback is added to the model as part of the nonlinear normalization function. This normalization function has only to satisfy some very broad requirements. When the neighborhood relaxation expands to all pairs of neurons, the system becomes complete lateral inhibition, and the common winner-take-all consequence should be expected. It is proved that those assignments with a winner in the neighborhood of each loser are asymptotically stable fixed points, and other fixed points are unstable