Competitive learning paradigms are usually defined with winner-take-all (WTA) activation rules. The paper develops a mathematical model for competitive learning paradigms using a generalization of the WTA activation rule (g-WTA). The model is a partial differential equation (PDE) relating the time rate of change in the ;density' of weight vectors to the divergence of a vector field called the neural flux. Characteristic trajectories are used to study solutions of the PDE model over scalar weight spaces. These solutions show how the model can be used to design competitive learning algorithms which estimate the modes of unknown probability density functions.
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