Dynamics of the Amari-Takeuchi competitive learning model

A rigorous analysis of an analog version of the Amari-Takeuchi (1978) theory of self-organization of category detecting nerve cells is given. Convergence of the learning is proven by constructing a Lyapunov function for the learning dynamics in a convenient set of coordinates. This function has separate terms reflecting the Hebbian learning and lateral inhibition components of the theory. This facilitates a theoretic characterization of the categories formed by the model. Also proposed is a different network interpretation of the equations, with the outputs implicit functions of the inputs.<<ETX>>