DYNAMICS OF LEARNING IN LINEAR FEATURE-DISCOVERY NETWORKS

In this paper I address the dynamics of learning in unsupervised neural feature-discovery networks. The models introduced incorporate feedforward connections modified by a Hebb law, and recurrent lateral connections modified by an anti-Hebb law. Conditions for stability of equilibria are derived, and bifurcation theory is used to explore the behaviour near loss of stability. Stability of the equilibria is shown to depend on the learning rates in the system, and on the statistics of the input signal. The bifurcation analyses reveal previously overlooked behaviours, including equilibria that consist of mixtures of the principal eigenvectors of the input autocorrelation, as well as limit cycles. The results provide a more complete picture of adaptation in Hebbian feature-discovery networks.