Analysis of Linsker-type Hebbian learning: rigorous results

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Abstract
In terms of a rigorous analysis of the nonlinear asymmetric dynamics of Linsker's unsupervised Hebbian learning network, the whole set of fixed point attractors of the network is determined, and the necessary and sufficient condition for the emergence of structured receptive fields are presented. New rigorous criteria for the division of parameter regimes to ensure the development of various structured connection patterns can be obtained explicitly. The shape of a receptive field is totally governed by the feedforward synaptic density function between the present layer and the preceding one, while the existence of a parameter regime for its occurrence is determined by the covariance matrix of cell activities in the present layer, i.e., by synaptic density functions of all preceding layers. The generation of center-surround and other oriented structures is re-interpreted with the aid of the authors' general theorems and numerical examples. The distribution of a few types of principal parameter regimes for varying system parameters and the relationship between these types are discussed.