Simplified Rules and Theoretical Analysis for Information Bottleneck Optimization and PCA with Spiking Neurons

We show that under suitable assumptions (primarily linearization) a simple and perspicuous online learning rule for Information Bottleneck optimization with spiking neurons can be derived. This rule performs on common benchmark tasks as well as a rather complex rule that has previously been proposed \cite{KlampflETAL:07b}. Furthermore, the transparency of this new learning rule makes a theoretical analysis of its convergence properties feasible. A variation of this learning rule (with sign changes) provides a theoretically founded method for performing Principal Component Analysis {(PCA)} with spiking neurons. By applying this rule to an ensemble of neurons, different principal components of the input can be extracted.