Optimal signal representation in neural spiking population codes: a model for the formation of simple cell receptive fields.
Résumé
Taking advantage of the constraints of spiking representations, we derive an unsupervised learning algorithm which we prove to efficiently code natural images and apply it to a model of the input to the primary visual cortex. In fact, spikes carry temporal event-based information in bundles of parallel fibers and may be considered as all-or-none binary events. This property may be used to formulate the efficiency of a representation problem as finding the L$_0$-norm sparsest representation, a ``hard" NP-complete problem. We propose a solution for a bundle of Integrate-and-Fire neurons which improves previous results based on an Adaptive Matching Pursuit scheme by explicitly implementing an homeostatic constraint in the choice function by a spiking gain control mechanism in the neural population. For comparison purposes, we applied this scheme to the learning of small images taken from natural images as in \sparsenet\ and compared the results and efficiency of this last algorithm with Matching Pursuit and the proposed algorithm. Results show that the different coding algorithm give similar efficiencies while the homeostasis provided an optimal balance which was crucial during the learning. This study provides a simpler and more efficient algorithm for learning independent components in a set of inputs such as natural images suggesting that this Sparse Spike Coding strategy may provide a generic computational module that help us understanding the efficiency of the Primary Visual Cortex.
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