What is required in the Natural Scene Environment for the Development of Orientation Selectivity: How Sparse is Sparse?

Brian Blais

collaborators: H. Shouval, N. Intrator, L. N Cooper

Recently several different learning rules have been proposed that develop simple cell-like receptive fields in a natural image environment(Law and Cooper, 1994; Olshausen and Field, 1995; Bell and Sejnowski, 1997). Some of these rules maximize a measure of sparse coding to obtain the receptive fields, motivated by the sparsity of the natural scenes and the necessity for the visual cortex to find an efficient representation scheme. We describe a method to directly find the sparsity of the representation a learning rule finds. We use this method to compare several statistically and biologically motivated learning rules using the same visual environment and neuronal architecture. This allows us to concentrate on the feature extraction and neuronal coding properties of these rules. Included in these rules are kurtosis and skew maximization, the quadratic form of the BCM learning rule, and single cell ICA. We find that the coding is indeed very sparse: many learning rules are coding only about one percent of the input structure. The algorithm for measuring sparsity can also be used to remove selectively the structure which the neuron is coding, in order to recursively pick out the most salient features in the environment.


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