The sparse structure of natural chemical environments

Sparse representations, in which sources are represented by neural ensembles with small average activity ratios, have many desirable properties including ease of learning, the capacity for generalization, and noise resistance. All of these are characteristic of the biological olfactory system, despite activity patterns across receptor arrays often being highly non-sparse. This is possible because the underlying chemosensory data are “signal sparse” - a distinct property, dependent on environmental statistics, that enables sparse coding algorithms to construct representational sparseness in subsequent processing layers. Whereas this can be accomplished by simple rotation in some systems, chemosensory sparse coding requires curvature in the isoresponse surfaces for each neuron owing to the diversity of chemical sources (overcompleteness). We propose that this functional curvature arises from statistical learning processes instantiated in plastic networks of the early olfactory system. Using models of the chemosensory environment, we illustrate the application of sparse coding algorithms to the analysis of chemical signals.