Analyzing the robustness of redundant population codes in sensory and feature extraction systems

Sensory systems often use groups of redundant neurons to represent stimulus information both during transduction and population coding of features. This redundancy makes the system more robust to corruption in the representation. We approximate neural coding as a projection of the stimulus onto a set of vectors, with the result encoded by spike trains. We use the formalism of frame theory to quantify the inherent noise reduction properties of such population codes. Additionally, computing features from the stimulus signal can also be thought of as projecting the coefficients of a sensory representation onto another set of vectors specific to the feature of interest. The conditions under which a combination of different features form a complete representation for the stimulus signal can be found through a recent extension to frame theory called “frames of subspaces.” We extend the frame of subspaces theory to quantify the noise reduction properties of a collection of redundant feature spaces.