Department of Mathematics and Statistics
Reconstruction of Sparse Connectivity and Stimuli in Neuronal Networks Using Compressive Sensing of Network Dynamics
Sparsity is a fundamental characteristic of numerous biological, social, and technological networks. Neuronal network connectivity demonstrates sparsity on multiple spatial scales and natural stimuli typically also possess sparse representations in appropriate domains. In this talk, we address the role of sparsity in the efficient encoding of network structure and inputs through nonlinear neuronal network dynamics. We develop a theoretical framework for reconstructing sparse network data by leveraging compressive sensing theory and the linearity of input-output mappings commonly underlying neuronal dynamics. Addressing the theoretical and experimental challenges in measuring structural network connectivity, we reconstruct model neuronal network connections using the evoked dynamics in response to a small ensemble of random stimuli. Using the reconstructed connectivity matrix, we then accurately recover detailed network inputs distinct from the random input ensemble. Analyzing several receptive field models, we investigate how the accuracy of input reconstructions depends on the network architecture, and demonstrate that the center-surround structure common in the early visual system facilitates marked improvements in natural scene processing well beyond the uniformly-random connectivity typical in compressive sensing theory. However, we show that the spatial localization inherent in receptive fields combined with information loss introduced by nonlinear neuronal dynamics may underlie deficiencies in processing specific classes of non-natural stimuli, yielding a novel explanation for the manifestation of certain illusory effects. We expect this talk will provide a new perspective for understanding compressive encoding in sensory systems as well as the structure-function relationship in neuronal networks.
A pizza lunch will be served.