RUI: Compressive Sensing and Neuronal Network Structure-Function Relationships

Swarthmore College, Swarthmore PA

Investigators

Abstract

The human brain is a complex network of billions of neurons whose intricate connectivity largely determines perception and behavior. To understand brain function, it is therefore paramount to efficiently measure and analyze neuronal network architecture. However, measuring the connectivity of large neuronal networks remains a challenge both experimentally and theoretically. An often more tractable approach to reconstructing connectivity in complex networks is to instead measure the dynamics of neurons of interest, and then use mathematical approaches to infer the network connectivity. This project will utilize the widespread sparsity found in brain networks to develop an efficient mathematical framework for reconstructing neuronal connectivity from limited measurements of neuronal dynamics. Upon accurately recovering the architecture of neuronal networks, this project will investigate how the sparse structure of natural stimuli impacts the early development of neuronal connectivity and what functional implication this has in the encoding of diverse classes of sensory signals. Analyzing the neuronal dynamics that optimally encode network connectivity and stimulus information, this project will provide new insights into sensory processing and abnormal brain function. In formulating novel methodologies for processing dynamic network data, this project will inform advances in artificial intelligence and prosthetics. This work will actively involve undergraduate students in all phases of research, promoting interdisciplinary scientific collaboration and deepening the scope of applied mathematics education for a diverse spectrum of students. With the increasing prevalence of network models in the mathematical sciences, accurately measuring network structure and understanding its relationship with network function is of broad scientific importance. In neuroscience in particular, efficiently measuring large-scale brain connectivity and determining its impact on cognitive function is inherently challenging yet fundamental in characterizing the nature of computation in the brain. This project will formulate a novel framework for the reconstruction and characterization of neuronal connectivity by taking advantage of the widespread network sparsity found in the brain and utilizing recent advances in compressive-sensing (CS) theory. Key facets of the project are to: (1) develop a novel CS-based mean-field approach for efficiently reconstructing sparse connections in physiological neuronal networks based on underlying input-output mappings embedded in the nonlinear network dynamics; (2) analyze the role of the balanced network operating regime in CS reconstruction of recurrent network connectivity; (3) investigate the basis for structural motifs in the visual system through supervised learning of neuronal connectivity aimed at optimized compressive encoding of sparse visual stimuli; and (4) characterize the functional role of receptive field structure in the encoding of natural scenes through compressive network dynamics and the manifestation of related deficiencies in processing non-natural scenes, such as illusory images. This work will underline how the network dynamical regime impacts the inference of structural connectivity and network inputs from neuronal dynamics, improving the scale over which neuronal connectivity can be determined and providing novel insights into abnormal information processing in the brain. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.