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Determining the structure of a network is of central importance to understanding its function in both neuroscience and applied mathematics. However, recovering the structural connectivity of neuronal networks remains a fundamental challenge both theoretically and experimentally. While neuronal networks operate in certain dynamical regimes, which may influence their connectivity reconstruction, there is widespread experimental evidence of a balanced neuronal operating state in which strong excitatory and inhibitory inputs are dynamically adjusted such that neuronal voltages primarily remain near resting potential. Utilizing the dynamics of model neurons in such a balanced regime in conjunction with the ubiquitous sparse connectivity structure of neuronal networks, we develop a compressive sensing theoretical framework for efficiently reconstructing network connections by measuring individual neuronal activity in response to a relatively small ensemble of random stimuli injected over a short time scale. By tuning the network dynamical regime, we determine that the highest fidelity reconstructions are achievable in the balanced state. We hypothesize the balanced dynamics observed  in vivo  may therefore be a result of evolutionary selection for optimal information encoding and expect the methodology developed to be generalizable for alternative model networks as well as experimental paradigms.

Compressive Sensing Inference of Neuronal Network Connectivity in Balanced Neuronal Dynamics