Exact statistical physics models of large-scale neural activity with loops

As experiments advance to record from large populations of neurons, statistical physics provides a framework for understanding how collective activity emerges from networks of fine-scale correlations. If these networks do not have loops, then many statistical physics problems become tractable, and one can construct models of very large systems. Yet in the brain, neurons cluster together into functional units, making loops an integral feature of neural circuitry. Here, for a class of networks with loops, we solve the maximum entropy problem exactly and efficiently. Moreover, we present a greedy algorithm to search for the optimal network of correlations that provides the most information about the population activity. We use this approach to analyze experiments on over 10,000 neurons in the mouse visual system, demonstrating that feedback loops play a critical role in understanding large-scale neuronal activity.