ATS and LT are corresponding authors.Abstract-Recent evidence suggests that neural information is encoded in packets and may be flexibly routed from region to region. We have hypothesized that neural circuits are split into sub-circuits where one sub-circuit controls information propagation via pulse gating and a second sub-circuit processes graded information under the control of the first sub-circuit. Using an explicit pulse-gating mechanism, we have been able to show how information may be processed by such pulsecontrolled circuits and also how, by allowing the information processing circuit to interact with the gating circuit, decisions can be made. Here, we demonstrate how Hebbian plasticity may be used to supplement our pulse-gated information processing framework by implementing a machine learning algorithm. The resulting neural circuit has a number of structures that are similar to biological neural systems, including a layered structure and information propagation driven by oscillatory gating with a complex frequency spectrum.
How the connectivity of cortical networks determines the neural dynamics and the resulting computations is one of the key questions in neuroscience. Previous works have pursued two complementary strategies to quantify the structure in connectivity, by specifying either the local statistics of connectivity motifs between small groups of neurons, or by defining network-wide low-rank patterns of connectivity that determine the resulting low-dimensional dynamics. A direct relationship between these two approaches is however currently missing,
and in particular it remains to be clarified how local connectivity statistics are related to the global connectivity structure and shape the low-dimensional activity. To bridge this gap, here we develop a method for mapping local connectivity statistics onto an approximate global low-rank structure. Our method rests on approximating the global connectivity matrix using dominant eigenvectors, which we compute using perturbation theory for random matrices. This approach demonstrates that multi-population networks defined from local connectivity properties can in general be approximated by low-rank connectivity with Gaussian-mixture statistics. We specifically apply this method to excitatory-inhibitory networks, and show that it leads to accurate predictions for both the low-dimensional dynamics, and for the activity of individual neurons. Altogether, our approach allows us to disentangle the effects of mean connectivity and reciprocal motifs on the global recurrent feedback, and provides an intuitive picture of how local connectivity shapes global network dynamics.
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