Geometry of population activity in spiking networks with low-rank structure

Recurrent network models are instrumental in investigating how behaviorally-relevant computations emerge from collective neural dynamics. A recently developed class of models based on low-rank connectivity provides an analytically tractable framework for understanding of how connectivity structure determines the geometry of low-dimensional dynamics and the ensuing computations. Such models however lack some fundamental biological constraints, and in particular represent individual neurons in terms of abstract units that communicate through continuous firing rates rather than discrete action potentials. Here we examine how far the theoretical insights obtained from low-rank rate networks transfer to more biologically plausible networks of spiking neurons. Adding a low-rank structure on top of random excitatory-inhibitory connectivity, we systematically compare the geometry of activity in networks of integrate-and-fire neurons to rate networks with statistically equivalent low-rank connectivity. We show that the mean-field predictions of rate networks allow us to identify low-dimensional dynamics at constant population-average activity in spiking networks, as well as novel non-linear regimes of activity such as out-of-phase oscillations and slow manifolds. We finally exploit these results to directly build spiking networks that perform nonlinear computations.Author summary: Behaviorally relevant information processing is believed to emerge from interactions among neurons forming networks in the brain, and computational modeling is an important approach for understanding this process. Models of neuronal networks have been developed at different levels of detail, with typically a trade off between analytic tractability and biological realism. The relation between network connectivity, dynamics and computations is best understood in abstract models where individual neurons are represented as simplified units with continuous firing activity. Here we examine how far the results obtained in an analytically-tractable class of rate models extend to more biologically realistic spiking networks where neurons interact through discrete action potentials. Our results show that abstract rate models provide accurate predictions for the collective dynamics and the resulting computations in more biologically faithful spiking networks.