Unifying mechanistic and functional models of cortical circuits with low-rank, E/I-balanced spiking networks

Network models are often designed to capture selective aspects of cortical circuits. On one end, mechanistic models such as balanced spiking networks resemble activity regimes observed in data, but are often limited to simple computations. On the other end, functional models like trained deep networks can show comparable performance and dynamical motifs, but are far removed from experimental physiology. Here, we put forth a new framework for excitatory-inhibitory spiking networks which retains key properties of both mechanistic and functional models. Based on previous studies of the geometry of spike-coding networks, we consider a population of spiking neurons with low-rank connectivity, allowing each neuron’s threshold to be cast as a boundary in a space of population modes, or latent variables. Each neuron’s boundary divides this latent space into subthreshold and suprathreshold areas, which determines its contribution to the input-output function of the network. Then, incorporating Dale’s law as a connectivity constraint, we demonstrate how a network of inhibitory (I) neurons forms a convex, stable boundary in the latent coding space, and a network of excitatory (E) neurons forms a concave, unstable boundary. Finally, we show how the combination of the two yields stable dynamics at the crossing of the E and I boundaries. The resultant E/I networks are balanced, inhibition-stabilized, and exhibit asynchronous irregular activity, thereby closely resembling cortical dynamics. Moreover, the latent variables can be mapped onto a constrained optimization problem, and are capable of universal function approximation. The combination of these dynamical and functional properties leads to unique insights, including specified computational roles for E/I balance and Dale’s law. Finally, the intuitive geometry of the representations, plus the link to constrained optimization, makes our framework a promising candidate for scalable and interpretable computation in biologically-plausible spiking networks.