Speaker
Description
Ring models are widely used in neuroscience to study fundamental mechanisms such as response sharpening and working memory. Ring networks composed of spiking neurons in the balanced state can reliably reproduce the irregular activity observed in vivo and exhibit phenomena like response sharpening through local inhibition and feature tuning emerging in random networks. In principle, balanced ring networks can be analyzed using powerful mean-field theory that captures even heterogeneous response profiles, but this approach has so far been applied only to binary networks and remains technically demanding.
Here, we present a class of analytically tractable spiking balanced ring models that allow for a rigorous dissection of response tuning mechanisms. We analyze networks with both cosine- and von Mises–shaped connectivity and input. In the von Mises case, the mean population activity profile is derived analytically as an infinite series of Bessel functions. This profile directly follows from the balance condition and is shown to be independent of the single-neuron model and intrinsic heterogeneity.
In contrast, for the cosine-tuned network—a limiting case of von Mises tuning—the balance equation alone is insufficient. Instead, the population profile depends on a set of self-consistency equations for the moments of the firing rate distribution, which we derive in closed form. We provide accurate approximate solutions and show how they determine the full distribution of heterogeneous tuning curves across the network. Our results strongly suggest that the population response profile is universal with respect to many biophysical parameters and specific neuron model properties.
