Abstract

Cortical networks feature strong recurrent excitation, posing them near potential instability. By and large, models of cortical dynamics have relied on single neuronal saturation to overcome such instability. However, throughout the cortical dynamic range, neurons’ activity tends to remain well below their saturation levels, and correspondingly their empirically measured input-output functions remain convex and supralinear. Such expansive nonlinearities at first appear to aggravate the problem of stability. Nevertheless we have recently shown that strong recurrent inhibition is sufficient to stabilize cortical networks against runaway excitation, without relying on single neuronal saturation (Ahmadian et al. 2013, Rubin et al. 2015). Moreover, as a consequence, such Stabilized Supralinear Networks (SSN) provide a robust and parsimonious mechanistic explanation for a plethora of contextual modulation phenomena observed across sensory cortical areas. These include surround suppression and divisive normalization, recently dubbed a canonical brain computation (Carandini & Heeger, 2011).

In this talk I will first review these published results. In the second half, I will focus on ongoing work using the SSN to model aspects of time-dependent cortical dynamics. Gamma rhythms are a robust feature of cortical dynamics, and have been hypothesized to play a central role in various cognitive tasks. Gamma rhythm characteristics such as their power and peak frequency, however, exhibit strong dependencies on stimulus and contextual parameters (it has in turn been argued that such dependencies may invalidate some hypothesized computational functions for gamma). I will describe how SSN is able to robustly account for such modulations in gamma characteristics. In particular, I will show how the model explains the particular dependence of gamma peak frequency on local stimulus contrast and stimulus size observed in the visual cortex. Time allowing, I will also elaborate on two possible mechanisms for attentional modulation of rates in SSN , which lead to opposite effects on gamma power, as observed, respectively, in V1 vs. higher visual cortical areas.