Ken Miller and Brent Doiron
Columbia University and University of Pittsburgh

The Stabilized Supralinear Network, or, The Importance of Being Loosely Balanced (Miller) / Spatiotemporal profiles of spiking variability in recurrent networks (Doiron)

Tuesday 15th of August 2017 at 12:00pm
560 Evans

Miller: I will describe the Stabilized Supralinear Network mechanism and its application to understanding sensory cortical behavior. The mechanism is based on a network of excitatory (E) and inhibitory (I) neurons with very simple assumptions: (1) Individual neurons have an expansive or supralinear input/output functions, e.g. a power law with power >1; (2) Feedback inhibition is sufficiently strong to drive the network to a stable fixed point for a given stable input. The expansive input/output function leads effective synaptic strengths to grow with network activation. The network then transitions, with increasing external input strength, between two regimes: (1) For weak activation, the network is very weakly coupled, with neuronal input dominated by external input (from outside the network) rather than network input. In this regime, responses to different stimuli sum supralinearly, and hence different stimuli tend to facilitate one another's response. (2) For stronger activation, the network becomes strongly coupled, with input dominated by network input; and recurrent excitation becomes strong enough to potentially create network instability, but the network is stabilized by feedback inhibition. With increasing activation the network input is more and more dominated by inhibitory input.
In this strongly-coupled regime, the network is loosely balanced: the E/I dynamics lead network input to partially cancel external input, so that the net input grows sublinearly as a function of the external input. This turns out to be equivalent to the "balanced network" of Van Vreeswijk and Sompolinsky, but in a regime in which the net input remaining after cancellation is comparable to the components that are cancelled ("loose balance") rather than being negligibly small in comparison ("tight balance"). This makes all the difference for network behavior: whereas tight balance yields network response that is a linear function of external input, loose balance yields nonlinear behaviors that look strikingly like sensory cortical behaviors. These behaviors include "normalization" or sublinear summation of responses to multiple stimuli that becomes linear for weak stimuli and becomes "winner-take-all" for stimuli of strongly unequal strength; and surround suppression that becomes surround facilitation for a weak center stimulus. In addition, whereas tight balance creates an asynchronous regime (without correlations), loose balance allows correlated variability that is gradually quenched by increasingly strong stimuli, as observed across multiple cortical systems. While the network's dynamical behavior will surely grow richer as multiple cell types and other aspects of cortical circuits are modeled, this basic mechanism -- E/I dynamics stabilizing against potential instability by loose balancing of excitatory and inhibitory input -- seems likely to underly many fundamental cortical behaviors.

Doiron: A signature feature of the cortex is the extreme trial-to-trial and temporal variability of neuronal spiking, with shared variability (noise correlations) across a population being low dimensional. Circuit models fail to capture these features, producing either asynchronous high dimensional variability or pathologic synchrony. We combine the attention-mediated decreases and increases of within and between area noise correlations in the visual system to constrain circuit models of cortical variability. Including realistic spatial and temporal profiles of synaptic architecture allow networks of spiking neurons with large recurrent excitation and inhibition to satisfy these constraints. Further, the spatiotemporal profile of inhibition determines the low dimensional nature of population-wide shared variability. Our model is an important bridge between circuit and systems neuroscience, showing how well-established circuit structure can explain previously mysterious aspects of population dynamics.

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