Abstract
Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in networks of deterministic, but randomly connected rate units. How this type of intrinsically generated fluctuations appears in more realistic networks of spiking neurons has been a long standing question. To ease the comparison between rate and spiking networks, recent works investigated the dynamical regimes of randomly-connected rate networks with segregated excitatory and inhibitory populations, and firing rates constrained to be positive. These works derived general dynamical mean field (DMF) equations describing the fluctuating dynamics, but solved these equations only in the case of purely inhibitory networks. Using a simplified excitatory-inhibitory architecture in which DMF equations are more easily tractable, here we show that the presence of excitation qualitatively modifies the fluctuating activity compared to purely inhibitory networks. In presence of excitation, intrinsically generated fluctuations induce a strong increase in mean firing rates, a phenomenon that is much weaker in purely inhibitory networks. Excitation moreover induces two different fluctuating regimes: for moderate overall coupling, recurrent inhibition is sufficient to stabilize fluctuations; for strong coupling, firing rates are stabilized solely by the upper bound imposed on activity, even if inhibition is stronger than excitation. These results extend to more general network architectures, and to rate networks receiving noisy inputs mimicking spiking activity. Finally, we show that signatures of the second dynamical regime appear in networks of integrate-and-fire neurons.
Highlights
Networks of excitatory and inhibitory neurons form the basic processing units in the cortex
We find that in presence of excitation, the coupling between mean and the auto-correlation of the activity leads to a strong increase of mean firing rates in the fluctuating regime [19], a phenomenon that is much weaker in purely inhibitory networks
In order to isolate the two contributions, we examined how the amplitude of fluctuating activity depends on the upper bound on firing rates φmax
Summary
Networks of excitatory and inhibitory neurons form the basic processing units in the cortex. The network displays a state in which the firing rates fluctuate strongly in time and across units, the dynamics are fully deterministic and there are no external inputs. Several works showed that the randomly connected rate network is able to learn complex temporal dynamics and input-output associations [6,7,8]. These computational properties may be related to the appearance of an exponential number of unstable fixed points at the transition [9], and to the fact that dynamics are slow and the signal-to-noise ratio maximal [10]
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