Mean-field theory

…network (CTLN) model is a mean-field theory for excitatory-inhibitory Hawkes networks, with clustered connectivity, in an inhibition-stabilized regime. This mapping allows us to leverage powerful analytical results for CTLN networks

Networks of interconnected neurons display diverse patterns of collective spiking activity. Relating this collective activity to the network's connectivity structure is a key goal of computational neuroscience. We approach this question for clustered networks, which can form via biologically realistic learning rules and allow for the re-activation of previously evoked patterns. Previous studies of clustered networks have focused on metastabilty between fixed points corresponding to individual clusters, leaving open the question of whether clustered spiking networks can display more rich dyna

…studied its dynamics by means of the mean-field theory and simulations. Our analysis uncovered a rich phase diagram: High-dimensional chaotic activity (microscopic chaos), common in homogeneous networks, is separated from the low-dimensional chaotic activity of strongly coherent modules (macroscop

The critical brain hypothesis proposes that neural networks operate near criticality to reap the computational benefits of accessing a wide range of timescales [1]. Proponents of this viewpoint highlight the presence of heavy-tailed (power-law) spatiotemporal correlations as markers of criticality in the brain [2]. Critics of this hypothesis argue that such correlations could be inherited from upstream sources, such as sensory input [3]. Similarly, Ref. [4] constructed a model of independent neurons driven by shared noise input that exhibited neural activity with power-law tails, which could b

…Using mean-field theory and large-scale network simulations of spiking cells (Fig. 1A), we reconcile these seemingly contradictory findings by demonstrating

A neuron’s input-output function is a central component of network dynamics and is commonly understood in terms of two fundamental operating regimes: 1) the mean-driven regime where the mean input drives regular and frequent firing, and 2) the fluctuation-driven regime where input fluctuations drive responses at relatively low firing frequency but with variable intervals. Active dendrites are expected to profoundly influence the input-output function by either controlling gain modulation or through the additive modulation by dendritic inputs that have been transformed nonlinearly as in an arti

…We propose a novel theory that shows the benefits of spiking dynamics on neural computation. In particular, we show that spiking neural dynamics

Behavioral states in humans and animals vary over time, and these shifts alter cortical processing and cognitive function. For example, one striking result is an observed inverted-U relationship between arousal and performance on signal detection tasks. However, there is currently a need for mechanistic models that can explain these state-dependent effects. Here we address this challenge in the context of arousal-dependent auditory processing in rodents. In experiments where mice were presented tones of different frequencies, we found that frequency information could be best decoded from popu