Topic: mean-field theory

Networks of interconnected neurons display diverse patterns of activity. Relating these patterns to the structure of the network is a central goal of theoretical neuroscience. Classic neural field and rate models have been powerful tools for this purpose due to their analytical tractability. Here, we show that the recently-developed combinatorial threshold-linear 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

Neuronal computation is mediated by spikes, yet it is unclear what the benefits of discrete spiking dynamics over continuous firing rates are. Many theoretical and computational studies treat single neurons as continuous units and their output as an effective firing rate. These works view spiking dynamics as a biophysical constraint, e.g., for energy efficiency. Conversely, other theories suggest that the exact timings of single spikes are meaningful. We propose a novel theory that shows the benefits of spiking dynamics on neural computation. In particular, we show that spiking neural dynamics

Cortical excitatory (E) neurons exhibit clear tuning to stimulus features, but the tuning properties of inhibitory interneurons remain ambiguous. While inhibitory neurons are traditionally viewed as functionally and structurally untuned [1-4], recent studies indicate that parvalbumin-expressing (PV) neurons do show feature selectivity and establish co-tuned reciprocal connections with individual pyramidal neurons at a pairwise level [5-7]. Using mean-field theory and large-scale network simulations of spiking cells (Fig. 1A), we reconcile these seemingly contradictory findings by demonstrating

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