We also discuss the emergence of metastability as a stochastic bifurcation, which can be interpreted as a static phase transition in the RMF limits. Importantly, we find that these rates specify probabilistic pseudo-equilibria which accurately capture the neural variability observed in the original finite-size network. We solve this original problem by combining the resolvent formalism and singular-perturbation theory. Technically, these stationary rates are determined as the solutions of a set of delayed differential equations under certain regularity conditions that any physical solutions shall satisfy. Within this setting, we show that metastable finite-size networks admit multistable RMF limits, which are fully characterized by stationary firing rates. Here, we extend the RMF computational framework to point-process-based neural network models with exponential stochastic intensities, allowing for mixed excitation and inhibition. However, metastable dynamics typically unfold in networks with mixed inhibition and excitation. Such randomization renders certain excitatory networks fully tractable at the cost of neglecting activity correlations, but with explicit dependence on the finite size of the neural constituents. In this limit, networks are made of infinitely many replicas of the finite network of interest, but with randomized interactions across replicas. We propose to address this challenge in the recently introduced replica-mean-field (RMF) limit. Characterizing metastable neural dynamics in finite-size spiking networks remains a daunting challenge.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |