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Metastable spiking networks in the replica-mean-field limit
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
Abstract
- Characterizing metastable neural dynamics in finite-size spiking networks remains a daunting challenge. We propose to address this challenge in the recently introduced replica-mean-field (RMF) limit. In this limit, networks are made of infinitely many replicas of the finite network of interest, but with randomized interactions across replicas. 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. However, metastable dynamics typically unfold in networks with mixed inhibition and excitation. Here, we extend the RMF computational framework to point-process-based neural network models with exponential stochastic intensities, allowing for mixed excitation and inhibition. Within this setting, we show that metastable finite-size networks admit multistable RMF limits, which are fully characterized by stationary firing rates. 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. We solve this original problem by combining the resolvent formalism and singular-perturbation theory. Importantly, we find that these rates specify probabilistic pseudo-equilibria which accurately capture the neural variability observed in the original finite-size network. We also discuss the emergence of metastability as a stochastic bifurcation, which can be interpreted as a static phase transition in the RMF limits. In turn, we expect to leverage the static picture of RMF limits to infer purely dynamical features of metastable finite-size networks, such as the transition rates between pseudo-equilibria.<br />Comment: 40 pages, 14 figures
- Subjects :
- Neurons
Ecology
Models, Neurological
Action Potentials
FOS: Physical sciences
Cellular and Molecular Neuroscience
Computational Theory and Mathematics
Biological Physics (physics.bio-ph)
Quantitative Biology - Neurons and Cognition
Modeling and Simulation
FOS: Biological sciences
Genetics
Neurons and Cognition (q-bio.NC)
Physics - Biological Physics
Neural Networks, Computer
Nerve Net
Molecular Biology
Ecology, Evolution, Behavior and Systematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....bc2f471994113c0a26ce4114bb1d81f0
- Full Text :
- https://doi.org/10.48550/arxiv.2105.01223