Metastable spiking networks in the replica-mean-field limit

Area of Science:

• Computational Neuroscience
• Theoretical Neuroscience
• Complex Systems

Background:

• Characterizing metastable dynamics in finite-size spiking neural networks is challenging.
• Existing replica-mean-field (RMF) methods are limited to excitatory networks and neglect correlations.

Purpose of the Study:

• Extend the RMF framework to analyze metastable dynamics in finite-size networks with mixed excitation and inhibition.
• Develop a tractable computational approach for complex neural systems.

Main Methods:

• Extended RMF to point-process neural network models with exponential stochastic intensities.
• Utilized resolvent formalism and singular-perturbation theory to solve delayed differential equations.
• Analyzed stationary firing rates to characterize multistable RMF limits.

Main Results:

• Metastable finite-size networks admit multistable RMF limits characterized by stationary firing rates.
• These rates define probabilistic pseudo-equilibria that accurately reflect neural variability.
• Identified metastability as a stochastic bifurcation, analogous to a static phase transition.

Conclusions:

• The extended RMF framework provides a powerful tool for studying metastable dynamics in biologically realistic neural networks.
• The static picture of RMF limits can infer dynamical features like transition rates between pseudo-equilibria.
• This work offers new insights into the stability and variability of neural activity.