# Complete Mean-Field Theory for Dynamics of Binary Recurrent Networks.

@article{Farkhooi2017CompleteMT, title={Complete Mean-Field Theory for Dynamics of Binary Recurrent Networks.}, author={Farzad Farkhooi and Wilhelm Stannat}, journal={Physical review letters}, year={2017}, volume={119 20}, pages={ 208301 } }

We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description of nonequilibrium fluctuations in networks with a finite size and finite degree of interactions. Our approach allows the investigation of systems for which a deterministic mean-field theory breaks down. To demonstrate this, we uncover a novel dynamic state in…

## 12 Citations

Ubiquity of collective irregular dynamics in balanced networks of spiking neurons

- PhysicsbioRxiv
- 2018

A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition prevails, the asymptotic regime is not asynchronous but rather characterized by a self-sustained irregular, macroscopic (collective) dynamics.

Ubiquity of collective irregular dynamics in balanced networks of spiking neurons.

- PhysicsChaos
- 2018

A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition prevails, the asymptotic regime is not asynchronous but rather characterized by a self-sustained irregular, macroscopic (collective) dynamics.

Mean-field Approximation for Stochastic Population Processes in Networks under Imperfect Information

- Mathematics, Computer ScienceArXiv
- 2021

General conditions on the network and policy dynamics for which a suitable mean-field approximation exists are provided and it is shown that as long as the network is well-connected, the macroscopic behavior of the population concentrates around the same mean- field system as the complete-graph case.

Mean Field Limits for Interacting Diffusions in a Two-Scale Potential

- MathematicsJ. Nonlinear Sci.
- 2018

It is shown that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit.

Dynamics of the Desai-Zwanzig model in multiwell and random energy landscapes.

- PhysicsPhysical review. E
- 2019

The structure and nature of bifurcations and phase transitions for this system of weakly interacting diffusions moving in a multiwell potential energy landscape, coupled via a Curie-Weiss type (quadratic) interaction potential are characterized.

A CHARACTERIZATION OF THE EDGE OF CRITICALITY IN BINARY ECHO STATE NETWORKS

- Computer Science2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)
- 2018

Binary ESNs are proposed, which are architecturally equivalent to standard ESNs but consider binary activation functions and binary recurrent weights, and a theoretical explanation for the fact that the variance of the input plays a major role in characterizing the EoC.

Spatial and temporal correlations in neural networks with structured connectivity

- Physics, Psychology
- 2022

Correlated ﬂuctuations in the activity of neural populations reﬂect the network’s dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. How-ever,…

Chaotic neural circuit dynamics

- Biology
- 2017

Novel numerical and analytical techniques from dynamical systems, stochastic processes and information theory are developed to characterize the evoked and spontaneous dynamics and phase space organization of large neural circuit models to determine how biophysical properties of neurons and network parameters influence information transmission.

Unfolding recurrence by Green's functions for optimized reservoir computing

- Computer ScienceNeurIPS
- 2020

The purpose of this work is to present a solvable recurrent network model that links to feed forward networks and transforms the time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels.

Mean Field Limits for Interacting Diffusions with Colored Noise: Phase Transitions and Spectral Numerical Methods

- Mathematics, PhysicsMultiscale Model. Simul.
- 2020

The spectral method that is developed in this paper can be used for solving linear and nonlinear, local and nonlocal (mean-field) Fokker-Planck equations, without requiring that they have a gradient structure.

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