Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks

Abstract

Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness found in experimental data being the overrepresentation of bidirectional connections among pyramidal cells. Using numerical and analytical methods, we investigated the effects of partially symmetric connectivity on dynamics in networks of rate units. We considered the two dynamical regimes exhibited by random neural networks: the weak-coupling regime, where the firing activity decays to a single fixed point unless the network is stimulated, and the strong-coupling or chaotic regime, characterized by internally generated fluctuating firing rates. In the weak-coupling regime, we computed analytically for an arbitrary degree of symmetry the auto-correlation of network activity in presence of external noise. In the chaotic regime, we performed simulations to determine the timescale of the intrinsic fluctuations. In both cases, symmetry increases the characteristic asymptotic decay time of the autocorrelation function and therefore slows down the dynamics in the network.

17 pages, 7 figures

References in corpus (5)

• Transition to chaos in random networks with cell-type-specific connectivity
• Topological and Dynamical Complexity of Random Neural Networks
• Dynamics of Random Neural Networks with Bistable Units
• Nonnormal amplification in random balanced neuronal networks
• Eigenvalue spectra of large correlated random matrices

Cited by in corpus (37)

• Dimension of activity in random neural networks
• Contrasting the effects of adaptation and synaptic filtering on the timescales of dynamics in recurrent networks
• Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
• Condition numbers for real eigenvalues in the real Elliptic Gaussian ensemble
• Transient chaotic dimensionality expansion by recurrent networks
• Universal transient behavior in large dynamical systems on networks
• Localization and universality of eigenvectors in directed random graphs
• Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations
• From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior
• Unified field theoretical approach to deep and recurrent neuronal networks
• Large Deviations Approach to Random Recurrent Neuronal Networks: Parameter Inference and Fluctuation-Induced Transitions
• Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
• Self-consistent formulations for stochastic nonlinear neuronal dynamics
• Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings
• Spectrum of non-Hermitian deep-Hebbian neural networks
• Power law decay for systems of randomly coupled differential equations
• Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World
• Analytic relationship of relative synchronizability to network structure and motifs
• Nonreciprocal Spin-Glass Transition and Aging
• Volcano transition in populations of phase oscillators with random nonreciprocal interactions
• Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model
• Gating creates slow modes and controls phase-space complexity in GRUs and LSTMs
• An optimization-based equilibrium measure describes non-equilibrium steady state dynamics: application to edge of chaos
• Dynamical Theory for Adaptive Systems
• Effect of Synaptic Heterogeneity on Neuronal Coordination
• Spontaneous and stimulus-induced coherent states of critically balanced neuronal networks
• Different eigenvalue distributions encode the same temporal tasks in recurrent neural networks
• Discontinuous transition to chaos in a canonical random neural network
• Irreversibility in Non-reciprocal Chaotic Systems
• Neuronal correlations shape the scaling behavior of memory capacity and nonlinear computational capability of reservoir recurrent neural networks
• Random matrix ensemble for the covariance matrix of Ornstein-Uhlenbeck processes with heterogeneous temperatures
• Phase transitions in in vivo or in vitro populations of spiking neurons belong to different universality classes
• Bifurcations of a neural network model with symmetry
• Hydrodynamics of Cooperation and Self-Interest in a Two-Population Occupation Model
• Learning recurrent dynamics in spiking networks
• A geometrical analysis of global stability in trained feedback networks
• Zero-temperature dynamics of the spherical model with non-reciprocal interactions