Nonnormal amplification in random balanced neuronal networks

Abstract

In dynamical models of cortical networks, the recurrent connectivity can amplify the input given to the network in two distinct ways. One is induced by the presence of near-critical eigenvalues in the connectivity matrix W, producing large but slow activity fluctuations along the corresponding eigenvectors (dynamical slowing). The other relies on W being nonnormal, which allows the network activity to make large but fast excursions along specific directions. Here we investigate the tradeoff between nonnormal amplification and dynamical slowing in the spontaneous activity of large random neuronal networks composed of excitatory and inhibitory neurons. We use a Schur decomposition of W to separate the two amplification mechanisms. Assuming linear stochastic dynamics, we derive an exact expression for the expected amount of purely nonnormal amplification. We find that amplification is very limited if dynamical slowing must be kept weak. We conclude that, to achieve strong transient amplification with little slowing, the connectivity must be structured. We show that unidirectional connections between neurons of the same type together with reciprocal connections between neurons of different types, allow for amplification already in the fast dynamical regime. Finally, our results also shed light on the differences between balanced networks in which inhibition exactly cancels excitation, and those where inhibition dominates.

13 pages, 7 figures

References in corpus (4)

• Scale-free brain functional networks
• Spectra and eigenvectors of scale-free networks
• Enhancing neural-network performance via assortativity
• Small-world spectra in mean field theory

Cited by in corpus (22)

• Non-Hermitian Physics
• Non-reciprocal phase transitions
• Full-density multi-scale account of structure and dynamics of macaque visual cortex
• Intrinsically-generated fluctuating activity in excitatory-inhibitory networks
• Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks
• Spectral Theory of Sparse Non-Hermitian Random Matrices
• Feedback Between Motion and Sensation Provides Nonlinear Boost in Run-and-tumble Navigation
• Topological resilience in non-normal networked systems
• Network structural origin of instabilities in large complex systems
• Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
• Transient chaotic dimensionality expansion by recurrent networks
• The Efficiency of Synchronization Dynamics and the Role of Network Syncreactivity
• From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior
• Broken detailed balance and entropy production in directed networks
• Non-normal Recurrent Neural Network (nnRNN): learning long time dependencies while improving expressivity with transient dynamics
• Non-normality and non-monotonic dynamics in complex reaction networks
• Power law decay for systems of randomly coupled differential equations
• Non normal amplification of stochastic quasi-cycles
• Balanced condition in networks leads to Weibull statistics
• Interplay of inhibition and multiplexing : Largest eigenvalue statistics
• Condition numbers for real eigenvalues of real elliptic ensemble: weak non-normality at the edge
• Hierarchical route to the emergence of leader nodes in real-world networks