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

Martí, Daniel; Brunel, Nicolas; Ostojic, Srdjan

doi:10.1103/physreve.97.062314

Cited by 63 publications

(95 citation statements)

References 69 publications

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“…the fact that the left-and right-eigenvectors of the connectivity matrix are not identical (Trefethen et al, 1993). A number of recent studies in theoretical neuroscience have pointed out the interesting dynamical properties of networks with non-normal connectivity (White et al, 2004;Ganguli et al, 2008;Murphy and Miller, 2009;Goldman, 2009;Hennequin et al, 2012Hennequin et al, , 2014Ahmadian et al, 2015;Martí et al, 2018). Several of these works (Murphy and Miller, 2009;Hennequin et al, 2012Hennequin et al, , 2014Ahmadian et al, 2015) have examined the amplification of the norm of the activity vector, as we do here.…”

Section: Discussionmentioning

confidence: 92%

Coding with transient trajectories in recurrent neural networks

Bondanelli

Ostojic

2020

PLoS Comput Biol

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Following a stimulus, the neural response typically strongly varies in time and across neurons before settling to a steady-state. While classical population coding theory disregards the temporal dimension, recent works have argued that trajectories of transient activity can be particularly informative about stimulus identity and may form the basis of computations through dynamics. Yet the dynamical mechanisms needed to generate a population code based on transient trajectories have not been fully elucidated. Here we examine transient coding in a broad class of high-dimensional linear networks of recurrently connected units. We start by reviewing a well-known result that leads to a distinction between two classes of networks: networks in which all inputs lead to weak, decaying transients, and networks in which specific inputs elicit strongly amplified transient responses and are mapped onto orthogonal output states during the dynamics. Theses two classes are simply distinguished based on the spectrum of the symmetric part of the connectivity matrix. For the second class of networks, which is a sub-class of non-normal networks, we provide a procedure to identify transiently amplified inputs and the corresponding readouts. We first apply these results to standard randomly-connected and two-population networks. We then build minimal, low-rank networks that robustly implement trajectories mapping a specific input onto a specific output state. Finally, we demonstrate that the capacity of the obtained networks increases proportionally with their size. Significance statementClassical theories of sensory coding consider the neural activity following a stimulus as constant in time. Recent works have however suggested that the temporal variations following the appearance and disappearance of a stimulus are strongly informative. Yet their dynamical origin remains little understood. Here we show that strong temporal variations in response to a stimulus can be generated by collective interactions within a network of neurons if the connectivity between neurons satisfies a simple mathematical criterion. We moreover determine the relationship between connectivity and the stimuli that are represented in the most informative manner by the variations of activity, and estimate the number of different stimuli a given network can encode using temporal variations of neural activity.

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Section: Discussionmentioning

confidence: 92%

Coding with transient trajectories in recurrent neural networks

Bondanelli

Ostojic

2020

PLoS Comput Biol

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“…Another possibility is that non-random features of the connectivity, such as the over-representation of reciprocal connections [65,66] slow down the dynamics away from any bifurcation. A recent study [67] has indeed found such a slowing-down. Weak connectivity structure of low-rank type provides yet another mechanism for the emergence of long timescales.…”

Section: Discussionmentioning

confidence: 78%

Contrasting the effects of adaptation and synaptic filtering on the timescales of dynamics in recurrent networks

Beirán

Ostojic

2019

PLoS Comput Biol

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Neural activity in awake behaving animals exhibits a vast range of timescales that can be several fold larger than the membrane time constant of individual neurons. Two types of mechanisms have been proposed to explain this conundrum. One possibility is that large timescales are generated by a network mechanism based on positive feedback, but this hypothesis requires fine-tuning of the strength or structure of the synaptic connections. A second possibility is that large timescales in the neural dynamics are inherited from large timescales of underlying biophysical processes, two prominent candidates being intrinsic adaptive ionic currents and synaptic transmission. How the timescales of adaptation or synaptic transmission influence the timescale of the network dynamics has however not been fully explored. To address this question, here we analyze large networks of randomly connected excitatory and inhibitory units with additional degrees of freedom that correspond to adaptation or synaptic filtering. We determine the fixed points of the systems, their stability to perturbations and the corresponding dynamical timescales. Furthermore, we apply dynamical mean field theory to study the temporal statistics of the activity in the fluctuating regime, and examine how the adaptation and synaptic timescales transfer from individual units to the whole population. Our overarching finding is that synaptic filtering and adaptation in single neurons have very different effects at the network level. Unexpectedly, the macroscopic network dynamics do not inherit the large timescale present in adaptive currents. In contrast, the timescales of network activity increase proportionally to the time constant of the synaptic filter. Altogether, our study demonstrates that the timescales of different biophysical processes have different effects on the network level, so that the slow processes within individual neurons do not necessarily induce slow activity in large recurrent neural networks.

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“…Contemporarily, the pivotal role of overlaps is understood in the simplest case of the evolution of complex Ginibre matrix -either in Smoluchowski-Fokker-Planck formalism [7,8] or in Langevin formalism [9], following the pioneering paper [10,11]. The effects of the overlaps of the Ginibre matrix for the temporal autocorrelation function of randomly connected networks was addressed analytically in the latest paper [5], confirming the numerical simulations in the weakly coupled regime of synaptic models.…”

Section: Introductionmentioning

confidence: 69%

“…In particular, the work of Marti et. al [5] shows that increasing the symmetry of the connectivity leads to a systematic slowing-down of the dynamics and vice versa, decreasing the symmetry of the matrix leads to the speeding of the dynamics. This non-normality of the matrix not only forces matrices to have complex spectrum (which challenges several traditional tools of random matrix theory), but more importantly, its study sheds new light on the role of Bell-Steinberger [6] matrix of overlaps between the left and right eigenvectors of the connectivity matrix.…”

Section: Introductionmentioning

confidence: 99%

From Synaptic Interactions to Collective Dynamics in Random Neuronal Networks Models: Critical Role of Eigenvectors and Transient Behavior

Gudowska–Nowak

Nowak

Chialvo³

et al. 2020

Neural Computation

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The study of neuronal interactions is currently at the center of several neuroscience big collaborative projects (including the Human Connectome, the Blue Brain, the Brainome, etc.) which attempt to obtain a detailed map of the entire brain matrix. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of such synaptic interaction matrix. This work explores the application of free random variables (FRV) to the study of large synaptic interaction matrices. Besides recovering in a straightforward way known results on eigenspectra of neural networks, we extend them to heavy-tailed distributions of interactions. More importantly, we derive analytically the behavior of eigenvector overlaps, which determine stability of the spectra. We observe that upon imposing the neuronal excitation/inhibition balance, although the eigenvalues remain unchanged, their stability dramatically decreases due to strong non-orthogonality of associated eigenvectors. It leads us to the conclusion that the understanding of the temporal evolution of asymmetric neural networks requires considering the entangled dynamics of both eigenvectors and eigenvalues, which might bear consequences for learning and memory processes in these models. Considering the success of FRV analysis in a wide variety of branches disciplines, we hope that the results presented here foster additional application of these ideas in the area of brain sciences.Recently, the two-point function associated with off-diagonal elements of the overlap matrix has become accessible within free probability [35].

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

Cited by 63 publications

References 69 publications

Coding with transient trajectories in recurrent neural networks

Coding with transient trajectories in recurrent neural networks

Contrasting the effects of adaptation and synaptic filtering on the timescales of dynamics in recurrent networks

From Synaptic Interactions to Collective Dynamics in Random Neuronal Networks Models: Critical Role of Eigenvectors and Transient Behavior

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