Strength of Correlations in Strongly Recurrent Neuronal Networks

Darshan, Ran; Vreeswijk, Carl van; Hansel, David

doi:10.1103/physrevx.8.031072

Cited by 41 publications

(60 citation statements)

References 67 publications

(127 reference statements)

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“…For example, in a two-dimensional balanced network with slow inhibitory kinetics, shared fluctuations arise from instability at some spatial frequency that generates rate chaos 24 . Similarly, in a one-dimensional balanced ring model, strong correlations arise from a feed-forward structure in some Fourier modes of connectivity 40 . However, in these models correlations arise from fluctuations around a global fixed point with a timescale defined by the mismatch between excitatory and inhibitory synaptic time-constants, i.e.…”

Section: Discussionmentioning

confidence: 99%

Influence of On-Off dynamics and selective attention on the spatial pattern of correlated variability in neocortex

Shi

Steinmetz

Moore

et al. 2020

Preprint

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Correlated activity fluctuations in neocortex influence sensory responses and behavior. Neural correlations reflect anatomical connectivity and change dynamically with cognitive states, such as attention. Yet, how anatomical connectivity and cognitive states define the population structure of correlations is not known. We measured correlations in single cortical columns and found that the magnitude of correlations, their attentional modulation and dependence on lateral distance are predicted by On-Off dynamics, synchronous fluctuations in population activity across cortical layers. We developed a network model, in which spatial connectivity correlates the On-Off dynamics across nearby columns. We show that attentional inputs modulate the spatial extent of On-Off dynamics, resulting in spatially non-uniform changes in correlations. We confirm this prediction in our columnar recordings by showing that attentional modulation of correlations depends on lateral distance. Our results reveal how heterogeneous spatial patterns of correlations arise from the connectivity and network dynamics during attention.

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Section: Discussionmentioning

confidence: 99%

Influence of On-Off dynamics and selective attention on the spatial pattern of correlated variability in neocortex

Shi

Steinmetz

Moore

et al. 2020

Preprint

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“…In order to achieve this it is necessary that the structured component embed an effectively-feedforward projection between a pair of orthogonal modes. In parallel, Darshan et al [5] have developed a theory for internally generated correlations 525 in excitation-inhibition networks of binary units. The underlying principle is similar: the recurrent connectivity embeds a purely feedforward structure.…”

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confidence: 99%

Coherent chaos in a recurrent neural network with structured connectivity

Landau

Sompolinsky

2018

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We present a simple model for coherent, spatially correlated chaos in a recurrent neural network. Networks of randomly connected neurons exhibit chaotic fluctuations and have been studied as a model for capturing the temporal variability of cortical activity. The dynamics generated by such networks, however, are spatially uncorrelated and do not generate coherent fluctuations, which are commonly observed across spatial scales of the 5 neocortex. In our model we introduce a structured component of connectivity, in addition to random connections, which effectively embeds a feedforward structure via unidirectional coupling between a pair of orthogonal modes.Local fluctuations driven by the random connectivity are summed by an output mode and drive coherent activity along an input mode. The orthogonality between input and output mode preserves chaotic fluctuations even as coherence develops. In the regime of weak structured connectivity we apply a perturbative approach to 10 solve the dynamic mean-field equations, showing that in this regime coherent fluctuations are driven passively by the chaos of local residual fluctuations. Strikingly, the chaotic dynamics are not subdued even by very strong structured connectivity if we add a row balance constraint on the random connectivity. In this regime the system displays longer time-scales and switching-like activity reminiscent of "Up-Down" states observed in cortical circuits. The level of coherence grows with increasing strength of structured connectivity until the 15 dynamics are almost entirely constrained to a single spatial mode. We describe how in this regime the model achieves intermittent self-tuned criticality in which the coherent component of the dynamics self-adjusts to yield periods of slow chaos. Furthermore, we show how the dynamics depend qualitatively on the particular realization of the connectivity matrix: a complex leading eigenvalue can yield coherent oscillatory chaos while a real leading eigenvalue can yield chaos with broken symmetry. We examine the effects of network-size scaling and show that 20 these results are not finite-size effects. Finally, we show that in the regime of weak structured connectivity, coherent chaos emerges also for a generalized structured connectivity with multiple input-output modes. Author SummaryNeural activity observed in the neocortex is temporally variable, displaying irregular temporal fluctuations at every accessible level of measurement. Furthermore, these temporal fluctuations are often found to be spatially correlated 25 whether at the scale of local measurements such as membrane potentials and spikes, or global measurements such as EEG and fMRI. A thriving field of study has developed models of recurrent networks which intrinsically generate irregular temporal variability, the paradigmatic example being networks of randomly connected rate neurons which exhibit chaotic dynamics. These models have been examined analytically and numerically in great detail, yet until now the intrinsic variability generated by thes...

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“…Balanced networks produce significant dynamic and trial-to-trial spiking variability through internal mechanisms 42,57 . While balanced networks with disordered connectivity produce asynchronous activity 44 , networks with structured wiring can produce correlated variability 45,48 , that under certain conditions can be population-wide 47 . These past models were concerned with the mechanics of neuronal variability and did not model a spatially distributed stimulus to drive network response.…”

Section: Resultsmentioning

confidence: 99%

Internally generated population activity in cortical networks hinders information transmission

Huang

Pouget

Doiron

2020

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4How neuronal variability impacts neuronal codes is a central question in systems neuroscience, often 5 with complex and model dependent answers. Most population models are parametric, with a tacitly 6 assumed structure of neuronal tuning and population-wide variability. While these models provide 7 key insights, they purposely divorce any mechanistic relationship between trial average and trial vari-8 able neuronal activity. By contrast, circuit based models produce activity with response statistics that 9 are reflection of the underlying circuit structure, and thus any relations between trial averaged and 10 trial variable activity are emergent rather than assumed. In this work, we study information transfer 11 in networks of spatially ordered spiking neuron models with strong excitatory and inhibitory interac-12 tions, capable of producing rich population-wide neuronal variability. Motivated by work in the visual 13 system we embed a columnar stimulus orientation map in the network and measure the population 14 estimation of an orientated input. We show that the spatial structure of feedforward and recurrent 15 connectivity are critical determinants for population code performance. In particular, when network 16 wiring supports stable firing rate activity then with a sufficiently large number of decoded neurons all 17 1 available stimulus information is transmitted. However, if the inhibitory projections place network ac-18 tivity in a pattern forming regime then the population-wide dynamics compromise information flow. 19 In total, network connectivity determines both the stimulus tuning as well as internally generated 20 population-wide fluctuations and thereby dictates population code performance in complicated ways 21 where modeling efforts provide essential understanding. 23A prominent feature of cortical response to sensory stimuli is that neuronal activity varies significantly 24 across presentation trials 1,2 , even when efforts are taken to control or account for variable animal 25 behavior 3-6 . A component of this variability is coordinated among neurons in a brain area, often 26 leading to shared fluctuations in spiking activity [7][8][9][10][11] . How stimulus processing is affected by this large, 27 population-wide neuronal variability is a longstanding question in both experimental and theoretical 28 neuroscience communities. 29 Recording from neuronal populations while simultaneously monitoring an animal's behavior dur-30 ing a structured task offers a glimpse into how neuronal activity supports computation. Correlations 31 between spike counts from pairs of neurons in response to repeated stimulus, often referred to as 32 noise correlations, are modulated by a variety of cognitive factors that are known to affect task perfor-33 mance 4 . For example, noise correlations decrease with animal arousal 12,13 or task engagement 14 . In 34 the visual pathway noise correlations are decreased when spatial attention is directed into the recep-35 tive field of a recorded population 15,16 ...

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Strength of Correlations in Strongly Recurrent Neuronal Networks

Cited by 41 publications

References 67 publications

Influence of On-Off dynamics and selective attention on the spatial pattern of correlated variability in neocortex

Influence of On-Off dynamics and selective attention on the spatial pattern of correlated variability in neocortex

Coherent chaos in a recurrent neural network with structured connectivity

Internally generated population activity in cortical networks hinders information transmission

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