How well do mean field theories of spiking quadratic-integrate-and-fire networks work in realistic parameter regimes?

Grabska-Barwińska, Agnieszka; Latham, Peter E.

doi:10.1007/s10827-013-0481-5

Cited by 11 publications

(11 citation statements)

References 28 publications

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“…Fig 4 (B) shows that the mean field approximation for the firing rates of neurons in the network matches simulations with great precision for a wide range of N and K , and that the average firing rates are independent of N and change monotonically with K , as expected from previous work [16, 47]. Later, we will make use of the quantities μ E , I and derived in Eq (6) to outline the difference between network and MF responses for fixed stimuli.…”

Section: Methodssupporting

confidence: 80%

“…This dip occurs because QIF dynamics produce a relative refractory period, leading to typical Fano Factors lower than one (between 0.77 and 1 in all of our simulations). This is refractory period can be regarded as a realistic feature; in any case, the use of assumption (ii) still leads to correct estimates for our dynamical regime, as was also observed in [47]. …”

Section: Methodssupporting

confidence: 75%

“…We follow a similar approach to [47, 48] where QIF neurons driven by noise and in a MF setting are studied for exponentially decaying synapses. In contrast to networks of leaky integrate-and-fire (LIF) neurons, QIF dynamics introduce some complications because their firing rate response to fluctuating drives is not straightforward to compute (c.f.…”

Section: Methodsmentioning

confidence: 99%

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Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems

et al. 2016

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Highly connected recurrent neural networks often produce chaotic dynamics, meaning their precise activity is sensitive to small perturbations. What are the consequences of chaos for how such networks encode streams of temporal stimuli? On the one hand, chaos is a strong source of randomness, suggesting that small changes in stimuli will be obscured by intrinsically generated variability. On the other hand, recent work shows that the type of chaos that occurs in spiking networks can have a surprisingly low-dimensional structure, suggesting that there may be room for fine stimulus features to be precisely resolved. Here we show that strongly chaotic networks produce patterned spikes that reliably encode time-dependent stimuli: using a decoder sensitive to spike times on timescales of 10’s of ms, one can easily distinguish responses to very similar inputs. Moreover, recurrence serves to distribute signals throughout chaotic networks so that small groups of cells can encode substantial information about signals arriving elsewhere. A conclusion is that the presence of strong chaos in recurrent networks need not exclude precise encoding of temporal stimuli via spike patterns.

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Section: Methodssupporting

confidence: 80%

Section: Methodssupporting

confidence: 75%

Section: Methodsmentioning

confidence: 99%

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Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems

et al. 2016

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“…Current-based LIF models are popular because of their relative simplicity (see e.g., Brunel, 2013) and they have the key advantage of facilitating the derivation of analytical closed-form solutions. Thus current-based synapses are convenient for developing mean field models (Grabska-Barwinska and Latham, 2013), event-based models (Touboul and Faugeras, 2011), or firing rate models (Helias et al, 2010; Ostojic and Brunel, 2011; Schaffer et al, 2013), as well as in studies examining the stability of neural states (Babadi and Abbott, 2010; Mongillo et al, 2012). Moreover, current-based models are often adopted, because of their simplicity, to investigate numerically network-scale phenomena (Memmesheimer, 2010; Renart and Van Rossum, 2012; Gutig et al, 2013; Lim and Goldman, 2013; Zhang et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Comparison of the dynamics of neural interactions between current-based and conductance-based integrate-and-fire recurrent networks

Cavallari

Panzeri

Mazzoni

2014

Front. Neural Circuits

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Models of networks of Leaky Integrate-and-Fire (LIF) neurons are a widely used tool for theoretical investigations of brain function. These models have been used both with current- and conductance-based synapses. However, the differences in the dynamics expressed by these two approaches have been so far mainly studied at the single neuron level. To investigate how these synaptic models affect network activity, we compared the single neuron and neural population dynamics of conductance-based networks (COBNs) and current-based networks (CUBNs) of LIF neurons. These networks were endowed with sparse excitatory and inhibitory recurrent connections, and were tested in conditions including both low- and high-conductance states. We developed a novel procedure to obtain comparable networks by properly tuning the synaptic parameters not shared by the models. The so defined comparable networks displayed an excellent and robust match of first order statistics (average single neuron firing rates and average frequency spectrum of network activity). However, these comparable networks showed profound differences in the second order statistics of neural population interactions and in the modulation of these properties by external inputs. The correlation between inhibitory and excitatory synaptic currents and the cross-neuron correlation between synaptic inputs, membrane potentials and spike trains were stronger and more stimulus-modulated in the COBN. Because of these properties, the spike train correlation carried more information about the strength of the input in the COBN, although the firing rates were equally informative in both network models. Moreover, the network activity of COBN showed stronger synchronization in the gamma band, and spectral information about the input higher and spread over a broader range of frequencies. These results suggest that the second order statistics of network dynamics depend strongly on the choice of synaptic model.

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“…The very first studies in neuroscience demonstrated analytically that the mean-field approximation was valid for homogenous neural networks when the numbers of neurons tend to infinity (Amari, 1972;Amari et al, 1977). Ever since, numerous studies have analysed the mean-field in neural networks under diverse conditions such as in finite neural networks (Mattia and Del Giduice, 2002;Touboul and Ermentrout, 2011), with different connectivity patterns (Cessac and Vieville, 2013;Moynot and Samuelides, 2002;Samuelides and Cessac, 2007;Brunel and hakim, 1999;Cessac, 1995), using different single-cell neuronal models (Abbot and Vreeswijk, 1993;Cessac, 2008;Treves, 1993)), using realistic parameter regimes (Grabska-Barwinska and Latham, 2013), or as a function of time (Molgedey et al, 2013;Moynot and Samuelides, 2002), the so-called dynamic mean-field approaches.…”

Section: Introductionmentioning

confidence: 99%

Comparing average network signals and neural mass signals in systems with low-synchrony

Tewarie

Daffertshofer

van

2017

Preprint

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1AbstractNeural mass models are accepted as efficient modelling techniques to model empirical observations such as disturbed oscillations or neuronal synchronization. Neural mass models are based on the mean-field assumption, i.e. they capture the mean-activity of a neuronal population. However, it is unclear if neural mass models still describe the mean activity of a neuronal population when the underlying neural network topology is not homogenous. Here, we test whether the mean activity of a neuronal population can be described by neural mass models when there is neuronal loss and when the connections in the network become sparse. To this end, we derive two neural mass models from a conductance based leaky integrate-and-firing (LIF) model. We then compared the power spectral densities of the mean activity of a network of inhibitory and excitatory LIF neurons with that of neural mass models by computing the Kolmogorov-Smirnov test statistic. Firstly, we found that when the number of neurons in a fully connected LIF-network is larger than 300, the neural mass model is a good description of the mean activity. Secondly, if the connection density in the LIF-network does not exceed a crtical value, this leads to desynchronization of neurons within the LIF-network and to failure of neural mass description. Therefore we conclude that neural mass models can be used for analysing empirical observations if the neuronal network of interest is large enough and when neurons in this system synchronize.

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How well do mean field theories of spiking quadratic-integrate-and-fire networks work in realistic parameter regimes?

Cited by 11 publications

References 28 publications

Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems

Encoding in Balanced Networks: Revisiting Spike Patterns and Chaos in Stimulus-Driven Systems

Comparison of the dynamics of neural interactions between current-based and conductance-based integrate-and-fire recurrent networks

Comparing average network signals and neural mass signals in systems with low-synchrony

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