Exact firing time statistics of neurons driven by discrete inhibitory noise

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimulations of infinitesimal amplitude, but they apply as well to finite amplitude post-synaptic potentials, thus being able to capture the effect of rare and large spikes. The developed methods are able to reproduce also the average firing properties of heterogeneous neuronal populations.Comment: 20 pages, 8 Figures, submitted to Scientific Report

Learning to Recognize Actions from Limited Training Examples Using a Recurrent Spiking Neural Model

A fundamental challenge in machine learning today is to build a model that can learn from few examples. Here, we describe a reservoir based spiking neural model for learning to recognize actions with a limited number of labeled videos. First, we propose a novel encoding, inspired by how microsaccades influence visual perception, to extract spike information from raw video data while preserving the temporal correlation across different frames. Using this encoding, we show that the reservoir generalizes its rich dynamical activity toward signature action/movements enabling it to learn from few training examples. We evaluate our approach on the UCF-101 dataset. Our experiments demonstrate that our proposed reservoir achieves 81.3%/87% Top-1/Top-5 accuracy, respectively, on the 101-class data while requiring just 8 video examples per class for training. Our results establish a new benchmark for action recognition from limited video examples for spiking neural models while yielding competetive accuracy with respect to state-of-the-art non-spiking neural models.Comment: 13 figures (includes supplementary information

Heterogeneous Mean Field for neural networks with short term plasticity

We report about the main dynamical features of a model of leaky-integrate-and fire excitatory neurons with short term plasticity defined on random massive networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation of the model, that is able to reproduce dynamical phases characterized by the presence of quasi-synchronous events. This formulation allows one to solve also the inverse problem of reconstructing the in-degree distribution for different network topologies from the knowledge of the global activity field. We study the robustness of this inversion procedure, by providing numerical evidence that the in-degree distribution can be recovered also in the presence of noise and disorder in the external currents. Finally, we discuss the validity of the heterogeneous mean-field approach for sparse networks, with a sufficiently large average in-degree

Collective irregular dynamics in balanced networks of leaky integrate-and-fire neurons

Open access via Springer Compact The authors acknowledge: N. Brunel, F. Farkhooi, G. Mato, S. Ostoijc, A. Roxin, and M. di Volo for useful discussions. One of us (AT) has been supported by the French government under the Excellence Initiative I-Site Paris Seine (No ANR-16-IDEX-008) and under the Labex MME-DII (No ANR-11-LBX-0023-01). The work has been mainly realized at the Max Planck Institute for the Physics of Complex Systems (Dresden, Germany) during the Advanced Study Group 2016/17 “From Microscopic to Collective Dynamics in Neural Circuits”.Peer reviewedPublisher PD

Theory of the asynchronous state of structured rotator networks and its application to recurrent networks of excitatory and inhibitory units

Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can nevertheless exhibit a rich temporal correlation statistics, that is generally difficult to capture theoretically. For randomly coupled rotator networks, it is possible to derive differential equations that determine the autocorrelation functions of the network noise and of the single elements in the network. So far, the theory has been restricted to statistically homogeneous networks, making it difficult to apply this framework to real-world networks, which are structured with respect to the properties of the single units and their connectivity. A particularly striking case are neural networks for which one has to distinguish between excitatory and inhibitory neurons, which drive their target neurons towards or away from firing threshold. To take into account network structures like that, here we extend the theory for rotator networks to the case of multiple populations. Specifically, we derive a system of differential equations that govern the self-consistent autocorrelation functions of the network fluctuations in the respective populations. We then apply this general theory to the special but important case of recurrent networks of excitatory and inhibitory units in the balanced case and compare our theory to numerical simulations. We inspect the effect of the network structure on the noise statistics by comparing our results to the case of an equivalent homogeneous network devoid of internal structure. Our results show that structured connectivity and heterogeneity of the oscillator type can both enhance or reduce the overall strength of the generated network noise and shape its temporal correlations.Comment: 11 pages, 4 figure

Recurrence-mediated suprathreshold stochastic resonance

It has previously been shown that the encoding of time-dependent signals by feedforward networks (FFNs) of processing units exhibits suprathreshold stochastic resonance (SSR), which is an optimal signal transmission for a finite level of independent, individual stochasticity in the single units. In this study, a recurrent spiking network is simulated to demonstrate that SSR can be also caused by network noise in place of intrinsic noise. The level of autonomously generated fluctuations in the network can be controlled by the strength of synapses, and hence the coding fraction (our measure of information transmission) exhibits a maximum as a function of the synaptic coupling strength. The presence of a coding peak at an optimal coupling strength is robust over a wide range of individual, network, and signal parameters, although the optimal strength and peak magnitude depend on the parameter being varied. We also perform control experiments with an FFN illustrating that the optimized coding fraction is due to the change in noise level and not from other effects entailed when changing the coupling strength. These results also indicate that the non-white (temporally correlated) network noise in general provides an extra boost to encoding performance compared to the FFN driven by intrinsic white noise fluctuations.Deutsche ForschungsgemeinschaftHumboldt-Universität zu Berlin (1034)Peer Reviewe

A unique method for stochastic models in computational and cognitive neuroscience

We review applications of the Fokker–Planck equation for the description of systems with event trains in computational and cognitive neuroscience. The most prominent example is the spike trains generated by integrate-and-fire neurons when driven by correlated (colored) fluctuations, by adaptation currents and/or by other neurons in a recurrent network. We discuss how for a general Gaussian colored noise and an adaptation current can be incorporated into a multidimensional Fokker–Planck equation by Markovian embedding for systems with a fire-and-reset condition and how in particular the spike-train power spectrum can be determined by this equation. We then review how this framework can be used to determine the self-consistent correlation statistics in a recurrent network in which the colored fluctuations arise from the spike trains of statistically similar neurons. We then turn to the popular drift-diffusion models for binary decisions in cognitive neuroscience and demonstrate that very similar Fokker–Planck equations (with two instead of only one threshold) can be used to study the statistics of sequences of decisions. Specifically, we present a novel two-dimensional model that includes an evidence variable and an expectancy variable that can reproduce salient features of key experiments in sequential decision making.Humboldt-Universität zu Berlin (1034)Peer Reviewe

Decorrelation of neural-network activity by inhibitory feedback

Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent theoretical and experimental studies demonstrate that spike correlations in recurrent neural networks are considerably smaller than expected based on the amount of shared presynaptic input. By means of a linear network model and simulations of networks of leaky integrate-and-fire neurons, we show that shared-input correlations are efficiently suppressed by inhibitory feedback. To elucidate the effect of feedback, we compare the responses of the intact recurrent network and systems where the statistics of the feedback channel is perturbed. The suppression of spike-train correlations and population-rate fluctuations by inhibitory feedback can be observed both in purely inhibitory and in excitatory-inhibitory networks. The effect is fully understood by a linear theory and becomes already apparent at the macroscopic level of the population averaged activity. At the microscopic level, shared-input correlations are suppressed by spike-train correlations: In purely inhibitory networks, they are canceled by negative spike-train correlations. In excitatory-inhibitory networks, spike-train correlations are typically positive. Here, the suppression of input correlations is not a result of the mere existence of correlations between excitatory (E) and inhibitory (I) neurons, but a consequence of a particular structure of correlations among the three possible pairings (EE, EI, II)