1,310 research outputs found
Spontaneous Dynamics of Asymmetric Random Recurrent Spiking Neural Networks
We study in this paper the effect of an unique initial stimulation on random
recurrent networks of leaky integrate and fire neurons. Indeed given a
stochastic connectivity this so-called spontaneous mode exhibits various non
trivial dynamics. This study brings forward a mathematical formalism that
allows us to examine the variability of the afterward dynamics according to the
parameters of the weight distribution. Provided independence hypothesis (e.g.
in the case of very large networks) we are able to compute the average number
of neurons that fire at a given time -- the spiking activity. In accordance
with numerical simulations, we prove that this spiking activity reaches a
steady-state, we characterize this steady-state and explore the transients.Comment: 28 pages, 7 figure
Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity
In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity
Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity
We study the storage and retrieval of phase-coded patterns as stable
dynamical attractors in recurrent neural networks, for both an analog and a
integrate-and-fire spiking model. The synaptic strength is determined by a
learning rule based on spike-time-dependent plasticity, with an asymmetric time
window depending on the relative timing between pre- and post-synaptic
activity. We store multiple patterns and study the network capacity.
For the analog model, we find that the network capacity scales linearly with
the network size, and that both capacity and the oscillation frequency of the
retrieval state depend on the asymmetry of the learning time window. In
addition to fully-connected networks, we study sparse networks, where each
neuron is connected only to a small number z << N of other neurons. Connections
can be short range, between neighboring neurons placed on a regular lattice, or
long range, between randomly chosen pairs of neurons. We find that a small
fraction of long range connections is able to amplify the capacity of the
network. This imply that a small-world-network topology is optimal, as a
compromise between the cost of long range connections and the capacity
increase.
Also in the spiking integrate and fire model the crucial result of storing
and retrieval of multiple phase-coded patterns is observed. The capacity of the
fully-connected spiking network is investigated, together with the relation
between oscillation frequency of retrieval state and window asymmetry
A mean-field model for conductance-based networks of adaptive exponential integrate-and-fire neurons
Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of
neocortical processing at mesoscopic scales. Since VSDi signals report the
average membrane potential, it seems natural to use a mean-field formalism to
model such signals. Here, we investigate a mean-field model of networks of
Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based
synaptic interactions. The AdEx model can capture the spiking response of
different cell types, such as regular-spiking (RS) excitatory neurons and
fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism,
together with a semi-analytic approach to the transfer function of AdEx
neurons. We compare the predictions of this mean-field model to simulated
networks of RS-FS cells, first at the level of the spontaneous activity of the
network, which is well predicted by the mean-field model. Second, we
investigate the response of the network to time-varying external input, and
show that the mean-field model accurately predicts the response time course of
the population. One notable exception was that the "tail" of the response at
long times was not well predicted, because the mean-field does not include
adaptation mechanisms. We conclude that the Master Equation formalism can yield
mean-field models that predict well the behavior of nonlinear networks with
conductance-based interactions and various electrophysiolgical properties, and
should be a good candidate to model VSDi signals where both excitatory and
inhibitory neurons contribute.Comment: 21 pages, 7 figure
Deterministic networks for probabilistic computing
Neural-network models of high-level brain functions such as memory recall and
reasoning often rely on the presence of stochasticity. The majority of these
models assumes that each neuron in the functional network is equipped with its
own private source of randomness, often in the form of uncorrelated external
noise. However, both in vivo and in silico, the number of noise sources is
limited due to space and bandwidth constraints. Hence, neurons in large
networks usually need to share noise sources. Here, we show that the resulting
shared-noise correlations can significantly impair the performance of
stochastic network models. We demonstrate that this problem can be overcome by
using deterministic recurrent neural networks as sources of uncorrelated noise,
exploiting the decorrelating effect of inhibitory feedback. Consequently, even
a single recurrent network of a few hundred neurons can serve as a natural
noise source for large ensembles of functional networks, each comprising
thousands of units. We successfully apply the proposed framework to a diverse
set of binary-unit networks with different dimensionalities and entropies, as
well as to a network reproducing handwritten digits with distinct predefined
frequencies. Finally, we show that the same design transfers to functional
networks of spiking neurons.Comment: 22 pages, 11 figure
Associative memory of phase-coded spatiotemporal patterns in leaky Integrate and Fire networks
We study the collective dynamics of a Leaky Integrate and Fire network in
which precise relative phase relationship of spikes among neurons are stored,
as attractors of the dynamics, and selectively replayed at differentctime
scales. Using an STDP-based learning process, we store in the connectivity
several phase-coded spike patterns, and we find that, depending on the
excitability of the network, different working regimes are possible, with
transient or persistent replay activity induced by a brief signal. We introduce
an order parameter to evaluate the similarity between stored and recalled
phase-coded pattern, and measure the storage capacity. Modulation of spiking
thresholds during replay changes the frequency of the collective oscillation or
the number of spikes per cycle, keeping preserved the phases relationship. This
allows a coding scheme in which phase, rate and frequency are dissociable.
Robustness with respect to noise and heterogeneity of neurons parameters is
studied, showing that, since dynamics is a retrieval process, neurons preserve
stablecprecise phase relationship among units, keeping a unique frequency of
oscillation, even in noisy conditions and with heterogeneity of internal
parameters of the units
Random Recurrent Neural Networks Dynamics
This paper is a review dealing with the study of large size random recurrent
neural networks. The connection weights are selected according to a probability
law and it is possible to predict the network dynamics at a macroscopic scale
using an averaging principle. After a first introductory section, the section 1
reviews the various models from the points of view of the single neuron
dynamics and of the global network dynamics. A summary of notations is
presented, which is quite helpful for the sequel. In section 2, mean-field
dynamics is developed.
The probability distribution characterizing global dynamics is computed. In
section 3, some applications of mean-field theory to the prediction of chaotic
regime for Analog Formal Random Recurrent Neural Networks (AFRRNN) are
displayed. The case of AFRRNN with an homogeneous population of neurons is
studied in section 4. Then, a two-population model is studied in section 5. The
occurrence of a cyclo-stationary chaos is displayed using the results of
\cite{Dauce01}. In section 6, an insight of the application of mean-field
theory to IF networks is given using the results of \cite{BrunelHakim99}.Comment: Review paper, 36 pages, 5 figure
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