2,924 research outputs found
Linear response for spiking neuronal networks with unbounded memory
We establish a general linear response relation for spiking neuronal
networks, based on chains with unbounded memory. This relation allows us to
predict the influence of a weak amplitude time-dependent external stimuli on
spatio-temporal spike correlations, from the spontaneous statistics (without
stimulus) in a general context where the memory in spike dynamics can extend
arbitrarily far in the past. Using this approach, we show how linear response
is explicitly related to neuronal dynamics with an example, the gIF model,
introduced by M. Rudolph and A. Destexhe. This example illustrates the
collective effect of the stimuli, intrinsic neuronal dynamics, and network
connectivity on spike statistics. We illustrate our results with numerical
simulations.Comment: 60 pages, 8 figure
A unified view on weakly correlated recurrent networks
The diversity of neuron models used in contemporary theoretical neuroscience
to investigate specific properties of covariances raises the question how these
models relate to each other. In particular it is hard to distinguish between
generic properties and peculiarities due to the abstracted model. Here we
present a unified view on pairwise covariances in recurrent networks in the
irregular regime. We consider the binary neuron model, the leaky
integrate-and-fire model, and the Hawkes process. We show that linear
approximation maps each of these models to either of two classes of linear rate
models, including the Ornstein-Uhlenbeck process as a special case. The classes
differ in the location of additive noise in the rate dynamics, which is on the
output side for spiking models and on the input side for the binary model. Both
classes allow closed form solutions for the covariance. For output noise it
separates into an echo term and a term due to correlated input. The unified
framework enables us to transfer results between models. For example, we
generalize the binary model and the Hawkes process to the presence of
conduction delays and simplify derivations for established results. Our
approach is applicable to general network structures and suitable for
population averages. The derived averages are exact for fixed out-degree
network architectures and approximate for fixed in-degree. We demonstrate how
taking into account fluctuations in the linearization procedure increases the
accuracy of the effective theory and we explain the class dependent differences
between covariances in the time and the frequency domain. Finally we show that
the oscillatory instability emerging in networks of integrate-and-fire models
with delayed inhibitory feedback is a model-invariant feature: the same
structure of poles in the complex frequency plane determines the population
power spectra
Spike train statistics and Gibbs distributions
This paper is based on a lecture given in the LACONEU summer school,
Valparaiso, January 2012. We introduce Gibbs distribution in a general setting,
including non stationary dynamics, and present then three examples of such
Gibbs distributions, in the context of neural networks spike train statistics:
(i) Maximum entropy model with spatio-temporal constraints; (ii) Generalized
Linear Models; (iii) Conductance based Inte- grate and Fire model with chemical
synapses and gap junctions.Comment: 23 pages, submitte
Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses
We investigate the effect of electric synapses (gap junctions) on collective
neuronal dynamics and spike statistics in a conductance-based
Integrate-and-Fire neural network, driven by a Brownian noise, where
conductances depend upon spike history. We compute explicitly the time
evolution operator and show that, given the spike-history of the network and
the membrane potentials at a given time, the further dynamical evolution can be
written in a closed form. We show that spike train statistics is described by a
Gibbs distribution whose potential can be approximated with an explicit
formula, when the noise is weak. This potential form encompasses existing
models for spike trains statistics analysis such as maximum entropy models or
Generalized Linear Models (GLM). We also discuss the different types of
correlations: those induced by a shared stimulus and those induced by neurons
interactions.Comment: 42 pages, 1 figure, submitte
Locking of correlated neural activity to ongoing oscillations
Population-wide oscillations are ubiquitously observed in mesoscopic signals
of cortical activity. In these network states a global oscillatory cycle
modulates the propensity of neurons to fire. Synchronous activation of neurons
has been hypothesized to be a separate channel of signal processing information
in the brain. A salient question is therefore if and how oscillations interact
with spike synchrony and in how far these channels can be considered separate.
Experiments indeed showed that correlated spiking co-modulates with the static
firing rate and is also tightly locked to the phase of beta-oscillations. While
the dependence of correlations on the mean rate is well understood in
feed-forward networks, it remains unclear why and by which mechanisms
correlations tightly lock to an oscillatory cycle. We here demonstrate that
such correlated activation of pairs of neurons is qualitatively explained by
periodically-driven random networks. We identify the mechanisms by which
covariances depend on a driving periodic stimulus. Mean-field theory combined
with linear response theory yields closed-form expressions for the
cyclostationary mean activities and pairwise zero-time-lag covariances of
binary recurrent random networks. Two distinct mechanisms cause time-dependent
covariances: the modulation of the susceptibility of single neurons (via the
external input and network feedback) and the time-varying variances of single
unit activities. For some parameters, the effectively inhibitory recurrent
feedback leads to resonant covariances even if mean activities show
non-resonant behavior. Our analytical results open the question of
time-modulated synchronous activity to a quantitative analysis.Comment: 57 pages, 12 figures, published versio
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
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)
A generative spike train model with time-structured higher order correlations
Emerging technologies are revealing the spiking activity in ever larger
neural ensembles. Frequently, this spiking is far from independent, with
correlations in the spike times of different cells. Understanding how such
correlations impact the dynamics and function of neural ensembles remains an
important open problem. Here we describe a new, generative model for correlated
spike trains that can exhibit many of the features observed in data. Extending
prior work in mathematical finance, this generalized thinning and shift (GTaS)
model creates marginally Poisson spike trains with diverse temporal correlation
structures. We give several examples which highlight the model's flexibility
and utility. For instance, we use it to examine how a neural network responds
to highly structured patterns of inputs. We then show that the GTaS model is
analytically tractable, and derive cumulant densities of all orders in terms of
model parameters. The GTaS framework can therefore be an important tool in the
experimental and theoretical exploration of neural dynamics
A Comprehensive Workflow for General-Purpose Neural Modeling with Highly Configurable Neuromorphic Hardware Systems
In this paper we present a methodological framework that meets novel
requirements emerging from upcoming types of accelerated and highly
configurable neuromorphic hardware systems. We describe in detail a device with
45 million programmable and dynamic synapses that is currently under
development, and we sketch the conceptual challenges that arise from taking
this platform into operation. More specifically, we aim at the establishment of
this neuromorphic system as a flexible and neuroscientifically valuable
modeling tool that can be used by non-hardware-experts. We consider various
functional aspects to be crucial for this purpose, and we introduce a
consistent workflow with detailed descriptions of all involved modules that
implement the suggested steps: The integration of the hardware interface into
the simulator-independent model description language PyNN; a fully automated
translation between the PyNN domain and appropriate hardware configurations; an
executable specification of the future neuromorphic system that can be
seamlessly integrated into this biology-to-hardware mapping process as a test
bench for all software layers and possible hardware design modifications; an
evaluation scheme that deploys models from a dedicated benchmark library,
compares the results generated by virtual or prototype hardware devices with
reference software simulations and analyzes the differences. The integration of
these components into one hardware-software workflow provides an ecosystem for
ongoing preparative studies that support the hardware design process and
represents the basis for the maturity of the model-to-hardware mapping
software. The functionality and flexibility of the latter is proven with a
variety of experimental results
- …