601 research outputs found
How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation
This paper addresses two questions in the context of neuronal networks
dynamics, using methods from dynamical systems theory and statistical physics:
(i) How to characterize the statistical properties of sequences of action
potentials ("spike trains") produced by neuronal networks ? and; (ii) what are
the effects of synaptic plasticity on these statistics ? We introduce a
framework in which spike trains are associated to a coding of membrane
potential trajectories, and actually, constitute a symbolic coding in important
explicit examples (the so-called gIF models). On this basis, we use the
thermodynamic formalism from ergodic theory to show how Gibbs distributions are
natural probability measures to describe the statistics of spike trains, given
the empirical averages of prescribed quantities. As a second result, we show
that Gibbs distributions naturally arise when considering "slow" synaptic
plasticity rules where the characteristic time for synapse adaptation is quite
longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure
KInNeSS: A Modular Framework for Computational Neuroscience
Making use of very detailed neurophysiological, anatomical, and behavioral data to build biological-realistic computational models of animal behavior is often a difficult task. Until recently, many software packages have tried to resolve this mismatched granularity with different approaches. This paper presents KInNeSS, the KDE Integrated NeuroSimulation Software environment, as an alternative solution to bridge the gap between data and model behavior. This open source neural simulation software package provides an expandable framework incorporating features such as ease of use, scalabiltiy, an XML based schema, and multiple levels of granularity within a modern object oriented programming design. KInNeSS is best suited to simulate networks of hundreds to thousands of branched multu-compartmental neurons with biophysical properties such as membrane potential, voltage-gated and ligand-gated channels, the presence of gap junctions of ionic diffusion, neuromodulation channel gating, the mechanism for habituative or depressive synapses, axonal delays, and synaptic plasticity. KInNeSS outputs include compartment membrane voltage, spikes, local-field potentials, and current source densities, as well as visualization of the behavior of a simulated agent. An explanation of the modeling philosophy and plug-in development is also presented. Further developement of KInNeSS is ongoing with the ultimate goal of creating a modular framework that will help researchers across different disciplines to effecitively collaborate using a modern neural simulation platform.Center for Excellence for Learning Education, Science, and Technology (SBE-0354378); Air Force Office of Scientific Research (F49620-01-1-0397); Office of Naval Research (N00014-01-1-0624
Spike timing-dependent plasticity induces non-trivial topology in the brain.
We study the capacity of Hodgkin-Huxley neuron in a network to change temporarily or permanently their connections and behavior, the so called spike timing-dependent plasticity (STDP), as a function of their synchronous behavior. We consider STDP of excitatory and inhibitory synapses driven by Hebbian rules. We show that the final state of networks evolved by a STDP depend on the initial network configuration. Specifically, an initial all-to-all topology evolves to a complex topology. Moreover, external perturbations can induce co-existence of clusters, those whose neurons are synchronous and those whose neurons are desynchronous. This work reveals that STDP based on Hebbian rules leads to a change in the direction of the synapses between high and low frequency neurons, and therefore, Hebbian learning can be explained in terms of preferential attachment between these two diverse communities of neurons, those with low-frequency spiking neurons, and those with higher-frequency spiking neurons
Self-Organization of Spiking Neural Networks for Visual Object Recognition
On one hand, the visual system has the ability to differentiate between very similar
objects. On the other hand, we can also recognize the same object in images that vary
drastically, due to different viewing angle, distance, or illumination. The ability to
recognize the same object under different viewing conditions is called invariant object
recognition. Such object recognition capabilities are not immediately available after
birth, but are acquired through learning by experience in the visual world.
In many viewing situations different views of the same object are seen in a tem-
poral sequence, e.g. when we are moving an object in our hands while watching it.
This creates temporal correlations between successive retinal projections that can be
used to associate different views of the same object. Theorists have therefore pro-
posed a synaptic plasticity rule with a built-in memory trace (trace rule).
In this dissertation I present spiking neural network models that offer possible
explanations for learning of invariant object representations. These models are based
on the following hypotheses:
1. Instead of a synaptic trace rule, persistent firing of recurrently connected groups
of neurons can serve as a memory trace for invariance learning.
2. Short-range excitatory lateral connections enable learning of self-organizing
topographic maps that represent temporal as well as spatial correlations.
3. When trained with sequences of object views, such a network can learn repre-
sentations that enable invariant object recognition by clustering different views
of the same object within a local neighborhood.
4. Learning of representations for very similar stimuli can be enabled by adaptive
inhibitory feedback connections.
The study presented in chapter 3.1 details an implementation of a spiking neural
network to test the first three hypotheses. This network was tested with stimulus
sets that were designed in two feature dimensions to separate the impact of tempo-
ral and spatial correlations on learned topographic maps. The emerging topographic
maps showed patterns that were dependent on the temporal order of object views
during training. Our results show that pooling over local neighborhoods of the to-
pographic map enables invariant recognition.
Chapter 3.2 focuses on the fourth hypothesis. There we examine how the adaptive
feedback inhibition (AFI) can improve the ability of a network to discriminate between
very similar patterns. The results show that with AFI learning is faster, and the
network learns selective representations for stimuli with higher levels of overlap
than without AFI.
Results of chapter 3.1 suggest a functional role for topographic object representa-
tions that are known to exist in the inferotemporal cortex, and suggests a mechanism
for the development of such representations. The AFI model implements one aspect
of predictive coding: subtraction of a prediction from the actual input of a system. The
successful implementation in a biologically plausible network of spiking neurons
shows that predictive coding can play a role in cortical circuits
On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses
We present a mathematical analysis of a networks with Integrate-and-Fire
neurons and adaptive conductances. Taking into account the realistic fact that
the spike time is only known within some \textit{finite} precision, we propose
a model where spikes are effective at times multiple of a characteristic time
scale , where can be \textit{arbitrary} small (in particular,
well beyond the numerical precision). We make a complete mathematical
characterization of the model-dynamics and obtain the following results. The
asymptotic dynamics is composed by finitely many stable periodic orbits, whose
number and period can be arbitrary large and can diverge in a region of the
synaptic weights space, traditionally called the "edge of chaos", a notion
mathematically well defined in the present paper. Furthermore, except at the
edge of chaos, there is a one-to-one correspondence between the membrane
potential trajectories and the raster plot. This shows that the neural code is
entirely "in the spikes" in this case. As a key tool, we introduce an order
parameter, easy to compute numerically, and closely related to a natural notion
of entropy, providing a relevant characterization of the computational
capabilities of the network. This allows us to compare the computational
capabilities of leaky and Integrate-and-Fire models and conductance based
models. The present study considers networks with constant input, and without
time-dependent plasticity, but the framework has been designed for both
extensions.Comment: 36 pages, 9 figure
Simulation of networks of spiking neurons: A review of tools and strategies
We review different aspects of the simulation of spiking neural networks. We
start by reviewing the different types of simulation strategies and algorithms
that are currently implemented. We next review the precision of those
simulation strategies, in particular in cases where plasticity depends on the
exact timing of the spikes. We overview different simulators and simulation
environments presently available (restricted to those freely available, open
source and documented). For each simulation tool, its advantages and pitfalls
are reviewed, with an aim to allow the reader to identify which simulator is
appropriate for a given task. Finally, we provide a series of benchmark
simulations of different types of networks of spiking neurons, including
Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based
or conductance-based synapses, using clock-driven or event-driven integration
strategies. The same set of models are implemented on the different simulators,
and the codes are made available. The ultimate goal of this review is to
provide a resource to facilitate identifying the appropriate integration
strategy and simulation tool to use for a given modeling problem related to
spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of
Computational Neuroscience, in press (2007
Computational modeling with spiking neural networks
This chapter reviews recent developments in the area of spiking neural networks (SNN) and summarizes the main contributions to this research field. We give background information about the functioning of biological neurons, discuss the most important mathematical neural models along with neural encoding techniques, learning algorithms, and applications of spiking neurons. As a specific application, the functioning of the evolving spiking neural network (eSNN) classification method is presented in detail and the principles of numerous eSNN based applications are highlighted and discussed
A spintronic Huxley-Hodgkin-analogue neuron implemented with a single magnetic tunnel junction
Spiking neural networks aim to emulate the brain's properties to achieve
similar parallelism and high-processing power. A caveat of these neural
networks is the high computational cost to emulate, while current proposals for
analogue implementations are energy inefficient and not scalable. We propose a
device based on a single magnetic tunnel junction to perform neuron firing for
spiking neural networks without the need of any resetting procedure. We
leverage two physics, magnetism and thermal effects, to obtain a bio-realistic
spiking behavior analogous to the Huxley-Hodgkin model of the neuron. The
device is also able to emulate the simpler Leaky-Integrate and Fire model.
Numerical simulations using experimental-based parameters demonstrate firing
frequency in the MHz to GHz range under constant input at room temperature. The
compactness, scalability, low cost, CMOS-compatibility, and power efficiency of
magnetic tunnel junctions advocate for their broad use in hardware
implementations of spiking neural networks.Comment: 23 pages, 6 figures, 2 table
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