208 research outputs found
Detecting and Estimating Signals in Noisy Cable Structures, II: Information Theoretical Analysis
This is the second in a series of articles that seek to recast classical single-neuron biophysics in information-theoretical terms. Classical cable theory focuses on analyzing the voltage or current attenuation of a synaptic signal as it propagates from its dendritic input location to the spike initiation zone. On the other hand, we are interested in analyzing the amount of information lost about the signal in this process due to the presence of various noise sources distributed throughout the neuronal membrane. We use a stochastic version of the linear one-dimensional cable equation to derive closed-form expressions for the second-order moments of the fluctuations of the membrane potential associated with different membrane current noise sources: thermal noise, noise due to the random opening and closing of sodium and potassium channels, and noise due to the presence of “spontaneous” synaptic input.
We consider two different scenarios. In the signal estimation paradigm, the time course of the membrane potential at a location on the cable is used to reconstruct the detailed time course of a random, band-limited current injected some distance away. Estimation performance is characterized in terms of the coding fraction and the mutual information. In the signal detection paradigm, the membrane potential is used to determine whether a distant synaptic event occurred within a given observation interval. In the light of our analytical results, we speculate that the length of weakly active apical dendrites might be limited by the information loss due to the accumulated noise between distal synaptic input sites and the soma and that the presence of dendritic nonlinearities probably serves to increase dendritic information transfer
Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective
On metrics of density and power efficiency, neuromorphic technologies have
the potential to surpass mainstream computing technologies in tasks where
real-time functionality, adaptability, and autonomy are essential. While
algorithmic advances in neuromorphic computing are proceeding successfully, the
potential of memristors to improve neuromorphic computing have not yet born
fruit, primarily because they are often used as a drop-in replacement to
conventional memory. However, interdisciplinary approaches anchored in machine
learning theory suggest that multifactor plasticity rules matching neural and
synaptic dynamics to the device capabilities can take better advantage of
memristor dynamics and its stochasticity. Furthermore, such plasticity rules
generally show much higher performance than that of classical Spike Time
Dependent Plasticity (STDP) rules. This chapter reviews the recent development
in learning with spiking neural network models and their possible
implementation with memristor-based hardware
The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
We study pairwise Ising models for describing the statistics of multi-neuron
spike trains, using data from a simulated cortical network. We explore
efficient ways of finding the optimal couplings in these models and examine
their statistical properties. To do this, we extract the optimal couplings for
subsets of size up to 200 neurons, essentially exactly, using Boltzmann
learning. We then study the quality of several approximate methods for finding
the couplings by comparing their results with those found from Boltzmann
learning. Two of these methods- inversion of the TAP equations and an
approximation proposed by Sessak and Monasson- are remarkably accurate. Using
these approximations for larger subsets of neurons, we find that extracting
couplings using data from a subset smaller than the full network tends
systematically to overestimate their magnitude. This effect is described
qualitatively by infinite-range spin glass theory for the normal phase. We also
show that a globally-correlated input to the neurons in the network lead to a
small increase in the average coupling. However, the pair-to-pair variation of
the couplings is much larger than this and reflects intrinsic properties of the
network. Finally, we study the quality of these models by comparing their
entropies with that of the data. We find that they perform well for small
subsets of the neurons in the network, but the fit quality starts to
deteriorate as the subset size grows, signalling the need to include higher
order correlations to describe the statistics of large networks.Comment: 12 pages, 10 figure
From Spiking Neuron Models to Linear-Nonlinear Models
Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates
Characterization and Compensation of Network-Level Anomalies in Mixed-Signal Neuromorphic Modeling Platforms
Advancing the size and complexity of neural network models leads to an ever
increasing demand for computational resources for their simulation.
Neuromorphic devices offer a number of advantages over conventional computing
architectures, such as high emulation speed or low power consumption, but this
usually comes at the price of reduced configurability and precision. In this
article, we investigate the consequences of several such factors that are
common to neuromorphic devices, more specifically limited hardware resources,
limited parameter configurability and parameter variations. Our final aim is to
provide an array of methods for coping with such inevitable distortion
mechanisms. As a platform for testing our proposed strategies, we use an
executable system specification (ESS) of the BrainScaleS neuromorphic system,
which has been designed as a universal emulation back-end for neuroscientific
modeling. We address the most essential limitations of this device in detail
and study their effects on three prototypical benchmark network models within a
well-defined, systematic workflow. For each network model, we start by defining
quantifiable functionality measures by which we then assess the effects of
typical hardware-specific distortion mechanisms, both in idealized software
simulations and on the ESS. For those effects that cause unacceptable
deviations from the original network dynamics, we suggest generic compensation
mechanisms and demonstrate their effectiveness. Both the suggested workflow and
the investigated compensation mechanisms are largely back-end independent and
do not require additional hardware configurability beyond the one required to
emulate the benchmark networks in the first place. We hereby provide a generic
methodological environment for configurable neuromorphic devices that are
targeted at emulating large-scale, functional neural networks
Spatio-temporal Learning with Arrays of Analog Nanosynapses
Emerging nanodevices such as resistive memories are being considered for
hardware realizations of a variety of artificial neural networks (ANNs),
including highly promising online variants of the learning approaches known as
reservoir computing (RC) and the extreme learning machine (ELM). We propose an
RC/ELM inspired learning system built with nanosynapses that performs both
on-chip projection and regression operations. To address time-dynamic tasks,
the hidden neurons of our system perform spatio-temporal integration and can be
further enhanced with variable sampling or multiple activation windows. We
detail the system and show its use in conjunction with a highly analog
nanosynapse device on a standard task with intrinsic timing dynamics- the TI-46
battery of spoken digits. The system achieves nearly perfect (99%) accuracy at
sufficient hidden layer size, which compares favorably with software results.
In addition, the model is extended to a larger dataset, the MNIST database of
handwritten digits. By translating the database into the time domain and using
variable integration windows, up to 95% classification accuracy is achieved. In
addition to an intrinsically low-power programming style, the proposed
architecture learns very quickly and can easily be converted into a spiking
system with negligible loss in performance- all features that confer
significant energy efficiency.Comment: 6 pages, 3 figures. Presented at 2017 IEEE/ACM Symposium on Nanoscale
architectures (NANOARCH
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