Synchronization of quadratic integrate-and-fire spiking neurons: Constant versus voltage-dependent couplings

Interspike interval (ISI) distributions of cortical neurons exhibit a range of different shapes. Wide ISI distributions are believed to stem from a balance of excitatory and inhibitory inputs that leads to a strongly fluctuating total drive. An important question is whether the full range of experimentally observed ISI distributions can be reproduced by modulating this balance. To address this issue, we investigate the shape of the ISI distributions of spiking neuron models receiving fluctuating inputs. Using analytical tools to describe the ISI distribution of a leaky integrate-and-fire (LIF) neuron, we identify three key features: 1) the ISI distribution displays an exponential decay at long ISIs independently of the strength of the fluctuating input; 2) as the amplitude of the input fluctuations is increased, the ISI distribution evolves progressively between three types, a narrow distribution (suprathreshold input), an exponential with an effective refractory period (subthreshold but suprareset input), and a bursting exponential (subreset input); 3) the shape of the ISI distribution is approximately independent of the mean ISI and determined only by the coefficient of variation. Numerical simulations show that these features are not specific to the LIF model but are also present in the ISI distributions of the exponential integrate-and-fire model and a Hodgkin-Huxley-like model. Moreover, we observe that for a fixed mean and coefficient of variation of ISIs, the full ISI distributions of the three models are nearly identical. We conclude that the ISI distributions of spiking neurons in the presence of fluctuating inputs are well described by gamma distributions.

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Classification of Correlated Patterns with a Configurable Analog VLSI Neural Network of Spiking Neurons and Self-Regulating Plastic Synapses

Neural Computation ◽

10.1162/neco.2009.08-07-599 ◽

2009 ◽

Vol 21 (11) ◽

pp. 3106-3129 ◽

Cited By ~ 16

Author(s):

Massimilian Giulioni ◽

Mario Pannunzi ◽

Davide Badoni ◽

Vittorio Dante ◽

Paolo Del Giudice

Keyword(s):

Marked Improvement ◽

Analog Vlsi ◽

Spiking Neurons ◽

Learning Performance ◽

Event Representation ◽

Plasticity Mechanism ◽

Integrate And Fire ◽

Correlated Patterns ◽

Synaptic Changes

We describe the implementation and illustrate the learning performance of an analog VLSI network of 32 integrate-and-fire neurons with spike-frequency adaptation and 2016 Hebbian bistable spike-driven stochastic synapses, endowed with a self-regulating plasticity mechanism, which avoids unnecessary synaptic changes. The synaptic matrix can be flexibly configured and provides both recurrent and external connectivity with address-event representation compliant devices. We demonstrate a marked improvement in the efficiency of the network in classifying correlated patterns, owing to the self-regulating mechanism.

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Hebbian Self-Organizing Integrate-and-Fire Networks for Data Clustering

Neural Computation ◽

10.1162/neco.2009.12-08-926 ◽

2010 ◽

Vol 22 (1) ◽

pp. 273-288 ◽

Cited By ~ 16

Author(s):

Florian Landis ◽

Thomas Ott ◽

Ruedi Stoop

Keyword(s):

Data Clustering ◽

Time Complexity ◽

Arbitrary Shape ◽

Clustering Algorithm ◽

Hebbian Learning ◽

Spiking Neurons ◽

Integrate And Fire ◽

Background Data ◽

Homogeneous Regions ◽

Noisy Background

We propose a Hebbian learning-based data clustering algorithm using spiking neurons. The algorithm is capable of distinguishing between clusters and noisy background data and finds an arbitrary number of clusters of arbitrary shape. These properties render the approach particularly useful for visual scene segmentation into arbitrarily shaped homogeneous regions. We present several application examples, and in order to highlight the advantages and the weaknesses of our method, we systematically compare the results with those from standard methods such as the k-means and Ward's linkage clustering. The analysis demonstrates that not only the clustering ability of the proposed algorithm is more powerful than those of the two concurrent methods, the time complexity of the method is also more modest than that of its generally used strongest competitor.

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Voltage-dependent K+ Channels Improve the Energy Efficiency of Signalling in Blowfly Photoreceptors

10.1101/090308 ◽

2016 ◽

Author(s):

Francisco J. H. Heras ◽

John Anderson ◽

Simon B. Laughlin ◽

Jeremy E. Niven

Keyword(s):

Energy Efficiency ◽

Energy Consumption ◽

Negative Feedback ◽

Light Adaptation ◽

Bright Light ◽

Spiking Neurons ◽

Delayed Rectifier ◽

Voltage Response ◽

Functional Requirements ◽

Voltage Dependent

AbstractVoltage-dependent conductances in many spiking neurons are tuned to reduce action potential energy consumption, so improving the energy efficiency of spike coding. However, the contribution of voltage-dependent conductances to the energy efficiency of analogue coding, by graded potentials in dendrites and non-spiking neurons, remains unclear. We investigate the contribution of voltage-dependent conductances to the energy efficiency of analogue coding by modelling blowfly R1-6 photoreceptor membrane. Two voltage-dependent delayed rectifier K+ conductances (DRs) shape the membrane's voltage response and contribute to light adaptation. They make two types of energy saving. By reducing membrane resistance upon depolarisation they convert the cheap, low bandwidth membrane needed in dim light to the expensive high bandwidth membrane needed in bright light. This investment of energy in bandwidth according to functional requirements can halve daily energy consumption. Second, DRs produce negative feedback that reduces membrane impedance and increases bandwidth. This negative feedback allows an active membrane with DRs to consume at least 30% less energy than a passive membrane with the same capacitance and bandwidth. Voltage gated conductances in other non-spiking neurons, and in dendrites, might be organized to make similar savings.

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Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking

Neural Computation ◽

10.1162/089976600300015899 ◽

2000 ◽

Vol 12 (1) ◽

pp. 43-89 ◽

Cited By ~ 249

Author(s):

Wulfram Gerstner

Keyword(s):

Integral Equation ◽

Population Dynamics ◽

Small Amplitude ◽

Spiking Neurons ◽

Linear Filter ◽

Population Activity ◽

Integrate And Fire ◽

Fast Transients ◽

The Stability ◽

Fire Type

An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate-and-fire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay, and a bifurcation diagram is derived. The response of a population of noisy integrate-and-fire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized “locked” solutions is analyzed.

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Spatiotemporal Coding in the Cortex: Information Flow-Based Learning in Spiking Neural Networks

Neural Computation ◽

10.1162/089976699300016502 ◽

1999 ◽

Vol 11 (4) ◽

pp. 919-934 ◽

Cited By ~ 6

Author(s):

Gustavo Deco ◽

Bernd Schürmann

Keyword(s):

Information Flow ◽

Cortical Neurons ◽

Spiking Neurons ◽

Reconstruction Method ◽

First Principle ◽

Information Theoretic ◽

Discrimination Ability ◽

Sensory Inputs ◽

Integrate And Fire ◽

Synchronous Firing

We introduce a learning paradigm for networks of integrate-and-fire spiking neurons that is based on an information-theoretic criterion. This criterion can be viewed as a first principle that demonstrates the experimentally observed fact that cortical neurons display synchronous firing for some stimuli and not for others. The principle can be regarded as the postulation of a nonparametric reconstruction method as optimization criteria for learning the required functional connectivity that justifies and explains synchronous firing for binding of features as a mechanism for spatiotemporal coding. This can be expressed in an information-theoretic way by maximizing the discrimination ability between different sensory inputs in minimal time.

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Correlation of physiologically and morphologically identified neuronal types in human association cortex in vitro

Journal of Neurophysiology ◽

10.1152/jn.1991.66.6.1825 ◽

1991 ◽

Vol 66 (6) ◽

pp. 1825-1837 ◽

Cited By ~ 79

Author(s):

R. C. Foehring ◽

N. M. Lorenzon ◽

P. Herron ◽

C. J. Wilson

Keyword(s):

Spiking Neurons ◽

Burst Firing ◽

Repetitive Firing ◽

Association Cortex ◽

Firing Behavior ◽

Voltage Dependent ◽

Low Threshold ◽

Fast Spiking ◽

Human Association

1. We examined whether the three physiologically defined neuron types described for rodent neocortex were also evident in human association cortex studied in an in vitro brain slice preparation. We also examined the relationship between physiological and morphological cell type in human neocortical neurons. In particular, we tested whether burst-firing neurons were numerous in regions of human cortex that are susceptible to seizures. 2. Although we sampled regular-spiking and fast-spiking neurons, we observed no true burst-firing neurons, as defined for rodent cortex. We did find neurons that displayed a voltage-dependent shift in firing behavior. Because this behavior was due, in large part, to a low-threshold calcium conductance, we called these cells low-threshold spike (LTS) neurons. 3. Regular-spiking neurons and LTS neurons only differed in the voltage dependence of firing behavior and the first few interspike intervals (ISIs) of repetitive firing in response to small current injections (from hyperpolarized membrane potentials). Because of the general similarities between the two types, we consider the LTS cells to be a subgroup of regular-spiking cells. 4. All biocytin-filled regular-spiking neurons were spiny and pyramidal and found in layers II-VI. The lone filled fast-spiking cell was aspiny and nonpyramidal (layer V). The LTS neurons were morphologically heterogeneous. We found 80% of LTS neurons to be spiny and pyramidal, but 20% were aspiny nonpyramidal cells. LTS neurons were located in layers II-VI. 5. In conclusion, human association cortex contains two of three physiological cell types described in rodent cortex: regular spiking and fast spiking. These physiological types corresponded to spiny, pyramidal, and aspiny, nonpyramidal cells, respectively. We sampled no intrinsic burst-firing neurons in human association cortex. LTS neurons exhibited voltage-dependent changes in firing behavior and were morphologically heterogeneous: most LTS cells were spiny and pyramidal, but two cells were found to be aspiny and nonpyramidal. It is not clear whether the absence of burst-firing neurons or the morphological heterogeneity of LTS neurons are due to species differences or differences in cortical areas.

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Response to Comment on ”Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons”

10.1101/020354 ◽

2015 ◽

Cited By ~ 2

Author(s):

Srdjan Ostojic

Keyword(s):

Action Potentials ◽

Spiking Neurons ◽

Inhibitory Neurons ◽

Synaptic Coupling ◽

Process Information ◽

Integrate And Fire ◽

Different Types ◽

Dominant Paradigm

Networks of excitatory and inhibitory neurons form the basic computational units in the mammalian cortex. Within the dominant paradigm, neurons in such networks encode and process information by asynchronously emitting action potentials. In a recent publication, I argued that unstructured, sparsely connected networks of integrate-and-fire neurons display a transition between two qualitatively different types of asynchronous activity as the synaptic coupling is increased. A comment by Engelken et al (bioRxiv doi: 10.1101/017798) disputes this finding. Here I provide additional evidence for a transition between two qualitatively different types of asynchronous activity and address the criticism raised in the comment. The claims that the original paper is "factually incorrect" and "conceptually misleading" are unsubstantiated and inappropriate.

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Image Segmentation by Networks of Spiking Neurons

Neural Computation ◽

10.1162/0899766053491913 ◽

2005 ◽

Vol 17 (5) ◽

pp. 1010-1031 ◽

Cited By ~ 18

Author(s):

Joachim M. Buhmann ◽

Tilman Lange ◽

Ulrich Ramacher

Keyword(s):

Image Segmentation ◽

Real World ◽

Network Architecture ◽

Spiking Neurons ◽

Local Smoothing ◽

Class Membership ◽

Local Competition ◽

Integrate And Fire ◽

Clustering Approach ◽

The Mean

A network of leaky integrate-and-fire (IAF) neurons is proposed to segment gray-scale images. The network architecture with local competition between neurons that encode segment assignments of image blocks is motivated by a histogram clustering approach to image segmentation. Lateral excitatory connections between neighboring image sites yield a local smoothing of segments. The mean firing rate of class membership neurons encodes the image segmentation. A weight modification scheme is proposed that estimates segment-specific prototypical histograms. The robustness properties of the network implementation make it amenable to an analog VLSI realization. Results on synthetic and real-world images demonstrate the effectiveness of the architecture.

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Computational Properties of Networks of Synchronous Groups of Spiking Neurons

Neural Computation ◽

10.1162/neco.2007.19.9.2433 ◽

2007 ◽

Vol 19 (9) ◽

pp. 2433-2467 ◽

Cited By ~ 2

Author(s):

Judith E. Dayhoff

Keyword(s):

Neural Network ◽

Artificial Neural Network ◽

Function Approximation ◽

Spiking Neurons ◽

Processing Unit ◽

Group Model ◽

Neuronal Group ◽

Integrate And Fire ◽

Artificial Neural ◽

Neuronal Groups

We demonstrate a model in which synchronously firing ensembles of neurons are networked to produce computational results. Each ensemble is a group of biological integrate-and-fire spiking neurons, with probabilistic interconnections between groups. An analogy is drawn in which each individual processing unit of an artificial neural network corresponds to a neuronal group in a biological model. The activation value of a unit in the artificial neural network corresponds to the fraction of active neurons, synchronously firing, in a biological neuronal group. Weights of the artificial neural network correspond to the product of the interconnection density between groups, the group size of the presynaptic group, and the postsynaptic potential heights in the synchronous group model. All three of these parameters can modulate connection strengths between neuronal groups in the synchronous group models. We give an example of nonlinear classification (XOR) and a function approximation example in which the capability of the artificial neural network can be captured by a neural network model with biological integrate-and-fire neurons configured as a network of synchronously firing ensembles of such neurons. We point out that the general function approximation capability proven for feedforward artificial neural networks appears to be approximated by networks of neuronal groups that fire in synchrony, where the groups comprise integrate-and-fire neurons. We discuss the advantages of this type of model for biological systems, its possible learning mechanisms, and the associated timing relationships.

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