Izhikevich Spiking Neuron Research Articles

Implementation of Izhikevich neuron based on stochastic computing using a novel inspired Omega‐Flip stochastic number generator

AbstractThis paper presents an optimized stochastic multiplier to implement Izhikevich spiking neuron model. A novel stochastic number generator is used as the main block for stochastic computing to design a stochastic multiplier. The designed multiplier was used to describe and implement Izhikevich neuron model equation which is capable to produce variant responses of spiking neurons. To the best of the author's knowledge, this work is the pioneer using a designed multiplier for computing all of the multiplication expressions in spiking neuron equation. The effect of increasing number of bit streams on the accuracy of stochastic computing is studied. Furthermore, some numerical intervals that are more prone to the error are found and illustrated upon stochastic computing usage, and a method is proposed to improve the error prone numerical intervals. In addition, the response accuracy is optimized by changing time step parameter in solving ordinary differential Izhikevich neuron model equation using Euler's method. Hence, a 13‐bit stochastic multiplier is designed. It is found that variations in parameters a and b have a profound effect on the accuracy of recovery variable u and, consequently, on the responses. Out of 20 responses of Izhikevich neuron model, 11 responses are generated using the proposed stochastic computing method and compared with piecewise linear method and some previous architectures of Izhikevich neuron model implementations.

Memristive Izhikevich Spiking Neuron Model and Its Application in Oscillatory Associative Memory.

The Izhikevich (IZH) spiking neuron model can display spiking and bursting behaviors of neurons. Based on the switching property and bio-plausibility of the memristor, the memristive Izhikevich (MIZH) spiking neuron model is built. Firstly, the MIZH spiking model is introduced and used to generate 23 spiking patterns. We compare the 23 spiking patterns produced by the IZH and MIZH spiking models. Secondly, the MIZH spiking model actively reproduces various neuronal behaviors, including the excitatory cortical neurons, the inhibitory cortical neurons, and other cortical neurons. Finally, the collective dynamic activities of the MIZH neuronal network are performed, and the MIZH oscillatory network is constructed. Experimental results illustrate that the constructed MIZH spiking neuron model performs high firing frequency and good frequency adaptation. The model can easily simulate various spiking and bursting patterns of distinct neurons in the brain. The MIZH neuronal network realizes the synchronous and asynchronous collective behaviors. The MIZH oscillatory network can memorize and retrieve the information patterns correctly and efficiently with high retrieval accuracy.

Protein Structured Reservoir Computing for Spike-Based Pattern Recognition

Nowadays we witness a miniaturisation trend in the semiconductor industry backed up by groundbreaking discoveries and designs in nanoscale characterisation and fabrication. To facilitate the trend and produce ever smaller, faster and cheaper computing devices, the size of nanoelectronic devices is now reaching the scale of atoms or molecules - a technical goal undoubtedly demanding for novel devices. Following the trend, we explore an unconventional route of implementing a reservoir computing on a single protein molecule and introduce neuromorphic connectivity with a small-world networking property. We have chosen Izhikevich spiking neurons as elementary processors, corresponding to the atoms of verotoxin protein, and its molecule as a 'hardware' architecture of the communication networks connecting the processors. We apply on a single readout layer various training methods in a supervised fashion to investigate whether the molecular structured Reservoir Computing (RC) system is capable to deal with machine learning benchmarks. We start with the Remote Supervised Method, based on Spike-Timing-Dependent-Plasticity, and carry on with linear regression and scaled conjugate gradient back-propagation training methods. The RC network is evaluated as a proof-of-concept on the handwritten digit images from the MNIST dataset and demonstrates acceptable classification accuracy in comparison with other similar approaches.

Neurodegeneration exposes firing rate dependent effects on oscillation dynamics in computational neural networks

Traumatic brain injury (TBI) can lead to neurodegeneration in the injured circuitry, either through primary structural damage to the neuron or secondary effects that disrupt key cellular processes. Moreover, traumatic injuries can preferentially impact subpopulations of neurons, but the functional network effects of these targeted degeneration profiles remain unclear. Although isolating the consequences of complex injury dynamics and long-term recovery of the circuit can be difficult to control experimentally, computational networks can be a powerful tool to analyze the consequences of injury. Here, we use the Izhikevich spiking neuron model to create networks representative of cortical tissue. After an initial settling period with spike-timing-dependent plasticity (STDP), networks developed rhythmic oscillations similar to those seen in vivo. As neurons were sequentially removed from the network, population activity rate and oscillation dynamics were significantly reduced. In a successive period of network restructuring with STDP, network activity levels returned to baseline for some injury levels and oscillation dynamics significantly improved. We next explored the role that specific neurons have in the creation and termination of oscillation dynamics. We determined that oscillations initiate from activation of low firing rate neurons with limited structural inputs. To terminate oscillations, high activity excitatory neurons with strong input connectivity activate downstream inhibitory circuitry. Finally, we confirm the excitatory neuron population role through targeted neurodegeneration. These results suggest targeted neurodegeneration can play a key role in the oscillation dynamics after injury.

Self-repairing Control against Actuator Failures Using a Spiking Neuron Model

This paper presents a new Self-repairing Control System (SRCS) for plants with actuator failures. The proposed SRCS uses the well-known Izhikevich spiking neuron model as a fault detector. When the actuator fails, the neuron model is excited and then spikes occur. Thus, counting up spikes makes it possible to find failures. Compared with the existing active fault-tolerant control systems, the SRCS has the following advantages: one can not only set a maximum detection time in advance, but also construct a simple control system whose structure is independent of the mathematical model of the plant. To confirm the effectiveness of the SRCS, this paper shows theoretical performance analysis and numerical simulation.

A Neuromorphic Model to Match the Spiking Activity of Merkel Mechanoreceptors With Biomimetic Tactile Sensors for Bioengineering Applications

A major challenge in upper limb neuroprostheses is to reproduce the tactile feedback as the one provided by the spiking activity of human mechanoreceptors. In this paper, we aim at emulating the firing behavior of Merkel mechanoreceptors, innervated by slowly adapting type I (SA1) receptors, in silico by means of a custom implementation of the Izhikevich spiking neuron model with a porting function of the sensors output. We matched the neuron model output with the sustained firing observed in neurophysiological experiments in response to constant stimuli to the skin. We compared different input transformation functions to find the proper trade-off between agreement with biological spiking activity and model leanness. We identified a porting function that converts the output of physical sensors into the input to artificial spiking models of mechanoreceptors. The porting function was then validated by comparing the firing rate-indentation curve of real mechanoreceptors with the one obtained from an MEMS-based biomimetic tactile sensor platform. From the analysis of the adjusted-residual variance, the two curves result coherent. Therefore, having applied the calibration inverse function to a sensor output, the proposed porting function allows obtaining the proper input to an artificial neuron model, enabling the generation of neuromorphic signals.

Firing-rate models for neurons with a broad repertoire of spiking behaviors

Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.

Building a Spiking Neural Network Model of the Basal Ganglia on SpiNNaker

We present a biologically inspired and scalable model of the basal ganglia (BG) simulated on the spiking neural network architecture (SpiNNaker) machine, a biologically inspired low-power hardware platform allowing parallel, asynchronous computing. Our BG model consists of six cell populations, where the neuro-computational unit is a conductance-based Izhikevich spiking neuron; the number of neurons in each population is proportional to that reported in anatomical literature. This model is treated as a single-channel of action-selection in the BG, and is scaled-up to three channels with lateral cross-channel connections. When tested with two competing inputs, this three-channel model demonstrates action-selection behavior. The SpiNNaker-based model is mapped exactly on to SpineML running on a conventional computer; both model responses show functional and qualitative similarity, thus validating the usability of SpiNNaker for simulating biologically plausible networks. Furthermore, the SpiNNaker-based model simulates in real time for time-steps $\geq {1}$ ms; power dissipated during model execution is $\approx {1.8}$ W.

Unsupervised heart-rate estimation in wearables with Liquid states and a probabilistic readout

Heart-rate estimation is a fundamental feature of modern wearable devices. In this paper we propose a machine learning technique to estimate heart-rate from electrocardiogram (ECG) data collected using wearable devices. The novelty of our approach lies in (1) encoding spatio-temporal properties of ECG signals directly into spike train and using this to excite recurrently connected spiking neurons in a Liquid State Machine computation model; (2) a novel learning algorithm; and (3) an intelligently designed unsupervised readout based on Fuzzy c-Means clustering of spike responses from a subset of neurons (Liquid states), selected using particle swarm optimization. Our approach differs from existing works by learning directly from ECG signals (allowing personalization), without requiring costly data annotations. Additionally, our approach can be easily implemented on state-of-the-art spiking-based neuromorphic systems, offering high accuracy, yet significantly low energy footprint, leading to an extended battery-life of wearable devices. We validated our approach with CARLsim, a GPU accelerated spiking neural network simulator modeling Izhikevich spiking neurons with Spike Timing Dependent Plasticity (STDP) and homeostatic scaling. A range of subjects is considered from in-house clinical trials and public ECG databases. Results show high accuracy and low energy footprint in heart-rate estimation across subjects with and without cardiac irregularities, signifying the strong potential of this approach to be integrated in future wearable devices.

Detecting invasive species with a bio-inspired semi-supervised neurocomputing approach: the case of Lagocephalus sceleratus

The need to protect the environment and biodiversity and to safeguard public health require the development of timely and reliable methods for the identification of particularly dangerous invasive species, before they become regulators of ecosystems. These species appear to be morphologically similar, despite their strong biological differences, something that complicates their identification process. Additionally, the localization of the broader space of dispersion and the development of invasive species are considered to be of critical importance in the effort to take proper management measures. The aim of this research is to create an advanced computational intelligence system for the automatic recognition, of invasive or another unknown species. The identification is performed based on the analysis of environmental DNA by employing machine learning methods. More specifically, this research effort proposes a hybrid bio-inspired computational intelligence detection approach. It employs extreme learning machines combined with an evolving Izhikevich spiking neuron model for the automated identification of the invasive fish species “Lagocephalus sceleratus” extremely dangerous for human health.

LEARNING STIMULUS-STIMULUS ASSOCIATION IN SPATIO-TEMPORAL NEURAL NETWORKS

We propose a stimulus-stimulus association learning by coupling firing rate and precise spike timing encoding for spatio-temporal neural networks. We simulate a generic recurrent network with random and sparse connectivity consisting of Izhikevich spiking neurons. The magnitude of weight adjustment in learning is dependent on pre- and postsynaptic spikes based on their spikes count and time correlation. As a result of learning, synchronisation of activity among inter- and intra-subpopulation neurons demonstrates association between two stimuli. The associations show in spill-over of activity between the two stimuli involved.

Computational simulation of dentate gyrus granule cell—The role of metaplasticity

After several decades of study, the dynamics of synaptic plasticity in neurons still remains somewhat a mystery. By conducting a series of simulations on a simulated version of an in-vivo experiment on the rat dentate gyrus granule cell, using the Izhikevich spiking neuron model, we compare and contrast several potential synaptic plasticity rules׳ applicability to the same experiment. Our simulations reveal that spike timing dependent plasticity (STDP), a more recent theory of synaptic plasticity, is insufficient to replicate the heterosynaptic LTD shown in the experiment without including aspects of the significantly older Bienenstock–Cooper–Munro (BCM) theory. The STDP rule modified by including the history of postsynaptic spiking seems most likely to be an accurate candidate for reproducing the heterosynaptic plasticity dynamics.

Formation and disruption of tonotopy in a large-scale model of the auditory cortex.

There is ample experimental evidence describing changes of tonotopic organisation in the auditory cortex due to environmental factors. In order to uncover the underlying mechanisms, we designed a large-scale computational model of the auditory cortex. The model has up to 100 000 Izhikevich's spiking neurons of 17 different types, almost 21 million synapses, which are evolved according to Spike-Timing-Dependent Plasticity (STDP) and have an architecture akin to existing observations. Validation of the model revealed alternating synchronised/desynchronised states and different modes of oscillatory activity. We provide insight into these phenomena via analysing the activity of neuronal subtypes and testing different causal interventions into the simulation. Our model is able to produce experimental predictions on a cell type basis. To study the influence of environmental factors on the tonotopy, different types of auditory stimulations during the evolution of the network were modelled and compared. We found that strong white noise resulted in completely disrupted tonotopy, which is consistent with in vivo experimental observations. Stimulation with pure tones or spontaneous activity led to a similar degree of tonotopy as in the initial state of the network. Interestingly, weak white noise led to a substantial increase in tonotopy. As the STDP was the only mechanism of plasticity in our model, our results suggest that STDP is a sufficient condition for the emergence and disruption of tonotopy under various types of stimuli. The presented large-scale model of the auditory cortex and the core simulator, SUSNOIMAC, have been made publicly available.

A spiking Basal Ganglia model of synchrony, exploration and decision making.

To make an optimal decision we need to weigh all the available options, compare them with the current goal, and choose the most rewarding one. Depending on the situation an optimal decision could be to either “explore” or “exploit” or “not to take any action” for which the Basal Ganglia (BG) is considered to be a key neural substrate. In an attempt to expand this classical picture of BG function, we had earlier hypothesized that the Indirect Pathway (IP) of the BG could be the subcortical substrate for exploration. In this study we build a spiking network model to relate exploration to synchrony levels in the BG (which are a neural marker for tremor in Parkinson's disease). Key BG nuclei such as the Sub Thalamic Nucleus (STN), Globus Pallidus externus (GPe) and Globus Pallidus internus (GPi) were modeled as Izhikevich spiking neurons whereas the Striatal output was modeled as Poisson spikes. The model is cast in reinforcement learning framework with the dopamine signal representing reward prediction error. We apply the model to two decision making tasks: a binary action selection task (similar to one used by Humphries et al., 2006) and an n-armed bandit task (Bourdaud et al., 2008). The model shows that exploration levels could be controlled by STN's lateral connection strength which also influenced the synchrony levels in the STN-GPe circuit. An increase in STN's lateral strength led to a decrease in exploration which can be thought as the possible explanation for reduced exploratory levels in Parkinson's patients. Our simulations also show that on complete removal of IP, the model exhibits only Go and No-Go behaviors, thereby demonstrating the crucial role of IP in exploration. Our model provides a unified account for synchronization, action section, and explorative behavior.

A Minimal Spiking Neural Network to Rapidly Train and Classify Handwritten Digits in Binary and 10-Digit Tasks

This paper reports the results of experiments to develop a minimal neural network for pattern classification. The network uses biologically plausible neural and learning mechanisms and is applied to a subset of the MNIST dataset of handwritten digits. The research goal is to assess the classification power of a very simple biologically motivated mechanism. The network architecture is primarily a feedforward spiking neural network (SNN) composed of Izhikevich regular spiking (RS) neurons and conductance-based synapses. The weights are trained with the spike timing-dependent plasticity (STDP) learning rule. The proposed SNN architecture contains three neuron layers which are connected by both static and adaptive synapses. Visual input signals are processed by the first layer to generate input spike trains. The second and third layers contribute to spike train segmentation and STDP learning, respectively. The network is evaluated by classification accuracy on the handwritten digit images from the MNIST dataset. The simulation results show that although the proposed SNN is trained quickly without error-feedbacks in a few number of iterations, it results in desirable performance (97.6%) in the binary classification (0 and 1). In addition, the proposed SNN gives acceptable recognition accuracy in 10-digit (0-9) classification in comparison with statistical methods such as support vector machine (SVM) and multi-perceptron neural network.

ASIC Implementation for Improved Character Recognition and Classification using SNN Model

The third generation of spiking neural networks raises the level of biological realism by using individual spikes. So instead of using rate coding, these neurons use pulse coding mechanisms where neurons receive and do send out individual pulses, allowing multiplexing of information. This work depicts how Spiking neural network model is used for character recognition and classification. Here, we adapt to the technique of using ASIC for large scale simulations of the Izhikevich model and use RTL Clock gating approach for reducing the dynamic power. Here the focus is on how power consumption and system cost can be reduced for large production run. The full custom biologically plausible spiking neural network model is implemented on ASIC with 90 nm Process. The Izhikevich spiking neuron model is best suited for large scale cortical simulations due to its accuracy, efficiency, power and simulation time. The classification efficiency of SNN based on MATLAB simulations is demonstrated in this work by its ability to classify the 27 characters correctly out of 30 noisy character images presented. The ASIC realizing the English character classification and recognition dissipates power of 2.8 mW and an area of 120312 μm2. This work brings about the application of using networks of these spiking neurons for character recognition and their suitability for custom realization with reduced power consumption.

Biologically Inspired Temporal Sequence Learning

We propose a temporal sequence learning model in spiking neural networks consisting of Izhikevich spiking neurons. In our reward-based learning model, we train a network to associate two stimuli with temporal delay and a target response. Learning rule is dependent on reward signals that modulate the weight changes derived from spike-timing dependent plasticity (STDP) function. The dynamic properties of our model can be attributed to the sparse and recurrent connectivity, synaptic transmission delays, background activity and inter-stimulus interval (ISI). We have tested the learning in visual recognition task, and temporal AND and XOR problems. The network can be trained to associate a stimulus pair with its target response and to discriminate the temporal sequence of the stimulus presentation.

Evolvable Neuronal Paths: A Novel Basis for Information and Search in the Brain

We propose a previously unrecognized kind of informational entity in the brain that is capable of acting as the basis for unlimited hereditary variation in neuronal networks. This unit is a path of activity through a network of neurons, analogous to a path taken through a hidden Markov model. To prove in principle the capabilities of this new kind of informational substrate, we show how a population of paths can be used as the hereditary material for a neuronally implemented genetic algorithm, (the swiss-army knife of black-box optimization techniques) which we have proposed elsewhere could operate at somatic timescales in the brain. We compare this to the same genetic algorithm that uses a standard ‘genetic’ informational substrate, i.e. non-overlapping discrete genotypes, on a range of optimization problems. A path evolution algorithm (PEA) is defined as any algorithm that implements natural selection of paths in a network substrate. A PEA is a previously unrecognized type of natural selection that is well suited for implementation by biological neuronal networks with structural plasticity. The important similarities and differences between a standard genetic algorithm and a PEA are considered. Whilst most experiments are conducted on an abstract network model, at the conclusion of the paper a slightly more realistic neuronal implementation of a PEA is outlined based on Izhikevich spiking neurons. Finally, experimental predictions are made for the identification of such informational paths in the brain.

Emergence of synchronicity in a self-organizing spiking neuron network: an approach via genetic algorithms

Based on the Theory of Neuronal Group Selection (TNGS), we have investigated the emergence of synchronicity in a network composed of spiking neurons via genetic algorithm. The TNGS establishes that a neuronal group is the most basic unit in the cortical area of the brain and, as a rule, it is not formed by a single neuron, but by a cluster of tightly coupled neural cells which fire and oscillate in synchrony at a predefined frequency. Thus, this paper describes a method of tuning the parameters of the Izhikevich spiking neuron model through genetic algorithm in order to enable the self-organization of the neural network. Computational experiments were performed considering a network composed of neurons of the same type and another composed of neurons of different types.

The polychronic economy

The polychronic economy