Homogeneous spiking neural P systems working in sequential mode induced by maximum spike number

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired by the way neurons communicate by means of spikes, where neurons work in parallel in the sense that each neuron that can fire should fire at each computation step, and neurons can be different in the sense that they can have different sets of spiking rules. In this work, we consider SN P systems with the restrictions: (1) all neurons are homogeneous in the sense that each neuron has the same set of rules; (2) at each step the neuron with the maximum number of spikes among the neurons that are active (can spike) will fire. These restrictions correspond to the fact that the system consists of only one kind of neurons and a global view of the whole network makes the system sequential. The computation power of homogeneous SN P systems working in the sequential mode induced by the maximum spike number is investigated. Specifically, it is proved that such systems are universal as both generating and accepting devices.     

Action Recognition Using a Bio-Inspired Feedforward Spiking Network

We propose a bio-inspired feedforward spiking network modeling two brain areas dedicated to motion (V1 and MT), and we show how the spiking output can be exploited in a computer vision application: action recognition. In order to analyze spike trains, we consider two characteristics of the neural code: mean firing rate of each neuron and synchrony between neurons. Interestingly, we show that they carry some relevant information for the action recognition application. We compare our results to Jhuang et al. (Proceedings of the 11th international conference on computer vision, pp. 1–8, 2007) on the Weizmann database. As a conclusion, we are convinced that spiking networks represent a powerful alternative framework for real vision applications that will benefit from recent advances in computational neuroscience.     

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.     

On computing Boolean functions by a spiking neuron

Computations by spiking neurons are performed using the timing of action potentials. We investigate the computational power of a simple model for such a spiking neuron in the Boolean domain by comparing it with traditional neuron models such as threshold gates (or McCulloch–Pitts neurons) and sigma-pi units (or polynomial threshold gates). In particular, we estimate the number of gates required to simulate a spiking neuron by a disjunction of threshold gates and we establish tight bounds for this threshold number. Furthermore, we analyze the degree of the polynomials that a sigma-pi unit must use for the simulation of a spiking neuron. We show that this degree cannot be bounded by any fixed value. Our results give evidence that the use of continuous time as a computational resource endows single-cell models with substantially larger computational capabilities. This revised version was published online in June 2006 with corrections to the Cover Date.     

Finding the event structure of neuronal spike trains

Neurons in sensory systems convey information about physical stimuli in their spike trains. In vitro, single neurons respond precisely and reliably to the repeated injection of the same fluctuating current, producing regions of elevated firing rate, termed events. Analysis of these spike trains reveals that multiple distinct spike patterns can be identified as trial-to-trial correlations between spike times (Fellous, Tiesinga, Thomas, & Sejnowski, 2004 ). Finding events in data with realistic spiking statistics is challenging because events belonging to different spike patterns may overlap. We propose a method for finding spiking events that uses contextual information to disambiguate which pattern a trial belongs to. The procedure can be applied to spike trains of the same neuron across multiple trials to detect and separate responses obtained during different brain states. The procedure can also be applied to spike trains from multiple simultaneously recorded neurons in order to identify volleys of near-synchronous activity or to distinguish between excitatory and inhibitory neurons. The procedure was tested using artificial data as well as recordings in vitro in response to fluctuating current waveforms.     

Spiking神经元输入脉冲扰动敏感性研究

脉冲神经网络是一种基于生物的网络模型,它的输入输出为具有时间特性的脉冲序列,其运行机制相比其他传统人工神经网络更加接近于生物神经网络。神经元之间通过脉冲序列传递信息,这些信息通过脉冲的激发时间编码能够更有效地发挥网络的学习性能。脉冲神经元的时间特性导致了其工作机制较为复杂,而spiking神经元的敏感性反映了当神经元输入发生扰动时输出的spike的变化情况,可以作为研究神经元内部工作机制的工具。不同于传统的神经网络,spiking神经元敏感性定义为输出脉冲的变化时刻个数与运行时间长度的比值,能直接反映出输入扰动对输出的影响程度。通过对不同形式的输入扰动敏感性的分析,可以看出spiking神经元的敏感性较为复杂,当全体突触发生扰动时,神经元为定值,而当部分突触发生扰动时,不同突触的扰动会导致不同大小的神经元敏感性。     

On the nonlearnability of a single spiking neuron

We study the computational complexity of training a single spiking neuron N with binary coded inputs and output that, in addition to adaptive weights and a threshold, has adjustable synaptic delays. A synchronization technique is introduced so that the results concerning the nonlearnability of spiking neurons with binary delays are generalized to arbitrary real-valued delays. In particular, the consistency problem for N with programmable weights, a threshold, and delays, and its approximation version are proven to be NP-complete. It follows that the spiking neurons with arbitrary synaptic delays are not properly PAC learnable and do not allow robust learning unless RP = NP. In addition, the representation problem for N, a question whether an n-variable Boolean function given in DNF (or as a disjunction of O(n) threshold gates) can be computed by a spiking neuron, is shown to be coNP-hard.     

Categorization of neural excitability using threshold models

A classification of spiking neurons according to the transition from quiescence to periodic firing of action potentials is commonly used. Nonbursting neurons are classified into two types, type I and type II excitability. We use simple phenomenological spiking neuron models to derive a criterion for the determination of the neural excitability based on the afterpotential following a spike. The crucial characteristic is the existence for type II model of a positive overshoot, that is, a delayed after depolarization, during the recovery process of the membrane potential. Our prediction is numerically tested using well-known type I and type II models including the Connor, Walter, & McKown (1977) model and the Hodgkin-Huxley (1952) model.     

Classification of motor imagery electroencephalography signals using spiking neurons with different input encoding strategies

Motor imagery-based brain–computer interfaces decode users’ intentions from the electroencephalogram; however, poor spatial resolution makes automatic recognition of these intentions a challenging task. New classification approaches with low computational costs and high classification performances need to be developed in order to increase the number of users benefitted by these systems. On the other hand, spiking neuron models, which are mathematical abstractions of real neurons, have shown good performances in several classification tasks, making these models suitable for motor imagery classification. In this work, two different encoding strategies for spiking neuron models, applied to the classification of motor imagery time–frequency features of stroke patients and healthy subjects, were evaluated. Classification performances and computational costs of spiking neuron models were compared against those of linear discriminant analysis, support vector machines and artificial neural networks. Results showed that a time-varying encoding strategy is more suitable for motor imagery classification, and its implementation computational cost is low. Therefore, a spiking neuron model with a time-varying encoding strategy could increase the number of potential users of brain–computer interfaces.

     

Higher-order statistics of input ensembles and the response of simple model neurons

Pairwise correlations among spike trains recorded in vivo have been frequently reported. It has been argued that correlated activity could play an important role in the brain, because it efficiently modulates the response of a postsynaptic neuron. We show here that a neuron's output firing rate critically depends on the higher-order statistics of the input ensemble. We constructed two statistical models of populations of spiking neurons that fired with the same rates and had identical pairwise correlations, but differed with regard to the higher-order interactions within the population. The first ensemble was characterized by clusters of spikes synchronized over the whole population. In the second ensemble, the size of spike clusters was, on average, proportional to the pairwise correlation. For both input models, we assessed the role of the size of the population, the firing rate, and the pairwise correlation on the output rate of two simple model neurons: a continuous firing-rate model and a conductance-based leaky integrate-and-fire neuron. An approximation to the mean output rate of the firing-rate neuron could be derived analytically with the help of shot noise theory. Interestingly, the essential features of the mean response of the two neuron models were similar. For both neuron models, the three input parameters played radically different roles with respect to the postsynaptic firing rate, depending on the interaction structure of the input. For instance, in the case of an ensemble with small and distributed spike clusters, the output firing rate was efficiently controlled by the size of the input population. In addition to the interaction structure, the ratio of inhibition to excitation was found to strongly modulate the effect of correlation on the postsynaptic firing rate.     

基于生物机制脉冲神经网络的特征提取

脉冲神经元可以被用于处理生物刺激并且可以解释大脑复杂的智能行为。脉冲神经网络以非常逼近生物的神经元模型作为处理单元,可以直接用来仿真脑科学中发现的神经网络计算模型,输出的脉冲信号还可与生物神经系统对接。而小波变换是一个非常有利的时频分析工具,它可以有效的压缩图像并且提取图像的特征。本文中将提出一种与人类视觉系统的开/关神经元阵列相结合的脉冲神经网络,来实现针对视觉图像的快速小波变换。仿真结果显示,这个脉冲神经网络可以很好地保留视觉图像的关键特征。     

Spiking neural P systems with neuron division and budding

Spiking neural P systems are a class of distributed and parallel computing models inspired by spiking neurons.In this work,the features of neuron division and neuron budding are introduced into the framework of spiking neural P systems,which are processes inspired by neural stem cell division. With neuron division and neuron budding,a spiking neural P system can generate exponential work space in polynomial time as the case for P systems with active membranes.In this way,spiking neural P systems can efficie...     

基于脉冲神经网络的红外目标提取

模拟生物信息处理机制,设计了一种用于红外目标提取的脉冲神经网络(SNN)。首先,利用输入层脉冲神经元将激励图像转化为脉冲序列;其次,采用中间层脉冲神经元输出脉冲的密度编码红外图像目标的轮廓像素和非目标轮廓像素;最后,根据输出层神经元输出脉冲的密度是否超过阈值提取红外目标。实验结果表明,设计的脉冲神经网络具有较好的红外目标提取性能,并且符合生物视觉信息处理机制。     

Delay learning and polychronization for reservoir computing

We propose a multi-timescale learning rule for spiking neuron networks, in the line of the recently emerging field of reservoir computing. The reservoir is a network model of spiking neurons, with random topology and driven by STDP (spike-time-dependent plasticity), a temporal Hebbian unsupervised learning mode, biologically observed. The model is further driven by a supervised learning algorithm, based on a margin criterion, that affects the synaptic delays linking the network to the readout neurons, with classification as a goal task. The network processing and the resulting performance can be explained by the concept of polychronization, proposed by Izhikevich [Polychronization: computation with spikes, Neural Comput. 18(2) (2006) 245–282], on physiological grounds. The model emphasizes that polychronization can be used as a tool for exploiting the computational power of synaptic delays and for monitoring the topology and activity of a spiking neuron network.     

Multiple resonances with time delays and enhancement by non-Gaussian noise in Newman-Watts networks of Hodgkin-Huxley neurons

In this paper, we study the effect of time delay on the spiking activity in Newman-Watts small-world networks of Hodgkin-Huxley neurons with non-Gaussian noise, and investigate how the non-Gaussian noise affects the delay-induced behaviors. It was found that, as the delay increases, the neuron spiking intermittently performs the most ordered and synchronized behavior when the delay lengths are integer multiples of the spiking periods, which shows multiple temporal resonances and spatial synchronizations, and reveals that the locking between the delay lengths and the spiking periods might be the mechanism behind the behaviors. It was also found that the delay-optimized spiking behaviors could be enhanced when non-Gaussian noise's deviation from the Gaussian noise is appropriate. These results show that time delay and non-Gaussian noise would cooperate to play more constructive and efficient roles in the information processing of neural networks.     

面向图像识别的多层脉冲神经网络学习算法综述

相较于第1代和第2代神经网络,第3代神经网络的脉冲神经网络是一种更加接近于生物神经网络的模型,因此更具有生物可解释性和低功耗性。基于脉冲神经元模型,脉冲神经网络可以通过脉冲信号的形式模拟生物信号在神经网络中的传播,通过脉冲神经元的膜电位变化来发放脉冲序列,脉冲序列通过时空联合表达不仅传递了空间信息还传递了时间信息。当前面向模式识别任务的脉冲神经网络模型性能还不及深度学习,其中一个重要原因在于脉冲神经网络的学习方法不成熟,深度学习中神经网络的人工神经元是基于实数形式的输出,这使得其可以使用全局性的反向传播算法对深度神经网络的参数进行训练,脉冲序列是二值性的离散输出,这直接导致对脉冲神经网络的训练存在一定困难,如何对脉冲神经网络进行高效训练是一个具有挑战的研究问题。本文首先总结了脉冲神经网络研究领域中的相关学习算法,然后对其中主要的方法:直接监督学习、无监督学习的算法以及ANN2SNN的转换算法进行分析介绍,并对其中代表性的工作进行对比分析,最后基于对当前主流方法的总结,对未来更高效、更仿生的脉冲神经网络参数学习方法进行展望。     

What can a neuron learn with spike-timing-dependent plasticity?

Spiking neurons are very flexible computational modules, which can implement with different values of their adjustable synaptic parameters an enormous variety of different transformations F from input spike trains to output spike trains. We examine in this letter the question to what extent a spiking neuron with biologically realistic models for dynamic synapses can be taught via spike-timing-dependent plasticity (STDP) to implement a given transformation F. We consider a supervised learning paradigm where during training, the output of the neuron is clamped to the target signal (teacher forcing). The well-known perceptron convergence theorem asserts the convergence of a simple supervised learning algorithm for drastically simplified neuron models (McCulloch-Pitts neurons). We show that in contrast to the perceptron convergence theorem, no theoretical guarantee can be given for the convergence of STDP with teacher forcing that holds for arbitrary input spike patterns. On the other hand, we prove that average case versions of the perceptron convergence theorem hold for STDP in the case of uncorrelated and correlated Poisson input spike trains and simple models for spiking neurons. For a wide class of cross-correlation functions of the input spike trains, the resulting necessary and sufficient condition can be formulated in terms of linear separability, analogously as the well-known condition of learnability by perceptrons. However, the linear separability criterion has to be applied here to the columns of the correlation matrix of the Poisson input. We demonstrate through extensive computer simulations that the theoretically predicted convergence of STDP with teacher forcing also holds for more realistic models for neurons, dynamic synapses, and more general input distributions. In addition, we show through computer simulations that these positive learning results hold not only for the common interpretation of STDP, where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.     

脉冲神经元环路振荡发放与环路选择

在Izhikevich提出的脉冲神经元模型中,引入随机变化的输入电流,使神经元的脉冲发放具有随机性,不同数量的神经元采用连接权值组成网络的脉冲发放。实验结果表明,选择适当的连接权值可以得到环路的持续振荡发放。通过脉冲发放,可以在网络中选择神经环路,完成环路记忆联想过程,并给出研究脉冲神经智能的新思路。     

基于卷积计算的多层脉冲神经网络的监督学习

针对脉冲神经元基于精确定时的多脉冲编码信息的特点,提出了一种基于卷积计算的多层脉冲神经网络监督学习的新算法。该算法应用核函数的卷积计算将离散的脉冲序列转换为连续函数,在多层前馈脉冲神经网络结构中,使用梯度下降的方法得到基于核函数卷积表示的学习规则,并用来调整神经元连接的突触权值。在实验部分,首先验证了该算法学习脉冲序列的效果,然后应用该算法对Iris数据集进行分类。结果显示,该算法能够实现脉冲序列复杂时空模式的学习,对非线性模式分类问题具有较高的分类正确率。