Spike pattern recognition using artificial neuron and spike-timing-dependent plasticity implemented on a multi-core embedded platform

The objective of this work is to use a multi-core embedded platform as computing architectures for neural applications relevant to neuromorphic engineering: e.g., robotics, and artificial and spiking neural networks. Recently, it has been shown how spike-timing-dependent plasticity (STDP) can play a key role in pattern recognition. In particular, multiple repeating arbitrary spatio-temporal spike patterns hidden in spike trains can be robustly detected and learned by multiple neurons equipped with spike-timing-dependent plasticity listening to the incoming spike trains. This paper presents an implementation on a biological time scale of STDP algorithm to localize a repeating spatio-temporal spike patterns on a multi-core embedded platform.     

脉冲神经网络:模型、学习算法与应用

脉冲神经网络是目前最具有生物解释性的人工神经网络,是类脑智能领域的核心组成部分.首先介绍各类常用的脉冲神经元模型以及前馈和循环型脉冲神经网络结构;然后介绍脉冲神经网络的时间编码方式,在此基础上,系统地介绍脉冲神经网络的学习算法,包括无监督学习和监督学习算法,其中监督学习算法按照梯度下降算法、结合STDP规则的算法和基于脉冲序列卷积核的算法3大类别分别展开详细介绍和总结;接着列举脉冲神经网络在控制领域、模式识别领域和类脑智能研究领域的应用,并在此基础上介绍各国脑计划中,脉冲神经网络与神经形态处理器相结合的案例;最后分析脉冲神经网络目前所存在的困难和挑战.     

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.     

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。     

Advances in Design and Application of Spiking Neural Networks

This paper presents new findings in the design and application of biologically plausible neural networks based on spiking neuron models, which represent a more plausible model of real biological neurons where time is considered as an important feature for information encoding and processing in the brain. The design approach consists of an evolutionary strategy based supervised training algorithm, newly developed by the authors, and the use of different biologically plausible neuronal models. A dynamic synapse (DS) based neuron model, a biologically more detailed model, and the spike response model (SRM) are investigated in order to demonstrate the efficacy of the proposed approach and to further our understanding of the computing capabilities of the nervous system. Unlike the conventional synapse, represented as a static entity with a fixed weight, employed in conventional and SRM-based neural networks, a DS is weightless and its strength changes upon the arrival of incoming input spikes. Therefore its efficacy depends on the temporal structure of the impinging spike trains. In the proposed approach, the training of the network free parameters is achieved using an evolutionary strategy where, instead of binary encoding, real values are used to encode the static and DS parameters which underlie the learning process. The results show that spiking neural networks based on both types of synapse are capable of learning non-linearly separable data by means of spatio-temporal encoding. Furthermore, a comparison of the obtained performance with classical neural networks (multi-layer perceptrons) is presented.     

A gradient descent rule for spiking neurons emitting multiple spikes

A supervised learning rule for Spiking Neural Networks (SNNs) is presented that can cope with neurons that spike multiple times. The rule is developed by extending the existing SpikeProp algorithm which could only be used for one spike per neuron. The problem caused by the discontinuity in the spike process is counteracted with a simple but effective rule, which makes the learning process more efficient. Our learning rule is successfully tested on a classification task of Poisson spike trains. We also applied the algorithm on a temporal version of the XOR problem and show that it is possible to learn this classical problem using only one spiking neuron making use of a hair-trigger situation.     

Analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity

Analyzing the dependencies between spike trains is an important step in understanding how neurons work in concert to represent biological signals. Usually this is done for pairs of neurons at a time using correlation-based techniques. Chornoboy, Schramm, and Karr (1988) proposed maximum likelihood methods for the simultaneous analysis of multiple pair-wise interactions among an ensemble of neurons. One of these methods is an iterative, continuous-time estimation algorithm for a network likelihood model formulated in terms of multiplicative conditional intensity functions. We devised a discrete-time version of this algorithm that includes a new, efficient computational strategy, a principled method to compute starting values, and a principled stopping criterion. In an analysis of simulated neural spike trains from ensembles of interacting neurons, the algorithm recovered the correct connectivity matrices and interaction parameters. In the analysis of spike trains from an ensemble of rat hippocampal place cells, the algorithm identified a connectivity matrix and interaction parameters consistent with the pattern of conjoined firing predicted by the overlap of the neurons' spatial receptive fields. These results suggest that the network likelihood model can be an efficient tool for the analysis of ensemble spiking activity.     

脉冲神经膜系统在穷举使用规则下产生的二进制字符串语言

脉冲神经膜系统是基于大脑中神经元之间通过突触相瓦协作、处理脉冲的生物现象提出的一种新的模型,文中在穷举使用规则的情况下考虑将脉冲神经膜系统作为串语言产生器:当输出神经元发送出一个或多个神经脉冲时,用数字1表示,否则用数字0表示,当计算停止时,把产生的二进制串定义为系统的计算结果.在文中,作者让明了在穷举使用规则的情况下,具有一个神经元的脉冲神经膜系统可以刻画二进制有限语言,并且证明了在不限制神经元个数的情况下,该系统可以刻画递归可枚举语言.     

A VLSI array of low-power spiking neurons and bistable synapses with spike-timing dependent plasticity

We present a mixed-mode analog/digital VLSI device comprising an array of leaky integrate-and-fire (I&F) neurons, adaptive synapses with spike-timing dependent plasticity, and an asynchronous event based communication infrastructure that allows the user to (re)configure networks of spiking neurons with arbitrary topologies. The asynchronous communication protocol used by the silicon neurons to transmit spikes (events) off-chip and the silicon synapses to receive spikes from the outside is based on the "address-event representation" (AER). We describe the analog circuits designed to implement the silicon neurons and synapses and present experimental data showing the neuron's response properties and the synapses characteristics, in response to AER input spike trains. Our results indicate that these circuits can be used in massively parallel VLSI networks of I&F neurons to simulate real-time complex spike-based learning algorithms.     

A low-order model of biological neural networks

A biologically plausible low-order model (LOM) of biological neural networks is proposed. LOM is a recurrent hierarchical network of models of dendritic nodes and trees; spiking and nonspiking neurons; unsupervised, supervised covariance and accumulative learning mechanisms; feedback connections; and a scheme for maximal generalization. These component models are motivated and necessitated by making LOM learn and retrieve easily without differentiation, optimization, or iteration, and cluster, detect, and recognize multiple and hierarchical corrupted, distorted, and occluded temporal and spatial patterns. Four models of dendritic nodes are given that are all described as a hyperbolic polynomial that acts like an exclusive-OR logic gate when the model dendritic nodes input two binary digits. A model dendritic encoder that is a network of model dendritic nodes encodes its inputs such that the resultant codes have an orthogonality property. Such codes are stored in synapses by unsupervised covariance learning, supervised covariance learning, or unsupervised accumulative learning, depending on the type of postsynaptic neuron. A masking matrix for a dendritic tree, whose upper part comprises model dendritic encoders, enables maximal generalization on corrupted, distorted, and occluded data. It is a mathematical organization and idealization of dendritic trees with overlapped and nested input vectors. A model nonspiking neuron transmits inhibitory graded signals to modulate its neighboring model spiking neurons. Model spiking neurons evaluate the subjective probability distribution (SPD) of the labels of the inputs to model dendritic encoders and generate spike trains with such SPDs as firing rates. Feedback connections from the same or higher layers with different numbers of unit-delay devices reflect different signal traveling times, enabling LOM to fully utilize temporally and spatially associated information. Biological plausibility of the component models is discussed. Numerical examples are given to demonstrate how LOM operates in retrieving, generalizing, and unsupervised and supervised learning.     

Efficient event-driven simulation of large networks of spiking neurons and dynamical synapses

A simulation procedure is described for making feasible large-scale simulations of recurrent neural networks of spiking neurons and plastic synapses. The procedure is applicable if the dynamic variables of both neurons and synapses evolve deterministically between any two successive spikes. Spikes introduce jumps in these variables, and since spike trains are typically noisy, spikes introduce stochasticity into both dynamics. Since all events in the simulation are guided by the arrival of spikes, at neurons or synapses, we name this procedure event-driven. The procedure is described in detail, and its logic and performance are compared with conventional (synchronous) simulations. The main impact of the new approach is a drastic reduction of the computational load incurred upon introduction of dynamic synaptic efficacies, which vary organically as a function of the activities of the pre- and postsynaptic neurons. In fact, the computational load per neuron in the presence of the synaptic dynamics grows linearly with the number of neurons and is only about 6% more than the load with fixed synapses. Even the latter is handled quite efficiently by the algorithm. We illustrate the operation of the algorithm in a specific case with integrate-and-fire neurons and specific spike-driven synaptic dynamics. Both dynamical elements have been found to be naturally implementable in VLSI. This network is simulated to show the effects on the synaptic structure of the presentation of stimuli, as well as the stability of the generated matrix to the neural activity it induces.     

Information encoding and computation with spikes and bursts

Neurons compute and communicate by transforming synaptic input patterns into output spike trains. The nature of this transformation depends crucially on the properties of voltage-gated conductances in neuronal membranes. These intrinsic membrane conductances can enable neurons to generate different spike patterns including brief, high-frequency bursts that are commonly observed in a variety of brain regions. Here we examine how the membrane conductances that generate bursts affect neural computation and encoding. We simulated a bursting neuron model driven by random current input signal and superposed noise. We consider two issues: the timing reliability of different spike patterns and the computation performed by the neuron. Statistical analysis of the simulated spike trains shows that the timing of bursts is much more precise than the timing of single spikes. Furthermore, the number of spikes per burst is highly robust to noise. Next we considered the computation performed by the neuron: how different features of the input current are mapped into specific output spike patterns. Dimensional reduction and statistical classification techniques were used to determine the stimulus features triggering different firing patterns. Our main result is that spikes, and bursts of different durations, code for different stimulus features, which can be quantified without a priori assumptions about those features. These findings lead us to propose that the biophysical mechanisms of spike generation enables individual neurons to encode different stimulus features into distinct spike patterns.     

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.     

Reinforcement learning through modulation of spike-timing-dependent synaptic plasticity

The persistent modification of synaptic efficacy as a function of the relative timing of pre- and postsynaptic spikes is a phenomenon known as spike-timing-dependent plasticity (STDP). Here we show that the modulation of STDP by a global reward signal leads to reinforcement learning. We first derive analytically learning rules involving reward-modulated spike-timing-dependent synaptic and intrinsic plasticity, by applying a reinforcement learning algorithm to the stochastic spike response model of spiking neurons. These rules have several features common to plasticity mechanisms experimentally found in the brain. We then demonstrate in simulations of networks of integrate-and-fire neurons the efficacy of two simple learning rules involving modulated STDP. One rule is a direct extension of the standard STDP model (modulated STDP), and the other one involves an eligibility trace stored at each synapse that keeps a decaying memory of the relationships between the recent pairs of pre- and postsynaptic spike pairs (modulated STDP with eligibility trace). This latter rule permits learning even if the reward signal is delayed. The proposed rules are able to solve the XOR problem with both rate coded and temporally coded input and to learn a target output firing-rate pattern. These learning rules are biologically plausible, may be used for training generic artificial spiking neural networks, regardless of the neural model used, and suggest the experimental investigation in animals of the existence of reward-modulated STDP.     

脉冲神经元的信息处理

介绍累积放电脉冲神经元的数学描述;讨论脉冲神经元如何将激励信号转化为脉冲序列;讨论脉冲神经元如何将输入脉冲序列转化为输出脉冲序列。实验结果表明脉冲神经元具有很好的信息表示能力、信号鉴别能力和图像信号重构能力。给出利用脉冲神经网络进行图像信号处理的方法。     

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。     

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。     

A novel spiking neural network of receptive field encoding with groups of neurons decision

Human information processing depends mainly on billions of neurons which constitute a complex neural network, and the information is transmitted in the form of neural spikes. In this paper, we propose a spiking neural network (SNN), named MD-SNN, with three key features: (1) using receptive field to encode spike trains from images; (2) randomly selecting partial spikes as inputs for each neuron to approach the absolute refractory period of the neuron; (3) using groups of neurons to make decisions. We test MD-SNN on the MNIST data set of handwritten digits, and results demonstrate that: (1) Different sizes of receptive fields influence classification results significantly. (2) Considering the neuronal refractory period in the SNN model, increasing the number of neurons in the learning layer could greatly reduce the training time, effectively reduce the probability of over-fitting, and improve the accuracy by 8.77%. (3) Compared with other SNN methods, MD-SNN achieves a better classification; compared with the convolution neural network, MD-SNN maintains flip and rotation invariance (the accuracy can remain at 90.44% on the test set), and it is more suitable for small sample learning (the accuracy can reach 80.15% for 1000 training samples, which is 7.8 times that of CNN).     

面向类脑计算的脉冲神经网络研究

随着深度学习在训练成本、泛化能力、可解释性以及可靠性等方面的不足日益突出,类脑计算已成为下一代人工智能的研究热点。脉冲神经网络能更好地模拟生物神经元的信息传递方式,且具有计算能力强、功耗低等特点,在模拟人脑学习、记忆、推理、判断和决策等复杂信息方面具有重要的潜力。本文对脉冲神经网络从以下几个方面进行总结:首先阐述脉冲神经网络的基本结构和工作原理;在结构优化方面,从脉冲神经网络的编码方式、脉冲神经元改进、拓扑结构、训练算法以及结合其他算法这5个方面进行总结;在训练算法方面,从基于反向传播方法、基于脉冲时序依赖可塑性规则方法、人工神经网络转脉冲神经网络和其他学习算法这4个方面进行总结;针对脉冲神经网络的不足与发展,从监督学习和无监督学习两方面剖析;最后,将脉冲神经网络应用到类脑计算和仿生任务中。本文对脉冲神经网络的基本原理、编码方式、网络结构和训练算法进行了系统归纳,对脉冲神经网络的研究发展具有一定的积极意义。