The current article introduces a supervised learning algorithm for multilayer spiking neural networks. The algorithm presented here overcomes some limitations of existing learning algorithms as it can be applied to neurons firing multiple spikes and it can in principle be applied to any linearisable neuron model. The algorithm is applied successfully to various benchmarks, such as the XOR problem and the Iris data set, as well as complex classifications problems. The simulations also show the flexibility of this supervised learning algorithm which permits different encodings of the spike timing patterns, including precise spike trains encoding.
Modern deep learning enabled artificial neural networks, such as Deep Neural Network (DNN) and Convolutional Neural Network (CNN), have achieved a series of breaking records on a broad spectrum of recognition applications. However, the enormous computation and storage requirements associated with such deep and complex neural network models greatly challenge their implementations on resource-limited platforms. Time-based spiking neural network has recently emerged as a promising solution in Neuromorphic Computing System designs for achieving remarkable computing and power efficiency within a si…
Information encoding in the nervous system is supported through the precise spike-timings of neurons; however, an understanding of the underlying processes by which such representations are formed in the first place remains unclear. Here we examine how networks of spiking neurons can learn to encode for input patterns using a fully temporal coding scheme. To this end, we introduce a learning rule for spiking networks containing hidden neurons which optimizes the likelihood of generating desired output spiking patterns. We show the proposed learning rule allows for a large number of accurate in…
Although widely used in machine learning, backpropagation cannot directly be applied to SNN training and is not feasible on a neuromorphic processor that emulates biological neuron and synapses. This work presents a spike-based backpropagation algorithm with biological plausible local update rules and adapts it to fit the constraint in a neuromorphic hardware. The algorithm is implemented on Intel Loihi chip enabling low power in-hardware supervised online learning of multilayered SNNs for mobile applications. We test this implementation on MNIST, Fashion-MNIST, CIFAR-10 and MSTAR datasets wit…
University of Surrey（萨里大学）；University of Applied Sciences Stralsund（施特拉尔松德应用技术大学）
Experimental studies support the notion of spike-based neuronal information processing in the brain, with neural circuits exhibiting a wide range of temporally-based coding strategies to rapidly and efficiently represent sensory stimuli. Accordingly, it would be desirable to apply spike-based computation to tackling real-world challenges, and in particular transferring such theory to neuromorphic systems for low-power embedded applications. Motivated by this, we propose a new supervised learning method that can train multilayer spiking neural networks to solve classification problems based on …
Few algorithms for supervised training of spiking neural networks exist that can deal with patterns of multiple spikes, and their computational properties are largely unexplored. We demonstrate in a set of simulations that the ReSuMe learning algorithm can be successfully applied to layered neural networks. Input and output patterns are encoded as spike trains of multiple precisely timed spikes, and the network learns to transform the input trains into target output trains. This is done by combining the ReSuMe learning algorithm with multiplicative scaling of the connections of downstream neur…
A new supervised learning algorithm, SNN/LP, is proposed for Spiking Neural Networks. This novel algorithm uses limited precision for both synaptic weights and synaptic delays; 3 bits in each case. Also a genetic algorithm is used for the supervised training. The results are comparable or better than previously published work. The results are applicable to the realization of large scale hardware neural networks. One of the trained networks is implemented in programmable hardware.
The spiking neural network (SNN) has been attracting considerable attention not only as a mathematical model for the brain, but also as an energy-efficient information processing model for real-world applications. In particular, SNNs based on temporal coding are expected to be much more efficient than those based on rate coding, because the former requires substantially fewer spikes to carry out tasks. As SNNs are continuous-state and continuous-time models, it is favorable to implement them with analog VLSI circuits. However, the construction of the entire system with continuous-time analog c…
We derive a synaptic weight update rule for learning temporally precise spike train to spike train transformations in multilayer feedforward networks of spiking neurons. The framework, aimed at seamlessly generalizing error backpropagation to the deterministic spiking neuron setting, is based strictly on spike timing and avoids invoking concepts pertaining to spike rates or probabilistic models of spiking. The derivation is founded on two innovations. First, an error functional is proposed that compares the spike train emitted by the output neuron of the network to the desired spike train by w…
Institute of Industrial Science, The University of Tokyo（东京大学生产技术研究所）；NEC Corporation（日本电气股份有限公司）；Interdisciplinary Graduate School of Engineering Sciences, Kyushu University（九州大学工学研究院跨学科工学研究科）；Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology（九州工业大学生命科学与系统工程研究生院）；International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo（东京大学高等研究院神经智能国际研究中心（WPI-IRCN））
Spiking neural networks (SNNs) are brain-inspired mathematical models with the ability to process information in the form of spikes. SNNs are expected to provide not only new machine-learning algorithms, but also energy-efficient computational models when implemented in VLSI circuits. In this paper, we propose a novel supervised learning algorithm for SNNs based on temporal coding. A spiking neuron in this algorithm is designed to facilitate analog VLSI implementations with analog resistive memory, by which ultra-high energy efficiency can be achieved. We also propose several techniques to imp…
Stanford University（斯坦福大学）；University of Oxford（牛津大学）
A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in-vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in-silico. Here we revisit the problem of supervised learning in temporally coding multi-layer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three factor learning rule capable of training multi-layer networks of dete…
Spiking neural networks have been referred to as the third generation of artificial neural networks where the information is coded as time of the spikes. There are a number of different spiking neuron models available and they are categorized based on their level of abstraction. In addition, there are two known learning methods, unsupervised and supervised learning. This thesis focuses on supervised learning where a new algorithm is proposed, based on genetic algorithms. The proposed algorithm is able to train both synaptic weights and delays and also allow each neuron to emit multiple spikes …
Learning synaptic weights of spiking neural network (SNN) models that can reproduce target spike trains from provided neural firing data is a central problem in computational neuroscience and spike-based computing. The discovery of the optimal weight values can be posed as a supervised learning task wherein the weights of the model network are chosen to maximize the similarity between the target spike trains and the model outputs. It is still largely unknown whether optimizing spike train similarity of highly recurrent SNNs produces weight matrices similar to those of the ground truth model. T…
Wuhan University（武汉大学）；Northwest Normal University（西北师范大学）
Using precise times of every spike, spiking supervised learning has more effects on complex spatial-temporal pattern than supervised learning only through neuronal firing rates. The purpose of spiking supervised learning after spatial-temporal encoding is to emit desired spike trains with precise times. Existing algorithms of spiking supervised learning have excellent performances, but mechanisms of them still have some problems, such as the limitation of neuronal types and complex computation. Based on an online regulative mechanism of biological synapses, this paper proposes an online superv…
Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal dynamics and responds to the history of inputs as opposed to the current inputs only. Because of such properties a spiking neural network has rich intrinsic capabilities to process spatiotemporal data. However, because the spikes are discontinuous 'yes or no' events, it is not trivial to apply traditional training procedures such as gradient descend to the spiking …
University of Minnesota（明尼苏达大学）；University of Surrey（萨里大学）；University of Applied Sciences, Stralsund（施特拉尔松德应用科学大学）
In this work we propose a new supervised learning method for temporally-encoded multilayer spiking networks to perform classification. The method employs a reinforcement signal that mimics backpropagation but is far less computationally intensive. The weight update calculation at each layer requires only local data apart from this signal. We also employ a rule capable of producing specific output spike trains; by setting the target spike time equal to the actual spike time with a slight negative offset for key high-value neurons the actual spike time becomes as early as possible. In simulated …
Biological neurons use spikes to process and learn temporally dynamic inputs in an energy and computationally efficient way. However, applying the state-of-the-art gradient-based supervised algorithms to spiking neural networks (SNN) is a challenge due to the non-differentiability of the activation function of spiking neurons. Employing surrogate gradients is one of the main solutions to overcome this challenge. Although SNNs naturally work in the temporal domain, recent studies have focused on developing SNNs to solve static image categorization tasks. In this paper, we employ a surrogate gra…
Compared with rate-based artificial neural networks, Spiking Neural Networks (SNN) provide a more biological plausible model for the brain. But how they perform supervised learning remains elusive. Inspired by recent works of Bengio et al., we propose a supervised learning algorithm based on Spike-Timing Dependent Plasticity (STDP) for a hierarchical SNN consisting of Leaky Integrate-and-fire (LIF) neurons. A time window is designed for the presynaptic neuron and only the spikes in this window take part in the STDP updating process. The model is trained on the MNIST dataset. The classification…
Precise spike timing as a means to encode information in neural networks is biologically supported, and is advantageous over frequency-based codes by processing input features on a much shorter time-scale. For these reasons, much recent attention has been focused on the development of supervised learning rules for spiking neural networks that utilise a temporal coding scheme. However, despite significant progress in this area, there still lack rules that have a theoretical basis, and yet can be considered biologically relevant. Here we examine the general conditions under which synaptic plasti…
Gradient descent training techniques are remarkably successful in training analog-valued artificial neural networks (ANNs). Such training techniques, however, do not transfer easily to spiking networks due to the spike generation hard non-linearity and the discrete nature of spike communication. We show that in a feedforward spiking network that uses a temporal coding scheme where information is encoded in spike times instead of spike rates, the network input-output relation is differentiable almost everywhere. Moreover, this relation is piece-wise linear after a transformation of variables. M…
Tokyo Institute of Technology（东京工业大学）；Saitama University（埼玉大学）；JST, PREST（日本科学技术振兴机构 PREST）
A semi-supervised learning method for spiking neural networks is proposed. The proposed method consists of supervised learning by backpropagation and subsequent unsupervised learning by spike-timing-dependent plasticity (STDP), which is a biologically plausible learning rule. Numerical experiments show that the proposed method improves the accuracy without additional labeling when a small amount of labeled data is used. This feature has not been achieved by existing semi-supervised learning methods of discriminative models. It is possible to implement the proposed learning method for event-dri…
This study adapts the highly-versatile siamese neural network model to the event data domain. We introduce a supervised training framework for optimizing Earth Mover's Distance (EMD) between spike trains with spiking neural networks (SNN). We train this model on images of the MNIST dataset converted into spiking domain with novel conversion schemes. The quality of the siamese embeddings of input images was evaluated by measuring the classifier performance for different dataset coding types. The models achieved performance similar to existing SNN-based approaches (F1-score of up to 0.9386) whil…
Reconstructing Spiking Neural Networks Using a Single Neuron with Autapses
Brain-Apparatus Communication Institute, University of Electronic Science and Technology of China（脑器通信研究院，电子科技大学）；School of Artificial Intelligence, Chongqing University of Education（人工智能学院，重庆教育学院）
Much of studies on neural computation are based on network models of static neurons that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete pulses called spikes. Research in spike-based computation has been impeded by the lack of efficient supervised learning algorithm for spiking networks. Here, we present a gradient descent method for optimizing spiking network models by introducing a differentiable formulation of spiking networks and deriving the exact gradient calculation. For demonstration,…
Spiking neural networks (SNN) are artificial computational models that have been inspired by the brain's ability to naturally encode and process information in the time domain. The added temporal dimension is believed to render them more computationally efficient than the conventional artificial neural networks, though their full computational capabilities are yet to be explored. Recently, computational memory architectures based on non-volatile memory crossbar arrays have shown great promise to implement parallel computations in artificial and spiking neural networks. In this work, we experim…
Spiking neural networks (SNN) are considered as a perspective basis for performing all kinds of learning tasks - unsupervised, supervised and reinforcement learning. Learning in SNN is implemented through synaptic plasticity - the rules which determine dynamics of synaptic weights depending usually on activity of the pre- and post-synaptic neurons. Diversity of various learning regimes assumes that different forms of synaptic plasticity may be most efficient for, for example, unsupervised and supervised learning, as it is observed in living neurons demonstrating many kinds of deviations from t…
Groningen Cognitive Systems and Materials Center（格罗宁根认知系统与材料中心）；University of Groningen（格罗宁根大学）
Memristive devices are a class of circuit elements that shows great promise as future building block for brain-inspired computing. One influential view in theoretical neuroscience sees the brain as a function-computing device: given input signals, the brain applies a function in order to generate new internal states and motor outputs. Therefore, being able to approximate functions is a fundamental axiom to build upon for future brain research and to derive more efficient computational machines. In this work we apply a novel supervised learning algorithm - based on controlling niobium-doped str…
Institute of Neuroinformatics, University of Z\"urich；ETH Z\"urich, Z\"urich, Switzerland
Spiking silicon cochlea sensors encode sound as an asynchronous stream of spikes from different frequency channels. The lack of labeled training datasets for spiking cochleas makes it difficult to train deep neural networks on the outputs of these sensors. This work proposes a self-supervised method called Temporal Network Grafting Algorithm (T-NGA), which grafts a recurrent network pretrained on spectrogram features so that the network works with the cochlea event features. T-NGA training requires only temporally aligned audio spectrograms and event features. Our experiments show that the acc…
Spiking Neural Networks are often touted as brain-inspired learning models for the third wave of Artificial Intelligence. Although recent SNNs trained with supervised backpropagation show classification accuracy comparable to deep networks, the performance of unsupervised learning-based SNNs remains much lower. This paper presents a heterogeneous recurrent spiking neural network (HRSNN) with unsupervised learning for spatio-temporal classification of video activity recognition tasks on RGB (KTH, UCF11, UCF101) and event-based datasets (DVS128 Gesture). The key novelty of the HRSNN is that the …
CERCO UMR 5549, CNRS – Université Toulouse 3（法国国家科学研究中心CERCO UMR 5549——图卢兹第三大学）；IRIT, Université de Toulouse（图卢兹大学IRIT研究所）
Recently, it has been shown that spiking neural networks (SNNs) can be trained efficiently, in a supervised manner, using backpropagation through time. Indeed, the most commonly used spiking neuron model, the leaky integrate-and-fire neuron, obeys a differential equation which can be approximated using discrete time steps, leading to a recurrent relation for the potential. The firing threshold causes optimization issues, but they can be overcome using a surrogate gradient. Here, we extend previous approaches in two ways. Firstly, we show that the approach can be used to train convolutional lay…
Raven's Progressive Matrices have been widely used for measuring abstract reasoning and intelligence in humans. However for artificial learning systems, abstract reasoning remains a challenging problem. In this paper we investigate how neural networks augmented with biologically inspired spiking modules gain a significant advantage in solving this problem. To illustrate this, we first investigate the performance of our networks with supervised learning, then with unsupervised learning. Experiments on the RAVEN dataset show that the overall accuracy of our supervised networks surpass human-leve…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences（中国科学院脑科学与智能技术卓越创新中心）
Spiking neural networks (SNNs) possess energy-efficient potential due to event-based computation. However, supervised training of SNNs remains a challenge as spike activities are non-differentiable. Previous SNNs training methods can be generally categorized into two basic classes, i.e., backpropagation-like training methods and plasticity-based learning methods. The former methods are dependent on energy-inefficient real-valued computation and non-local transmission, as also required in artificial neural networks (ANNs), whereas the latter are either considered to be biologically implausible …
We propose a new supervised learning rule for multilayer spiking neural networks (SNNs) that use a form of temporal coding known as rank-order-coding. With this coding scheme, all neurons fire exactly one spike per stimulus, but the firing order carries information. In particular, in the readout layer, the first neuron to fire determines the class of the stimulus. We derive a new learning rule for this sort of network, named S4NN, akin to traditional error backpropagation, yet based on latencies. We show how approximated error gradients can be computed backward in a feedforward network with an…
In machine learning, error back-propagation in multi-layer neural networks (deep learning) has been impressively successful in supervised and reinforcement learning tasks. As a model for learning in the brain, however, deep learning has long been regarded as implausible, since it relies in its basic form on a non-local plasticity rule. To overcome this problem, energy-based models with local contrastive Hebbian learning were proposed and tested on a classification task with networks of rate neurons. We extended this work by implementing and testing such a model with networks of leaky integrate…
The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While nonlinear computations can be implemented successfully in spiking neural networks, this requires supervised training and the resulting connectivity can be hard to interpret. In contrast, the required connectivity for any computation in the form of a linear dynamical system can be directly derived and understood with the spike coding network (SCN) framework. These networks also have biologically realistic activity patterns and are highly robust to …
The field of neuromorphic computing promises extremely low-power and low-latency sensing and processing. Challenges in transferring learning algorithms from traditional artificial neural networks (ANNs) to spiking neural networks (SNNs) have so far prevented their application to large-scale, complex regression tasks. Furthermore, realizing a truly asynchronous and fully neuromorphic pipeline that maximally attains the abovementioned benefits involves rethinking the way in which this pipeline takes in and accumulates information. In the case of perception, spikes would be passed as-is and one-b…
There has been a strong push recently to examine biological scale simulations of neuromorphic algorithms to achieve stronger inference capabilities. This paper presents a set of piecewise linear spiking neuron models, which can reproduce different behaviors, similar to the biological neuron, both for a single neuron as well as a network of neurons. The proposed models are investigated, in terms of digital implementation feasibility and costs, targeting large scale hardware implementation. Hardware synthesis and physical implementations on FPGA show that the proposed models can produce precise …
A Cloud-Edge Framework for Energy-Efficient Event-Driven Control: An Integration of Online Supervised Learning, Spiking Neural Networks and Local Plasticity Rules
University of Louisiana at Lafayette（路易斯安那大学拉斐特分校）；Monash University（莫纳什大学）；Kharazmi University（哈拉齐米大学）；CNRS-Université de Toulouse 3（法国国家科学研究中心-图卢兹第三大学）
In recent years, deep learning has been a revolution in the field of machine learning, for computer vision in particular. In this approach, a deep (multilayer) artificial neural network (ANN) is trained in a supervised manner using backpropagation. Huge amounts of labeled examples are required, but the resulting classification accuracy is truly impressive, sometimes outperforming humans. Neurons in an ANN are characterized by a single, static, continuous-valued activation. Yet biological neurons use discrete spikes to compute and transmit information, and the spike times, in addition to the sp…
One of the most exciting advancements in AI over the last decade is the wide adoption of ANNs, such as DNN and CNN, in many real-world applications. However, the underlying massive amounts of computation and storage requirement greatly challenge their applicability in resource-limited platforms like the drone, mobile phone, and IoT devices etc. The third generation of neural network model--Spiking Neural Network (SNN), inspired by the working mechanism and efficiency of human brain, has emerged as a promising solution for achieving more impressive computing and power efficiency within light-we…
Conventional modeling approaches have found limitations in matching the increasingly detailed neural network structures and dynamics recorded in experiments to the diverse brain functionalities. On another approach, studies have demonstrated to train spiking neural networks for simple functions using supervised learning. Here, we introduce a modified SpikeProp learning algorithm, which achieved better learning stability in different activity states. In addition, we show biological realistic features such as lateral connections and sparse activities can be included in the network. We demonstrat…
Ghent University（根特大学）；Institute for Infocomm Research, A*STAR（新加坡科技研究局资讯通信研究院）
The information of spiking neural networks (SNNs) are propagated between the adjacent biological neuron by spikes, which provides a computing paradigm with the promise of simulating the human brain. Recent studies have found that the time delay of neurons plays an important role in the learning process. Therefore, configuring the precise timing of the spike is a promising direction for understanding and improving the transmission process of temporal information in SNNs. However, most of the existing learning methods for spiking neurons are focusing on the adjustment of synaptic weight, while v…
Peking University（北京大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）；Peng Cheng Laboratory（鹏城实验室）
Spiking neural networks (SNNs) with event-based computation are promising brain-inspired models for energy-efficient applications on neuromorphic hardware. However, most supervised SNN training methods, such as conversion from artificial neural networks or direct training with surrogate gradients, require complex computation rather than spike-based operations of spiking neurons during training. In this paper, we study spike-based implicit differentiation on the equilibrium state (SPIDE) that extends the recently proposed training method, implicit differentiation on the equilibrium state (IDE),…
The timing of individual neuronal spikes is essential for biological brains to make fast responses to sensory stimuli. However, conventional artificial neural networks lack the intrinsic temporal coding ability present in biological networks. We propose a spiking neural network model that encodes information in the relative timing of individual neuron spikes. In classification tasks, the output of the network is indicated by the first neuron to spike in the output layer. This temporal coding scheme allows the supervised training of the network with backpropagation, using locally exact derivati…
