Spiking Neural Networks (SNNs) are being explored for their potential energy efficiency resulting from sparse, event-driven computations. Many recent works have demonstrated effective backpropagation for deep Spiking Neural Networks (SNNs) by approximating gradients over discontinuous neuron spikes or firing events. A beneficial side-effect of these surrogate gradient spiking backpropagation algorithms is that the spikes, which trigger additional computations, may now themselves be directly considered in the gradient calculations. We propose an explicit inclusion of spike counts in the loss function, along with a traditional error loss, causing the backpropagation learning algorithms to optimize weight parameters for both accuracy and spiking sparsity. As supported by existing theory of over-parameterized neural networks, there are many solution states with effectively equivalent accuracy. As such, appropriate weighting of the two loss goals during training in this multi-objective optimization process can yield an improvement in spiking sparsity without a significant loss of accuracy. We additionally explore a simulated annealing-inspired loss weighting technique to increase the weighting for sparsity as training time increases. Our preliminary results on the Cifar-10 dataset show up to 70.1% reduction in spiking activity with iso-accuracy compared to an equivalent SNN trained only for accuracy and up to 73.3% reduction in spiking activity if allowed a trade-off of 1% reduction in classification accuracy.
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 …
University of California, Santa Barbara（加州大学圣巴巴拉分校）
Spiking neural networks (SNNs) are well suited for spatio-temporal learning and implementations on energy-efficient event-driven neuromorphic processors. However, existing SNN error backpropagation (BP) methods lack proper handling of spiking discontinuities and suffer from low performance compared with the BP methods for traditional artificial neural networks. In addition, a large number of time steps are typically required to achieve decent performance, leading to high latency and rendering spike-based computation unscalable to deep architectures. We present a novel Temporal Spike Sequence L…
University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）
Spiking neural networks (SNNs) well support spatiotemporal learning and energy-efficient event-driven hardware neuromorphic processors. As an important class of SNNs, recurrent spiking neural networks (RSNNs) possess great computational power. However, the practical application of RSNNs is severely limited by challenges in training. Biologically-inspired unsupervised learning has limited capability in boosting the performance of RSNNs. On the other hand, existing backpropagation (BP) methods suffer from high complexity of unrolling in time, vanishing and exploding gradients, and approximate di…
Advancing Training Efficiency of Deep Spiking Neural Networks through Rate-based Backpropagation
College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息与电子工程学院）；ZJU-UIUC Institute, Zhejiang University（浙江大学-伊利诺伊大学厄巴纳-香槟分校联合学院）
Recent advances in event-based neuromorphic systems have resulted in significant interest in the use and development of spiking neural networks (SNNs). However, the non-differentiable nature of spiking neurons makes SNNs incompatible with conventional backpropagation techniques. In spite of the significant progress made in training conventional deep neural networks (DNNs), training methods for SNNs still remain relatively poorly understood. In this paper, we present a novel framework for training recurrent SNNs. Analogous to the benefits presented by recurrent neural networks (RNNs) in learnin…
Towards Memory- and Time-Efficient Backpropagation for Training Spiking Neural Networks
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）；Peking University（北京大学）；Peng Cheng Laboratory（鹏城实验室）
Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities. For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative j…
Deep spiking neural networks (SNNs) hold great potential for improving the latency and energy efficiency of deep neural networks through event-based computation. However, training such networks is difficult due to the non-differentiable nature of asynchronous spike events. In this paper, we introduce a novel technique, which treats the membrane potentials of spiking neurons as differentiable signals, where discontinuities at spike times are only considered as noise. This enables an error backpropagation mechanism for deep SNNs, which works directly on spike signals and membrane potentials. Thu…
Spiking neural networks (SNNs) are positioned to enable spatio-temporal information processing and ultra-low power event-driven neuromorphic hardware. However, SNNs are yet to reach the same performances of conventional deep artificial neural networks (ANNs), a long-standing challenge due to complex dynamics and non-differentiable spike events encountered in training. The existing SNN error backpropagation (BP) methods are limited in terms of scalability, lack of proper handling of spiking discontinuities, and/or mismatch between the rate-coded loss function and computed gradient. We present a…
In this work we explore recurrent representations of leaky integrate and fire neurons operating at a timescale equal to their absolute refractory period. Our coarse time scale approximation is obtained using a probability distribution function for spike arrivals that is homogeneously distributed over this time interval. This leads to a discrete representation that exhibits the same dynamics as the continuous model, enabling efficient large scale simulations and backpropagation through the recurrent implementation. We use this approach to explore the training of deep spiking neural networks inc…
School of Microelectronics, Xidian University（西安电子科技大学微电子学院）；Guangzhou Institute of Technology, Xidian University（西安电子科技大学广州研究院）
Spiking neural networks (SNNs) can utilize spatio-temporal information and have a nature of energy efficiency which is a good alternative to deep neural networks(DNNs). The event-driven information processing makes SNNs can reduce the expensive computation of DNNs and save a lot of energy consumption. However, high training and inference latency is a limitation of the development of deeper SNNs. SNNs usually need tens or even hundreds of time steps during the training and inference process which causes not only the increase of latency but also the waste of energy consumption. To overcome this …
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…
Indian Institute of Technology Bombay（印度理工学院孟买分校）；New Jersey Institute of Technology（新泽西理工学院）
Spiking neural networks (SNNs) have garnered a great amount of interest for supervised and unsupervised learning applications. This paper deals with the problem of training multi-layer feedforward SNNs. The non-linear integrate-and-fire dynamics employed by spiking neurons make it difficult to train SNNs to generate desired spike trains in response to a given input. To tackle this, first the problem of training a multi-layer SNN is formulated as an optimization problem such that its objective function is based on the deviation in membrane potential rather than the spike arrival instants. Then,…
Event-based neuromorphic systems promise to reduce the energy consumption of deep learning tasks by replacing expensive floating point operations on dense matrices by low power sparse and asynchronous operations on spike events. While these systems can be trained increasingly well using approximations of the back-propagation algorithm, these implementations usually require high precision errors for training and are therefore incompatible with the typical communication infrastructure of neuromorphic circuits. In this work, we analyze how the gradient can be discretized into spike events when tr…
Brigham Young University–Idaho（爱达荷州杨百翰大学）；Purdue University（普渡大学）
Spiking Neural Networks (SNNs) are being explored for their potential energy efficiency benefits due to sparse, event-driven computation. Non-spiking artificial neural networks are typically trained with stochastic gradient descent using backpropagation. The calculation of true gradients for backpropagation in spiking neural networks is impeded by the non-differentiable firing events of spiking neurons. On the other hand, using approximate gradients is effective, but computationally expensive over many time steps. One common technique, then, for training a spiking neural network is to train a …
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…
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…
The increasing need for intelligent sensors in a wide range of everyday objects requires the existence of low power information processing systems which can operate autonomously in their environment. In particular, merging and processing the outputs of different sensors efficiently is a necessary requirement for mobile agents with cognitive abilities. In this work, we present a multi-layer spiking neural network for inference of relations between stimuli patterns in dedicated neuromorphic systems. The system is trained with a new version of the backpropagation algorithm adapted to on-chip lear…
Recent advances in Voice Activity Detection (VAD) are driven by artificial and Recurrent Neural Networks (RNNs), however, using a VAD system in battery-operated devices requires further power efficiency. This can be achieved by neuromorphic hardware, which enables Spiking Neural Networks (SNNs) to perform inference at very low energy consumption. Spiking networks are characterized by their ability to process information efficiently, in a sparse cascade of binary events in time called spikes. However, a big performance gap separates artificial from spiking networks, mostly due to a lack of powe…
Department of Electrical and Computer Engineering, National University of Singapore（新加坡国立大学电气与计算机工程系）；School of Computing, Department of Computer Science, National University of Singapore（新加坡国立大学计算机学院计算机科学系）；School of Computer Science and Engineering, University of Electronic Science and Technology of China（电子科技大学计算机科学与工程学院）；Department of Computer and Information Sciences, Faculty of Engineering and Environment, Northumbria University（诺森比亚大学工程与环境学院计算机与信息科学系）；Zhejiang Lab（浙江实验室）
Spiking Neural Networks (SNNs) use spatio-temporal spike patterns to represent and transmit information, which is not only biologically realistic but also suitable for ultra-low-power event-driven neuromorphic implementation. Motivated by the success of deep learning, the study of Deep Spiking Neural Networks (DeepSNNs) provides promising directions for artificial intelligence applications. However, training of DeepSNNs is not straightforward because the well-studied error back-propagation (BP) algorithm is not directly applicable. In this paper, we first establish an understanding as to why e…
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…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；University of California–Irvine（加州大学尔湾分校）
Directly training spiking neural networks (SNNs) has remained challenging due to complex neural dynamics and intrinsic non-differentiability in firing functions. The well-known backpropagation through time (BPTT) algorithm proposed to train SNNs suffers from large memory footprint and prohibits backward and update unlocking, making it impossible to exploit the potential of locally-supervised training methods. This work proposes an efficient and direct training algorithm for SNNs that integrates a locally-supervised training method with a temporally-truncated BPTT algorithm. The proposed algori…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Future Technology, University of Chinese Academy of Sciences（中国科学院大学未来技术学院）；Research Center for Brain-Inspired Intelligence, CASIA（中国科学院自动化研究所脑启发智能研究中心）；National Laboratory of Pattern Recognition, CASIA（中国科学院自动化研究所模式识别国家重点实验室）；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）
The spiking neural network (SNN) mimics the information processing operation in the human brain, represents and transmits information in spike trains containing wealthy spatial and temporal information, and shows superior performance on many cognitive tasks. In addition, the event-driven information processing enables the energy-efficient implementation on neuromorphic chips. The success of deep learning is inseparable from backpropagation. Due to the discrete information transmission, directly applying the backpropagation to the training of the SNN still has a performance gap compared with th…
Compared with artificial neural networks (ANNs), spiking neural networks (SNNs) are promising to explore the brain-like behaviors since the spikes could encode more spatio-temporal information. Although pre-training from ANN or direct training based on backpropagation (BP) makes the supervised training of SNNs possible, these methods only exploit the networks' spatial domain information which leads to the performance bottleneck and requires many complicated training skills. Another fundamental issue is that the spike activity is naturally non-differentiable which causes great difficulties in t…
Desire Backpropagation: A Lightweight Training Algorithm for Multi-Layer Spiking Neural Networks based on Spike-Timing-Dependent Plasticity
Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局高性能计算研究所）；National University of Singapore（新加坡国立大学）
Amirkabir University of Technology（阿米尔卡比尔理工大学）；Shahid Beheshti University（沙希德·贝赫什提大学）；CNRS Université Toulouse 3（法国国家科学研究中心图卢兹第三大学）
We recently proposed the STiDi-BP algorithm, which avoids backward recursive gradient computation, for training multi-layer spiking neural networks (SNNs) with single-spike-based temporal coding. The algorithm employs a linear approximation to compute the derivative of the spike latency with respect to the membrane potential and it uses spiking neurons with piecewise linear postsynaptic potential to reduce the computational cost and the complexity of neural processing. In this paper, we extend the STiDi-BP algorithm to employ it in deeper and convolutional architectures. The evaluation results…
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 …
The emergence of brain-inspired neuromorphic computing as a paradigm for edge AI is motivating the search for high-performance and efficient spiking neural networks to run on this hardware. However, compared to classical neural networks in deep learning, current spiking neural networks lack competitive performance in compelling areas. Here, for sequential and streaming tasks, we demonstrate how a novel type of adaptive spiking recurrent neural network (SRNN) is able to achieve state-of-the-art performance compared to other spiking neural networks and almost reach or exceed the performance of c…
Stochastic Quantum Spiking Neural Networks with Quantum Memory and Local Learning
Department of Engineering, King’s College London（伦敦国王学院工程系）；Institute for Intelligent Networked Systems, Northeastern University London（伦敦东北大学智能网络系统研究所）
University of Michigan（密歇根大学）；University of Western Australia（西澳大利亚大学）
Spiking neural networks can compensate for quantization error by encoding information either in the temporal domain, or by processing discretized quantities in hidden states of higher precision. In theory, a wide dynamic range state-space enables multiple binarized inputs to be accumulated together, thus improving the representational capacity of individual neurons. This may be achieved by increasing the firing threshold, but make it too high and sparse spike activity turns into no spike emission. In this paper, we propose the use of `threshold annealing' as a warm-up method for firing thresho…
Seoul National University（首尔国立大学）；Stanford University（斯坦福大学）
Nowadays deep learning is dominating the field of machine learning with state-of-the-art performance in various application areas. Recently, spiking neural networks (SNNs) have been attracting a great deal of attention, notably owning to their power efficiency, which can potentially allow us to implement a low-power deep learning engine suitable for real-time/mobile applications. However, implementing SNN-based deep learning remains challenging, especially gradient-based training of SNNs by error backpropagation. We cannot simply propagate errors through SNNs in conventional way because of the…
Spiking Neural Networks (SNNs) have recently emerged as a prominent neural computing paradigm. However, the typical shallow SNN architectures have limited capacity for expressing complex representations while training deep SNNs using input spikes has not been successful so far. Diverse methods have been proposed to get around this issue such as converting off-the-shelf trained deep Artificial Neural Networks (ANNs) to SNNs. However, the ANN-SNN conversion scheme fails to capture the temporal dynamics of a spiking system. On the other hand, it is still a difficult problem to directly train deep…
Spiking neural networks (SNNs) offer a promising alternative to current artificial neural networks to enable low-power event-driven neuromorphic hardware. Spike-based neuromorphic applications require processing and extracting meaningful information from spatio-temporal data, represented as series of spike trains over time. In this paper, we propose a method to synthesize images from multiple modalities in a spike-based environment. We use spiking auto-encoders to convert image and audio inputs into compact spatio-temporal representations that is then decoded for image synthesis. For this, we …
Donders Institute for Brain, Cognition and Behaviour（唐德斯脑、认知与行为研究所）
Spiking neural networks are a promising approach towards next-generation models of the brain in computational neuroscience. Moreover, compared to classic artificial neural networks, they could serve as an energy-efficient deployment of AI by enabling fast computation in specialized neuromorphic hardware. However, training deep spiking neural networks, especially in an unsupervised manner, is challenging and the performance of a spiking model is significantly hindered by dead or bursting neurons. Here, we apply end-to-end learning with membrane potential-based backpropagation to a spiking convo…
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…
As the scales of neural networks increase, techniques that enable them to run with low computational cost and energy efficiency are required. From such demands, various efficient neural network paradigms, such as spiking neural networks (SNNs) or binary neural networks (BNNs), have been proposed. However, they have sticky drawbacks, such as degraded inference accuracy and latency. To solve these problems, we propose a single-step spiking neural network (S$^3$NN), an energy-efficient neural network with low computational cost and high precision. The proposed S$^3$NN processes the information be…
Training Spiking Neural Networks Using Lessons From Deep Learning
UC Santa Cruz（加州大学圣克鲁兹分校）；University of Michigan（密歇根大学）；UWA（西澳大学）；Harvard University（哈佛大学）；Forschungszentrum Jülich（于利希研究中心）；RWTH Aachen（亚琛工业大学）；SynSense（SynSense（类脑智能公司））；Hanyang University（汉阳大学）
FZI Research Center For Information Technology（FZI信息技术研究中心）；University of California Irvine（加州大学欧文分校）
Spike-based communication between biological neurons is sparse and unreliable. This enables the brain to process visual information from the eyes efficiently. Taking inspiration from biology, artificial spiking neural networks coupled with silicon retinas attempt to model these computations. Recent findings in machine learning allowed the derivation of a family of powerful synaptic plasticity rules approximating backpropagation for spiking networks. Are these rules capable of processing real-world visual sensory data? In this paper, we evaluate the performance of Event-Driven Random Back-Propa…
Inspired by the operation of biological brains, Spiking Neural Networks (SNNs) have the unique ability to detect information encoded in spatio-temporal patterns of spiking signals. Examples of data types requiring spatio-temporal processing include logs of time stamps, e.g., of tweets, and outputs of neural prostheses and neuromorphic sensors. In this paper, the second of a series of three review papers on SNNs, we first review models and training algorithms for the dominant approach that considers SNNs as a Recurrent Neural Network (RNN) and adapt learning rules based on backpropagation throu…
The event-driven and sparse nature of communication between spiking neurons in the brain holds great promise for flexible and energy-efficient AI. Recent advances in learning algorithms have demonstrated that recurrent networks of spiking neurons can be effectively trained to achieve competitive performance compared to standard recurrent neural networks. Still, as these learning algorithms use error-backpropagation through time (BPTT), they suffer from high memory requirements, are slow to train, and are incompatible with online learning. This limits the application of these learning algorithm…
