Spiking Neural Networks (SNNs) provide a promising framework for energy-efficient and biologically grounded computation; however, scalable learning in deep recurrent architectures with sparse connectivity remains a major challenge. In this work, we propose a structured multi-layer recurrent SNN architecture composed of locally dense recurrent layers augmented with sparse small-world long-range projections to a readout population. The long-range connectivity is largely fixed, preserving routing efficiency and hardware scalability, while synaptic adaptation is performed using strictly local plasticity mechanisms. To enable supervised learning without backpropagation or surrogate gradients, we introduce a biologically motivated learning framework that combines: (i) population-based winner-take-all (WTA) teaching signals at the output layer, (ii) fixed random broadcast alignment feedback pathways, and (iii) low-dimensional modulatory neuron populations that gate synaptic updates through three-factor learning rules with eligibility traces. This design supports deep recurrent computation with sparse global communication and purely local synaptic updates. We analyze the algorithmic properties, computational complexity, and hardware feasibility of the proposed approach, and demonstrate stable learning and competitive performance on benchmark classification tasks. The results highlight the potential of structured recurrence and neuromodulatory learning to enable scalable, hardware-compatible SNN training beyond gradient-based methods.
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…
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…
Feedback-driven recurrent spiking neural networks (RSNNs) are powerful computational models that can mimic dynamical systems. However, the presence of a feedback loop from the readout to the recurrent layer de-stabilizes the learning mechanism and prevents it from converging. Here, we propose a supervised training procedure for RSNNs, where a second network is introduced only during the training, to provide hint for the target dynamics. The proposed training procedure consists of generating targets for both recurrent and readout layers (i.e., for a full RSNN system). It uses the recursive leas…
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…
Loss shaping enhances exact gradient learning with Eventprop in spiking neural networks
School of Engineering and Informatics, University of Sussex（萨塞克斯大学工程与信息学院）；Information & Communication Technologies, Imperial College London（伦敦帝国理工学院信息与通信技术系）
TESS: A Scalable Temporally and Spatially Local Learning Rule for Spiking Neural Networks
School of Electrical and Computer Engineering, Purdue University, Indiana, USA（电气与计算机工程学院，普渡大学，印第安纳州，美国）；Microelectronics Department, Delft University of Technology, Delft, NL（微电子系，代尔夫特理工大学，代尔夫特，荷兰）
SparseProp: Efficient Event-Based Simulation and Training of Sparse Recurrent Spiking Neural Networks
Zuckerman Mind Brain Behavior Institute, Columbia University（哥伦比亚大学祖克曼心智脑行为研究所）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；Göttingen Campus Institute for Dynamics of Biological Networks（哥廷根校区生物网络动力学研究所）
We present a fully memristive spiking neural network (MSNN) consisting of novel memristive neurons trained using the backpropagation through time (BPTT) learning rule. Gradient descent is applied directly to the memristive integrated-and-fire (MIF) neuron designed using analog SPICE circuit models, which generates distinct depolarization, hyperpolarization, and repolarization voltage waveforms. Synaptic weights are trained by BPTT using the membrane potential of the MIF neuron model and can be processed on memristive crossbars. The natural spiking dynamics of the MIF neuron model are fully dif…
EAS-SNN: End-to-End Adaptive Sampling and Representation for Event-based Detection with Recurrent Spiking Neural Networks
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；State Key Laboratory of Brain-Machine Intelligence, Zhejiang University（浙江大学脑机智能国家重点实验室）
Intelligent Systems Research Centre（智能系统研究中心）；University of Ulster（阿尔斯特大学）
The practical applications based on recurrent spiking neurons are limited due to their non-trivial learning algorithms. The temporal nature of spiking neurons is more favorable for hardware implementation where signals can be represented in binary form and communication can be done through the use of spikes. This work investigates the potential of recurrent spiking neurons implementations on reconfigurable platforms and their applicability in temporal based applications. A theoretical framework of reservoir computing is investigated for hardware/software implementation. In this framework, only…
Ohio University（俄亥俄大学）；University of Kentucky（肯塔基大学）；Wright State University（莱特州立大学）
Over the past decade, artificial neural networks (ANNs) have made tremendous advances, in part due to the increased availability of annotated data. However, ANNs typically require significant power and memory consumptions to reach their full potential. Spiking neural networks (SNNs) have recently emerged as a low-power alternative to ANNs due to their sparsity nature. SNN, however, are not as easy to train as ANNs. In this work, we propose a hybrid SNN training scheme and apply it to segment human hippocampi from magnetic resonance images. Our approach takes ANN-SNN conversion as an initializa…
Department of Information Engineering (DEI), University of Padova, Italy（帕多瓦大学信息工程系）；Department of Information Engineering (DII), University of Brescia, Italy（布雷西亚大学信息工程系）；Department of Methematics ``Tullio-Levi Civita'', University of Padova, Italy（帕多瓦大学数学系）
Adaptive Robotic Arm Control with a Spiking Recurrent Neural Network on a Digital Accelerator
University of Sevilla（塞维利亚大学）；Politecnico di Torino（都灵理工大学）；Graz University of Technology（格拉茨工业大学）；University of Zurich（苏黎世大学）；Delft University of Technology（代尔夫特理工大学）
Purdue University（普渡大学）；Nanoelectronics Research Laboratory（纳米电子学研究实验室）
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 fu…
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 …
National Engineering School of Tunis（突尼斯国立工程学院）；Université Tunis El Manar（突尼斯艾尔马纳尔大学）
Synaptic plasticity seems to be a capital aspect of the dynamics of neural networks. It is about the physiological modifications of the synapse, which have like consequence a variation of the value of the synaptic weight. The information encoding is based on the precise timing of single spike events that is based on the relative timing of the pre- and post-synaptic spikes, local synapse competitions within a single neuron and global competition via lateral connections. In order to classify temporal sequences, we present in this paper how to use a local hebbian learning, spike-timing dependent …
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…
We have presented a Spiking Convolutional Neural Network (SCNN) that incorporates retinal foveal-pit inspired Difference of Gaussian filters and rank-order encoding. The model is trained using a variant of the backpropagation algorithm adapted to work with spiking neurons, as implemented in the Nengo library. We have evaluated the performance of our model on two publicly available datasets - one for digit recognition task, and the other for vehicle recognition task. The network has achieved up to 90% accuracy, where loss is calculated using the cross-entropy function. This is an improvement ov…
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…
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…
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）
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…
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…
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…
Laboratory of Biological Modeling, NIDDK/NIH（美国国立糖尿病、消化系统疾病和肾病研究所（NIDDK）/美国国立卫生研究院（NIH）生物建模实验室）
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that emerge after learning remains unknown. Here we show that modifying the recurrent connectivity with a recursive least squares algorithm provides sufficient flexibility for synaptic and spiking rate dynamics of spiking networks to produce a wide range of spatiotemporal activity. We apply the training method to learn arbitrary firing patterns, stabilize irregular sp…
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 (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…
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,…
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 …
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…
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 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…
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…
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…
We present RNNbow, an interactive tool for visualizing the gradient flow during backpropagation training in recurrent neural networks. RNNbow is a web application that displays the relative gradient contributions from Recurrent Neural Network (RNN) cells in a neighborhood of an element of a sequence. We describe the calculation of backpropagation through time (BPTT) that keeps track of itemized gradients, or gradient contributions from one element of a sequence to previous elements of a sequence. By visualizing the gradient, as opposed to activations, RNNbow offers insight into how the network…
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 …
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…
Spiking neural networks (SNNs) in neuromorphic systems are more energy efficient compared to deep learning-based methods, but there is no clear competitive learning algorithm for training such SNNs. Eligibility propagation (e-prop) offers an efficient and biologically plausible way to train competitive recurrent SNNs in low-power neuromorphic hardware. In this report, previous performance of e-prop on a speech classification task is reproduced, and the effects of including STDP-like behavior are analyzed. Including STDP to the ALIF neuron model improves the classification performance, but this…
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…
CWI（CWI研究所）；Stichting IMEC Netherlands, Holst Centre（荷兰IMEC基金会荷尔斯特中心）；Univ of Amsterdam（阿姆斯特丹大学）；Rijksuniversiteit Groningen（格罗宁根大学）
Inspired by more detailed modeling of biological neurons, Spiking neural networks (SNNs) have been investigated both as more biologically plausible and potentially more powerful models of neural computation, and also with the aim of extracting biological neurons' energy efficiency; the performance of such networks however has remained lacking compared to classical artificial neural networks (ANNs). Here, we demonstrate how a novel surrogate gradient combined with recurrent networks of tunable and adaptive spiking neurons yields state-of-the-art for SNNs on challenging benchmarks in the time-do…
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…
GRSN: Gated Recurrent Spiking Neurons for POMDPs and MARL
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；College of Computer Science, Zhejiang University of Technology（浙江工业大学计算机学院）
University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）
As an important class of spiking neural networks (SNNs), recurrent spiking neural networks (RSNNs) possess great computational power and have been widely used for processing sequential data like audio and text. However, most RSNNs suffer from two problems. 1. Due to a lack of architectural guidance, random recurrent connectivity is often adopted, which does not guarantee good performance. 2. Training of RSNNs is in general challenging, bottlenecking achievable model accuracy. To address these problems, we propose a new type of RSNNs called Skip-Connected Self-Recurrent SNNs (ScSr-SNNs). Recurr…
