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 including convolutional, all-to-all connectivity, and maxpool layers directly in Pytorch. We found that the recurrent model leads to high classification accuracy using just 4-long spike trains during training. We also observed a good transfer back to continuous implementations of leaky integrate and fire neurons. Finally, we applied this approach to some of the standard control problems as a first step to explore reinforcement learning using neuromorphic chips.
Computational Brain Lab, Department of Computer Science, Rutgers University（罗格斯大学计算机科学系计算大脑实验室）
Energy-efficient mapless navigation is crucial for mobile robots as they explore unknown environments with limited on-board resources. Although the recent deep reinforcement learning (DRL) approaches have been successfully applied to navigation, their high energy consumption limits their use in several robotic applications. Here, we propose a neuromorphic approach that combines the energy-efficiency of spiking neural networks with the optimality of DRL and benchmark it in learning control policies for mapless navigation. Our hybrid framework, spiking deep deterministic policy gradient (SDDPG),…
The process of continuously reallocating funds into financial assets, aiming to increase the expected return of investment and minimizing the risk, is known as portfolio management. Processing speed and energy consumption of portfolio management have become crucial as the complexity of their real-world applications increasingly involves high-dimensional observation and action spaces and environment uncertainty, which their limited onboard resources cannot offset. Emerging neuromorphic chips inspired by the human brain increase processing speed by up to 1000 times and reduce power consumption b…
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…
Neuromorphic computing is a new paradigm for design of both the computing hardware and algorithms inspired by biological neural networks. The event-based nature and the inherent parallelism make neuromorphic computing a promising paradigm for building efficient neural network based architectures for control of fast and agile robots. In this paper, we present a spiking neural network architecture that uses sensory feedback to control rotational velocity of a robotic vehicle. When the velocity reaches the target value, the mapping from the target velocity of the vehicle to the correct motor comm…
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 …
We describe a method to train spiking deep networks that can be run using leaky integrate-and-fire (LIF) neurons, achieving state-of-the-art results for spiking LIF networks on five datasets, including the large ImageNet ILSVRC-2012 benchmark. Our method for transforming deep artificial neural networks into spiking networks is scalable and works with a wide range of neural nonlinearities. We achieve these results by softening the neural response function, such that its derivative remains bounded, and by training the network with noise to provide robustness against the variability introduced by…
This paper presents a three layer spiking neural network based region proposal network operating on data generated by neuromorphic vision sensors. The proposed architecture consists of refractory, convolution and clustering layers designed with bio-realistic leaky integrate and fire (LIF) neurons and synapses. The proposed algorithm is tested on traffic scene recordings from a DAVIS sensor setup. The performance of the region proposal network has been compared with event based mean shift algorithm and is found to be far superior (~50% better) in recall for similar precision (~85%). Computation…
In this work we have extended AutoML inspired approaches to the exploration and optimization of neuromorphic architectures. Through the integration of a parallel asynchronous model-based search approach with a simulation framework to simulate spiking architectures, we are able to efficiently explore the configuration space of neuromorphic architectures and identify the subset of conditions leading to the highest performance in a targeted application. We have demonstrated this approach on an exemplar case of real time, on-chip learning application. Our results indicate that we can effectively u…
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…
Neuromorphic architectures achieve low-power operation by using many simple spiking neurons in lieu of traditional hardware. Here, we develop methods for precise linear computations in spiking neural networks and use these methods to map the evolution of a linear dynamical system (LDS) onto an existing neuromorphic chip: IBM's TrueNorth. We analytically characterize, and numerically validate, the discrepancy between the spiking LDS state sequence and that of its non-spiking counterpart. These analytical results shed light on the multiway tradeoff between time, space, energy, and accuracy in ne…
In the last few years, spiking neural networks have been demonstrated to perform on par with regular convolutional neural networks. Several works have proposed methods to convert a pre-trained CNN to a Spiking CNN without a significant sacrifice of performance. We demonstrate first that quantization-aware training of CNNs leads to better accuracy in SNNs. One of the benefits of converting CNNs to spiking CNNs is to leverage the sparse computation of SNNs and consequently perform equivalent computation at a lower energy consumption. Here we propose an efficient optimization strategy to train sp…
In this paper, we propose a design methodology to partition and map the neurons and synapses of online learning SNN-based applications to neuromorphic architectures at {run-time}. Our design methodology operates in two steps -- step 1 is a layer-wise greedy approach to partition SNNs into clusters of neurons and synapses incorporating the constraints of the neuromorphic architecture, and step 2 is a hill-climbing optimization algorithm that minimizes the total spikes communicated between clusters, improving energy consumption on the shared interconnect of the architecture. We conduct experimen…
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…
Institute of Neuroinformatics, University of Zurich（苏黎世大学神经信息学研究所）；ETH Zurich（苏黎世联邦理工学院）；Istituto Italiano di Tecnologia（意大利技术研究院）
Despite neuromorphic engineering promises the deployment of low latency, adaptive and low power systems that can lead to the design of truly autonomous artificial agents, the development of a fully neuromorphic artificial agent is still missing. While neuromorphic sensing and perception, as well as decision-making systems, are now mature, the control and actuation part is lagging behind. In this paper, we present a closed-loop motor controller implemented on mixed-signal analog-digital neuromorphic hardware using a spiking neural network. The network performs a proportional control action by e…
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…
Energy-Efficient Neuromorphic Computing for Edge AI: A Framework with Adaptive Spiking Neural Networks and Hardware-Aware Optimization
Department of Applied Mathematics and Computer Science (DTU Compute)（应用数学与计算机科学系（DTU计算））；Department of Engineering（工程系）；Department of Computer Engineering（计算机工程系）；Department of Mathematics（数学系）；Department of Computer Systems（计算机系统系）
Heidelberg University（海德堡大学）；Friedrich Miescher Institute for Biomedical Research（弗里德里希·米歇尔生物医学研究所）
To rapidly process temporal information at a low metabolic cost, biological neurons integrate inputs as an analog sum but communicate with spikes, binary events in time. Analog neuromorphic hardware uses the same principles to emulate spiking neural networks with exceptional energy-efficiency. However, instantiating high-performing spiking networks on such hardware remains a significant challenge due to device mismatch and the lack of efficient training algorithms. Here, we introduce a general in-the-loop learning framework based on surrogate gradients that resolves these issues. Using the Bra…
The widely parallel, spiking neural networks of neuromorphic processors can enable computationally powerful formulations. While recent interest has focused on primarily machine learning tasks, the space of appropriate applications is wide and continually expanding. Here, we leverage the parallel and event-driven structure to solve a steady state heat equation using a random walk method. The random walk can be executed fully within a spiking neural network using stochastic neuron behavior, and we provide results from both IBM TrueNorth and Intel Loihi implementations. Additionally, we position …
Spiking Neural Networks (SNNs) are widely deployed to solve complex pattern recognition, function approximation and image classification tasks. With the growing size and complexity of these networks, hardware implementation becomes challenging because scaling up the size of a single array (crossbar) of fully connected neurons is no longer feasible due to strict energy budget. Modern neromorphic hardware integrates small-sized crossbars with time-multiplexed interconnects. Partitioning SNNs becomes essential in order to map them on neuromorphic hardware with the major aim to reduce the global c…
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…
Recently, both industry and academia have proposed several different neuromorphic systems to execute machine learning applications that are designed using Spiking Neural Networks (SNNs). With the growing complexity on design and technology fronts, programming such systems to admit and execute a machine learning application is becoming increasingly challenging. Additionally, neuromorphic systems are required to guarantee real-time performance, consume lower energy, and provide tolerance to logic and memory failures. Consequently, there is a clear need for system software frameworks that can imp…
The increasing need for compact and low-power computing solutions for machine learning applications has triggered significant interest in energy-efficient neuromorphic systems. However, most of these architectures rely on spiking neural networks, which typically perform poorly compared to their non-spiking counterparts in terms of accuracy. In this paper, we propose a new adaptive spiking neuron model that can be abstracted as a low-pass filter. This abstraction enables faster and better training of spiking networks using back-propagation, without simulating spikes. We show that this model dra…
The approximation of quantum states with artificial neural networks has gained a lot of attention during the last years. Meanwhile, analog neuromorphic chips, inspired by structural and dynamical properties of the biological brain, show a high energy efficiency in running artificial neural-network architectures for the profit of generative applications. This encourages employing such hardware systems as platforms for simulations of quantum systems. Here we report on the realization of a prototype using the latest spike-based BrainScaleS hardware allowing us to represent few-qubit maximally ent…
Synergies between wireless communications and artificial intelligence are increasingly motivating research at the intersection of the two fields. On the one hand, the presence of more and more wirelessly connected devices, each with its own data, is driving efforts to export advances in machine learning (ML) from high performance computing facilities, where information is stored and processed in a single location, to distributed, privacy-minded, processing at the end user. On the other hand, ML can address algorithm and model deficits in the optimization of communication protocols. However, im…
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 introduce an optoelectronic spiking artificial neuron capable of operating at ultrafast rates ($\approx$ 100 ps/optical spike) and with low energy consumption ($<$ pJ/spike). The proposed system combines an excitable resonant tunnelling diode (RTD) element exhibiting negative differential conductance, coupled to a nanoscale light source (forming a master node) or a photodetector (forming a receiver node). We study numerically the spiking dynamical responses and information propagation functionality of an interconnected master-receiver RTD node system. Using the key functionali…
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…
We present results related to the performance of an algorithm for community detection which incorporates event-driven computation. We define a mapping which takes a graph G to a system of spiking neurons. Using a fully connected spiking neuron system, with both inhibitory and excitatory synaptic connections, the firing patterns of neurons within the same community can be distinguished from firing patterns of neurons in different communities. On a random graph with 128 vertices and known community structure we show that by using binary decoding and a Hamming-distance based metric, individual co…
Technische Universität Wien（维也纳工业大学）；Politecnico di Torino（都灵理工大学）；New York University（纽约大学）
Autonomous Driving (AD) related features provide new forms of mobility that are also beneficial for other kind of intelligent and autonomous systems like robots, smart transportation, and smart industries. For these applications, the decisions need to be made fast and in real-time. Moreover, in the quest for electric mobility, this task must follow low power policy, without affecting much the autonomy of the mean of transport or the robot. These two challenges can be tackled using the emerging Spiking Neural Networks (SNNs). When deployed on a specialized neuromorphic hardware, SNNs can achiev…
The increasing rise in machine learning and deep learning applications is requiring ever more computational resources to successfully meet the growing demands of an always-connected, automated world. Neuromorphic technologies based on Spiking Neural Network algorithms hold the promise to implement advanced artificial intelligence using a fraction of the computations and power requirements by modeling the functioning, and spiking, of the human brain. With the proliferation of tools and platforms aiding data scientists and machine learning engineers to develop the latest innovations in artificia…
Spiking neural networks have shown great promise for the design of low-power sensory-processing and edge-computing hardware platforms. However, implementing on-chip learning algorithms on such architectures is still an open challenge, especially for multi-layer networks that rely on the back-propagation algorithm. In this paper, we present a spike-based learning method that approximates back-propagation using local weight update mechanisms and which is compatible with mixed-signal analog/digital neuromorphic circuits. We introduce a network architecture that enables synaptic weight update mech…
Developing intelligent neuromorphic solutions remains a challenging endeavour. It requires a solid conceptual understanding of the hardware's fundamental building blocks. Beyond this, accessible and user-friendly prototyping is crucial to speed up the design pipeline. We developed an open source Loihi emulator based on the neural network simulator Brian that can easily be incorporated into existing simulation workflows. We demonstrate errorless Loihi emulation in software for a single neuron and for a recurrently connected spiking neural network. On-chip learning is also reviewed and implement…
The Lobula Giant Movement Detector (LGMD) is an identified neuron of the locust that detects looming objects and triggers the insect's escape responses. Understanding the neural principles and network structure that lead to these fast and robust responses can facilitate the design of efficient obstacle avoidance strategies for robotic applications. Here we present a neuromorphic spiking neural network model of the LGMD driven by the output of a neuromorphic Dynamic Vision Sensor (DVS), which incorporates spiking frequency adaptation and synaptic plasticity mechanisms, and which can be mapped o…
After several decades of continuously optimizing computing systems, the Moore's law is reaching itsend. However, there is an increasing demand for fast and efficient processing systems that can handlelarge streams of data while decreasing system footprints. Neuromorphic computing answers thisneed by creating decentralized architectures that communicate with binary events over time. Despiteits rapid growth in the last few years, novel algorithms are needed that can leverage the potential ofthis emerging computing paradigm and can stimulate the design of advanced neuromorphic chips.In this work,…
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）
SpikingJelly: An open-source machine learning infrastructure platform for spike-based intelligence
Peking University（北京大学）；Peng Cheng Laboratory（鹏城实验室）；Shanghai Jiao Tong University（上海交通大学）；Chinese Academy of Sciences（中国科学院）；Centre de Recherche Cerveau et Cognition (CERCO), UMR5549 CNRS - Univ. Toulouse 3（大脑与认知研究中心（CERCO），CNRS UMR5549 - 图卢兹第三大学）；University of Chinese Academy of Sciences（中国科学院大学）
Recent research has demonstrated the usefulness of neural networks as variational ansatz functions for quantum many-body states. However, high-dimensional sampling spaces and transient autocorrelations confront these approaches with a challenging computational bottleneck. Compared to conventional neural networks, physical-model devices offer a fast, efficient and inherently parallel substrate capable of related forms of Markov chain Monte Carlo sampling. Here, we demonstrate the ability of a neuromorphic chip to represent the ground states of quantum spin models by variational energy minimizat…
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…
All-optical binary convolution with a photonic spiking vertical-cavity surface-emitting laser (VCSEL) neuron is proposed and demonstrated experimentally for the first time. Optical inputs, extracted from digital images and temporally encoded using rectangular pulses, are injected in the VCSEL neuron which delivers the convolution result in the number of fast (<100 ps long) spikes fired. Experimental and numerical results show that binary convolution is achieved successfully with a single spiking VCSEL neuron and that all-optical binary convolution can be used to calculate image gradient magnit…
Spiking Neural Networks (SNN) are an emerging computation model, which uses event-driven activation and bio-inspired learning algorithms. SNN-based machine-learning programs are typically executed on tile- based neuromorphic hardware platforms, where each tile consists of a computation unit called crossbar, which maps neurons and synapses of the program. However, synthesizing such programs on an off-the-shelf neuromorphic hardware is challenging. This is because of the inherent resource and latency limitations of the hardware, which impact both model performance, e.g., accuracy, and hardware p…
A Spiking Sequence Generator for Polar Trajectories on Neuromorphic Hardware
Mechanical & Aerospace Engineering, Case Western Reserve University（机械与航空航天工程，凯斯西储大学）；Mechanical & Aerospace Engineering, West Virginia University（机械与航空航天工程，西弗吉尼亚大学）
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…
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,…
How spiking networks are able to perform probabilistic inference is an intriguing question, not only for understanding information processing in the brain, but also for transferring these computational principles to neuromorphic silicon circuits. A number of computationally powerful spiking network models have been proposed, but most of them have only been tested, under ideal conditions, in software simulations. Any implementation in an analog, physical system, be it in vivo or in silico, will generally lead to distorted dynamics due to the physical properties of the underlying substrate. In t…
With more and more event-based neuromorphic hardware systems being developed at universities and in industry, there is a growing need for assessing their performance with domain specific measures. In this work, we use the methodology of converting pre-trained non-spiking to spiking neural networks to evaluate the performance loss and measure the energy-per-inference for three neuromorphic hardware systems (BrainScaleS, Spikey, SpiNNaker) and common simulation frameworks for CPU (NEST) and CPU/GPU (GeNN). For analog hardware we further apply a re-training technique known as hardware-in-the-loop…
