Rapid feedforward computation by temporal encoding and learning with spiking neurons

Improving Multispike Learning With Plastic Synaptic Delays

Emulating the spike-based processing in the brain, spiking neural networks (SNNs) are developed and act as a promising candidate for the new generation of artificial neural networks that aim to produce efficient cognitions as the brain. Due to the complex dynamics and nonlinearity of SNNs, designing efficient learning algorithms has remained a major difficulty, which attracts great research attention. Most existing ones focus on the adjustment of synaptic weights. However, other components, such as synaptic delays, are found to be adaptive and important in modulating neural behavior. How could plasticity on different components cooperate to improve the learning of SNNs remains as an interesting question. Advancing our previous multispike learning, we propose a new joint weight-delay plasticity rule, named TDP-DL, in this article. Plastic delays are integrated into the learning framework, and as a result, the performance of multispike learning is significantly improved. Simulation results highlight the effectiveness and efficiency of our TDP-DL rule compared to baseline ones. Moreover, we reveal the underlying principle of how synaptic weights and delays cooperate with each other through a synthetic task of interval selectivity and show that plastic delays can enhance the selectivity and flexibility of neurons by shifting information across time. Due to this capability, useful information distributed away in the time domain can be effectively integrated for a better accuracy performance, as highlighted in our generalization tasks of the image, speech, and event-based object recognitions. Our work is thus valuable and significant to improve the performance of spike-based neuromorphic computing.

Efficient multi-scale representation of visual objects using a biologically plausible spike-latency code and winner-take-all inhibition

Deep neural networks have surpassed human performance in key visual challenges such as object recognition, but require a large amount of energy, computation, and memory. In contrast, spiking neural networks (SNNs) have the potential to improve both the efficiency and biological plausibility of object recognition systems. Here we present a SNN model that uses spike-latency coding and winner-take-all inhibition (WTA-I) to efficiently represent visual stimuli using multi-scale parallel processing. Mimicking neuronal response properties in early visual cortex, images were preprocessed with three different spatial frequency (SF) channels, before they were fed to a layer of spiking neurons whose synaptic weights were updated using spike-timing-dependent-plasticity. We investigate how the quality of the represented objects changes under different SF bands and WTA-I schemes. We demonstrate that a network of 200 spiking neurons tuned to three SFs can efficiently represent objects with as little as 15 spikes per neuron. Studying how core object recognition may be implemented using biologically plausible learning rules in SNNs may not only further our understanding of the brain, but also lead to novel and efficient artificial vision systems.

An overview of brain-like computing: Architecture, applications, and future trends

With the development of technology, Moore's law will come to an end, and scientists are trying to find a new way out in brain-like computing. But we still know very little about how the brain works. At the present stage of research, brain-like models are all structured to mimic the brain in order to achieve some of the brain's functions, and then continue to improve the theories and models. This article summarizes the important progress and status of brain-like computing, summarizes the generally accepted and feasible brain-like computing models, introduces, analyzes, and compares the more mature brain-like computing chips, outlines the attempts and challenges of brain-like computing applications at this stage, and looks forward to the future development of brain-like computing. It is hoped that the summarized results will help relevant researchers and practitioners to quickly grasp the research progress in the field of brain-like computing and acquire the application methods and related knowledge in this field.

Temporal Encoding and Multispike Learning Framework for Efficient Recognition of Visual Patterns

Biological systems under a parallel and spike-based computation endow individuals with abilities to have prompt and reliable responses to different stimuli. Spiking neural networks (SNNs) have thus been developed to emulate their efficiency and to explore principles of spike-based processing. However, the design of a biologically plausible and efficient SNN for image classification still remains as a challenging task. Previous efforts can be generally clustered into two major categories in terms of coding schemes being employed: rate and temporal. The rate-based schemes suffer inefficiency, whereas the temporal-based ones typically end with a relatively poor performance in accuracy. It is intriguing and important to develop an SNN with both efficiency and efficacy being considered. In this article, we focus on the temporal-based approaches in a way to advance their accuracy performance by a great margin while keeping the efficiency on the other hand. A new temporal-based framework integrated with the multispike learning is developed for efficient recognition of visual patterns. Different approaches of encoding and learning under our framework are evaluated with the MNIST and Fashion-MNIST data sets. Experimental results demonstrate the efficient and effective performance of our temporal-based approaches across a variety of conditions, improving accuracies to higher levels that are even comparable to rate-based ones but importantly with a lighter network structure and far less number of spikes. This article attempts to extend the advanced multispike learning to the challenging task of image recognition and bring state of the arts in temporal-based approaches to a novel level. The experimental results could be potentially favorable to low-power and high-speed requirements in the field of artificial intelligence and contribute to attract more efforts toward brain-like computing.

Constructing Accurate and Efficient Deep Spiking Neural Networks With Double-Threshold and Augmented Schemes

Spiking neural networks (SNNs) are considered as a potential candidate to overcome current challenges, such as the high-power consumption encountered by artificial neural networks (ANNs); however, there is still a gap between them with respect to the recognition accuracy on various tasks. A conversion strategy was, thus, introduced recently to bridge this gap by mapping a trained ANN to an SNN. However, it is still unclear that to what extent this obtained SNN can benefit both the accuracy advantage from ANN and high efficiency from the spike-based paradigm of computation. In this article, we propose two new conversion methods, namely TerMapping and AugMapping. The TerMapping is a straightforward extension of a typical threshold-balancing method with a double-threshold scheme, while the AugMapping additionally incorporates a new scheme of augmented spike that employs a spike coefficient to carry the number of typical all-or-nothing spikes occurring at a time step. We examine the performance of our methods based on the MNIST, Fashion-MNIST, and CIFAR10 data sets. The results show that the proposed double-threshold scheme can effectively improve the accuracies of the converted SNNs. More importantly, the proposed AugMapping is more advantageous for constructing accurate, fast, and efficient deep SNNs compared with other state-of-the-art approaches. Our study, therefore, provides new approaches for further integration of advanced techniques in ANNs to improve the performance of SNNs, which could be of great merit to applied developments with spike-based neuromorphic computing.

Toward Efficient Processing and Learning With Spikes: New Approaches for Multispike Learning

Spikes are the currency in central nervous systems for information transmission and processing. They are also believed to play an essential role in low-power consumption of the biological systems, whose efficiency attracts increasing attentions to the field of neuromorphic computing. However, efficient processing and learning of discrete spikes still remain a challenging problem. In this article, we make our contributions toward this direction. A simplified spiking neuron model is first introduced with the effects of both synaptic input and firing output on the membrane potential being modeled with an impulse function. An event-driven scheme is then presented to further improve the processing efficiency. Based on the neuron model, we propose two new multispike learning rules which demonstrate better performance over other baselines on various tasks, including association, classification, and feature detection. In addition to efficiency, our learning rules demonstrate high robustness against the strong noise of different types. They can also be generalized to different spike coding schemes for the classification task, and notably, the single neuron is capable of solving multicategory classifications with our learning rules. In the feature detection task, we re-examine the ability of unsupervised spike-timing-dependent plasticity with its limitations being presented, and find a new phenomenon of losing selectivity. In contrast, our proposed learning rules can reliably solve the task over a wide range of conditions without specific constraints being applied. Moreover, our rules cannot only detect features but also discriminate them. The improved performance of our methods would contribute to neuromorphic computing as a preferable choice.

Synaptic Learning With Augmented Spikes

Traditional neuron models use analog values for information representation and computation, while all-or-nothing spikes are employed in the spiking ones. With a more brain-like processing paradigm, spiking neurons are more promising for improvements in efficiency and computational capability. They extend the computation of traditional neurons with an additional dimension of time carried by all-or-nothing spikes. Could one benefit from both the accuracy of analog values and the time-processing capability of spikes? In this article, we introduce a concept of augmented spikes to carry complementary information with spike coefficients in addition to spike latencies. New augmented spiking neuron model and synaptic learning rules are proposed to process and learn patterns of augmented spikes. We provide systematic insights into the properties and characteristics of our methods, including classification of augmented spike patterns, learning capacity, construction of causality, feature detection, robustness, and applicability to practical tasks, such as acoustic and visual pattern recognition. Our augmented approaches show several advanced learning properties and reliably outperform the baseline ones that use typical all-or-nothing spikes. Our approaches significantly improve the accuracies of a temporal-based approach on sound and MNIST recognition tasks to 99.38% and 97.90%, respectively, highlighting the effectiveness and potential merits of our methods. More importantly, our augmented approaches are versatile and can be easily generalized to other spike-based systems, contributing to a potential development for them, including neuromorphic computing.

A Cost-Efficient High-Speed VLSI Architecture for Spiking Convolutional Neural Network Inference Using Time-Step Binary Spike Maps

Neuromorphic hardware systems have been gaining ever-increasing focus in many embedded applications as they use a brain-inspired, energy-efficient spiking neural network (SNN) model that closely mimics the human cortex mechanism by communicating and processing sensory information via spatiotemporally sparse spikes. In this paper, we fully leverage the characteristics of spiking convolution neural network (SCNN), and propose a scalable, cost-efficient, and high-speed VLSI architecture to accelerate deep SCNN inference for real-time low-cost embedded scenarios. We leverage the snapshot of binary spike maps at each time-step, to decompose the SCNN operations into a series of regular and simple time-step CNN-like processing to reduce hardware resource consumption. Moreover, our hardware architecture achieves high throughput by employing a pixel stream processing mechanism and fine-grained data pipelines. Our Zynq-7045 FPGA prototype reached a high processing speed of 1250 frames/s and high recognition accuracies on the MNIST and Fashion-MNIST image datasets, demonstrating the plausibility of our SCNN hardware architecture for many embedded applications.

A Survey of Encoding Techniques for Signal Processing in Spiking Neural Networks

Biologically inspired spiking neural networks are increasingly popular in the field of artificial intelligence due to their ability to solve complex problems while being power efficient. They do so by leveraging the timing of discrete spikes as main information carrier. Though, industrial applications are still lacking, partially because the question of how to encode incoming data into discrete spike events cannot be uniformly answered. In this paper, we summarise the signal encoding schemes presented in the literature and propose a uniform nomenclature to prevent the vague usage of ambiguous definitions. Therefore we survey both, the theoretical foundations as well as applications of the encoding schemes. This work provides a foundation in spiking signal encoding and gives an overview over different application-oriented implementations which utilise the schemes.

Computing Primitive of Fully VCSEL-Based All-Optical Spiking Neural Network for Supervised Learning and Pattern Classification

We propose computing primitive for an all-optical spiking neural network (SNN) based on vertical-cavity surface-emitting lasers (VCSELs) for supervised learning by using biologically plausible mechanisms. The spike-timing-dependent plasticity (STDP) model was established based on the dynamics of the vertical-cavity semiconductor optical amplifier (VCSOA) subject to dual-optical pulse injection. The neuron-synapse self-consistent unified model of the all-optical SNN was developed, which enables reproducing the essential neuron-like dynamics and STDP function. Optical character numbers are trained and tested by the proposed fully VCSEL-based all-optical SNN. Simulation results show that the proposed all-optical SNN is capable of recognizing ten numbers by a supervised learning algorithm, in which the input and output patterns as well as the teacher signals of the all-optical SNN are represented by spatiotemporal fashions. Moreover, the lateral inhibition is not required in our proposed architecture, which is friendly to the hardware implementation. The system-level unified model enables architecture-algorithm codesigns and optimization of all-optical SNN. To the best of our knowledge, the computing primitive of an all-optical SNN based on VCSELs for supervised learning has not yet been reported, which paves the way toward fully VCSEL-based large-scale photonic neuromorphic systems with low power consumption.

Numerical Spiking Neural P Systems

Spiking neural P (SN P) systems are a class of discrete neuron-inspired computation models, where information is encoded by the numbers of spikes in neurons and the timing of spikes. However, due to the discontinuous nature of the integrate-and-fire behavior of neurons and the symbolic representation of information, SN P systems are incompatible with the gradient descent-based training algorithms, such as the backpropagation algorithm, and lack the capability of processing the numerical representation of information. In this work, motivated by the numerical nature of numerical P (NP) systems in the area of membrane computing, a novel class of SN P systems is proposed, called numerical SN P (NSN P) systems. More precisely, information is encoded by the values of variables, and the integrate-and-fire way of neurons and the distribution of produced values are described by continuous production functions. The computation power of NSN P systems is investigated. We prove that NSN P is Turing universal as number generating devices, where the production functions in each neuron are linear functions, each involving at most one variable; as number accepting devices, NSN P systems are proved to be universal as well, even if each neuron contains only one production function. These results show that even if a single neuron is simple in the sense that it contains one or two production functions and the production functions in each neuron are linear functions with one variable, a network of simple neurons are still computationally powerful. With the powerful computation power and the characteristic of continuous production functions, developing learning algorithms for NSN P systems is potentially exploitable.

Efficient learning with augmented spikes: A case study with image classification

Efficient learning of spikes plays a valuable role in training spiking neural networks (SNNs) to have desired responses to input stimuli. However, current learning rules are limited to a binary form of spikes. The seemingly ubiquitous phenomenon of burst in nervous systems suggests a new way to carry more information with spike bursts in addition to times. Based on this, we introduce an advanced form, the augmented spikes, where spike coefficients are used to carry additional information. How could neurons learn and benefit from augmented spikes remains unclear. In this paper, we propose two new efficient learning rules to process spatiotemporal patterns composed of augmented spikes. Moreover, we examine the learning abilities of our methods with a synthetic recognition task of augmented spike patterns and two practical ones for image classification. Experimental results demonstrate that our rules are capable of extracting information carried by both the timing and coefficient of spikes. Our proposed approaches achieve remarkable performance and good robustness under various noise conditions, as compared to benchmarks. The improved performance indicates the merits of augmented spikes and our learning rules, which could be beneficial and generalized to a broad range of spike-based platforms.

Robust Environmental Sound Recognition With Sparse Key-Point Encoding and Efficient Multispike Learning

The capability for environmental sound recognition (ESR) can determine the fitness of individuals in a way to avoid dangers or pursue opportunities when critical sound events occur. It still remains mysterious about the fundamental principles of biological systems that result in such a remarkable ability. Additionally, the practical importance of ESR has attracted an increasing amount of research attention, but the chaotic and nonstationary difficulties continue to make it a challenging task. In this article, we propose a spike-based framework from a more brain-like perspective for the ESR task. Our framework is a unifying system with consistent integration of three major functional parts which are sparse encoding, efficient learning, and robust readout. We first introduce a simple sparse encoding, where key points are used for feature representation, and demonstrate its generalization to both spike- and nonspike-based systems. Then, we evaluate the learning properties of different learning rules in detail with our contributions being added for improvements. Our results highlight the advantages of multispike learning, providing a selection reference for various spike-based developments. Finally, we combine the multispike readout with the other parts to form a system for ESR. Experimental results show that our framework performs the best as compared to other baseline approaches. In addition, we show that our spike-based framework has several advantageous characteristics including early decision making, small dataset acquiring, and ongoing dynamic processing. Our framework is the first attempt to apply the multispike characteristic of nervous neurons to ESR. The outstanding performance of our approach would potentially contribute to draw more research efforts to push the boundaries of spike-based paradigm to a new horizon.

Unsupervised AER Object Recognition Based on Multiscale Spatio-Temporal Features and Spiking Neurons

This article proposes an unsupervised address event representation (AER) object recognition approach. The proposed approach consists of a novel multiscale spatio-temporal feature (MuST) representation of input AER events and a spiking neural network (SNN) using spike-timing-dependent plasticity (STDP) for object recognition with MuST. MuST extracts the features contained in both the spatial and temporal information of AER event flow, and forms an informative and compact feature spike representation. We show not only how MuST exploits spikes to convey information more effectively, but also how it benefits the recognition using SNN. The recognition process is performed in an unsupervised manner, which does not need to specify the desired status of every single neuron of SNN, and thus can be flexibly applied in real-world recognition tasks. The experiments are performed on five AER datasets including a new one named GESTURE-DVS. Extensive experimental results show the effectiveness and advantages of the proposed approach.

A High-Speed Low-Cost VLSI System Capable of On-Chip Online Learning for Dynamic Vision Sensor Data Classification

This paper proposes a high-speed low-cost VLSI system capable of on-chip online learning for classifying address-event representation (AER) streams from dynamic vision sensor (DVS) retina chips. The proposed system executes a lightweight statistic algorithm based on simple binary features extracted from AER streams and a Random Ferns classifier to classify these features. The proposed system’s characteristics of multi-level pipelines and parallel processing circuits achieves a high throughput up to 1 spike event per clock cycle for AER data processing. Thanks to the nature of the lightweight algorithm, our hardware system is realized in a low-cost memory-centric paradigm. In addition, the system is capable of on-chip online learning to flexibly adapt to different in-situ application scenarios. The extra overheads for on-chip learning in terms of time and resource consumption are quite low, as the training procedure of the Random Ferns is quite simple, requiring few auxiliary learning circuits. An FPGA prototype of the proposed VLSI system was implemented with 9.5~96.7% memory consumption and <11% computational and logic resources on a Xilinx Zynq-7045 chip platform. It was running at a clock frequency of 100 MHz and achieved a peak processing throughput up to 100 Meps (Mega events per second), with an estimated power consumption of 690 mW leading to a high energy efficiency of 145 Meps/W or 145 event/μJ. We tested the prototype system on MNIST-DVS, Poker-DVS, and Posture-DVS datasets, and obtained classification accuracies of 77.9%, 99.4% and 99.3%, respectively. Compared to prior works, our VLSI system achieves higher processing speeds, higher computing efficiency, comparable accuracy, and lower resource costs.

Supervised learning in spiking neural networks: A review of algorithms and evaluations

As a new brain-inspired computational model of the artificial neural network, a spiking neural network encodes and processes neural information through precisely timed spike trains. Spiking neural networks are composed of biologically plausible spiking neurons, which have become suitable tools for processing complex temporal or spatiotemporal information. However, because of their intricately discontinuous and implicit nonlinear mechanisms, the formulation of efficient supervised learning algorithms for spiking neural networks is difficult, and has become an important problem in this research field. This article presents a comprehensive review of supervised learning algorithms for spiking neural networks and evaluates them qualitatively and quantitatively. First, a comparison between spiking neural networks and traditional artificial neural networks is provided. The general framework and some related theories of supervised learning for spiking neural networks are then introduced. Furthermore, the state-of-the-art supervised learning algorithms in recent years are reviewed from the perspectives of applicability to spiking neural network architecture and the inherent mechanisms of supervised learning algorithms. A performance comparison of spike train learning of some representative algorithms is also made. In addition, we provide five qualitative performance evaluation criteria for supervised learning algorithms for spiking neural networks and further present a new taxonomy for supervised learning algorithms depending on these five performance evaluation criteria. Finally, some future research directions in this research field are outlined.

Reinforcement Learning in Spiking Neural Networks with Stochastic and Deterministic Synapses

Though succeeding in solving various learning tasks, most existing reinforcement learning (RL) models have failed to take into account the complexity of synaptic plasticity in the neural system. Models implementing reinforcement learning with spiking neurons involve only a single plasticity mechanism. Here, we propose a neural realistic reinforcement learning model that coordinates the plasticities of two types of synapses: stochastic and deterministic. The plasticity of the stochastic synapse is achieved by the hedonistic rule through modulating the release probability of synaptic neurotransmitter, while the plasticity of the deterministic synapse is achieved by a variant of a reward-modulated spike-timing-dependent plasticity rule through modulating the synaptic strengths. We evaluate the proposed learning model on two benchmark tasks: learning a logic gate function and the 19-state random walk problem. Experimental results show that the coordination of diverse synaptic plasticities can make the RL model learn in a rapid and stable form.

A review of learning in biologically plausible spiking neural networks

Artificial neural networks have been used as a powerful processing tool in various areas such as pattern recognition, control, robotics, and bioinformatics. Their wide applicability has encouraged researchers to improve artificial neural networks by investigating the biological brain. Neurological research has significantly progressed in recent years and continues to reveal new characteristics of biological neurons. New technologies can now capture temporal changes in the internal activity of the brain in more detail and help clarify the relationship between brain activity and the perception of a given stimulus. This new knowledge has led to a new type of artificial neural network, the Spiking Neural Network (SNN), that draws more faithfully on biological properties to provide higher processing abilities. A review of recent developments in learning of spiking neurons is presented in this paper. First the biological background of SNN learning algorithms is reviewed. The important elements of a learning algorithm such as the neuron model, synaptic plasticity, information encoding and SNN topologies are then presented. Then, a critical review of the state-of-the-art learning algorithms for SNNs using single and multiple spikes is presented. Additionally, deep spiking neural networks are reviewed, and challenges and opportunities in the SNN field are discussed.

SpykeTorch: Efficient Simulation of Convolutional Spiking Neural Networks With at Most One Spike per Neuron

Application of deep convolutional spiking neural networks (SNNs) to artificial intelligence (AI) tasks has recently gained a lot of interest since SNNs are hardware-friendly and energy-efficient. Unlike the non-spiking counterparts, most of the existing SNN simulation frameworks are not practically efficient enough for large-scale AI tasks. In this paper, we introduce SpykeTorch, an open-source high-speed simulation framework based on PyTorch. This framework simulates convolutional SNNs with at most one spike per neuron and the rank-order encoding scheme. In terms of learning rules, both spike-timing-dependent plasticity (STDP) and reward-modulated STDP (R-STDP) are implemented, but other rules could be implemented easily. Apart from the aforementioned properties, SpykeTorch is highly generic and capable of reproducing the results of various studies. Computations in the proposed framework are tensor-based and totally done by PyTorch functions, which in turn brings the ability of just-in-time optimization for running on CPUs, GPUs, or Multi-GPU platforms.

Spike Timing or Rate? Neurons Learn to Make Decisions for Both Through Threshold-Driven Plasticity

Spikes play an essential role in information transmission in central nervous system, but how neurons learn from them remains a challenging question. Most algorithms studied how to train spiking neurons to process patterns encoded with a sole assumption of either a rate or a temporal code. Is there a general learning algorithm capable of processing both codes regardless of the intense debate on them within neuroscience community? In this paper, we propose several threshold-driven plasticity algorithms to address the above question. In addition to formulating the algorithms, we also provide proofs with respect to several properties, such as robustness and convergence. The experimental results illustrate that our algorithms are simple, effective and yet efficient for training neurons to learn spike patterns. Due to their simplicity and high efficiency, our algorithms would be potentially beneficial for both software and hardware implementations. Neurons with our algorithms can also detect and recognize embedded features from a background sensory activity. With the as-proposed algorithms, a single neuron can successfully perform multicategory classifications by making decisions based on its output spike number in response to each category. Spike patterns being processed can be encoded with both spike rates and precise timings. When afferent spike timings matter, neurons will automatically extract temporal features without being explicitly instructed as to which point to fire.

Event-Driven Continuous STDP Learning With Deep Structure for Visual Pattern Recognition

Human beings can achieve reliable and fast visual pattern recognition with limited time and learning samples. Underlying this capability, ventral stream plays an important role in object representation and form recognition. Modeling the ventral steam may shed light on further understanding the visual brain in humans and building artificial vision systems for pattern recognition. The current methods to model the mechanism of ventral stream are far from exhibiting fast, continuous, and event-driven learning like the human brain. To create a visual system similar to ventral stream in human with fast learning capability, in this paper, we propose a new spiking neural system with an event-driven continuous spike timing dependent plasticity (STDP) learning method using specific spiking timing sequences. Two novel continuous input mechanisms have been used to obtain the continuous input spiking pattern sequence. With the event-driven STDP learning rule, the proposed learning procedure will be activated if the neuron receive one pre- or post-synaptic spike event. The experimental results on MNIST database show that the proposed method outperforms all other methods in fast learning scenarios and most of the current models in exhaustive learning experiments.

A structure-time parallel implementation of spike-based deep learning

Motivated by the recent progress of deep spiking neural networks (SNNs), we propose a structure-time parallel strategy based on layered structure and one-time computation over a time window to speed up the prominent spike-based deep learning algorithm named broadcast alignment. Furthermore, a well-designed deep hierarchical model based on the parallel broadcast alignment is proposed for object recognition. The parallel broadcast alignment achieves a significant 137× speedup compared to its original implementation on MNIST dataset. The object recognition model achieves higher accuracy than that of the latest spiking deep convolutional neural networks on the ETH-80 dataset. The proposed parallel strategy and the object recognition model will facilitate both the simulation of deep SNNs for studying spiking neural dynamics and also the applications of spike-based deep learning in real-world problems.

A 0.086-mm 2 12.7-pJ/SOP 64k-Synapse 256-Neuron Online-Learning Digital Spiking Neuromorphic Processor in 28-nm CMOS

Shifting computing architectures from von Neumann to event-based spiking neural networks (SNNs) uncovers new opportunities for low-power processing of sensory data in applications such as vision or sensorimotor control. Exploring roads toward cognitive SNNs requires the design of compact, low-power and versatile experimentation platforms with the key requirement of online learning in order to adapt and learn new features in uncontrolled environments. However, embedding online learning in SNNs is currently hindered by high incurred complexity and area overheads. In this paper, we present ODIN, a 0.086-mm ² 64k-synapse 256-neuron online-learning digital spiking neuromorphic processor in 28-nm FDSOI CMOS achieving a minimum energy per synaptic operation (SOP) of 12.7 pJ. It leverages an efficient implementation of the spike-driven synaptic plasticity (SDSP) learning rule for high-density embedded online learning with only 0.68  μm ² per 4-bit synapse. Neurons can be independently configured as a standard leaky integrate-and-fire model or as a custom phenomenological model that emulates the 20 Izhikevich behaviors found in biological spiking neurons. Using a single presentation of 6k 16 × 16 MNIST training images to a single-layer fully-connected 10-neuron network with on-chip SDSP-based learning, ODIN achieves a classification accuracy of 84.5%, while consuming only 15 nJ/inference at 0.55 V using rank order coding. ODIN thus enables further developments toward cognitive neuromorphic devices for low-power, adaptive and low-cost processing.

A Highly Effective and Robust Membrane Potential-Driven Supervised Learning Method for Spiking Neurons

Spiking neurons are becoming increasingly popular owing to their biological plausibility and promising computational properties. Unlike traditional rate-based neural models, spiking neurons encode information in the temporal patterns of the transmitted spike trains, which makes them more suitable for processing spatiotemporal information. One of the fundamental computations of spiking neurons is to transform streams of input spike trains into precisely timed firing activity. However, the existing learning methods, used to realize such computation, often result in relatively low accuracy performance and poor robustness to noise. In order to address these limitations, we propose a novel highly effective and robust membrane potential-driven supervised learning (MemPo-Learn) method, which enables the trained neurons to generate desired spike trains with higher precision, higher efficiency, and better noise robustness than the current state-of-the-art spiking neuron learning methods. While the traditional spike-driven learning methods use an error function based on the difference between the actual and desired output spike trains, the proposed MemPo-Learn method employs an error function based on the difference between the output neuron membrane potential and its firing threshold. The efficiency of the proposed learning method is further improved through the introduction of an adaptive strategy, called skip scan training strategy, that selectively identifies the time steps when to apply weight adjustment. The proposed strategy enables the MemPo-Learn method to effectively and efficiently learn the desired output spike train even when much smaller time steps are used. In addition, the learning rule of MemPo-Learn is improved further to help mitigate the impact of the input noise on the timing accuracy and reliability of the neuron firing dynamics. The proposed learning method is thoroughly evaluated on synthetic data and is further demonstrated on real-world classification tasks. Experimental results show that the proposed method can achieve high learning accuracy with a significant improvement in learning time and better robustness to different types of noise.

Hough Transform Implementation For Event-Based Systems: Concepts and Challenges

Hough transform (HT) is one of the most well-known techniques in computer vision that has been the basis of many practical image processing algorithms. HT however is designed to work for frame-based systems such as conventional digital cameras. Recently, event-based systems such as Dynamic Vision Sensor (DVS) cameras, has become popular among researchers. Event-based cameras have a significantly high temporal resolution (1 μs), but each pixel can only detect change and not color. As such, the conventional image processing algorithms cannot be readily applied to event-based output streams. Therefore, it is necessary to adapt the conventional image processing algorithms for event-based cameras. This paper provides a systematic explanation, starting from extending conventional HT to 3D HT, adaptation to event-based systems, and the implementation of the 3D HT using Spiking Neural Networks (SNNs). Using SNN enables the proposed solution to be easily realized on hardware using FPGA, without requiring CPU or additional memory. In addition, we also discuss techniques for optimal SNN-based implementation using efficient number of neurons for the required accuracy and resolution along each dimension, without increasing the overall computational complexity. We hope that this will help to reduce the gap between event-based and frame-based systems.

First-Spike-Based Visual Categorization Using Reward-Modulated STDP

Reinforcement learning (RL) has recently regained popularity with major achievements such as beating the European game of Go champion. Here, for the first time, we show that RL can be used efficiently to train a spiking neural network (SNN) to perform object recognition in natural images without using an external classifier. We used a feedforward convolutional SNN and a temporal coding scheme where the most strongly activated neurons fire first, while less activated ones fire later, or not at all. In the highest layers, each neuron was assigned to an object category, and it was assumed that the stimulus category was the category of the first neuron to fire. If this assumption was correct, the neuron was rewarded, i.e., spike-timing-dependent plasticity (STDP) was applied, which reinforced the neuron's selectivity. Otherwise, anti-STDP was applied, which encouraged the neuron to learn something else. As demonstrated on various image data sets (Caltech, ETH-80, and NORB), this reward-modulated STDP (R-STDP) approach has extracted particularly discriminative visual features, whereas classic unsupervised STDP extracts any feature that consistently repeats. As a result, R-STDP has outperformed STDP on these data sets. Furthermore, R-STDP is suitable for online learning and can adapt to drastic changes such as label permutations. Finally, it is worth mentioning that both feature extraction and classification were done with spikes, using at most one spike per neuron. Thus, the network is hardware friendly and energy efficient.

Sparse Temporal Encoding of Visual Features for Robust Object Recognition by Spiking Neurons

Robust object recognition in spiking neural systems remains a challenging in neuromorphic computing area as it needs to solve both the effective encoding of sensory information and also its integration with downstream learning neurons. We target this problem by developing a spiking neural system consisting of sparse temporal encoding and temporal classifier. We propose a sparse temporal encoding algorithm which exploits both spatial and temporal information derived from an spike-timing-dependent plasticity-based HMAX feature extraction process. The temporal feature representation, thus, becomes more appropriate to be integrated with a temporal classifier based on spiking neurons rather than with nontemporal classifier. The algorithm has been validated on two benchmark data sets and the results show the temporal feature encoding and learning-based method achieves high recognition accuracy. The proposed model provides an efficient approach to perform feature representation and recognition in a consistent temporal learning framework, which is easily adapted to neuromorphic implementations.

A Spiking Neural Network Framework for Robust Sound Classification

Environmental sounds form part of our daily life. With the advancement of deep learning models and the abundance of training data, the performance of automatic sound classification (ASC) systems has improved significantly in recent years. However, the high computational cost, hence high power consumption, remains a major hurdle for large-scale implementation of ASC systems on mobile and wearable devices. Motivated by the observations that humans are highly effective and consume little power whilst analyzing complex audio scenes, we propose a biologically plausible ASC framework, namely SOM-SNN. This framework uses the unsupervised self-organizing map (SOM) for representing frequency contents embedded within the acoustic signals, followed by an event-based spiking neural network (SNN) for spatiotemporal spiking pattern classification. We report experimental results on the RWCP environmental sound and TIDIGITS spoken digits datasets, which demonstrate competitive classification accuracies over other deep learning and SNN-based models. The SOM-SNN framework is also shown to be highly robust to corrupting noise after multi-condition training, whereby the model is trained with noise-corrupted sound samples. Moreover, we discover the early decision making capability of the proposed framework: an accurate classification can be made with an only partial presentation of the input.

Experimental Study of Artificial Neural Networks Using a Digital Memristor Simulator

This paper presents a fully digital implementation of a memristor hardware (HW) simulator, as the core of an emulator, based on a behavioral model of voltage-controlled threshold-type bipolar memristors. Compared to other analog solutions, the proposed digital design is compact, easily reconfigurable, demonstrates very good matching with the mathematical model on which it is based, and complies with all the required features for memristor emulators. We validated its functionality using Altera Quartus II and ModelSim tools targeting low-cost yet powerful field-programmable gate array families. We tested its suitability for complex memristive circuits as well as its synapse functioning in artificial neural networks, implementing examples of associative memory and unsupervised learning of spatiotemporal correlations in parallel input streams using a simplified spike-timing-dependent plasticity. We provide the full circuit schematics of all our digital circuit designs and comment on the required HW resources and their scaling trends, thus presenting a design framework for applications based on our HW simulator.

Online Supervised Learning for Hardware-Based Multilayer Spiking Neural Networks Through the Modulation of Weight-Dependent Spike-Timing-Dependent Plasticity

In this paper, we propose an online learning algorithm for supervised learning in multilayer spiking neural networks (SNNs). It is found that the spike timings of neurons in an SNN can be exploited to estimate the gradients that are associated with each synapse. With the proposed method of estimating gradients, learning similar to the stochastic gradient descent process employed in a conventional artificial neural network (ANN) can be achieved. In addition to the conventional layer-by-layer backpropagation, a one-pass direct backpropagation is possible using the proposed learning algorithm. Two neural networks, with one and two hidden layers, are employed as examples to demonstrate the effectiveness of the proposed learning algorithms. Several techniques for more effective learning are discussed, including utilizing a random refractory period to avoid saturation of spikes, employing a quantization noise injection technique and pseudorandom initial conditions to decorrelate spike timings, in addition to leveraging the progressive precision in an SNN to reduce the inference latency and energy. Extensive parametric simulations are conducted to examine the aforementioned techniques. The learning algorithm is developed with the considerations of ease of hardware implementation and relative compatibility with the classic ANN-based learning. Therefore, the proposed algorithm not only enjoys the high energy efficiency and good scalability of an SNN in its specialized hardware but also benefits from the well-developed theory and techniques of conventional ANN-based learning. The Modified National Institute of Standards and Technology database benchmark test is conducted to verify the newly proposed learning algorithm. Classification correct rates of 97.2% and 97.8% are achieved for the one-hidden-layer and two-hidden-layer neural networks, respectively. Moreover, a brief discussion of the hardware implementations is presented for two mainstream architectures.

Exploiting Lightweight Statistical Learning for Event-Based Vision Processing

This paper presents a lightweight statistical learning framework potentially suitable for low-cost event-based vision systems, where visual information is captured by a dynamic vision sensor (DVS) and represented as an asynchronous stream of pixel addresses (events) indicating a relative intensity change on those locations. A simple random ferns classifier based on randomly selected patch-based binary features is employed to categorize pixel event flows. Our experimental results demonstrate that compared to existing event-based processing algorithms, such as spiking convolutional neural networks (SCNNs) and the state-of-the-art bag-of-events (BoE)-based statistical algorithms, our framework excels in high processing speed (2× faster than the BoE statistical methods and >100× faster than previous SCNNs in training speed) with extremely simple online learning process, and achieves state-of-the-art classification accuracy on four popular address-event representation data sets: MNIST-DVS, Poker-DVS, Posture-DVS, and CIFAR10-DVS. Hardware estimation shows that our algorithm will be preferable for low-cost embedded system implementations.

SPANNER: A Self-Repairing Spiking Neural Network Hardware Architecture

Recent research has shown that a glial cell of astrocyte underpins a self-repair mechanism in the human brain, where spiking neurons provide direct and indirect feedbacks to presynaptic terminals. These feedbacks modulate the synaptic transmission probability of release (PR). When synaptic faults occur, the neuron becomes silent or near silent due to the low PR of synapses; whereby the PRs of remaining healthy synapses are then increased by the indirect feedback from the astrocyte cell. In this paper, a novel hardware architecture of Self-rePAiring spiking Neural NEtwoRk (SPANNER) is proposed, which mimics this self-repairing capability in the human brain. This paper demonstrates that the hardware can self-detect and self-repair synaptic faults without the conventional components for the fault detection and fault repairing. Experimental results show that SPANNER can maintain the system performance with fault densities of up to 40%, and more importantly SPANNER has only a 20% performance degradation when the self-repairing architecture is significantly damaged at a fault density of 80%.

Model-Driven Analysis of Eyeblink Classical Conditioning Reveals the Underlying Structure of Cerebellar Plasticity and Neuronal Activity

The cerebellum plays a critical role in sensorimotor control. However, how the specific circuits and plastic mechanisms of the cerebellum are engaged in closed-loop processing is still unclear. We developed an artificial sensorimotor control system embedding a detailed spiking cerebellar microcircuit with three bidirectional plasticity sites. This proved able to reproduce a cerebellar-driven associative paradigm, the eyeblink classical conditioning (EBCC), in which a precise time relationship between an unconditioned stimulus (US) and a conditioned stimulus (CS) is established. We challenged the spiking model to fit an experimental data set from human subjects. Two subsequent sessions of EBCC acquisition and extinction were recorded and transcranial magnetic stimulation (TMS) was applied on the cerebellum to alter circuit function and plasticity. Evolutionary algorithms were used to find the near-optimal model parameters to reproduce the behaviors of subjects in the different sessions of the protocol. The main finding is that the optimized cerebellar model was able to learn to anticipate (predict) conditioned responses with accurate timing and success rate, demonstrating fast acquisition, memory stabilization, rapid extinction, and faster reacquisition as in EBCC in humans. The firing of Purkinje cells (PCs) and deep cerebellar nuclei (DCN) changed during learning under the control of synaptic plasticity, which evolved at different rates, with a faster acquisition in the cerebellar cortex than in DCN synapses. Eventually, a reduced PC activity released DCN discharge just after the CS, precisely anticipating the US and causing the eyeblink. Moreover, a specific alteration in cortical plasticity explained the EBCC changes induced by cerebellar TMS in humans. In this paper, for the first time, it is shown how closed-loop simulations, using detailed cerebellar microcircuit models, can be successfully used to fit real experimental data sets. Thus, the changes of the model parameters in the different sessions of the protocol unveil how implicit microcircuit mechanisms can generate normal and altered associative behaviors.The cerebellum plays a critical role in sensorimotor control. However, how the specific circuits and plastic mechanisms of the cerebellum are engaged in closed-loop processing is still unclear. We developed an artificial sensorimotor control system embedding a detailed spiking cerebellar microcircuit with three bidirectional plasticity sites. This proved able to reproduce a cerebellar-driven associative paradigm, the eyeblink classical conditioning (EBCC), in which a precise time relationship between an unconditioned stimulus (US) and a conditioned stimulus (CS) is established. We challenged the spiking model to fit an experimental data set from human subjects. Two subsequent sessions of EBCC acquisition and extinction were recorded and transcranial magnetic stimulation (TMS) was applied on the cerebellum to alter circuit function and plasticity. Evolutionary algorithms were used to find the near-optimal model parameters to reproduce the behaviors of subjects in the different sessions of the protocol. The main finding is that the optimized cerebellar model was able to learn to anticipate (predict) conditioned responses with accurate timing and success rate, demonstrating fast acquisition, memory stabilization, rapid extinction, and faster reacquisition as in EBCC in humans. The firing of Purkinje cells (PCs) and deep cerebellar nuclei (DCN) changed during learning under the control of synaptic plasticity, which evolved at different rates, with a faster acquisition in the cerebellar cortex than in DCN synapses. Eventually, a reduced PC activity released DCN discharge just after the CS, precisely anticipating the US and causing the eyeblink. Moreover, a specific alteration in cortical plasticity explained the EBCC changes induced by cerebellar TMS in humans. In this paper, for the first time, it is shown how closed-loop simulations, using detailed cerebellar microcircuit models, can be successfully used to fit real experimental data sets. Thus, the changes of the model parameters in the different sessions of the protocol unveil how implicit microcircuit mechanisms can generate normal and altered associative behaviors.

A new approach to optimal control of conductance-based spiking neurons

This paper presents an algorithm for solving the minimum-energy optimal control problem of conductance-based spiking neurons. The basic procedure is (1) to construct a conductance-based spiking neuron oscillator as an affine nonlinear system, (2) to formulate the optimal control problem of the affine nonlinear system as a boundary value problem based on Pontryagin's maximum principle, and (3) to solve the boundary value problem using the homotopy perturbation method. The construction of the minimum-energy optimal control in the framework of the homotopy perturbation technique is novel and valid for a broad class of nonlinear conductance-based neuron models. The applicability of our method in the FitzHugh-Nagumo and Hindmarsh-Rose models is validated by simulations.

Triplet Spike Time-Dependent Plasticity in a Floating-Gate Synapse

Synapse plays an important role in learning in a neural network; the learning rules that modify the synaptic strength based on the timing difference between the pre- and postsynaptic spike occurrence are termed spike time-dependent plasticity (STDP) rules. The most commonly used rule posits weight change based on time difference between one presynaptic spike and one postsynaptic spike and is hence termed doublet STDP (D-STDP). However, D-STDP could not reproduce results of many biological experiments; a triplet STDP (T-STDP) that considers triplets of spikes as the fundamental unit has been proposed recently to explain these observations. This paper describes the compact implementation of a synapse using a single floating-gate (FG) transistor that can store a weight in a nonvolatile manner and demonstrates the T-STDP learning rule by modifying drain voltages according to triplets of spikes. We describe a mathematical procedure to obtain control voltages for the FG device for T-STDP and also show measurement results from an FG synapse fabricated in TSMC 0.35-μm CMOS process to support the theory. Possible very large scale integration implementation of drain voltage waveform generator circuits is also presented with the simulation results.