Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network's topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper.

Probabilistic Neural Computing with Stochastic Devices

The brain has effectively proven a powerful inspiration for the development of computing architectures in which processing is tightly integrated with memory, communication is event-driven, and analog computation can be performed at scale. These neuromorphic systems increasingly show an ability to improve the efficiency and speed of scientific computing and artificial intelligence applications. Herein, it is proposed that the brain's ubiquitous stochasticity represents an additional source of inspiration for expanding the reach of neuromorphic computing to probabilistic applications. To date, many efforts exploring probabilistic computing have focused primarily on one scale of the microelectronics stack, such as implementing probabilistic algorithms on deterministic hardware or developing probabilistic devices and circuits with the expectation that they will be leveraged by eventual probabilistic architectures. A co-design vision is described by which large numbers of devices, such as magnetic tunnel junctions and tunnel diodes, can be operated in a stochastic regime and incorporated into a scalable neuromorphic architecture that can impact a number of probabilistic computing applications, such as Monte Carlo simulations and Bayesian neural networks. Finally, a framework is presented to categorize increasingly advanced hardware-based probabilistic computing technologies.

Sharing leaky-integrate-and-fire neurons for memory-efficient spiking neural networks

Spiking Neural Networks (SNNs) have gained increasing attention as energy-efficient neural networks owing to their binary and asynchronous computation. However, their non-linear activation, that is Leaky-Integrate-and-Fire (LIF) neuron, requires additional memory to store a membrane voltage to capture the temporal dynamics of spikes. Although the required memory cost for LIF neurons significantly increases as the input dimension goes larger, a technique to reduce memory for LIF neurons has not been explored so far. To address this, we propose a simple and effective solution, EfficientLIF-Net, which shares the LIF neurons across different layers and channels. Our EfficientLIF-Net achieves comparable accuracy with the standard SNNs while bringing up to ~4.3× forward memory efficiency and ~21.9× backward memory efficiency for LIF neurons. We conduct experiments on various datasets including CIFAR10, CIFAR100, TinyImageNet, ImageNet-100, and N-Caltech101. Furthermore, we show that our approach also offers advantages on Human Activity Recognition (HAR) datasets, which heavily rely on temporal information. The code has been released at https://github.com/Intelligent-Computing-Lab-Yale/EfficientLIF-Net.

Coherent noise enables probabilistic sequence replay in spiking neuronal networks

Animals rely on different decision strategies when faced with ambiguous or uncertain cues. Depending on the context, decisions may be biased towards events that were most frequently experienced in the past, or be more explorative. A particular type of decision making central to cognition is sequential memory recall in response to ambiguous cues. A previously developed spiking neuronal network implementation of sequence prediction and recall learns complex, high-order sequences in an unsupervised manner by local, biologically inspired plasticity rules. In response to an ambiguous cue, the model deterministically recalls the sequence shown most frequently during training. Here, we present an extension of the model enabling a range of different decision strategies. In this model, explorative behavior is generated by supplying neurons with noise. As the model relies on population encoding, uncorrelated noise averages out, and the recall dynamics remain effectively deterministic. In the presence of locally correlated noise, the averaging effect is avoided without impairing the model performance, and without the need for large noise amplitudes. We investigate two forms of correlated noise occurring in nature: shared synaptic background inputs, and random locking of the stimulus to spatiotemporal oscillations in the network activity. Depending on the noise characteristics, the network adopts various recall strategies. This study thereby provides potential mechanisms explaining how the statistics of learned sequences affect decision making, and how decision strategies can be adjusted after learning.

Neural sampling machine with stochastic synapse allows brain-like learning and inference

Many real-world mission-critical applications require continual online learning from noisy data and real-time decision making with a defined confidence level. Brain-inspired probabilistic models of neural network can explicitly handle the uncertainty in data and allow adaptive learning on the fly. However, their implementation in a compact, low-power hardware remains a challenge. In this work, we introduce a novel hardware fabric that can implement a new class of stochastic neural network called Neural Sampling Machine (NSM) by exploiting the stochasticity in the synaptic connections for approximate Bayesian inference. We experimentally demonstrate an in silico hybrid stochastic synapse by pairing a ferroelectric field-effect transistor (FeFET)-based analog weight cell with a two-terminal stochastic selector element. We show that the stochastic switching characteristic of the selector between the insulator and the metallic states resembles the multiplicative synaptic noise of the NSM. We perform network-level simulations to highlight the salient features offered by the stochastic NSM such as performing autonomous weight normalization for continual online learning and Bayesian inferencing. We show that the stochastic NSM can not only perform highly accurate image classification with 98.25% accuracy on standard MNIST dataset, but also estimate the uncertainty in prediction (measured in terms of the entropy of prediction) when the digits of the MNIST dataset are rotated. Building such a probabilistic hardware platform that can support neuroscience inspired models can enhance the learning and inference capability of the current artificial intelligence (AI).

Neural sampling machines make use of noise to perform learning. Here, Dutta et al. present a hybrid stochastic synapse composed out of a ferroelectric transistor combined with a stochastic selector exhibiting multiplicative synaptic noise required for implementing a neural sample machine.

Phase-change memtransistive synapses for mixed-plasticity neural computations

In the mammalian nervous system, various synaptic plasticity rules act, either individually or synergistically, over wide-ranging timescales to enable learning and memory formation. Hence, in neuromorphic computing platforms, there is a significant need for artificial synapses that can faithfully express such multi-timescale plasticity mechanisms. Although some plasticity rules have been emulated with elaborate complementary metal oxide semiconductor and memristive circuitry, device-level hardware realizations of long-term and short-term plasticity with tunable dynamics are lacking. Here we introduce a phase-change memtransistive synapse that leverages both the non-volatility of the phase configurations and the volatility of field-effect modulation for implementing tunable plasticities. We show that these mixed-plasticity synapses can enable plasticity rules such as short-term spike-timing-dependent plasticity that helps with the modelling of dynamic environments. Further, we demonstrate the efficacy of the memtransistive synapses in realizing accelerators for Hopfield neural networks for solving combinatorial optimization problems.

Exploiting Non-idealities of Resistive Switching Memories for Efficient Machine Learning

Novel computing architectures based on resistive switching memories (also known as memristors or RRAMs) have been shown to be promising approaches for tackling the energy inefficiency of deep learning and spiking neural networks. However, resistive switch technology is immature and suffers from numerous imperfections, which are often considered limitations on implementations of artificial neural networks. Nevertheless, a reasonable amount of variability can be harnessed to implement efficient probabilistic or approximate computing. This approach turns out to improve robustness, decrease overfitting and reduce energy consumption for specific applications, such as Bayesian and spiking neural networks. Thus, certain non-idealities could become opportunities if we adapt machine learning methods to the intrinsic characteristics of resistive switching memories. In this short review, we introduce some key considerations for circuit design and the most common non-idealities. We illustrate the possible benefits of stochasticity and compression with examples of well-established software methods. We then present an overview of recent neural network implementations that exploit the imperfections of resistive switching memory, and discuss the potential and limitations of these approaches.

Probabilistic Spike Propagation for Efficient Hardware Implementation of Spiking Neural Networks

Spiking neural networks (SNNs) have gained considerable attention in recent years due to their ability to model temporal event streams, be trained using unsupervised learning rules, and be realized on low-power event-driven hardware. Notwithstanding the intrinsic desirable attributes of SNNs, there is a need to further optimize their computational efficiency to enable their deployment in highly resource-constrained systems. The complexity of evaluating an SNN is strongly correlated to the spiking activity in the network, and can be measured in terms of a fundamental unit of computation, viz. spike propagation along a synapse from a single source neuron to a single target neuron. We propose probabilistic spike propagation, an approach to optimize rate-coded SNNs by interpreting synaptic weights as probabilities, and utilizing these probabilities to regulate spike propagation. The approach results in 2.4-3.69× reduction in spikes propagated, leading to reduced time and energy consumption. We propose Probabilistic Spiking Neural Network Application Processor (P-SNNAP), a specialized SNN accelerator with support for probabilistic spike propagation. Our evaluations across a suite of benchmark SNNs demonstrate that probabilistic spike propagation results in 1.39-2× energy reduction with simultaneous speedups of 1.16-1.62× compared to the traditional model of SNN evaluation.

Adaptive Extreme Edge Computing for Wearable Devices

Wearable devices are a fast-growing technology with impact on personal healthcare for both society and economy. Due to the widespread of sensors in pervasive and distributed networks, power consumption, processing speed, and system adaptation are vital in future smart wearable devices. The visioning and forecasting of how to bring computation to the edge in smart sensors have already begun, with an aspiration to provide adaptive extreme edge computing. Here, we provide a holistic view of hardware and theoretical solutions toward smart wearable devices that can provide guidance to research in this pervasive computing era. We propose various solutions for biologically plausible models for continual learning in neuromorphic computing technologies for wearable sensors. To envision this concept, we provide a systematic outline in which prospective low power and low latency scenarios of wearable sensors in neuromorphic platforms are expected. We successively describe vital potential landscapes of neuromorphic processors exploiting complementary metal-oxide semiconductors (CMOS) and emerging memory technologies (e.g., memristive devices). Furthermore, we evaluate the requirements for edge computing within wearable devices in terms of footprint, power consumption, latency, and data size. We additionally investigate the challenges beyond neuromorphic computing hardware, algorithms and devices that could impede enhancement of adaptive edge computing in smart wearable devices.

Biologically Plausible Class Discrimination Based Recurrent Neural Network Training for Motor Pattern Generation

Biological brain stores massive amount of information. Inspired by features of the biological memory, we propose an algorithm to efficiently store different classes of spatio-temporal information in a Recurrent Neural Network (RNN). A given spatio-temporal input triggers a neuron firing pattern, known as an attractor, and it conveys information about the class to which the input belongs. These attractors are the basic elements of the memory in our RNN. Preparing a set of good attractors is the key to efficiently storing temporal information in an RNN. We achieve this by means of enhancing the “separation” and “approximation” properties associated with the attractors, during the RNN training. We furthermore elaborate how these attractors can trigger an action via the readout in the RNN, similar to the sensory motor action processing in the cerebellum cortex. We show how different voice commands by different speakers trigger hand drawn impressions of the spoken words, by means of our separation and approximation based learning. The method further recognizes the gender of the speaker. The method is evaluated on the TI-46 speech data corpus, and we have achieved 98.6% classification accuracy on the TI-46 digit corpus.

Discrete Langevin machine: Bridging the gap between thermodynamic and neuromorphic systems

A formulation of Langevin dynamics for discrete systems is derived as a class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a network architecture which is implemented by the Langevin machine. The Langevin machine represents a promising approach to compute successfully quantitative exact results of Boltzmann distributed systems by LIF neurons. Besides a detailed introduction of the dynamics, different simplified models of a neuromorphic hardware system are studied with respect to a control of emerging sources of errors.

Effects of synaptic integration on the dynamics and computational performance of spiking neural network

Neurons in the brain receive thousands of synaptic inputs from other neurons. This afferent information is processed by neurons through synaptic integration, which is an important information processing mechanism in biological neural networks. Synaptic currents integrated from spiking trains of presynaptic neurons have complex nonlinear dynamics which endow neurons with significant computational abilities. However, in many computational studies of neural networks, external input currents are often simply taken as a direct current that is static. In this paper, the influences of synaptic and noise external currents on the dynamics of spiking neural network and its computational capability have been investigated in detail. Our results show that due to the nonlinear synaptic integration, both of fast and slow excitatory synaptic currents have much more complex and oscillatory fluctuations than the noise current with the same average intensity. Thus network driven by synaptic external current exhibits remarkably more complex dynamics than that driven by noise external current. Interestingly, the enhancement of network activity is beneficial for information transmission, which is further supported by two computational tasks conducted on the liquid state machine (LSM) network. LSM with synaptic external current displays considerably better performance in both nonlinear fitting and pattern classification than that with noise external current. Synaptic integration can significantly enhance the entropy of activity patterns and computational performance of LSM. Our results demonstrate that the complex dynamics of nonlinear synaptic integration play a critical role in the computational abilities of neural networks and should be more broadly considered in the modelling studies of spiking neural networks.

A neuromorphic systems approach to in-memory computing with non-ideal memristive devices: from mitigation to exploitation

Memristive devices represent a promising technology for building neuromorphic electronic systems. In addition to their compactness and non-volatility, they are characterized by their computationally relevant physical properties, such as their state-dependence, non-linear conductance changes, and intrinsic variability in both their switching threshold and conductance values, that make them ideal devices for emulating the bio-physics of real synapses. In this paper we present a spiking neural network architecture that supports the use of memristive devices as synaptic elements and propose mixed-signal analog-digital interfacing circuits that mitigate the effect of variability in their conductance values and exploit their variability in the switching threshold for implementing stochastic learning. The effect of device variability is mitigated using pairs of memristive devices configured in a complementary push-pull mechanism and interfaced to a current-mode normalizer circuit. The stochastic learning mechanism is obtained by mapping the desired change in synaptic weight into a corresponding switching probability that is derived from the intrinsic stochastic behavior of memristive devices. We demonstrate the features of the CMOS circuits and apply the architecture proposed to a standard neural network hand-written digit classification benchmark based on the MNIST data-set. We evaluate the performance of the approach proposed in this benchmark using behavioral-level spiking neural network simulation, showing both the effect of the reduction in conductance variability produced by the current-mode normalizer circuit and the increase in performance as a function of the number of memristive devices used in each synapse.

Deterministic networks for probabilistic computing

Neuronal network models of high-level brain functions such as memory recall and reasoning often rely on the presence of some form of noise. The majority of these models assumes that each neuron in the functional network is equipped with its own private source of randomness, often in the form of uncorrelated external noise. In vivo, synaptic background input has been suggested to serve as the main source of noise in biological neuronal networks. However, the finiteness of the number of such noise sources constitutes a challenge to this idea. Here, we show that shared-noise correlations resulting from a finite number of independent noise sources can substantially impair the performance of stochastic network models. We demonstrate that this problem is naturally overcome by replacing the ensemble of independent noise sources by a deterministic recurrent neuronal network. By virtue of inhibitory feedback, such networks can generate small residual spatial correlations in their activity which, counter to intuition, suppress the detrimental effect of shared input. We exploit this mechanism to show that a single recurrent network of a few hundred neurons can serve as a natural noise source for a large ensemble of functional networks performing probabilistic computations, each comprising thousands of units.

ConvPath: A software tool for lung adenocarcinoma digital pathological image analysis aided by a convolutional neural network

BACKGROUND

The spatial distributions of different types of cells could reveal a cancer cell's growth pattern, its relationships with the tumor microenvironment and the immune response of the body, all of which represent key "hallmarks of cancer". However, the process by which pathologists manually recognize and localize all the cells in pathology slides is extremely labor intensive and error prone.

METHODS

In this study, we developed an automated cell type classification pipeline, ConvPath, which includes nuclei segmentation, convolutional neural network-based tumor cell, stromal cell, and lymphocyte classification, and extraction of tumor microenvironment-related features for lung cancer pathology images. To facilitate users in leveraging this pipeline for their research, all source scripts for ConvPath software are available at https://qbrc.swmed.edu/projects/cnn/.

FINDINGS

The overall classification accuracy was 92.9% and 90.1% in training and independent testing datasets, respectively. By identifying cells and classifying cell types, this pipeline can convert a pathology image into a "spatial map" of tumor, stromal and lymphocyte cells. From this spatial map, we can extract features that characterize the tumor micro-environment. Based on these features, we developed an image feature-based prognostic model and validated the model in two independent cohorts. The predicted risk group serves as an independent prognostic factor, after adjusting for clinical variables that include age, gender, smoking status, and stage.

INTERPRETATION

The analysis pipeline developed in this study could convert the pathology image into a "spatial map" of tumor cells, stromal cells and lymphocytes. This could greatly facilitate and empower comprehensive analysis of the spatial organization of cells, as well as their roles in tumor progression and metastasis.

Versatile stochastic dot product circuits based on nonvolatile memories for high performance neurocomputing and neurooptimization

The key operation in stochastic neural networks, which have become the state-of-the-art approach for solving problems in machine learning, information theory, and statistics, is a stochastic dot-product. While there have been many demonstrations of dot-product circuits and, separately, of stochastic neurons, the efficient hardware implementation combining both functionalities is still missing. Here we report compact, fast, energy-efficient, and scalable stochastic dot-product circuits based on either passively integrated metal-oxide memristors or embedded floating-gate memories. The circuit’s high performance is due to mixed-signal implementation, while the efficient stochastic operation is achieved by utilizing circuit’s noise, intrinsic and/or extrinsic to the memory cell array. The dynamic scaling of weights, enabled by analog memory devices, allows for efficient realization of different annealing approaches to improve functionality. The proposed approach is experimentally verified for two representative applications, namely by implementing neural network for solving a four-node graph-partitioning problem, and a Boltzmann machine with 10-input and 8-hidden neurons.

Providing efficient and scalable specialized hardware for stochastic neural networks remains a challenge. Here, the authors propose a fast, energy-efficient and scalable stochastic dot-product circuit that may use either of two types of memory devices – metal-oxide memristors and floating-gate memories.

Stochasticity from function - Why the Bayesian brain may need no noise

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise statistical properties of neural activity are important in this context, many models assume an ad-hoc source of well-behaved, explicit noise, either on the input or on the output side of single neuron dynamics, most often assuming an independent Poisson process in either case. However, these assumptions are somewhat problematic: neighboring neurons tend to share receptive fields, rendering both their input and their output correlated; at the same time, neurons are known to behave largely deterministically, as a function of their membrane potential and conductance. We suggest that spiking neural networks may have no need for noise to perform sampling-based Bayesian inference. We study analytically the effect of auto- and cross-correlations in functional Bayesian spiking networks and demonstrate how their effect translates to synaptic interaction strengths, rendering them controllable through synaptic plasticity. This allows even small ensembles of interconnected deterministic spiking networks to simultaneously and co-dependently shape their output activity through learning, enabling them to perform complex Bayesian computation without any need for noise, which we demonstrate in silico, both in classical simulation and in neuromorphic emulation. These results close a gap between the abstract models and the biology of functionally Bayesian spiking networks, effectively reducing the architectural constraints imposed on physical neural substrates required to perform probabilistic computing, be they biological or artificial.

Analysis of Liquid Ensembles for Enhancing the Performance and Accuracy of Liquid State Machines

Liquid state machine (LSM), a bio-inspired computing model consisting of the input sparsely connected to a randomly interlinked reservoir (or liquid) of spiking neurons followed by a readout layer, finds utility in a range of applications varying from robot control and sequence generation to action, speech, and image recognition. LSMs stand out among other Recurrent Neural Network (RNN) architectures due to their simplistic structure and lower training complexity. Plethora of recent efforts have been focused toward mimicking certain characteristics of biological systems to enhance the performance of modern artificial neural networks. It has been shown that biological neurons are more likely to be connected to other neurons in the close proximity, and tend to be disconnected as the neurons are spatially far apart. Inspired by this, we propose a group of locally connected neuron reservoirs, or an ensemble of liquids approach, for LSMs. We analyze how the segmentation of a single large liquid to create an ensemble of multiple smaller liquids affects the latency and accuracy of an LSM. In our analysis, we quantify the ability of the proposed ensemble approach to provide an improved representation of the input using the Separation Property (SP) and Approximation Property (AP). Our results illustrate that the ensemble approach enhances class discrimination (quantified as the ratio between the SP and AP), leading to better accuracy in speech and image recognition tasks, when compared to a single large liquid. Furthermore, we obtain performance benefits in terms of improved inference time and reduced memory requirements, due to lowered number of connections and the freedom to parallelize the liquid evaluation process.

Using Memristors for Robust Local Learning of Hardware Restricted Boltzmann Machines

One of the biggest stakes in nanoelectronics today is to meet the needs of Artificial Intelligence by designing hardware neural networks which, by fusing computation and memory, process and learn from data with limited energy. For this purpose, memristive devices are excellent candidates to emulate synapses. A challenge, however, is to map existing learning algorithms onto a chip: for a physical implementation, a learning rule should ideally be tolerant to the typical intrinsic imperfections of such memristive devices, and local. Restricted Boltzmann Machines (RBM), for their local learning rule and inherent tolerance to stochasticity, comply with both of these constraints and constitute a highly attractive algorithm towards achieving memristor-based Deep Learning. On simulation grounds, this work gives insights into designing simple memristive devices programming protocols to train on chip Boltzmann Machines. Among other RBM-based neural networks, we advocate using a Discriminative RBM, with two hardware-oriented adaptations. We propose a pulse width selection scheme based on the sign of two successive weight updates, and show that it removes the constraint to precisely tune the initial programming pulse width as a hyperparameter. We also propose to evaluate the weight update requested by the algorithm across several samples and stochastic realizations. We show that this strategy brings a partial immunity against the most severe memristive device imperfections such as the non-linearity and the stochasticity of the conductance updates, as well as device-to-device variability.

Hierarchical Bayesian Inference and Learning in Spiking Neural Networks

Numerous experimental data from neuroscience and psychological science suggest that human brain utilizes Bayesian principles to deal the complex environment. Furthermore, hierarchical Bayesian inference has been proposed as an appropriate theoretical framework for modeling cortical processing. However, it remains unknown how such a computation is organized in the network of biologically plausible spiking neurons. In this paper, we propose a hierarchical network of winner-take-all circuits which can carry out hierarchical Bayesian inference and learning through a spike-based variational expectation maximization (EM) algorithm. Particularly, we show how the firing activities of spiking neurons in response to the input stimuli and the spike-timing-dependent plasticity rule can be understood, respectively, as variational E-step and M-step of variational EM. Finally, we demonstrate the utility of this spiking neural network on the MNIST benchmark for unsupervised classification of handwritten digits.

Large-Scale Neuromorphic Spiking Array Processors: A Quest to Mimic the Brain

Neuromorphic engineering (NE) encompasses a diverse range of approaches to information processing that are inspired by neurobiological systems, and this feature distinguishes neuromorphic systems from conventional computing systems. The brain has evolved over billions of years to solve difficult engineering problems by using efficient, parallel, low-power computation. The goal of NE is to design systems capable of brain-like computation. Numerous large-scale neuromorphic projects have emerged recently. This interdisciplinary field was listed among the top 10 technology breakthroughs of 2014 by the MIT Technology Review and among the top 10 emerging technologies of 2015 by the World Economic Forum. NE has two-way goals: one, a scientific goal to understand the computational properties of biological neural systems by using models implemented in integrated circuits (ICs); second, an engineering goal to exploit the known properties of biological systems to design and implement efficient devices for engineering applications. Building hardware neural emulators can be extremely useful for simulating large-scale neural models to explain how intelligent behavior arises in the brain. The principal advantages of neuromorphic emulators are that they are highly energy efficient, parallel and distributed, and require a small silicon area. Thus, compared to conventional CPUs, these neuromorphic emulators are beneficial in many engineering applications such as for the porting of deep learning algorithms for various recognitions tasks. In this review article, we describe some of the most significant neuromorphic spiking emulators, compare the different architectures and approaches used by them, illustrate their advantages and drawbacks, and highlight the capabilities that each can deliver to neural modelers. This article focuses on the discussion of large-scale emulators and is a continuation of a previous review of various neural and synapse circuits (Indiveri et al., 2011). We also explore applications where these emulators have been used and discuss some of their promising future applications.

Deep Learning With Spiking Neurons: Opportunities and Challenges

Spiking neural networks (SNNs) are inspired by information processing in biology, where sparse and asynchronous binary signals are communicated and processed in a massively parallel fashion. SNNs on neuromorphic hardware exhibit favorable properties such as low power consumption, fast inference, and event-driven information processing. This makes them interesting candidates for the efficient implementation of deep neural networks, the method of choice for many machine learning tasks. In this review, we address the opportunities that deep spiking networks offer and investigate in detail the challenges associated with training SNNs in a way that makes them competitive with conventional deep learning, but simultaneously allows for efficient mapping to hardware. A wide range of training methods for SNNs is presented, ranging from the conversion of conventional deep networks into SNNs, constrained training before conversion, spiking variants of backpropagation, and biologically motivated variants of STDP. The goal of our review is to define a categorization of SNN training methods, and summarize their advantages and drawbacks. We further discuss relationships between SNNs and binary networks, which are becoming popular for efficient digital hardware implementation. Neuromorphic hardware platforms have great potential to enable deep spiking networks in real-world applications. We compare the suitability of various neuromorphic systems that have been developed over the past years, and investigate potential use cases. Neuromorphic approaches and conventional machine learning should not be considered simply two solutions to the same classes of problems, instead it is possible to identify and exploit their task-specific advantages. Deep SNNs offer great opportunities to work with new types of event-based sensors, exploit temporal codes and local on-chip learning, and we have so far just scratched the surface of realizing these advantages in practical applications.

On Practical Issues for Stochastic STDP Hardware With 1-bit Synaptic Weights

In computational neuroscience, synaptic plasticity learning rules are typically studied using the full 64-bit floating point precision computers provide. However, for dedicated hardware implementations, the precision used not only penalizes directly the required memory resources, but also the computing, communication, and energy resources. When it comes to hardware engineering, a key question is always to find the minimum number of necessary bits to keep the neurocomputational system working satisfactorily. Here we present some techniques and results obtained when limiting synaptic weights to 1-bit precision, applied to a Spike-Timing-Dependent-Plasticity (STDP) learning rule in Spiking Neural Networks (SNN). We first illustrate the 1-bit synapses STDP operation by replicating a classical biological experiment on visual orientation tuning, using a simple four neuron setup. After this, we apply 1-bit STDP learning to the hidden feature extraction layer of a 2-layer system, where for the second (and output) layer we use already reported SNN classifiers. The systems are tested on two spiking datasets: a Dynamic Vision Sensor (DVS) recorded poker card symbols dataset and a Poisson-distributed spike representation MNIST dataset version. Tests are performed using the in-house MegaSim event-driven behavioral simulator and by implementing the systems on FPGA (Field Programmable Gate Array) hardware.

Computational roles of plastic probabilistic synapses

The probabilistic nature of synaptic transmission has remained enigmatic. However, recent developments have started to shed light on why the brain may rely on probabilistic synapses. Here, we start out by reviewing experimental evidence on the specificity and plasticity of synaptic response statistics. Next, we overview different computational perspectives on the function of plastic probabilistic synapses for constrained, statistical and deep learning. We highlight that all of these views require some form of optimisation of probabilistic synapses, which has recently gained support from theoretical analysis of long-term synaptic plasticity experiments. Finally, we contrast these different computational views and propose avenues for future research. Overall, we argue that the time is ripe for a better understanding of the computational functions of probabilistic synapses.

Nonvolatile Memory Materials for Neuromorphic Intelligent Machines

Recent progress in deep learning extends the capability of artificial intelligence to various practical tasks, making the deep neural network (DNN) an extremely versatile hypothesis. While such DNN is virtually built on contemporary data centers of the von Neumann architecture, physical (in part) DNN of non-von Neumann architecture, also known as neuromorphic computing, can remarkably improve learning and inference efficiency. Particularly, resistance-based nonvolatile random access memory (NVRAM) highlights its handy and efficient application to the multiply-accumulate (MAC) operation in an analog manner. Here, an overview is given of the available types of resistance-based NVRAMs and their technological maturity from the material- and device-points of view. Examples within the strategy are subsequently addressed in comparison with their benchmarks (virtual DNN in deep learning). A spiking neural network (SNN) is another type of neural network that is more biologically plausible than the DNN. The successful incorporation of resistance-based NVRAM in SNN-based neuromorphic computing offers an efficient solution to the MAC operation and spike timing-based learning in nature. This strategy is exemplified from a material perspective. Intelligent machines are categorized according to their architecture and learning type. Also, the functionality and usefulness of NVRAM-based neuromorphic computing are addressed.

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.

Neural and Synaptic Array Transceiver: A Brain-Inspired Computing Framework for Embedded Learning

Embedded, continual learning for autonomous and adaptive behavior is a key application of neuromorphic hardware. However, neuromorphic implementations of embedded learning at large scales that are both flexible and efficient have been hindered by a lack of a suitable algorithmic framework. As a result, most neuromorphic hardware are trained off-line on large clusters of dedicated processors or GPUs and transferred post hoc to the device. We address this by introducing the neural and synaptic array transceiver (NSAT), a neuromorphic computational framework facilitating flexible and efficient embedded learning by matching algorithmic requirements and neural and synaptic dynamics. NSAT supports event-driven supervised, unsupervised and reinforcement learning algorithms including deep learning. We demonstrate the NSAT in a wide range of tasks, including the simulation of Mihalas-Niebur neuron, dynamic neural fields, event-driven random back-propagation for event-based deep learning, event-based contrastive divergence for unsupervised learning, and voltage-based learning rules for sequence learning. We anticipate that this contribution will establish the foundation for a new generation of devices enabling adaptive mobile systems, wearable devices, and robots with data-driven autonomy.

Data and Power Efficient Intelligence with Neuromorphic Learning Machines

The success of deep networks and recent industry involvement in brain-inspired computing is igniting a widespread interest in neuromorphic hardware that emulates the biological processes of the brain on an electronic substrate. This review explores interdisciplinary approaches anchored in machine learning theory that enable the applicability of neuromorphic technologies to real-world, human-centric tasks. We find that (1) recent work in binary deep networks and approximate gradient descent learning are strikingly compatible with a neuromorphic substrate; (2) where real-time adaptability and autonomy are necessary, neuromorphic technologies can achieve significant advantages over main-stream ones; and (3) challenges in memory technologies, compounded by a tradition of bottom-up approaches in the field, block the road to major breakthroughs. We suggest that a neuromorphic learning framework, tuned specifically for the spatial and temporal constraints of the neuromorphic substrate, will help guiding hardware algorithm co-design and deploying neuromorphic hardware for proactive learning of real-world data.

A Learning Framework for Winner-Take-All Networks with Stochastic Synapses

Many recent generative models make use of neural networks to transform the probability distribution of a simple low-dimensional noise process into the complex distribution of the data. This raises the question of whether biological networks operate along similar principles to implement a probabilistic model of the environment through transformations of intrinsic noise processes. The intrinsic neural and synaptic noise processes in biological networks, however, are quite different from the noise processes used in current abstract generative networks. This, together with the discrete nature of spikes and local circuit interactions among the neurons, raises several difficulties when using recent generative modeling frameworks to train biologically motivated models. In this letter, we show that a biologically motivated model based on multilayer winner-take-all circuits and stochastic synapses admits an approximate analytical description. This allows us to use the proposed networks in a variational learning setting where stochastic backpropagation is used to optimize a lower bound on the data log likelihood, thereby learning a generative model of the data. We illustrate the generality of the proposed networks and learning technique by using them in a structured output prediction task and a semisupervised learning task. Our results extend the domain of application of modern stochastic network architectures to networks where synaptic transmission failure is the principal noise mechanism.

Ultralow power artificial synapses using nanotextured magnetic Josephson junctions

Neuromorphic computing promises to markedly improve the efficiency of certain computational tasks, such as perception and decision-making. Although software and specialized hardware implementations of neural networks have made tremendous accomplishments, both implementations are still many orders of magnitude less energy efficient than the human brain. We demonstrate a new form of artificial synapse based on dynamically reconfigurable superconducting Josephson junctions with magnetic nanoclusters in the barrier. The spiking energy per pulse varies with the magnetic configuration, but in our demonstration devices, the spiking energy is always less than 1 aJ. This compares very favorably with the roughly 10 fJ per synaptic event in the human brain. Each artificial synapse is composed of a Si barrier containing Mn nanoclusters with superconducting Nb electrodes. The critical current of each synapse junction, which is analogous to the synaptic weight, can be tuned using input voltage spikes that change the spin alignment of Mn nanoclusters. We demonstrate synaptic weight training with electrical pulses as small as 3 aJ. Further, the Josephson plasma frequencies of the devices, which determine the dynamical time scales, all exceed 100 GHz. These new artificial synapses provide a significant step toward a neuromorphic platform that is faster, more energy-efficient, and thus can attain far greater complexity than has been demonstrated with other technologies.

An Event-Driven Classifier for Spiking Neural Networks Fed with Synthetic or Dynamic Vision Sensor Data

This paper introduces a novel methodology for training an event-driven classifier within a Spiking Neural Network (SNN) System capable of yielding good classification results when using both synthetic input data and real data captured from Dynamic Vision Sensor (DVS) chips. The proposed supervised method uses the spiking activity provided by an arbitrary topology of prior SNN layers to build histograms and train the classifier in the frame domain using the stochastic gradient descent algorithm. In addition, this approach can cope with leaky integrate-and-fire neuron models within the SNN, a desirable feature for real-world SNN applications, where neural activation must fade away after some time in the absence of inputs. Consequently, this way of building histograms captures the dynamics of spikes immediately before the classifier. We tested our method on the MNIST data set using different synthetic encodings and real DVS sensory data sets such as N-MNIST, MNIST-DVS, and Poker-DVS using the same network topology and feature maps. We demonstrate the effectiveness of our approach by achieving the highest classification accuracy reported on the N-MNIST (97.77%) and Poker-DVS (100%) real DVS data sets to date with a spiking convolutional network. Moreover, by using the proposed method we were able to retrain the output layer of a previously reported spiking neural network and increase its performance by 2%, suggesting that the proposed classifier can be used as the output layer in works where features are extracted using unsupervised spike-based learning methods. In addition, we also analyze SNN performance figures such as total event activity and network latencies, which are relevant for eventual hardware implementations. In summary, the paper aggregates unsupervised-trained SNNs with a supervised-trained SNN classifier, combining and applying them to heterogeneous sets of benchmarks, both synthetic and from real DVS chips.

Event-Driven Random Back-Propagation: Enabling Neuromorphic Deep Learning Machines

An ongoing challenge in neuromorphic computing is to devise general and computationally efficient models of inference and learning which are compatible with the spatial and temporal constraints of the brain. One increasingly popular and successful approach is to take inspiration from inference and learning algorithms used in deep neural networks. However, the workhorse of deep learning, the gradient descent Gradient Back Propagation (BP) rule, often relies on the immediate availability of network-wide information stored with high-precision memory during learning, and precise operations that are difficult to realize in neuromorphic hardware. Remarkably, recent work showed that exact backpropagated gradients are not essential for learning deep representations. Building on these results, we demonstrate an event-driven random BP (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations. Using a two-compartment Leaky Integrate & Fire (I&F) neuron, the rule requires only one addition and two comparisons for each synaptic weight, making it very suitable for implementation in digital or mixed-signal neuromorphic hardware. Our results show that using eRBP, deep representations are rapidly learned, achieving classification accuracies on permutation invariant datasets comparable to those obtained in artificial neural network simulations on GPUs, while being robust to neural and synaptic state quantizations during learning.

A Hierarchical Predictive Coding Model of Object Recognition in Natural Images

Predictive coding has been proposed as a model of the hierarchical perceptual inference process performed in the cortex. However, results demonstrating that predictive coding is capable of performing the complex inference required to recognise objects in natural images have not previously been presented. This article proposes a hierarchical neural network based on predictive coding for performing visual object recognition. This network is applied to the tasks of categorising hand-written digits, identifying faces, and locating cars in images of street scenes. It is shown that image recognition can be performed with tolerance to position, illumination, size, partial occlusion, and within-category variation. The current results, therefore, provide the first practical demonstration that predictive coding (at least the particular implementation of predictive coding used here; the PC/BC-DIM algorithm) is capable of performing accurate visual object recognition.

Benchmarking Spike-Based Visual Recognition: A Dataset and Evaluation

Today, increasing attention is being paid to research into spike-based neural computation both to gain a better understanding of the brain and to explore biologically-inspired computation. Within this field, the primate visual pathway and its hierarchical organization have been extensively studied. Spiking Neural Networks (SNNs), inspired by the understanding of observed biological structure and function, have been successfully applied to visual recognition and classification tasks. In addition, implementations on neuromorphic hardware have enabled large-scale networks to run in (or even faster than) real time, making spike-based neural vision processing accessible on mobile robots. Neuromorphic sensors such as silicon retinas are able to feed such mobile systems with real-time visual stimuli. A new set of vision benchmarks for spike-based neural processing are now needed to measure progress quantitatively within this rapidly advancing field. We propose that a large dataset of spike-based visual stimuli is needed to provide meaningful comparisons between different systems, and a corresponding evaluation methodology is also required to measure the performance of SNN models and their hardware implementations. In this paper we first propose an initial NE (Neuromorphic Engineering) dataset based on standard computer vision benchmarksand that uses digits from the MNIST database. This dataset is compatible with the state of current research on spike-based image recognition. The corresponding spike trains are produced using a range of techniques: rate-based Poisson spike generation, rank order encoding, and recorded output from a silicon retina with both flashing and oscillating input stimuli. In addition, a complementary evaluation methodology is presented to assess both model-level and hardware-level performance. Finally, we demonstrate the use of the dataset and the evaluation methodology using two SNN models to validate the performance of the models and their hardware implementations. With this dataset we hope to (1) promote meaningful comparison between algorithms in the field of neural computation, (2) allow comparison with conventional image recognition methods, (3) provide an assessment of the state of the art in spike-based visual recognition, and (4) help researchers identify future directions and advance the field.