Training Deep Spiking Convolutional Neural Networks With STDP-Based Unsupervised Pre-training Followed by Supervised Fine-Tuning

Convolutional spiking neural networks for intent detection based on anticipatory brain potentials using electroencephalogram

Spiking neural networks (SNNs) are receiving increased attention because they mimic synaptic connections in biological systems and produce spike trains, which can be approximated by binary values for computational efficiency. Recently, the addition of convolutional layers to combine the feature extraction power of convolutional networks with the computational efficiency of SNNs has been introduced. This paper studies the feasibility of using a convolutional spiking neural network (CSNN) to detect anticipatory slow cortical potentials (SCPs) related to braking intention in human participants using an electroencephalogram (EEG). Data was collected during an experiment wherein participants operated a remote-controlled vehicle on a testbed designed to simulate an urban environment. Participants were alerted to an incoming braking event via an audio countdown to elicit anticipatory potentials that were measured using an EEG. The CSNN's performance was compared to a standard CNN, EEGNet and three graph neural networks via 10-fold cross-validation. The CSNN outperformed all the other neural networks, and had a predictive accuracy of 99.06% with a true positive rate of 98.50%, a true negative rate of 99.20% and an F1-score of 0.98. Performance of the CSNN was comparable to the CNN in an ablation study using a subset of EEG channels that localized SCPs. Classification performance of the CSNN degraded only slightly when the floating-point EEG data were converted into spike trains via delta modulation to mimic synaptic connections.

Brain-guided manifold transferring to improve the performance of spiking neural networks in image classification

Spiking neural networks (SNNs), as the third generation of neural networks, are based on biological models of human brain neurons. In this work, a shallow SNN plays the role of an explicit image decoder in the image classification. An LSTM-based EEG encoder is used to construct the EEG-based feature space, which is a discriminative space in viewpoint of classification accuracy by SVM. Then, the visual feature vectors extracted from SNN is mapped to the EEG-based discriminative features space by manifold transferring based on mutual k-Nearest Neighbors (Mk-NN MT). This proposed "Brain-guided system" improves the separability of the SNN-based visual feature space. In the test phase, the spike patterns extracted by SNN from the input image is mapped to LSTM-based EEG feature space, and then classified without need for the EEG signals. The SNN-based image encoder is trained by the conversion method and the results are evaluated and compared with other training methods on the challenging small ImageNet-EEG dataset. Experimental results show that the proposed transferring the manifold of the SNN-based feature space to LSTM-based EEG feature space leads to 14.25% improvement at most in the accuracy of image classification. Thus, embedding SNN in the brain-guided system which is trained on a small set, improves its performance in image classification.

Gradient-based feature-attribution explainability methods for spiking neural networks

Introduction

Spiking neural networks (SNNs) are a model of computation that mimics the behavior of biological neurons. SNNs process event data (spikes) and operate more sparsely than artificial neural networks (ANNs), resulting in ultra-low latency and small power consumption. This paper aims to adapt and evaluate gradient-based explainability methods for SNNs, which were originally developed for conventional ANNs.

Methods

The adapted methods aim to create input feature attribution maps for SNNs trained through backpropagation that process either event-based spiking data or real-valued data. The methods address the limitations of existing work on explainability methods for SNNs, such as poor scalability, limited to convolutional layers, requiring the training of another model, and providing maps of activation values instead of true attribution scores. The adapted methods are evaluated on classification tasks for both real-valued and spiking data, and the accuracy of the proposed methods is confirmed through perturbation experiments at the pixel and spike levels.

Results and discussion

The results reveal that gradient-based SNN attribution methods successfully identify highly contributing pixels and spikes with significantly less computation time than model-agnostic methods. Additionally, we observe that the chosen coding technique has a noticeable effect on the input features that will be most significant. These findings demonstrate the potential of gradient-based explainability methods for SNNs in improving our understanding of how these networks process information and contribute to the development of more efficient and accurate SNNs.

HybridSNN: Combining Bio-Machine Strengths by Boosting Adaptive Spiking Neural Networks

Spiking neural networks (SNNs), inspired by the neuronal network in the brain, provide biologically relevant and low-power consuming models for information processing. Existing studies either mimic the learning mechanism of brain neural networks as closely as possible, for example, the temporally local learning rule of spike-timing-dependent plasticity (STDP), or apply the gradient descent rule to optimize a multilayer SNN with fixed structure. However, the learning rule used in the former is local and how the real brain might do the global-scale credit assignment is still not clear, which means that those shallow SNNs are robust but deep SNNs are difficult to be trained globally and could not work so well. For the latter, the nondifferentiable problem caused by the discrete spike trains leads to inaccuracy in gradient computing and difficulties in effective deep SNNs. Hence, a hybrid solution is interesting to combine shallow SNNs with an appropriate machine learning (ML) technique not requiring the gradient computing, which is able to provide both energy-saving and high-performance advantages. In this article, we propose a HybridSNN, a deep and strong SNN composed of multiple simple SNNs, in which data-driven greedy optimization is used to build powerful classifiers, avoiding the derivative problem in gradient descent. During the training process, the output features (spikes) of selected weak classifiers are fed back to the pool for the subsequent weak SNN training and selection. This guarantees HybridSNN not only represents the linear combination of simple SNNs, as what regular AdaBoost algorithm generates, but also contains neuron connection information, thus closely resembling the neural networks of a brain. HybridSNN has the benefits of both low power consumption in weak units and overall data-driven optimizing strength. The network structure in HybridSNN is learned from training samples, which is more flexible and effective compared with existing fixed multilayer SNNs. Moreover, the topological tree of HybridSNN resembles the neural system in the brain, where pyramidal neurons receive thousands of synaptic input signals through their dendrites. Experimental results show that the proposed HybridSNN is highly competitive among the state-of-the-art SNNs.

An unsupervised STDP-based spiking neural network inspired by biologically plausible learning rules and connections

The backpropagation algorithm has promoted the rapid development of deep learning, but it relies on a large amount of labeled data and still has a large gap with how humans learn. The human brain can quickly learn various conceptual knowledge in a self-organized and unsupervised manner, accomplished through coordinating various learning rules and structures in the human brain. Spike-timing-dependent plasticity (STDP) is a general learning rule in the brain, but spiking neural networks (SNNs) trained with STDP alone is inefficient and perform poorly. In this paper, taking inspiration from short-term synaptic plasticity, we design an adaptive synaptic filter and introduce the adaptive spiking threshold as the neuron plasticity to enrich the representation ability of SNNs. We also introduce an adaptive lateral inhibitory connection to adjust the spikes balance dynamically to help the network learn richer features. To speed up and stabilize the training of unsupervised spiking neural networks, we design a samples temporal batch STDP (STB-STDP), which updates weights based on multiple samples and moments. By integrating the above three adaptive mechanisms and STB-STDP, our model greatly accelerates the training of unsupervised spiking neural networks and improves the performance of unsupervised SNNs on complex tasks. Our model achieves the current state-of-the-art performance of unsupervised STDP-based SNNs in the MNIST and FashionMNIST datasets. Further, we tested on the more complex CIFAR10 dataset, and the results fully illustrate the superiority of our algorithm. Our model is also the first work to apply unsupervised STDP-based SNNs to CIFAR10. At the same time, in the small-sample learning scenario, it will far exceed the supervised ANN using the same structure.

Spiking Recurrent Neural Networks Represent Task-Relevant Neural Sequences in Rule-Dependent Computation

Background

Prefrontal cortical neurons play essential roles in performing rule-dependent tasks and working memory-based decision making.

Methods

Motivated by PFG recordings of task-performing mice, we developed an excitatory-inhibitory spiking recurrent neural network (SRNN) to perform a rule-dependent two-alternative forced choice (2AFC) task. We imposed several important biological constraints onto the SRNN, and adapted spike frequency adaptation (SFA) and SuperSpike gradient methods to train the SRNN efficiently.

Results

The trained SRNN produced emergent rule-specific tunings in single-unit representations, showing rule-dependent population dynamics that resembled experimentally observed data. Under varying test conditions, we manipulated the SRNN parameters or configuration in computer simulations, and we investigated the impacts of rule-coding error, delay duration, recurrent weight connectivity and sparsity, and excitation/inhibition (E/I) balance on both task performance and neural representations.

Conclusions

Overall, our modeling study provides a computational framework to understand neuronal representations at a fine timescale during working memory and cognitive control, and provides new experimentally testable hypotheses in future experiments.

EXODUS: Stable and efficient training of spiking neural networks

Introduction

Spiking Neural Networks (SNNs) are gaining significant traction in machine learning tasks where energy-efficiency is of utmost importance. Training such networks using the state-of-the-art back-propagation through time (BPTT) is, however, very time-consuming. Previous work employs an efficient GPU-accelerated backpropagation algorithm called SLAYER, which speeds up training considerably. SLAYER, however, does not take into account the neuron reset mechanism while computing the gradients, which we argue to be the source of numerical instability. To counteract this, SLAYER introduces a gradient scale hyper parameter across layers, which needs manual tuning.

Methods

In this paper, we modify SLAYER and design an algorithm called EXODUS, that accounts for the neuron reset mechanism and applies the Implicit Function Theorem (IFT) to calculate the correct gradients (equivalent to those computed by BPTT). We furthermore eliminate the need for ad-hoc scaling of gradients, thus, reducing the training complexity tremendously.

Results

We demonstrate, via computer simulations, that EXODUS is numerically stable and achieves comparable or better performance than SLAYER especially in various tasks with SNNs that rely on temporal features.

NeuroCARE: A generic neuromorphic edge computing framework for healthcare applications

Highly accurate classification methods for multi-task biomedical signal processing are reported, including neural networks. However, reported works are computationally expensive and power-hungry. Such bottlenecks make it hard to deploy existing approaches on edge platforms such as mobile and wearable devices. Gaining motivation from the good performance and high energy-efficiency of spiking neural networks (SNNs), a generic neuromorphic framework for edge healthcare and biomedical applications are proposed and evaluated on various tasks, including electroencephalography (EEG) based epileptic seizure prediction, electrocardiography (ECG) based arrhythmia detection, and electromyography (EMG) based hand gesture recognition. This approach, NeuroCARE, uses a unique sparse spike encoder to generate spike sequences from raw biomedical signals and makes classifications using the spike-based computing engine that combines the advantages of both CNN and SNN. An adaptive weight mapping method specifically co-designed with the spike encoder can efficiently convert CNN to SNN without performance deterioration. The evaluation results show that the overall performance, including the classification accuracy, sensitivity and F1 score, achieve 92.7, 96.7, and 85.7% for seizure prediction, arrhythmia detection and hand gesture recognition, respectively. In comparison with CNN topologies, the computation complexity is reduced by over 80.7% while the energy consumption and area occupation are reduced by over 80% and over 64.8%, respectively, indicating that the proposed neuromorphic computing approach is energy and area efficient and of high precision, which paves the way for deployment at edge platforms.

Supervised Learning Algorithm Based on Spike Train Inner Product for Deep Spiking Neural Networks

By mimicking the hierarchical structure of human brain, deep spiking neural networks (DSNNs) can extract features from a lower level to a higher level gradually, and improve the performance for the processing of spatio-temporal information. Due to the complex hierarchical structure and implicit nonlinear mechanism, the formulation of spike train level supervised learning methods for DSNNs remains an important problem in this research area. Based on the definition of kernel function and spike trains inner product (STIP) as well as the idea of error backpropagation (BP), this paper firstly proposes a deep supervised learning algorithm for DSNNs named BP-STIP. Furthermore, in order to alleviate the intrinsic weight transport problem of the BP mechanism, feedback alignment (FA) and broadcast alignment (BA) mechanisms are utilized to optimize the error feedback mode of BP-STIP, and two deep supervised learning algorithms named FA-STIP and BA-STIP are also proposed. In the experiments, the effectiveness of the proposed three DSNN algorithms is verified on the MNIST digital image benchmark dataset, and the influence of different kernel functions on the learning performance of DSNNs with different network scales is analyzed. Experimental results show that the FA-STIP and BP-STIP algorithms can achieve 94.73% and 95.65% classification accuracy, which apparently possess better learning performance and stability compared with the benchmark algorithm BP-STIP.

Efficient training of spiking neural networks with temporally-truncated local backpropagation through time

Directly training spiking neural networks (SNNs) has remained challenging due to complex neural dynamics and intrinsic non-differentiability in firing functions. The well-known backpropagation through time (BPTT) algorithm proposed to train SNNs suffers from large memory footprint and prohibits backward and update unlocking, making it impossible to exploit the potential of locally-supervised training methods. This work proposes an efficient and direct training algorithm for SNNs that integrates a locally-supervised training method with a temporally-truncated BPTT algorithm. The proposed algorithm explores both temporal and spatial locality in BPTT and contributes to significant reduction in computational cost including GPU memory utilization, main memory access and arithmetic operations. We thoroughly explore the design space concerning temporal truncation length and local training block size and benchmark their impact on classification accuracy of different networks running different types of tasks. The results reveal that temporal truncation has a negative effect on the accuracy of classifying frame-based datasets, but leads to improvement in accuracy on event-based datasets. In spite of resulting information loss, local training is capable of alleviating overfitting. The combined effect of temporal truncation and local training can lead to the slowdown of accuracy drop and even improvement in accuracy. In addition, training deep SNNs' models such as AlexNet classifying CIFAR10-DVS dataset leads to 7.26% increase in accuracy, 89.94% reduction in GPU memory, 10.79% reduction in memory access, and 99.64% reduction in MAC operations compared to the standard end-to-end BPTT. Thus, the proposed method has shown high potential to enable fast and energy-efficient on-chip training for real-time learning at the edge.

Voltage-dependent synaptic plasticity: Unsupervised probabilistic Hebbian plasticity rule based on neurons membrane potential

This study proposes voltage-dependent-synaptic plasticity (VDSP), a novel brain-inspired unsupervised local learning rule for the online implementation of Hebb’s plasticity mechanism on neuromorphic hardware. The proposed VDSP learning rule updates the synaptic conductance on the spike of the postsynaptic neuron only, which reduces by a factor of two the number of updates with respect to standard spike timing dependent plasticity (STDP). This update is dependent on the membrane potential of the presynaptic neuron, which is readily available as part of neuron implementation and hence does not require additional memory for storage. Moreover, the update is also regularized on synaptic weight and prevents explosion or vanishing of weights on repeated stimulation. Rigorous mathematical analysis is performed to draw an equivalence between VDSP and STDP. To validate the system-level performance of VDSP, we train a single-layer spiking neural network (SNN) for the recognition of handwritten digits. We report 85.01 ± 0.76% (Mean ± SD) accuracy for a network of 100 output neurons on the MNIST dataset. The performance improves when scaling the network size (89.93 ± 0.41% for 400 output neurons, 90.56 ± 0.27 for 500 neurons), which validates the applicability of the proposed learning rule for spatial pattern recognition tasks. Future work will consider more complicated tasks. Interestingly, the learning rule better adapts than STDP to the frequency of input signal and does not require hand-tuning of hyperparameters.

Spike-Based Approximate Backpropagation Algorithm of Brain-Inspired Deep SNN for Sonar Target Classification

With the development of neuromorphic computing, more and more attention has been paid to a brain-inspired spiking neural network (SNN) because of its ultralow energy consumption and high-performance spatiotemporal information processing. Due to the discontinuity of the spiking neuronal activation function, it is still a difficult problem to train brain-inspired deep SNN directly, so SNN has not yet shown performance comparable to that of an artificial neural network. For this reason, the spike-based approximate backpropagation (SABP) algorithm and a general brain-inspired SNN framework are proposed in this paper. The combination of the two can be used for end-to-end direct training of brain-inspired deep SNN. Experiments show that compared with other spike-based methods of directly training SNN, the classification accuracy of this method is close to the best results on MNIST and CIFAR-10 datasets and achieves the best classification accuracy on sonar image target classification (SITC) of small sample datasets. Further analysis shows that compared with artificial neural networks, our brain-inspired SNN has great advantages in computational complexity and energy consumption in sonar target classification.

Spike Timing-Dependent Plasticity with Enhanced Long-Term Depression Leads to an Increase of Statistical Complexity

Synaptic plasticity is characterized by remodeling of existing synapses caused by strengthening and/or weakening of connections. This is represented by long-term potentiation (LTP) and long-term depression (LTD). The occurrence of a presynaptic spike (or action potential) followed by a temporally nearby postsynaptic spike induces LTP; conversely, if the postsynaptic spike precedes the presynaptic spike, it induces LTD. This form of synaptic plasticity induction depends on the order and timing of the pre- and postsynaptic action potential, and has been termed spike time-dependent plasticity (STDP). After an epileptic seizure, LTD plays an important role as a depressor of synapses, which may lead to their complete disappearance together with that of their neighboring connections until days after the event. Added to the fact that after an epileptic seizure the network seeks to regulate the excess activity through two key mechanisms: depressed connections and neuronal death (eliminating excitatory neurons from the network), LTD becomes of great interest in our study. To investigate this phenomenon, we develop a biologically plausible model that privileges LTD at the triplet level while maintaining the pairwise structure in the STPD and study how network dynamics are affected as neuronal damage increases. We find that the statistical complexity is significantly higher for the network where LTD presented both types of interactions. While in the case where the STPD is defined with purely pairwise interactions an increase is observed as damage becomes higher for both Shannon Entropy and Fisher information.

Decision-Tree-Initialized Dendritic Neuron Model for Fast and Accurate Data Classification

This work proposes a decision tree (DT)-based method for initializing a dendritic neuron model (DNM). Neural networks become larger and larger, thus consuming more and more computing resources. This calls for a strong need to prune neurons that do not contribute much to their network's output. Pruning those with low contribution may lead to a loss of accuracy of DNM. Our proposed method is novel because 1) it can reduce the number of dendrites in DNM while improving training efficiency without affecting accuracy and 2) it can select proper initialization weight and threshold of neurons. The Adam algorithm is used to train DNM after its initialization with our proposed DT-based method. To verify its effectiveness, we apply it to seven benchmark datasets. The results show that decision-tree-initialized DNM is significantly better than the original DNM, k-nearest neighbor, support vector machine, back-propagation neural network, and DT classification methods. It exhibits the lowest model complexity and highest training speed without losing any accuracy. The interactions among attributes can also be observed in its dendritic neurons.

Effective Conversion of a Convolutional Neural Network into a Spiking Neural Network for Image Recognition Tasks

Due to energy efficiency, spiking neural networks (SNNs) have gradually been considered as an alternative to convolutional neural networks (CNNs) in various machine learning tasks. In image recognition tasks, leveraging the superior capability of CNNs, the CNN–SNN conversion is considered one of the most successful approaches to training SNNs. However, previous works assume a rather long inference time period called inference latency to be allowed, while having a trade-off between inference latency and accuracy. One of the main reasons for this phenomenon stems from the difficulty in determining proper a firing threshold for spiking neurons. The threshold determination procedure is called a threshold balancing technique in the CNN–SNN conversion approach. This paper proposes a CNN–SNN conversion method with a new threshold balancing technique that obtains converted SNN models with good accuracy even with low latency. The proposed method organizes the SNN models with soft-reset IF spiking neurons. The threshold balancing technique estimates the thresholds for spiking neurons based on the maximum input current in a layerwise and channelwise manner. The experiment results have shown that our converted SNN models attain even higher accuracy than the corresponding trained CNN model for the MNIST dataset with low latency. In addition, for the Fashion-MNIST and CIFAR-10 datasets, our converted SNNs have shown less conversion loss than other methods in low latencies. The proposed method can be beneficial in deploying efficient SNN models for recognition tasks on resource-limited systems because the inference latency is strongly associated with energy consumption.

Neuroevolution Guided Hybrid Spiking Neural Network Training

Neuromorphic computing algorithms based on Spiking Neural Networks (SNNs) are evolving to be a disruptive technology driving machine learning research. The overarching goal of this work is to develop a structured algorithmic framework for SNN training that optimizes unique SNN-specific properties like neuron spiking threshold using neuroevolution as a feedback strategy. We provide extensive results for this hybrid bio-inspired training strategy and show that such a feedback-based learning approach leads to explainable neuromorphic systems that adapt to the specific underlying application. Our analysis reveals 53.8, 28.8, and 28.2% latency improvement for the neuroevolution-based SNN training strategy on CIFAR-10, CIFAR-100, and ImageNet datasets, respectively in contrast to state-of-the-art conversion based approaches. The proposed algorithm can be easily extended to other application domains like image classification in presence of adversarial attacks where 43.2 and 27.9% latency improvements were observed on CIFAR-10 and CIFAR-100 datasets, respectively.

MONETA: A Processing-In-Memory-Based Hardware Platform for the Hybrid Convolutional Spiking Neural Network With Online Learning

We present a processing-in-memory (PIM)-based hardware platform, referred to as MONETA, for on-chip acceleration of inference and learning in hybrid convolutional spiking neural network. MONETAuses 8T static random-access memory (SRAM)-based PIM cores for vector matrix multiplication (VMM) augmented with spike-time-dependent-plasticity (STDP) based weight update. The spiking neural network (SNN)-focused data flow is presented to minimize data movement in MONETAwhile ensuring learning accuracy. MONETAsupports on-line and on-chip training on PIM architecture. The STDP-trained convolutional neural network within SNN (ConvSNN) with the proposed data flow, 4-bit input precision, and 8-bit weight precision shows only 1.63% lower accuracy in CIFAR-10 compared to the STDP accuracy implemented by the software. Further, the proposed architecture is used to accelerate a hybrid SNN architecture that couples off-chip supervised (back propagation through time) and on-chip unsupervised (STDP) training. We also evaluate the hybrid network architecture with the proposed data flow. The accuracy of this hybrid network is 10.84% higher than STDP trained accuracy result and 1.4% higher compared to the backpropagated training-based ConvSNN result with the CIFAR-10 dataset. Physical design of MONETAin 65 nm complementary metal-oxide-semiconductor (CMOS) shows 18.69 tera operation per second (TOPS)/W, 7.25 TOPS/W and 10.41 TOPS/W power efficiencies for the inference mode, learning mode, and hybrid learning mode, respectively.

Advancements in Algorithms and Neuromorphic Hardware for Spiking Neural Networks

Artificial neural networks (ANNs) have experienced a rapid advancement for their success in various application domains, including autonomous driving and drone vision. Researchers have been improving the performance efficiency and computational requirement of ANNs inspired by the mechanisms of the biological brain. Spiking neural networks (SNNs) provide a power-efficient and brain-inspired computing paradigm for machine learning applications. However, evaluating large-scale SNNs on classical von Neumann architectures (central processing units/graphics processing units) demands a high amount of power and time. Therefore, hardware designers have developed neuromorphic platforms to execute SNNs in and approach that combines fast processing and low power consumption. Recently, field-programmable gate arrays (FPGAs) have been considered promising candidates for implementing neuromorphic solutions due to their varied advantages, such as higher flexibility, shorter design, and excellent stability. This review aims to describe recent advances in SNNs and the neuromorphic hardware platforms (digital, analog, hybrid, and FPGA based) suitable for their implementation. We present that biological background of SNN learning, such as neuron models and information encoding techniques, followed by a categorization of SNN training. In addition, we describe state-of-the-art SNN simulators. Furthermore, we review and present FPGA-based hardware implementation of SNNs. Finally, we discuss some future directions for research in this field.

Robust Spike-Based Continual Meta-Learning Improved by Restricted Minimum Error Entropy Criterion

The spiking neural network (SNN) is regarded as a promising candidate to deal with the great challenges presented by current machine learning techniques, including the high energy consumption induced by deep neural networks. However, there is still a great gap between SNNs and the online meta-learning performance of artificial neural networks. Importantly, existing spike-based online meta-learning models do not target the robust learning based on spatio-temporal dynamics and superior machine learning theory. In this invited article, we propose a novel spike-based framework with minimum error entropy, called MeMEE, using the entropy theory to establish the gradient-based online meta-learning scheme in a recurrent SNN architecture. We examine the performance based on various types of tasks, including autonomous navigation and the working memory test. The experimental results show that the proposed MeMEE model can effectively improve the accuracy and the robustness of the spike-based meta-learning performance. More importantly, the proposed MeMEE model emphasizes the application of the modern information theoretic learning approach on the state-of-the-art spike-based learning algorithms. Therefore, in this invited paper, we provide new perspectives for further integration of advanced information theory in machine learning to improve the learning performance of SNNs, which could be of great merit to applied developments with spike-based neuromorphic systems.

Training Deep Convolutional Spiking Neural Networks With Spike Probabilistic Global Pooling

Recent work on spiking neural networks (SNNs) has focused on achieving deep architectures. They commonly use backpropagation (BP) to train SNNs directly, which allows SNNs to go deeper and achieve higher performance. However, the BP training procedure is computing intensive and complicated by many trainable parameters. Inspired by global pooling in convolutional neural networks (CNNs), we present the spike probabilistic global pooling (SPGP) method based on a probability function for training deep convolutional SNNs. It aims to remove the difficult of too many trainable parameters brought by multiple layers in the training process, which can reduce the risk of overfitting and get better performance for deep SNNs (DSNNs). We use the discrete leaky-integrate-fire model and the spatiotemporal BP algorithm for training DSNNs directly. As a result, our model trained with the SPGP method achieves competitive performance compared to the existing DSNNs on image and neuromorphic data sets while minimizing the number of trainable parameters. In addition, the proposed SPGP method shows its effectiveness in performance improvement, convergence, and generalization ability.

Memristive Devices Based on Two-Dimensional Transition Metal Chalcogenides for Neuromorphic Computing

Two-dimensional (2D) transition metal chalcogenides (TMC) and their heterostructures are appealing as building blocks in a wide range of electronic and optoelectronic devices, particularly futuristic memristive and synaptic devices for brain-inspired neuromorphic computing systems. The distinct properties such as high durability, electrical and optical tunability, clean surface, flexibility, and LEGO-staking capability enable simple fabrication with high integration density, energy-efficient operation, and high scalability. This review provides a thorough examination of high-performance memristors based on 2D TMCs for neuromorphic computing applications, including the promise of 2D TMC materials and heterostructures, as well as the state-of-the-art demonstration of memristive devices. The challenges and future prospects for the development of these emerging materials and devices are also discussed. The purpose of this review is to provide an outlook on the fabrication and characterization of neuromorphic memristors based on 2D TMCs.

Hierarchical Network Connectivity and Partitioning for Reconfigurable Large-Scale Neuromorphic Systems

We present an efficient and scalable partitioning method for mapping large-scale neural network models with locally dense and globally sparse connectivity onto reconfigurable neuromorphic hardware. Scalability in computational efficiency, i.e., amount of time spent in actual computation, remains a huge challenge in very large networks. Most partitioning algorithms also struggle to address the scalability in network workloads in finding a globally optimal partition and efficiently mapping onto hardware. As communication is regarded as the most energy and time-consuming part of such distributed processing, the partitioning framework is optimized for compute-balanced, memory-efficient parallel processing targeting low-latency execution and dense synaptic storage, with minimal routing across various compute cores. We demonstrate highly scalable and efficient partitioning for connectivity-aware and hierarchical address-event routing resource-optimized mapping, significantly reducing the total communication volume recursively when compared to random balanced assignment. We showcase our results working on synthetic networks with varying degrees of sparsity factor and fan-out, small-world networks, feed-forward networks, and a hemibrain connectome reconstruction of the fruit-fly brain. The combination of our method and practical results suggest a promising path toward extending to very large-scale networks and scalable hardware-aware partitioning.

Opportunities for neuromorphic computing algorithms and applications

Neuromorphic computing technologies will be important for the future of computing, but much of the work in neuromorphic computing has focused on hardware development. Here, we review recent results in neuromorphic computing algorithms and applications. We highlight characteristics of neuromorphic computing technologies that make them attractive for the future of computing and we discuss opportunities for future development of algorithms and applications on these systems.

Toward Learning in Neuromorphic Circuits Based on Quantum Phase Slip Junctions

We explore the use of superconducting quantum phase slip junctions (QPSJs), an electromagnetic dual to Josephson Junctions (JJs), in neuromorphic circuits. These small circuits could serve as the building blocks of neuromorphic circuits for machine learning applications because they exhibit desirable properties such as inherent ultra-low energy per operation, high speed, dense integration, negligible loss, and natural spiking responses. In addition, they have a relatively straight-forward micro/nano fabrication, which shows promise for implementation of an enormous number of lossless interconnections that are required to realize complex neuromorphic systems. We simulate QPSJ-only, as well as hybrid QPSJ + JJ circuits for application in neuromorphic circuits including artificial synapses and neurons, as well as fan-in and fan-out circuits. We also design and simulate learning circuits, where a simplified spike timing dependent plasticity rule is realized to provide potential learning mechanisms. We also take an alternative approach, which shows potential to overcome some of the expected challenges of QPSJ-based neuromorphic circuits, via QPSJ-based charge islands coupled together to generate non-linear charge dynamics that result in a large number of programmable weights or non-volatile memory states. Notably, we show that these weights are a function of the timing and frequency of the input spiking signals and can be programmed using a small number of DC voltage bias signals, therefore exhibiting spike-timing and rate dependent plasticity, which are mechanisms to realize learning in neuromorphic circuits.

SSTDP: Supervised Spike Timing Dependent Plasticity for Efficient Spiking Neural Network Training

Spiking Neural Networks (SNNs) are a pathway that could potentially empower low-power event-driven neuromorphic hardware due to their spatio-temporal information processing capability and high biological plausibility. Although SNNs are currently more efficient than artificial neural networks (ANNs), they are not as accurate as ANNs. Error backpropagation is the most common method for directly training neural networks, promoting the prosperity of ANNs in various deep learning fields. However, since the signals transmitted in the SNN are non-differentiable discrete binary spike events, the activation function in the form of spikes presents difficulties for the gradient-based optimization algorithms to be directly applied in SNNs, leading to a performance gap (i.e., accuracy and latency) between SNNs and ANNs. This paper introduces a new learning algorithm, called SSTDP, which bridges the gap between backpropagation (BP)-based learning and spike-time-dependent plasticity (STDP)-based learning to train SNNs efficiently. The scheme incorporates the global optimization process from BP and the efficient weight update derived from STDP. It not only avoids the non-differentiable derivation in the BP process but also utilizes the local feature extraction property of STDP. Consequently, our method can lower the possibility of vanishing spikes in BP training and reduce the number of time steps to reduce network latency. In SSTDP, we employ temporal-based coding and use Integrate-and-Fire (IF) neuron as the neuron model to provide considerable computational benefits. Our experiments show the effectiveness of the proposed SSTDP learning algorithm on the SNN by achieving the best classification accuracy 99.3% on the Caltech 101 dataset, 98.1% on the MNIST dataset, and 91.3% on the CIFAR-10 dataset compared to other SNNs trained with other learning methods. It also surpasses the best inference accuracy of the directly trained SNN with 25~32× less inference latency. Moreover, we analyze event-based computations to demonstrate the efficacy of the SNN for inference operation in the spiking domain, and SSTDP methods can achieve 1.3~37.7× fewer addition operations per inference. The code is available at: https://github.com/MXHX7199/SNN-SSTDP.

BlocTrain: Block-Wise Conditional Training and Inference for Efficient Spike-Based Deep Learning

Spiking neural networks (SNNs), with their inherent capability to learn sparse spike-based input representations over time, offer a promising solution for enabling the next generation of intelligent autonomous systems. Nevertheless, end-to-end training of deep SNNs is both compute- and memory-intensive because of the need to backpropagate error gradients through time. We propose BlocTrain, which is a scalable and complexity-aware incremental algorithm for memory-efficient training of deep SNNs. We divide a deep SNN into blocks, where each block consists of few convolutional layers followed by a classifier. We train the blocks sequentially using local errors from the classifier. Once a given block is trained, our algorithm dynamically figures out easy vs. hard classes using the class-wise accuracy, and trains the deeper block only on the hard class inputs. In addition, we also incorporate a hard class detector (HCD) per block that is used during inference to exit early for the easy class inputs and activate the deeper blocks only for the hard class inputs. We trained ResNet-9 SNN divided into three blocks, using BlocTrain, on CIFAR-10 and obtained 86.4% accuracy, which is achieved with up to 2.95× lower memory requirement during the course of training, and 1.89× compute efficiency per inference (due to early exit strategy) with 1.45× memory overhead (primarily due to classifier weights) compared to end-to-end network. We also trained ResNet-11, divided into four blocks, on CIFAR-100 and obtained 58.21% accuracy, which is one of the first reported accuracy for SNN trained entirely with spike-based backpropagation on CIFAR-100.

Event-Based Trajectory Prediction Using Spiking Neural Networks

In recent years, event-based sensors have been combined with spiking neural networks (SNNs) to create a new generation of bio-inspired artificial vision systems. These systems can process spatio-temporal data in real time, and are highly energy efficient. In this study, we used a new hybrid event-based camera in conjunction with a multi-layer spiking neural network trained with a spike-timing-dependent plasticity learning rule. We showed that neurons learn from repeated and correlated spatio-temporal patterns in an unsupervised way and become selective to motion features, such as direction and speed. This motion selectivity can then be used to predict ball trajectory by adding a simple read-out layer composed of polynomial regressions, and trained in a supervised manner. Hence, we show that a SNN receiving inputs from an event-based sensor can extract relevant spatio-temporal patterns to process and predict ball trajectories.

Exploring Optimized Spiking Neural Network Architectures for Classification Tasks on Embedded Platforms

In recent times, the usage of modern neuromorphic hardware for brain-inspired SNNs has grown exponentially. In the context of sparse input data, they are undertaking low power consumption for event-based neuromorphic hardware, specifically in the deeper layers. However, using deep ANNs for training spiking models is still considered as a tedious task. Until recently, various ANN to SNN conversion methods in the literature have been proposed to train deep SNN models. Nevertheless, these methods require hundreds to thousands of time-steps for training and still cannot attain good SNN performance. This work proposes a customized model (VGG, ResNet) architecture to train deep convolutional spiking neural networks. In this current study, the training is carried out using deep convolutional spiking neural networks with surrogate gradient descent backpropagation in a customized layer architecture similar to deep artificial neural networks. Moreover, this work also proposes fewer time-steps for training SNNs with surrogate gradient descent. During the training with surrogate gradient descent backpropagation, overfitting problems have been encountered. To overcome these problems, this work refines the SNN based dropout technique with surrogate gradient descent. The proposed customized SNN models achieve good classification results on both private and public datasets. In this work, several experiments have been carried out on an embedded platform (NVIDIA JETSON TX2 board), where the deployment of customized SNN models has been extensively conducted. Performance validations have been carried out in terms of processing time and inference accuracy between PC and embedded platforms, showing that the proposed customized models and training techniques are feasible for achieving a better performance on various datasets such as CIFAR-10, MNIST, SVHN, and private KITTI and Korean License plate dataset.

A Heterogeneous Spiking Neural Network for Unsupervised Learning of Spatiotemporal Patterns

This paper introduces a heterogeneous spiking neural network (H-SNN) as a novel, feedforward SNN structure capable of learning complex spatiotemporal patterns with spike-timing-dependent plasticity (STDP) based unsupervised training. Within H-SNN, hierarchical spatial and temporal patterns are constructed with convolution connections and memory pathways containing spiking neurons with different dynamics. We demonstrate analytically the formation of long and short term memory in H-SNN and distinct response functions of memory pathways. In simulation, the network is tested on visual input of moving objects to simultaneously predict for object class and motion dynamics. Results show that H-SNN achieves prediction accuracy on similar or higher level than supervised deep neural networks (DNN). Compared to SNN trained with back-propagation, H-SNN effectively utilizes STDP to learn spatiotemporal patterns that have better generalizability to unknown motion and/or object classes encountered during inference. In addition, the improved performance is achieved with 6x fewer parameters than complex DNNs, showing H-SNN as an efficient approach for applications with constrained computation resources.

Robust Trajectory Generation for Robotic Control on the Neuromorphic Research Chip Loihi

Neuromorphic hardware has several promising advantages compared to von Neumann architectures and is highly interesting for robot control. However, despite the high speed and energy efficiency of neuromorphic computing, algorithms utilizing this hardware in control scenarios are still rare. One problem is the transition from fast spiking activity on the hardware, which acts on a timescale of a few milliseconds, to a control-relevant timescale on the order of hundreds of milliseconds. Another problem is the execution of complex trajectories, which requires spiking activity to contain sufficient variability, while at the same time, for reliable performance, network dynamics must be adequately robust against noise. In this study we exploit a recently developed biologically-inspired spiking neural network model, the so-called anisotropic network. We identified and transferred the core principles of the anisotropic network to neuromorphic hardware using Intel's neuromorphic research chip Loihi and validated the system on trajectories from a motor-control task performed by a robot arm. We developed a network architecture including the anisotropic network and a pooling layer which allows fast spike read-out from the chip and performs an inherent regularization. With this, we show that the anisotropic network on Loihi reliably encodes sequential patterns of neural activity, each representing a robotic action, and that the patterns allow the generation of multidimensional trajectories on control-relevant timescales. Taken together, our study presents a new algorithm that allows the generation of complex robotic movements as a building block for robotic control using state of the art neuromorphic hardware.

Toward Scalable, Efficient, and Accurate Deep Spiking Neural Networks With Backward Residual Connections, Stochastic Softmax, and Hybridization

Spiking Neural Networks (SNNs) may offer an energy-efficient alternative for implementing deep learning applications. In recent years, there have been several proposals focused on supervised (conversion, spike-based gradient descent) and unsupervised (spike timing dependent plasticity) training methods to improve the accuracy of SNNs on large-scale tasks. However, each of these methods suffer from scalability, latency, and accuracy limitations. In this paper, we propose novel algorithmic techniques of modifying the SNN configuration with backward residual connections, stochastic softmax, and hybrid artificial-and-spiking neuronal activations to improve the learning ability of the training methodologies to yield competitive accuracy, while, yielding large efficiency gains over their artificial counterparts. Note, artificial counterparts refer to conventional deep learning/artificial neural networks. Our techniques apply to VGG/Residual architectures, and are compatible with all forms of training methodologies. Our analysis reveals that the proposed solutions yield near state-of-the-art accuracy with significant energy-efficiency and reduced parameter overhead translating to hardware improvements on complex visual recognition tasks, such as, CIFAR10, Imagenet datatsets.

Enabling Spike-Based Backpropagation for Training Deep Neural Network Architectures

Spiking Neural Networks (SNNs) have recently emerged as a prominent neural computing paradigm. However, the typical shallow SNN architectures have limited capacity for expressing complex representations while training deep SNNs using input spikes has not been successful so far. Diverse methods have been proposed to get around this issue such as converting off-the-shelf trained deep Artificial Neural Networks (ANNs) to SNNs. However, the ANN-SNN conversion scheme fails to capture the temporal dynamics of a spiking system. On the other hand, it is still a difficult problem to directly train deep SNNs using input spike events due to the discontinuous, non-differentiable nature of the spike generation function. To overcome this problem, we propose an approximate derivative method that accounts for the leaky behavior of LIF neurons. This method enables training deep convolutional SNNs directly (with input spike events) using spike-based backpropagation. Our experiments show the effectiveness of the proposed spike-based learning on deep networks (VGG and Residual architectures) by achieving the best classification accuracies in MNIST, SVHN, and CIFAR-10 datasets compared to other SNNs trained with a spike-based learning. Moreover, we analyze sparse event-based computations to demonstrate the efficacy of the proposed SNN training method for inference operation in the spiking domain.

Towards spike-based machine intelligence with neuromorphic computing

Guided by brain-like 'spiking' computational frameworks, neuromorphic computing-brain-inspired computing for machine intelligence-promises to realize artificial intelligence while reducing the energy requirements of computing platforms. This interdisciplinary field began with the implementation of silicon circuits for biological neural routines, but has evolved to encompass the hardware implementation of algorithms with spike-based encoding and event-driven representations. Here we provide an overview of the developments in neuromorphic computing for both algorithms and hardware and highlight the fundamentals of learning and hardware frameworks. We discuss the main challenges and the future prospects of neuromorphic computing, with emphasis on algorithm-hardware codesign.

A biologically plausible supervised learning method for spiking neural networks using the symmetric STDP rule

Spiking neural networks (SNNs) possess energy-efficient potential due to event-based computation. However, supervised training of SNNs remains a challenge as spike activities are non-differentiable. Previous SNNs training methods can be generally categorized into two basic classes, i.e., backpropagation-like training methods and plasticity-based learning methods. The former methods are dependent on energy-inefficient real-valued computation and non-local transmission, as also required in artificial neural networks (ANNs), whereas the latter are either considered to be biologically implausible or exhibit poor performance. Hence, biologically plausible (bio-plausible) high-performance supervised learning (SL) methods for SNNs remain deficient. In this paper, we proposed a novel bio-plausible SNN model for SL based on the symmetric spike-timing dependent plasticity (sym-STDP) rule found in neuroscience. By combining the sym-STDP rule with bio-plausible synaptic scaling and intrinsic plasticity of the dynamic threshold, our SNN model implemented SL well and achieved good performance in the benchmark recognition task (MNIST dataset). To reveal the underlying mechanism of our SL model, we visualized both layer-based activities and synaptic weights using the t-distributed stochastic neighbor embedding (t-SNE) method after training and found that they were well clustered, thereby demonstrating excellent classification ability. Furthermore, to verify the robustness of our model, we trained it on another more realistic dataset (Fashion-MNIST), which also showed good performance. As the learning rules were bio-plausible and based purely on local spike events, our model could be easily applied to neuromorphic hardware for online training and may be helpful for understanding SL information processing at the synaptic level in biological neural systems.

A Spiking Neural Network Based on the Model of VO2—Neuron

In this paper, we present an electrical circuit of a leaky integrate-and-fire neuron with one VO2 switch, which models the properties of biological neurons. Based on VO2 neurons, a two-layer spiking neural network consisting of nine input and three output neurons is modeled in the SPICE simulator. The network contains excitatory and inhibitory couplings, and implements the winner-takes-all principle in pattern recognition. Using a supervised Spike-Timing-Dependent Plasticity training method and a timing method of information coding, the network was trained to recognize three patterns with dimensions of 3 × 3 pixels. The neural network is able to recognize up to 105 images per second, and has the potential to increase the recognition speed further.

Rethinking the performance comparison between SNNS and ANNS

Artificial neural networks (ANNs), a popular path towards artificial intelligence, have experienced remarkable success via mature models, various benchmarks, open-source datasets, and powerful computing platforms. Spiking neural networks (SNNs), a category of promising models to mimic the neuronal dynamics of the brain, have gained much attention for brain inspired computing and been widely deployed on neuromorphic devices. However, for a long time, there are ongoing debates and skepticisms about the value of SNNs in practical applications. Except for the low power attribute benefit from the spike-driven processing, SNNs usually perform worse than ANNs especially in terms of the application accuracy. Recently, researchers attempt to address this issue by borrowing learning methodologies from ANNs, such as backpropagation, to train high-accuracy SNN models. The rapid progress in this domain continuously produces amazing results with ever-increasing network size, whose growing path seems similar to the development of deep learning. Although these ways endow SNNs the capability to approach the accuracy of ANNs, the natural superiorities of SNNs and the way to outperform ANNs are potentially lost due to the use of ANN-oriented workloads and simplistic evaluation metrics. In this paper, we take the visual recognition task as a case study to answer the questions of "what workloads are ideal for SNNs and how to evaluate SNNs makes sense". We design a series of contrast tests using different types of datasets (ANN-oriented and SNN-oriented), diverse processing models, signal conversion methods, and learning algorithms. We propose comprehensive metrics on the application accuracy and the cost of memory & compute to evaluate these models, and conduct extensive experiments. We evidence the fact that on ANN-oriented workloads, SNNs fail to beat their ANN counterparts; while on SNN-oriented workloads, SNNs can fully perform better. We further demonstrate that in SNNs there exists a trade-off between the application accuracy and the execution cost, which will be affected by the simulation time window and firing threshold. Based on these abundant analyses, we recommend the most suitable model for each scenario. To the best of our knowledge, this is the first work using systematical comparisons to explicitly reveal that the straightforward workload porting from ANNs to SNNs is unwise although many works are doing so and a comprehensive evaluation indeed matters. Finally, we highlight the urgent need to build a benchmarking framework for SNNs with broader tasks, datasets, and metrics.

Reinforcement Learning With Low-Complexity Liquid State Machines

We propose reinforcement learning on simple networks consisting of random connections of spiking neurons (both recurrent and feed-forward) that can learn complex tasks with very little trainable parameters. Such sparse and randomly interconnected recurrent spiking networks exhibit highly non-linear dynamics that transform the inputs into rich high-dimensional representations based on the current and past context. The random input representations can be efficiently interpreted by an output (or readout) layer with trainable parameters. Systematic initialization of the random connections and training of the readout layer using Q-learning algorithm enable such small random spiking networks to learn optimally and achieve the same learning efficiency as humans on complex reinforcement learning (RL) tasks like Atari games. In fact, the sparse recurrent connections cause these networks to retain fading memory of past inputs, thereby enabling them to perform temporal integration across successive RL time-steps and learn with partial state inputs. The spike-based approach using small random recurrent networks provides a computationally efficient alternative to state-of-the-art deep reinforcement learning networks with several layers of trainable parameters.

Locally connected spiking neural networks for unsupervised feature learning

In recent years, spiking neural networks (SNNs) have demonstrated great success in completing various machine learning tasks. We introduce a method for learning image features with locally connected layers in SNNs using a spike-timing-dependent plasticity (STDP) rule. In our approach, sub-networks compete via inhibitory interactions to learn features from different locations of the input space. These locally-connected SNNs (LC-SNNs) manifest key topological features of the spatial interaction of biological neurons. We explore a biologically inspired n-gram classification approach allowing parallel processing over various patches of the image space. We report the classification accuracy of simple two-layer LC-SNNs on two image datasets, which respectively match state-of-art performance and are the first results to date. LC-SNNs have the advantage of fast convergence to a dataset representation, and they require fewer learnable parameters than other SNN approaches with unsupervised learning. Robustness tests demonstrate that LC-SNNs exhibit graceful degradation of performance despite the random deletion of large numbers of synapses and neurons. Our results have been obtained using the BindsNET library, which allows efficient machine learning implementations of spiking neural networks.