Adaptive learning rate of SpikeProp based on weight convergence analysis

Effective Active Learning Method for Spiking Neural Networks

A large quantity of labeled data is required to train high-performance deep spiking neural networks (SNNs), but obtaining labeled data is expensive. Active learning is proposed to reduce the quantity of labeled data required by deep learning models. However, conventional active learning methods in SNNs are not as effective as that in conventional artificial neural networks (ANNs) because of the difference in feature representation and information transmission. To address this issue, we propose an effective active learning method for a deep SNN model in this article. Specifically, a loss prediction module ActiveLossNet is proposed to extract features and select valuable samples for deep SNNs. Then, we derive the corresponding active learning algorithm for deep SNN models. Comprehensive experiments are conducted on CIFAR-10, MNIST, Fashion-MNIST, and SVHN on different SNN frameworks, including seven-layer CIFARNet and 20-layer ResNet-18. The comparison results demonstrate that the proposed active learning algorithm outperforms random selection and conventional ANN active learning methods. In addition, our method converges faster than conventional active learning methods.

Training multi-layer spiking neural networks with plastic synaptic weights and delays

Spiking neural networks are usually considered as the third generation of neural networks, which hold the potential of ultra-low power consumption on corresponding hardware platforms and are very suitable for temporal information processing. However, how to efficiently train the spiking neural networks remains an open question, and most existing learning methods only consider the plasticity of synaptic weights. In this paper, we proposed a new supervised learning algorithm for multiple-layer spiking neural networks based on the typical SpikeProp method. In the proposed method, both the synaptic weights and delays are considered as adjustable parameters to improve both the biological plausibility and the learning performance. In addition, the proposed method inherits the advantages of SpikeProp, which can make full use of the temporal information of spikes. Various experiments are conducted to verify the performance of the proposed method, and the results demonstrate that the proposed method achieves a competitive learning performance compared with the existing related works. Finally, the differences between the proposed method and the existing mainstream multi-layer training algorithms are discussed.

AdaSAM: Boosting sharpness-aware minimization with adaptive learning rate and momentum for training deep neural networks

Sharpness aware minimization (SAM) optimizer has been extensively explored as it can generalize better for training deep neural networks via introducing extra perturbation steps to flatten the landscape of deep learning models. Integrating SAM with adaptive learning rate and momentum acceleration, dubbed AdaSAM, has already been explored empirically to train large-scale deep neural networks without theoretical guarantee due to the triple difficulties in analyzing the coupled perturbation step, adaptive learning rate and momentum step. In this paper, we try to analyze the convergence rate of AdaSAM in the stochastic non-convex setting. We theoretically show that AdaSAM admits a O(1/bT) convergence rate, which achieves linear speedup property with respect to mini-batch size b. Specifically, to decouple the stochastic gradient steps with the adaptive learning rate and perturbed gradient, we introduce the delayed second-order momentum term to decompose them to make them independent while taking an expectation during the analysis. Then we bound them by showing the adaptive learning rate has a limited range, which makes our analysis feasible. To the best of our knowledge, we are the first to provide the non-trivial convergence rate of SAM with an adaptive learning rate and momentum acceleration. At last, we conduct several experiments on several NLP tasks and the synthetic task, which show that AdaSAM could achieve superior performance compared with SGD, AMSGrad, and SAM optimizers.

Supervised Learning in Multilayer Spiking Neural Networks With Spike Temporal Error Backpropagation

The brain-inspired spiking neural networks (SNNs) hold the advantages of lower power consumption and powerful computing capability. However, the lack of effective learning algorithms has obstructed the theoretical advance and applications of SNNs. The majority of the existing learning algorithms for SNNs are based on the synaptic weight adjustment. However, neuroscience findings confirm that synaptic delays can also be modulated to play an important role in the learning process. Here, we propose a gradient descent-based learning algorithm for synaptic delays to enhance the sequential learning performance of single spiking neuron. Moreover, we extend the proposed method to multilayer SNNs with spike temporal-based error backpropagation. In the proposed multilayer learning algorithm, information is encoded in the relative timing of individual neuronal spikes, and learning is performed based on the exact derivatives of the postsynaptic spike times with respect to presynaptic spike times. Experimental results on both synthetic and realistic datasets show significant improvements in learning efficiency and accuracy over the existing spike temporal-based learning algorithms. We also evaluate the proposed learning method in an SNN-based multimodal computational model for audiovisual pattern recognition, and it achieves better performance compared with its counterparts.

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.

Effective Transfer Learning Algorithm in Spiking Neural Networks

As the third generation of neural networks, spiking neural networks (SNNs) have gained much attention recently because of their high energy efficiency on neuromorphic hardware. However, training deep SNNs requires many labeled data that are expensive to obtain in real-world applications, as traditional artificial neural networks (ANNs). In order to address this issue, transfer learning has been proposed and widely used in traditional ANNs, but it has limited use in SNNs. In this article, we propose an effective transfer learning framework for deep SNNs based on the domain in-variance representation. Specifically, we analyze the rationality of centered kernel alignment (CKA) as a domain distance measurement relative to maximum mean discrepancy (MMD) in deep SNNs. In addition, we study the feature transferability across different layers by testing on the Office-31, Office-Caltech-10, and PACS datasets. The experimental results demonstrate the transferability of SNNs and show the effectiveness of the proposed transfer learning framework by using CKA in SNNs.

Spiking Neural Network Regularization With Fixed and Adaptive Drop-Keep Probabilities

Dropout and DropConnect are two techniques to facilitate the regularization of neural network models, having achieved the state-of-the-art results in several benchmarks. In this paper, to improve the generalization capability of spiking neural networks (SNNs), the two drop techniques are first applied to the state-of-the-art SpikeProp learning algorithm resulting in two improved learning algorithms called SPDO (SpikeProp with Dropout) and SPDC (SpikeProp with DropConnect). In view that a higher membrane potential of a biological neuron implies a higher probability of neural activation, three adaptive drop algorithms, SpikeProp with Adaptive Dropout (SPADO), SpikeProp with Adaptive DropConnect (SPADC), and SpikeProp with Group Adaptive Drop (SPGAD), are proposed by adaptively adjusting the keep probability for training SNNs. A convergence theorem for SPDC is proven under the assumptions of the bounded norm of connection weights and a finite number of equilibria. In addition, the five proposed algorithms are carried out in a collaborative neurodynamic optimization framework to improve the learning performance of SNNs. The experimental results on the four benchmark data sets demonstrate that the three adaptive algorithms converge faster than SpikeProp, SPDO, and SPDC, and the generalization errors of the five proposed algorithms are significantly smaller than that of SpikeProp. Furthermore, the experimental results also show that the five algorithms based on collaborative neurodynamic optimization can be improved in terms of several measures.

Toward Reflective Spiking Neural Networks Exploiting Memristive Devices

The design of modern convolutional artificial neural networks (ANNs) composed of formal neurons copies the architecture of the visual cortex. Signals proceed through a hierarchy, where receptive fields become increasingly more complex and coding sparse. Nowadays, ANNs outperform humans in controlled pattern recognition tasks yet remain far behind in cognition. In part, it happens due to limited knowledge about the higher echelons of the brain hierarchy, where neurons actively generate predictions about what will happen next, i.e., the information processing jumps from reflex to reflection. In this study, we forecast that spiking neural networks (SNNs) can achieve the next qualitative leap. Reflective SNNs may take advantage of their intrinsic dynamics and mimic complex, not reflex-based, brain actions. They also enable a significant reduction in energy consumption. However, the training of SNNs is a challenging problem, strongly limiting their deployment. We then briefly overview new insights provided by the concept of a high-dimensional brain, which has been put forward to explain the potential power of single neurons in higher brain stations and deep SNN layers. Finally, we discuss the prospect of implementing neural networks in memristive systems. Such systems can densely pack on a chip 2D or 3D arrays of plastic synaptic contacts directly processing analog information. Thus, memristive devices are a good candidate for implementing in-memory and in-sensor computing. Then, memristive SNNs can diverge from the development of ANNs and build their niche, cognitive, or reflective computations.

Rectified Linear Postsynaptic Potential Function for Backpropagation in Deep Spiking Neural Networks

Spiking neural networks (SNNs) use spatiotemporal spike patterns to represent and transmit information, which are not only biologically realistic but also suitable for ultralow-power event-driven neuromorphic implementation. Just like other deep learning techniques, deep SNNs (DeepSNNs) benefit from the deep architecture. However, the training of DeepSNNs is not straightforward because the well-studied error backpropagation (BP) algorithm is not directly applicable. In this article, we first establish an understanding as to why error BP does not work well in DeepSNNs. We then propose a simple yet efficient rectified linear postsynaptic potential function (ReL-PSP) for spiking neurons and a spike-timing-dependent BP (STDBP) learning algorithm for DeepSNNs where the timing of individual spikes is used to convey information (temporal coding), and learning (BP) is performed based on spike timing in an event-driven manner. We show that DeepSNNs trained with the proposed single spike time-based learning algorithm can achieve the state-of-the-art classification accuracy. Furthermore, by utilizing the trained model parameters obtained from the proposed STDBP learning algorithm, we demonstrate ultralow-power inference operations on a recently proposed neuromorphic inference accelerator. The experimental results also show that the neuromorphic hardware consumes 0.751 mW of the total power consumption and achieves a low latency of 47.71 ms to classify an image from the Modified National Institute of Standards and Technology (MNIST) dataset. Overall, this work investigates the contribution of spike timing dynamics for information encoding, synaptic plasticity, and decision-making, providing a new perspective to the design of future DeepSNNs and neuromorphic hardware.

Analyzing and Accelerating the Bottlenecks of Training Deep SNNs With Backpropagation

Spiking neural networks (SNNs) with the event-driven manner of transmitting spikes consume ultra-low power on neuromorphic chips. However, training deep SNNs is still challenging compared to convolutional neural networks (CNNs). The SNN training algorithms have not achieved the same performance as CNNs. In this letter, we aim to understand the intrinsic limitations of SNN training to design better algorithms. First, the pros and cons of typical SNN training algorithms are analyzed. Then it is found that the spatiotemporal backpropagation algorithm (STBP) has potential in training deep SNNs due to its simplicity and fast convergence. Later, the main bottlenecks of the STBP algorithm are analyzed, and three conditions for training deep SNNs with the STBP algorithm are derived. By analyzing the connection between CNNs and SNNs, we propose a weight initialization algorithm to satisfy the three conditions. Moreover, we propose an error minimization method and a modified loss function to further improve the training performance. Experimental results show that the proposed method achieves 91.53% accuracy on the CIFAR10 data set with 1% accuracy increase over the STBP algorithm and decreases the training epochs on the MNIST data set to 15 epochs (over 13 times speed-up compared to the STBP algorithm). The proposed method also decreases classification latency by over 25 times compared to the CNN-SNN conversion algorithms. In addition, the proposed method works robustly for very deep SNNs, while the STBP algorithm fails in a 19-layer SNN.

SpiFoG: an efficient supervised learning algorithm for the network of spiking neurons

There has been a lot of research on supervised learning in spiking neural network (SNN) for a couple of decades to improve computational efficiency. However, evolutionary algorithm based supervised learning for SNN has not been investigated thoroughly which is still in embryo stage. This paper introduce an efficient algorithm (SpiFoG) to train multilayer feed forward SNN in supervised manner that uses elitist floating point genetic algorithm with hybrid crossover. The evidence from neuroscience claims that the brain uses spike times with random synaptic delays for information processing. Therefore, leaky-integrate-and-fire spiking neuron is used in this research introducing random synaptic delays. The SpiFoG allows both excitatory and inhibitory neurons by allowing a mixture of positive and negative synaptic weights. In addition, random synaptic delays are also trained with synaptic weights in an efficient manner. Moreover, computational efficiency of SpiFoG was increased by reducing the total simulation time and increasing the time step since increasing time step within the total simulation time takes less iteration. The SpiFoG is benchmarked on Iris and WBC dataset drawn from the UCI machine learning repository and found better performance than state-of-the-art techniques.

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

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

A review of learning in biologically plausible spiking neural networks

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

Deep Learning in the Biomedical Applications: Recent and Future Status

Deep neural networks represent, nowadays, the most effective machine learning technology in biomedical domain. In this domain, the different areas of interest concern the Omics (study of the genome—genomics—and proteins—transcriptomics, proteomics, and metabolomics), bioimaging (study of biological cell and tissue), medical imaging (study of the human organs by creating visual representations), BBMI (study of the brain and body machine interface) and public and medical health management (PmHM). This paper reviews the major deep learning concepts pertinent to such biomedical applications. Concise overviews are provided for the Omics and the BBMI. We end our analysis with a critical discussion, interpretation and relevant open challenges.

An Interclass Margin Maximization Learning Algorithm for Evolving Spiking Neural Network

This paper presents a new learning algorithm developed for a three layered spiking neural network for pattern classification problems. The learning algorithm maximizes the interclass margin and is referred to as the two stage margin maximization spiking neural network (TMM-SNN). In the structure learning stage, the learning algorithm completely evolves the hidden layer neurons in the first epoch. Further, TMM-SNN updates the weights of the hidden neurons for multiple epochs using the newly developed normalized membrane potential learning rule such that the interclass margins (based on the response of hidden neurons) are maximized. The normalized membrane potential learning rule considers both the local information in the spike train generated by a presynaptic neuron and the existing knowledge (synaptic weights) stored in the network to update the synaptic weights. After the first stage, the number of hidden neurons and their parameters are not updated. In the output weights learning stage, TMM-SNN updates the weights of the output layer neurons for multiple epochs to maximize the interclass margins (based on the response of output neurons). Performance of TMM-SNN is evaluated using ten benchmark data sets from the UCI machine learning repository. Statistical performance comparison of TMM-SNN with other existing learning algorithms for SNNs is conducted using the nonparametric Friedman test followed by a pairwise comparison using the Fisher's least significant difference method. The results clearly indicate that TMM-SNN achieves better generalization performance in comparison to other algorithms.

A Supervised Learning Algorithm for Learning Precise Timing of Multiple Spikes in Multilayer Spiking Neural Networks

There is a biological evidence to prove information is coded through precise timing of spikes in the brain. However, training a population of spiking neurons in a multilayer network to fire at multiple precise times remains a challenging task. Delay learning and the effect of a delay on weight learning in a spiking neural network (SNN) have not been investigated thoroughly. This paper proposes a novel biologically plausible supervised learning algorithm for learning precisely timed multiple spikes in a multilayer SNNs. Based on the spike-timing-dependent plasticity learning rule, the proposed learning method trains an SNN through the synergy between weight and delay learning. The weights of the hidden and output neurons are adjusted in parallel. The proposed learning method captures the contribution of synaptic delays to the learning of synaptic weights. Interaction between different layers of the network is realized through biofeedback signals sent by the output neurons. The trained SNN is used for the classification of spatiotemporal input patterns. The proposed learning method also trains the spiking network not to fire spikes at undesired times which contribute to misclassification. Experimental evaluation on benchmark data sets from the UCI machine learning repository shows that the proposed method has comparable results with classical rate-based methods such as deep belief network and the autoencoder models. Moreover, the proposed method can achieve higher classification accuracies than single layer and a similar multilayer SNN.

Robustness to Training Disturbances in SpikeProp Learning

Stability is a key issue during spiking neural network training using SpikeProp. The inherent nonlinearity of Spiking Neuron means that the learning manifold changes abruptly; therefore, we need to carefully choose the learning steps at every instance. Other sources of instability are the external disturbances that come along with training sample as well as the internal disturbances that arise due to modeling imperfection. The unstable learning scenario can be indirectly observed in the form of surges, which are sudden increases in the learning cost and are a common occurrence during SpikeProp training. Research in the past has shown that proper learning step size is crucial to minimize surges during training process. To determine proper learning step in order to avoid steep learning manifolds, we perform weight convergence analysis of SpikeProp learning in the presence of disturbance signals. The weight convergence analysis is further extended to robust stability analysis linked with overall system error. This ensures boundedness of the total learning error with minimal assumption of bounded disturbance signals. These analyses result in the learning rate normalization scheme, which are the key results of this paper. The performance of learning using this scheme has been compared with the prevailing methods for different benchmark data sets and the results show that this method has stable learning reflected by minimal surges during learning, higher success in training instances, and faster learning as well.

SuperSpike: Supervised Learning in Multilayer Spiking Neural Networks

A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in silico. Here we revisit the problem of supervised learning in temporally coding multilayer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three-factor learning rule capable of training multilayer networks of deterministic integrate-and-fire neurons to perform nonlinear computations on spatiotemporal spike patterns. Second, inspired by recent results on feedback alignment, we compare the performance of our learning rule under different credit assignment strategies for propagating output errors to hidden units. Specifically, we test uniform, symmetric, and random feedback, finding that simpler tasks can be solved with any type of feedback, while more complex tasks require symmetric feedback. In summary, our results open the door to obtaining a better scientific understanding of learning and computation in spiking neural networks by advancing our ability to train them to solve nonlinear problems involving transformations between different spatiotemporal spike time patterns.

A Scalable Weight-Free Learning Algorithm for Regulatory Control of Cell Activity in Spiking Neuronal Networks

Recent developments in neural stimulation and recording technologies are providing scientists with the ability of recording and controlling the activity of individual neurons in vitro or in vivo, with very high spatial and temporal resolution. Tools such as optogenetics, for example, are having a significant impact in the neuroscience field by delivering optical firing control with the precision and spatiotemporal resolution required for investigating information processing and plasticity in biological brains. While a number of training algorithms have been developed to date for spiking neural network (SNN) models of biological neuronal circuits, exiting methods rely on learning rules that adjust the synaptic strengths (or weights) directly, in order to obtain the desired network-level (or functional-level) performance. As such, they are not applicable to modifying plasticity in biological neuronal circuits, in which synaptic strengths only change as a result of pre- and post-synaptic neuron firings or biological mechanisms beyond our control. This paper presents a weight-free training algorithm that relies solely on adjusting the spatiotemporal delivery of neuron firings in order to optimize the network performance. The proposed weight-free algorithm does not require any knowledge of the SNN model or its plasticity mechanisms. As a result, this training approach is potentially realizable in vitro or in vivo via neural stimulation and recording technologies, such as optogenetics and multielectrode arrays, and could be utilized to control plasticity at multiple scales of biological neuronal circuits. The approach is demonstrated by training SNNs with hundreds of units to control a virtual insect navigating in an unknown environment.

Robust spike-train learning in spike-event based weight update

Supervised learning algorithms in a spiking neural network either learn a spike-train pattern for a single neuron receiving input spike-train from multiple input synapses or learn to output the first spike time in a feedforward network setting. In this paper, we build upon spike-event based weight update strategy to learn continuous spike-train in a spiking neural network with a hidden layer using a dead zone on-off based adaptive learning rate rule which ensures convergence of the learning process in the sense of weight convergence and robustness of the learning process to external disturbances. Based on different benchmark problems, we compare this new method with other relevant spike-train learning algorithms. The results show that the speed of learning is much improved and the rate of successful learning is also greatly improved.

A Cross-Correlated Delay Shift Supervised Learning Method for Spiking Neurons with Application to Interictal Spike Detection in Epilepsy

This study introduces a novel learning algorithm for spiking neurons, called CCDS, which is able to learn and reproduce arbitrary spike patterns in a supervised fashion allowing the processing of spatiotemporal information encoded in the precise timing of spikes. Unlike the Remote Supervised Method (ReSuMe), synapse delays and axonal delays in CCDS are variants which are modulated together with weights during learning. The CCDS rule is both biologically plausible and computationally efficient. The properties of this learning rule are investigated extensively through experimental evaluations in terms of reliability, adaptive learning performance, generality to different neuron models, learning in the presence of noise, effects of its learning parameters and classification performance. Results presented show that the CCDS learning method achieves learning accuracy and learning speed comparable with ReSuMe, but improves classification accuracy when compared to both the Spike Pattern Association Neuron (SPAN) learning rule and the Tempotron learning rule. The merit of CCDS rule is further validated on a practical example involving the automated detection of interictal spikes in EEG records of patients with epilepsy. Results again show that with proper encoding, the CCDS rule achieves good recognition performance.

Robust learning in SpikeProp

Training a Spiking Neural Network using SpikeProp and its derivatives faces stability issues. Surges, marked by a sudden rise in learning cost, are a common occurrence during the learning process. They disrupt the learning process and often destabilize the process resulting in failure. A proper learning rate, which is neither too small nor too big, is important to minimize surges. Furthermore, external disturbances due to imperfection in sample data as well as internal disturbances are additional destabilizing source during the learning process. In this paper, we perform error system analysis incorporating external disturbance, followed by weight convergence analysis along with detailed robust stability analysis of SpikeProp learning process to ensure error bound of the learning process. Based on these results, we propose a robust adaptive learning rate scheme that aligns with the results of theoretical analysis. The performance of the proposed method has been compared with other prevalent methods based on different benchmark datasets and the results demonstrate that our method indeed has better performance in terms of convergence and learning speed as well.