Multilayer Spiking Neural Networks Research Articles

Fractional-order spike-timing-dependent gradient descent for multi-layer spiking neural networks

Accumulated detailed knowledge about the neuronal activities in human brains has brought more attention to bio-inspired spiking neural networks (SNNs). In contrast to non-spiking deep neural networks (DNNs), SNNs can encode and transmit spatiotemporal information more efficiently by exploiting biologically realistic and low-power event-driven neuromorphic architectures. However, the supervised learning of SNNs still remains a challenge because the spike-timing-dependent plasticity (STDP) of connected spiking neurons is difficult to implement and interpret in existing backpropagation learning schemes. This paper proposes a fractional-order spike-timing-dependent gradient descent (FO-STDGD) learning model by considering a derived nonlinear activation function that describes the relationship between the quasi-instantaneous firing rate and the temporal membrane potentials of nonleaky integrate-and-fire neurons. The training strategy can be generalized to any fractional orders between 0 and 2 since the FO-STDGD incorporates the fractional gradient descent method into the calculation of spike-timing-dependent loss gradients. The proposed FO-STDGD model is tested on the MNIST and DVS128 Gesture datasets and its accuracy under different network structure and fractional orders is analyzed. It can be found that the classification accuracy increases as the fractional order increases, and specifically, the case of fractional order 1.9 improves by 155 % relative to the case of fractional order 1 (traditional gradient descent). In addition, our scheme demonstrates the state-of-the-art computational efficacy for the same SNN structure and training epochs.

Adaptive structure generation and neuronal differentiation for memory encoding in SNNs

Memory is the core of cognition. The exploration of the memory encoding mechanism or the representation mechanism of information in the Spiking Neural Network (SNN) is the basis for the in-depth study of memory. In this paper, we study the memory encoding mechanism of multilayer SNN models from a biomimetic perspective and explore a method using the high biological likelihood of SNN to enable the network to effectively simulate memory effects. We proposed a series of heuristic neuron-growing connection algorithms and supervised network weight learning algorithms, which were applied to the unsupervised and supervised training process of the presentation layer. These methods optimized the structure of the representation layer, achieved functional differentiation of neurons, and enabled the network to generate differentiated representations for different data modes. Under our algorithm, the proposed model achieves stable convergence with identical pattern inputs, demonstrating distinct representations and sensitivities to different visual modalities. To achieve stable information expression within the network, we conducted various comparative experiments to determine diverse parameters of the complex network. This paper contributes to the development of Brain-inspired Intelligence by bridging the gap between computer science and neuroscience by using simulations to validate biological hypotheses and guide machine learning.

A bio-inspired ferroelectric tunnel FET-based spiking neuron for high-speed energy efficient neuromorphic computing

In this study, a novel spiking neuron based on double-gate ferroelectric tunnel field effect transistor (DG-FE-TFET) is proposed in the 50 nm technology node. Through calibrated simulations in Atlas TCAD, it is verified that by leveraging the forward transfer characteristics, the device accurately emulates the spiking patterns exhibited by biological neurons. The device works on tunneling mechanism which ensures low voltage operation and thereby reduces overall energy consumption. The proposed neuron consumes an energy of 0.58 aJ per spike, which is 1.29, 41.38, 7.75 × 105, 12.9 × 105, 1.89 × 105, 13.79 × 106, and 7.75 × 107 times lesser than V-DGTFET, FE-JLFET, Z2-FET, DG-TFET, FD-MOSFET, Ge-MOSFET, and Si-MOSFET. Notably, the neuron operates without the need for additional reset circuitry and achieves spiking frequency of 344 GHz, which can be attributed to the sharp switching characteristics of the proposed device. This greatly simplifies implementation and facilitates a higher neuron density for energy-efficient neuromorphic chips with high-speed capabilities. Finally, based upon the proposed neuron, a multi-layer spiking neural network (SNN) is designed in Python platform. The network is implemented for signal classification with an accuracy of 84.4%.

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.

Fully Spiking Actor Network With Intralayer Connections for Reinforcement Learning.

With the help of special neuromorphic hardware, spiking neural networks (SNNs) are expected to realize artificial intelligence (AI) with less energy consumption. It provides a promising energy-efficient way for realistic control tasks by combining SNNs with deep reinforcement learning (DRL). In this article, we focus on the task where the agent needs to learn multidimensional deterministic policies to control, which is very common in real scenarios. Recently, the surrogate gradient method has been utilized for training multilayer SNNs, which allows SNNs to achieve comparable performance with the corresponding deep networks in this task. Most existing spike-based reinforcement learning (RL) methods take the firing rate as the output of SNNs, and convert it to represent continuous action space (i.e., the deterministic policy) through a fully connected (FC) layer. However, the decimal characteristic of the firing rate brings the floating-point matrix operations to the FC layer, making the whole SNN unable to deploy on the neuromorphic hardware directly. To develop a fully spiking actor network (SAN) without any floating-point matrix operations, we draw inspiration from the nonspiking interneurons found in insects and employ the membrane voltage of the nonspiking neurons to represent the action. Before the nonspiking neurons, multiple population neurons are introduced to decode different dimensions of actions. Since each population is used to decode a dimension of action, we argue that the neurons in each population should be connected in time domain and space domain. Hence, the intralayer connections are used in output populations to enhance the representation capacity. This mechanism exists extensively in animals and has been demonstrated effectively. Finally, we propose a fully SAN with intralayer connections (ILC-SAN). Extensive experimental results demonstrate that the proposed method outperforms the state-of-the-art performance on continuous control tasks from OpenAI gym. Moreover, we estimate the theoretical energy consumption when deploying ILC-SAN on neuromorphic chips to illustrate its high energy efficiency.

MorphBungee: A 65-nm 7.2-mm2 27-μJ/image Digital Edge Neuromorphic Chip with On-Chip 802-frame/s Multi-Layer Spiking Neural Network Learning.

This paper presents a digital edge neuromorphic spiking neural network (SNN) processor chip for a variety of edge intelligent cognitive applications. This processor allows high-speed, high-accuracy and fully on-chip spike-timing-based multi-layer SNN learning. It is characteristic of hierarchical multi-core architecture, event-driven processing paradigm, meta-crossbar for efficient spike communication, and hybrid and reconfigurable parallelism. A prototype chip occupying an active silicon area of 7.2 mm2 was fabricated using a 65-nm 1P9M CMOS process. when running a 256-256-256-256-200 4-layer fully-connected SNN on downscaled 16 × 16 MNIST images. it typically achieved a high-speed throughput of 802 and 2270 frames/s for on-chip learning and inference, respectively, with a relatively low power dissipation of around 61 mW at a 100 MHz clock rate under a 1.0V core power supply, Our on-chip learning results in comparably high visual recognition accuracies of 96.06%, 83.38%, 84.53%, 99.22% and 100% on the MNIST, Fashion-MNIST, ETH-80, Yale-10 and ORL-10 datasets, respectively. In addition, we have successfully applied our neuromorphic chip to demonstrate high-resolution satellite cloud image segmentation and non-visual tasks including olfactory classification and textural news categorization. These results indicate that our neuromorphic chip is suitable for various intelligent edge systems under restricted cost, energy and latency budgets while requiring in-situ self-adaptative learning capability.

Sparse-firing regularization methods for spiking neural networks with time-to-first-spike coding

The training of multilayer spiking neural networks (SNNs) using the error backpropagation algorithm has made significant progress in recent years. Among the various training schemes, the error backpropagation method that directly uses the firing time of neurons has attracted considerable attention because it can realize ideal temporal coding. This method uses time-to-first-spike (TTFS) coding, in which each neuron fires at most once, and this restriction on the number of firings enables information to be processed at a very low firing frequency. This low firing frequency increases the energy efficiency of information processing in SNNs. However, only an upper limit has been provided for TTFS-coded SNNs, and the information-processing capability of SNNs at lower firing frequencies has not been fully investigated. In this paper, we propose two spike-timing-based sparse-firing (SSR) regularization methods to further reduce the firing frequency of TTFS-coded SNNs. Both methods are characterized by the fact that they only require information about the firing timing and associated weights. The effects of these regularization methods were investigated on the MNIST, Fashion-MNIST, and CIFAR-10 datasets using multilayer perceptron networks and convolutional neural network structures.

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.

Desire backpropagation: A lightweight training algorithm for multi-layer spiking neural networks based on spike-timing-dependent plasticity

Spiking neural networks (SNNs) are a viable alternative to conventional artificial neural networks when resource efficiency and computational complexity are of importance. A major advantage of SNNs is their binary information transfer through spike trains which eliminates multiplication operations. The training of SNNs has, however, been a challenge, since neuron models are non-differentiable and traditional gradient-based backpropagation algorithms cannot be applied directly. Furthermore, spike-timing-dependent plasticity (STDP), albeit being a spike-based learning rule, updates weights locally and does not optimize for the output error of the network. We present desire backpropagation, a method to derive the desired spike activity of all neurons, including the hidden ones, from the output error. By incorporating this desire value into the local STDP weight update, we can efficiently capture the neuron dynamics while minimizing the global error and attaining a high classification accuracy. That makes desire backpropagation a spike-based supervised learning rule. We trained three-layer networks to classify MNIST and Fashion-MNIST images and reached an accuracy of 98.41% and 87.56%, respectively. In addition, by eliminating a multiplication during the backward pass, we reduce computational complexity and balance arithmetic resources between forward and backward pass, making desire backpropagation a candidate for training on low-resource devices.

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.

Time-Reduced Model for Multilayer Spiking Neural Networks

Spiking neural networks (SNNs) is a type of biological neural network model, which is more biologically plausible and computationally powerful than traditional artificial neural networks (ANNs). SNNs can achieve the same goals as ANNs, and can build a large-scale network structure (i.e. deep spiking neural network) to accomplish complex tasks. However, training deep spiking neural network is difficult due to the non-differentiable nature of spike events, and it requires much computation time during the training period. In this paper, a time-reduced model adopting two methods is presented for reducing the computation time of a deep spiking neural network (i.e. approximating the spike response function by the piecewise linear method, and choosing the suitable number of sub-synapses). The experimental results show that the methods of piecewise linear approximation and choosing the suitable number of sub-synapses is effective. This method can not only reduce the training time but also simplify the network structure. With the piecewise linear approximation method, the half of computation time of the original model can be reduced by at least. With the rule of choosing the number of sub-synapses, the computation time of less than one-tenth of the original model can be reduced for XOR and Iris tasks.

Modulating STDP With Back-Propagated Error Signals to Train SNNs for Audio Classification

Audio classification has many practical applications such as noise pollution detection, wildlife monitoring, speech recognition, and more. For many of these applications, deploying classifiers on low powered devices for persistent deployment is desirable. Artificial neural networks (ANN) have achieved state-of-the-art performance on audio classification tasks; however, it is not always feasible to deploy modern ANNs to embedded devices due to their high power consumption. Biologically inspired spiking neural networks (SNN) have been shown to significantly reduce power consumption during inference when compared with equivalent ANNs, and they have also been theoretically proven to be more computationally powerful than stateless ANNs. This work proposes an audio classification system using SNNs, and a learning algorithm is developed for classification with multilayer SNNs which combines biologically plausible spike-timing-dependent plasticity (STDP) with spatial error backpropagation. By allowing the STDP process to account for both temporal dependencies and the non-differentiable activation function derivative, the proposed learning rule successfully trains multilayer SNNs for the considered classification tasks. Through the STDP process, the proposed learning rule is also capable of online learning; explicit storage of values from previous timesteps is not required, in contrast to the widely adopted backpropagation through time (BPTT) algorithm. The proposed approach approaches the performance of SNNs trained via BPTT on the classification tasks. SNNs trained with the proposed learning rule are evaluated on the Iris Flower dataset, the Real-World Computing Partnership sounds dataset, the Free Spoken Digits Dataset, and the UrbanSound8k dataset.

An Optimized Multi-layer Spiking Neural Network implementation in FPGA Without Multipliers

This paper presents an expansion and evaluation of the hardware architecture for the Optimized Deep Event-driven Spiking Neural Network Architecture (ODESA). ODESA is a state-of-the-art, event-driven multi-layer Spiking Neural Network (SNN) architecture that offers an end-to-end, online, and local supervised training method. In previous work, ODESA was successfully implemented on Field-Programmable Gate Array (FPGA) hardware, showcasing its effectiveness in resource-constrained hardware environments. Building upon the previous implementation, this research focuses on optimizing the ODESA network hardware by introducing a novel approach. Specifically, we propose substituting the dot product multipliers in the Neurons with a low-cost shift-register design. This optimization strategy significantly reduces the hardware resources required for implementing a neuron, thereby enabling more complex SNNs to be accommodated within a single FPGA. Additionally, this optimization results in a reduction in power consumption, further enhancing the practicality and efficiency of the hardware implementation. To evaluate the effectiveness of the proposed optimization, extensive experiments and measurements were conducted. The results demonstrate the successful reduction in hardware resource utilization while maintaining the network's functionality and performance. Moreover, the power consumption reduction contributes to the overall energy efficiency of the hardware implementation.

A Supervised Learning Algorithm for Multilayer Spiking Neural Networks Based on Temporal Coding Toward Energy-Efficient VLSI Processor Design.

Spiking neural networks (SNNs) are brain-inspired mathematical models with the ability to process information in the form of spikes. SNNs are expected to provide not only new machine-learning algorithms but also energy-efficient computational models when implemented in very-large-scale integration (VLSI) circuits. In this article, we propose a novel supervised learning algorithm for SNNs based on temporal coding. A spiking neuron in this algorithm is designed to facilitate analog VLSI implementations with analog resistive memory, by which ultrahigh energy efficiency can be achieved. We also propose several techniques to improve the performance on recognition tasks and show that the classification accuracy of the proposed algorithm is as high as that of the state-of-the-art temporal coding SNN algorithms on the MNIST and Fashion-MNIST datasets. Finally, we discuss the robustness of the proposed SNNs against variations that arise from the device manufacturing process and are unavoidable in analog VLSI implementation. We also propose a technique to suppress the effects of variations in the manufacturing process on the recognition performance.

A summary of image recognition-relevant multi-layer spiking neural networks learning algorithms

A summary of image recognition-relevant multi-layer spiking neural networks learning algorithms

Wearable Fabric μ Brain Enabling On-Garment Edge-Based Sensor Data Processing

Advances in artificial intelligence (AI) is an enabler for innovative wearable on-garment edge-driven AI. Such AI technologies are leveraging bioinspired methods to develop spiking neural networks (SNNs) that mimic the workings of the human brain to produce higher performance edge-based processing capabilities. Such advancements are driving the development and emergence of neuromorphic computing with SNN architectural designs. Taking inspiration from these, this article proposes and demonstrates a wearable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> Brain multilayer SNN smart garment, with an event-driven artificial SNN embedded into the garments fabric. The fabric-based multilayer SNN is interchangeable and scalable through its fabric hidden layer (FHL) and fabric patch design and can be interconnected with textile-based analog monitoring sensors. The prototype was tested to check the functionality of the individual and collective nodes of the SNN as well as evaluating the wearable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> Brain for fault tolerance scenarios (ripping and fraying) proving the prototype remained intact following the disconnection of fabric node Patches 5 and 8. Two application demonstrators were identified and tested. The first application focused on the detection of touch sensation on a forearm using the wearable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> Brain; here, real-world use cases were checked against the expected output. Fluctuations were encountered when voltage output readings were above and below the set threshold level of 2.3 V. The second application interfaced the wearable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> Brain to live neurons to demonstrate how textile pressure sensors on the surface can lead to stimulation of neurons, when validated we observed an 11-s timeframe where the brain slice was stimulated.

A multi-layer spiking neural network-based approach to bearing fault diagnosis

Effective fault diagnosis is a crucial way to reduce the occurrence of severe damages of many industrial products. With the increasing amount of condition monitoring data, deep-learning-based methods have become promising ways for intelligent fault diagnosis thanks to their automatic feature extraction capability. Most recently, the third-generation neural network, called spiking neural network (SNN), has been introduced as an effective tool for fault diagnosis. However, the internal state and the error function of neurons in the SNN model cannot satisfy the conditions of continuity and differentiability, resulting in the difficulty of the gradient back-propagation, and it, therefore, prevents the extension of the SNN to a deep manner. In this article, a probabilistic spiking response model (PSRM) with a multi-layer structure is put forth to enhance the performance of the SNN in terms of bearing fault diagnosis. In the PSRM, the extracted features from the local mean decomposition (LMD) method are converted into the probability pulse sequences, and a multi-layer learning algorithm is developed to facilitate the multi-layer network training. The fault diagnosis results from three bearing databases, i.e., CWRU, MFPT, and Paderborn University datasets, demonstrate that the proposed PSRM exceeds a majority of the state-of-the-art machine learning methods. The proposed multi-layer SNN can also provide transparency to different bearing fault patterns by the membrane potentials of the spiking neurons in the output layer.

Multilayer Photonic Spiking Neural Networks: Generalized Supervised Learning Algorithm and Network Optimization

We propose a generalized supervised learning algorithm for multilayer photonic spiking neural networks (SNNs) by combining the spike-timing dependent plasticity (STDP) rule and the gradient descent mechanism. A vertical-cavity surface-emitting laser with an embedded saturable absorber (VCSEL-SA) is employed as a photonic leaky-integrate-and-fire (LIF) neuron. The temporal coding strategy is employed to transform information into the precise firing time. With the modified supervised learning algorithm, the trained multilayer photonic SNN successfully solves the XOR problem and performs well on the Iris and Wisconsin breast cancer datasets. This indicates that a generalized supervised learning algorithm is realized for multilayer photonic SNN. In addition, network optimization is performed by considering different network sizes.

Supervised learning algorithm based on spike optimization mechanism for multilayer spiking neural networks

Supervised learning algorithm based on spike optimization mechanism for multilayer spiking neural networks

MSPAN: A Memristive Spike-Based Computing Engine With Adaptive Neuron for Edge Arrhythmia Detection.

In this work, a memristive spike-based computing in memory (CIM) system with adaptive neuron (MSPAN) is proposed to realize energy-efficient remote arrhythmia detection with high accuracy in edge devices by software and hardware co-design. A multi-layer deep integrative spiking neural network (DiSNN) is first designed with an accuracy of 93.6% in 4-class ECG classification tasks. Then a memristor-based CIM architecture and the corresponding mapping method are proposed to deploy the DiSNN. By evaluation, the overall system achieves an accuracy of over 92.25% on the MIT-BIH dataset while the area is 3.438 mm2 and the power consumption is 0.178 μJ per heartbeat at a clock frequency of 500 MHz. These results reveal that the proposed MSPAN system is promising for arrhythmia detection in edge devices.