Training Deep Spiking Neural Networks for Energy-Efficient Neuromorphic Computing

The problem with training spiking neural networks (SNNs) is relevant due to the ultra-low power consumption these networks could exhibit when implemented in neuromorphic hardware. The ongoing progress in the fabrication of memristors, a prospective basis for analogue synapses, gives relevance to studying the possibility of SNN learning on the base of synaptic plasticity models, obtained by fitting the experimental measurements of the memristor conductance change. The dynamics of memristor conductances is (necessarily) nonlinear, because conductance changes depend on the spike timings, which neurons emit in an all-or-none fashion. The ability to solve classification tasks was previously shown for spiking network models based on the bio-inspired local learning mechanism of spike-timing-dependent plasticity (STDP), as well as with the plasticity that models the conductance change of nanocomposite (NC) memristors. Input data were presented to the network encoded into the intensities of Poisson input spike sequences. This work considers another approach for encoding input data into input spike sequences presented to the network: temporal encoding, in which an input vector is transformed into relative timing of individual input spikes. Since temporal encoding uses fewer input spikes, the processing of each input vector by the network can be faster and more energy-efficient. The aim of the current work is to show the applicability of temporal encoding to training spiking networks with three synaptic plasticity models: STDP, NC memristor approximation, and PPX memristor approximation. We assess the accuracy of the proposed approach on several benchmark classification tasks: Fisher’s Iris, Wisconsin breast cancer, and the pole balancing task (CartPole). The accuracies achieved by SNN with memristor plasticity and conventional STDP are comparable and are on par with classic machine learning approaches.

Spiking Neural Networks (SNNs), An alternative to sigmoidal neural networks, include time into their operations using discrete signals called spikes. Employing spikes enables SNNs to mimic any feedforward sigmoidal neural network with lower power consumption. Recently a new type of SNN has been introduced for classification problems, known as Degree of Belonging SNN (DoB-SNN). DoB-SNN is a two-layer spiking neural network that shows significant potential as an alternative SNN architecture and learning algorithm. This paper introduces a new variant of Spike-Timing Dependent Plasticity (STDP), which is based on the assembly of neurons and expands the DoB-SNN's training algorithm for multilayer architectures. The new learning rule, known as assembly-based STDP, employs trained DoBs in each layer to train the next layer and build strong connections between neurons from the same assembly while creating inhibitory connections between neurons from different assemblies in two consecutive layers. The performance of the multilayer DoB-SNN is evaluated on five datasets from the UCI machine learning repository. Detailed comparisons on these datasets with other supervised learning algorithms show that the multilayer DoB-SNN can achieve better performance on 4/5 datasets and comparable performance on 5th when compared to multilayer algorithms that employ considerably more trainable parameters.

A forecast-based STDP rule suitable for neuromorphic implementation

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.

Spiking Neural Networks (SNNs) mimic the behavior of biological neurons. Unlike traditional Artificial Neural Networks (ANNs) that operate in a continuous time domain and use activation functions to process information, SNNs operate discrete event-driven, where data is encoded and communicated through spikes or discrete events. This unique approach offers several advantages, such as efficient computation and lower power consumption, making SNNs particularly attractive for energy-constrained and neuromorphic applications. However, training SNNs poses significant challenges due to the discrete nature of spikes and the non-differentiable behavior they exhibit. As a result, converting pre-trained ANNs into SNNs has gained attention as a convenient approach. While this approach simplifies the training process, it introduces certain drawbacks, including high latency. The conversion of ANNs to SNNs typically leads to a loss of accuracy, which can be attributed to various factors, including quantization, clipping, and timing errors. Previous studies have proposed techniques to mitigate quantization and clipping errors during the conversion process. However, they do not consider timing errors, degrading SNN accuracies at low latency conditions. This work introduces the MiCE conversion method, which offers a comprehensive joint optimization strategy to simultaneously alleviate quantization, clipping, and timing errors. At a moderate latency of 8 time-steps, our converted ResNet-20 achieves classification accuracies of 79.02% and 95.74% on the CIFAR-100 and CIFAR-10 datasets, respectively.

Neuromorphic computing is emerging as a promising Beyond Moore computing paradigm that employs event-triggered computation and non-von Neumann hardware. Spike Timing Dependent Plasticity (STDP) is a well-known bio-inspired learning rule that relies on activities of locally connected neurons to adjust the weights of their respective synapses. In this work, we analyze a basic STDP rule and its sensitivity on the different hyperparameters for training spiking neural networks (SNNs) with supervision, customized for a neuromorphic hardware implementation with integer weights. We compare the classification performance on four UCI datasets (iris, wine, breast cancer and digits) that depict varying levels of complexity. We perform a search for optimal set of hyperparameters using both grid search and Bayesian optimization. Through the use of Bayesian optimization, we show the general trends in hyperparameter sensitivity in SNN classification problem. With the best sets of hyperparameters, we achieve accuracies comparable to some of the best performing SNNs on these four datasets. With a highly optimized supervised STDP rule we show that these accuracies can be achieved with just 20 epochs of training.

Joint A-SNN: Joint training of artificial and spiking neural networks via self-Distillation and weight factorization

Spiking Neural Networks (SNNs) have emerged as an attractive alternative to traditional deep learning frameworks, since they provide higher computational efficiency in event driven neuromorphic hardware. However, the state-of-the-art (SOTA) SNNs suffer from high inference latency, resulting from inefficient input encoding and training techniques. The most widely used input coding schemes, such as Poisson based rate-coding, do not leverage the temporal learning capabilities of SNNs. This paper presents a training framework for low-latency energy-efficient SNNs that uses a hybrid encoding scheme at the input layer in which the analog pixel values of an image are directly applied during the first timestep and a novel variant of spike temporal coding is used during subsequent timesteps. In particular, neurons in every hidden layer are restricted to fire at most once per image which increases activation sparsity. To train these hybrid-encoded SNNs, we propose a variant of the gradient descent based spike timing dependent backpropagation (STDB) mechanism using a novel cross entropy loss function based on both the output neurons' spike time and membrane potential. The resulting SNNs have reduced latency and high activation sparsity, yielding significant improvements in computational efficiency. In particular, we evaluate our proposed training scheme on image classification tasks from CIFAR-10 and CIFAR-100 datasets on several VGG architectures. We achieve top-l accuracy of 66.46% with 5 timesteps on the CIFAR-100 dataset with ~125x less compute energy than an equivalent standard ANN. Additionally, our proposed SNN performs 5–300 x faster inference compared to other state-of-the-art rate or temporally coded SNN models.

Artificial neural network (ANN) research is inspired by how information is dynamically and massively processed in parallel by biological neural networks. Spiking neural networks (SNNs) are versions of artificial neural networks that are more biologically realistic than commonly used static models. As in actual brains, neurons signal each other through current spikes (rather than constant inputs, as in conventional ANNs), and spike timing plays a key role in SNN functioning. In this work, we give an overview of SNNs, and we describe and implement three different mathematical models (integrate and fire, leaky integrate and fire, conductance-based) using the Brian2 software simulator. We also describe the training of SNNs using the spike-timing-dependent plasticity (STDP) algorithm, and discuss an experiment by Diehl and Cook that shows the ability of SNNs to learn to distinguish handwritten digits. Lastly, we describe a few available software SNN simulators and hardware SNN implementations with possible practical applications of SNNs.

Spiking neural networks (SNN) are more realistic and powerful than the preceding generations of the neural networks (e.g. multi-layer perceptron networks). The SNN can be applied for simulating the brain and its functions, as well as it is able to be employed for different applications such as pattern classification. Different methods have been proposed for supervised training of SNN, however, most of them were validated based on using the classical XOR problem, and they consume long training time if other problems are considered. This paper proposes a new supervised training method for SNN by adapting the Enhanced-Mussels Wandering Optimization algorithm. In addition, a SNN model for pattern classification is proposed. The proposed work is used for pattern classification of real-world problems. The obtained results indicate that the proposed method is competitive alternative in terms of classification accuracy and training time.

Spiking neural networks (SNNs) have attracted many researchers’ interests due to its biological plausibility and event-driven characteristic. In particular, recently, many studies on high-performance SNNs comparable to the conventional analog-valued neural networks (ANNs) have been reported by converting weights trained from ANNs into SNNs. However, unlike ANNs, SNNs have an inherent latency that is required to reach the best performance because of differences in operations of neuron. In SNNs, not only spatial integration but also temporal integration exists, and the information is encoded by spike trains rather than values in ANNs. Therefore, it takes time to achieve a steady-state of the performance in SNNs. The latency is worse in deep networks and required to be reduced for the practical applications. In this work, we propose a pre-charged membrane potential (PCMP) for the latency reduction in SNN. A variety of neural network applications (e.g., classification, autoencoder using MNIST and CIFAR-10 datasets) are trained and converted to SNNs to demonstrate the effect of the proposed approach. The latency of SNNs is successfully reduced without accuracy loss. In addition, we propose a delayed evaluation method (DE), by which the errors during the initial transient are discarded. The error spikes occurring in the initial transient is removed by DE, resulting in the further latency reduction. DE can be used in combination with PCMP for further latency reduction. Finally, we also show the advantages of the proposed methods in improving the number of spikes required to reach a steady-state of the performance in SNNs for energy-efficient computing.

Spiking Neural Networks (SNN) is one special implementation of Artificial Neural Networks (ANN), where the input signals are encoded in the temporal relationship between consecutive spikes (spike trains) instead of real-numbered values. Nevertheless, SNN is believed to be a closer representation of the biological neural system, because it imitates the current spikes that are transmitted between neurons in real biological systems. Practical and simplified SNN models include the Leaky Integrate-and-Fire (LIF) function of the neurons and the Spiking Timing Dependent Plasticity (STDP) function of the synapses. While most ANN architectures can be implemented with digital logic gates, SNN is more suitable to be implemented in analog circuits. In this paper, we propose revised analog circuit implementations of SNN neurons with LIF and STDP functions. Compared with previous works by other researchers, our proposed analog designs use fewer components and can be cascaded to form a complete neural system. The circuits are designed and simulated with SMIC 55nm CMOS LP process. The simulated results demonstrate that the analog neural system can work under a very small current (less than 10 µA) and voltage supply (1.0 Volts), and consumes less power consumption than digital implementations.

Artificial neural systems for computation were first proposed three quarters of a century ago and the concepts developed by the pioneers still shape the field today. The first generation of neural systems was developed in the nineteen forties in the context of analogue electronics and the theoretical research in logic and mathematics that led to the first digital computers in nineteen forties and fifties. The second generation of neural systems implemented on digital computers was born in the nineteen fifties and great progress was made in the subsequent half century with neural networks being applied to many problems in pattern recognition and machine learning. Through this history there has been an interplay between biologically inspired neural systems and their implementation by engineers on digital machines. This thesis concerns the third generation of neural networks, Spiking Neural Networks, which is making possible the creation of new kinds of brain inspired computing architectures that offer the potential to increase the level of realism and sophistication in terms of autonomous machine behaviour and cognitive computing. This thesis presents the development and demonstration of a new theoretical architecture for third generation neural systems, the Integrate-and-Fire based Spiking Neural Model with extended Neuro-modulated Spike Timing Dependent Plasticity capabilities. This proposed architecture overcomes the limitation of the homosynaptic architecture underlying existing implementations of spiking neural networks that it lacks a natural spike timing dependent plasticity regulation mechanism, and this results in ‘run away’ dynamics. To overcome this ad hoc procedures have been implemented to overcome the ‘run away’ dynamics that emerge from the use of spike timing dependent plasticity among other hebbian-based plasticity rules. The new heterosynaptic architecture presented, explicitly abstracts the modulation of complex biochemical mechanisms into a simplified mechanism that is suitable for the engineering of artificial systems with low computational complexity. Neurons work by receiving input signals from other neurons through synapses. The difference between homosynaptic and heterosynaptic plasticity is that, in the former the change in the properties of a synapse (e.g. synaptic efficacy) depends on the point to point activity in either of the sending and receiving neurons, in contrast for heterosynaptic plasticity the change in the properties of a synapse can be elicited by neurons that are not necessary presynaptic or postsynaptic to the synapse in question. The new architecture is tested by a number of implementations in simulated and real environments. This includes experiments with a simulation environment implemented in Netlogo, and an implementation using Lego Mindstorms as the physical robot platform. These experiments demonstrate the problems with the traditional Spike timing dependent plasticity homosynaptic architecture and how the new heterosynaptic approach can overcome them. It is concluded that the new theoretical architecture provides a natural, theoretically sound, and practical new direction for research into the role of modulatory neural systems applied to spiking neural networks.

We present a new back propagation based training algorithm for discrete-time spiking neural networks (SNN). Inspired by recent deep learning algorithms on binarized neural networks, binary activation with a straight-through gradient estimator is used to model the leaky integrate-fire spiking neuron, overcoming the difficulty in training SNNs using back propagation. Two SNN training algorithms are proposed: (1) SNN with discontinuous integration, which is suitable for rate-coded input spikes, and (2) SNN with continuous integration, which is more general and can handle input spikes with temporal information. Neuromorphic hardware designed in 28nm CMOS exploits the spike sparsity and demonstrates high classification accuracy (>98% on MNIST) and low energy (51.4-773 nJ/image).

How can we bring both privacy and energy-efficiency to a neural system? In this paper, we propose PrivateSNN, which aims to build low-power Spiking Neural Networks (SNNs) from a pre-trained ANN model without leaking sensitive information contained in a dataset. Here, we tackle two types of leakage problems: 1) Data leakage is caused when the networks access real training data during an ANN-SNN conversion process. 2) Class leakage is caused when class-related features can be reconstructed from network parameters. In order to address the data leakage issue, we generate synthetic images from the pre-trained ANNs and convert ANNs to SNNs using the generated images. However, converted SNNs remain vulnerable to class leakage since the weight parameters have the same (or scaled) value with respect to ANN parameters. Therefore, we encrypt SNN weights by training SNNs with a temporal spike-based learning rule. Updating weight parameters with temporal data makes SNNs difficult to be interpreted in the spatial domain. We observe that the encrypted PrivateSNN eliminates data and class leakage issues with a slight performance drop (less than ~2%) and significant energy-efficiency gain (about 55x) compared to the standard ANN. We conduct extensive experiments on various datasets including CIFAR10, CIFAR100, and TinyImageNet, highlighting the importance of privacy-preserving SNN training.