Enhanced representation learning with temporal coding in sparsely spiking neural networks

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.

Spiking Neural Networks (SNNs), widely known as the third generation of neural networks, encode input information temporally using sparse spiking events, which can be harnessed to achieve higher computational efficiency for cognitive tasks. However, considering the rapid strides in accuracy enabled by state-of-the-art Analog Neural Networks (ANNs), SNN training algorithms are much less mature, leading to accuracy gap between SNNs and ANNs. In this paper, we propose different SNN training methodologies, varying in degrees of biofidelity, and evaluate their efficacy on complex image recognition datasets. First, we present biologically plausible Spike Timing Dependent Plasticity (STDP) based deterministic and stochastic algorithms for unsupervised representation learning in SNNs. Our analysis on the CIFAR-10 dataset indicates that STDP-based learning rules enable the convolutional layers to self-learn low-level input features using fewer training examples. However, STDP-based learning is limited in applicability to shallow SNNs (≤4 layers) while yielding considerably lower than state-of-the-art accuracy. In order to scale the SNNs deeper and improve the accuracy further, we propose conversion methodology to map off-the-shelf trained ANN to SNN for energy-efficient inference. We demonstrate 69.96% accuracy for VGG16-SNN on ImageNet. However, ANN-to-SNN conversion leads to high inference latency for achieving the best accuracy. In order to minimize the inference latency, we propose spike-based error backpropagation algorithm using differentiable approximation for the spiking neuron. Our preliminary experiments on CIFAR-10 show that spike-based error backpropagation effectively captures temporal statistics to reduce the inference latency by up to 8× compared to converted SNNs while yielding comparable accuracy

A forecast-based STDP rule suitable for neuromorphic implementation

Delay learning based on temporal coding in Spiking Neural Networks

In neuromorphic computing, the coding method of spiking neurons serves as the foundation and is crucial for various aspects of network operation. Existing mainstream coding methods, such as rate coding and temporal coding, have different focuses, and each has its own advantages and limitations. This paper proposes a novel coding scheme called activeness coding that integrates the strengths of both rate and temporal coding methods. It encompasses precise timing information of the most recent neuronal spike as well as the historical firing rate information. The results of basic characteristic tests demonstrate that this encoding method accurately expresses input information and exhibits robustness. Furthermore, an unsupervised learning method based on activeness-coding triplet spike-timing dependent plasticity (STDP) is introduced, with the MNIST classification task used as an example to assess the performance of this encoding method in solving cognitive tasks. Test results show an improvement in accuracy of approximately 4.5%. Additionally, activeness coding also exhibits potential advantages in terms of resource conservation. Overall, activeness offers a promising approach for spiking neural network encoding with implications for various applications in the field of neural computation.

Spiking Neural Network (SNN) is a sparse-driven network that can be used in low-power neuromorphic applications. Training such a network is still a challenge. In this paper, we have implemented and analyzed a biologically plausible unsupervised Spike Time Dependent Plasticity (STDP) algorithm for training SNNs. The implementation was done in 90nm CMOS Technology using Cadence Virtuoso circuit simulator. The implementation was verified using MNIST dataset for handwritten digits. The MNIST images were converted to time-dependent spike trains by rate encoding technique using the Google Colab platform. The parameter specifications were analyzed in Cadence Virtuoso. Dependency of each parameter on the circuit characteristics was obtained and simulations show that the time constant and value of the capacitor in the circuit are linearly dependent.

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.

Spike timing dependent plasticity (STDP) learning rule is one of hot topics in neurobiology since it's been widely believed that synaptic plasticity mainly contribute to learning and memory in brain. Up to now, STDP has been observed in a wide variety of areas of brain, hippocampus, cortex and so on. Competition among synapses is an important behavior for this learning rule. In present study, we propose a single layer spiking neural network model using STDP learning rule in inhibitory synapses to investigate the competitive behavior. The experiments show that the synapses among neurons are both strengthened on the whole training process. Thus neurons inhibit the activities of one another, eventually the neuron with the highest input spike rate win the competition. We have found that the behavior is efficient when the differences of firing rates of input neurons without STDP are great than 5Hz, otherwise the winner neuron is random. In order to use the principle to artificial intelligent system, we use a mechanism of dynamic learning rate to let the neuron with the highest input to be selected by the competitive behavior as the winner. Therefore, a robust competitive spiking neural network is obtained.

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.

We present a compact mixed-signal implementation of synaptic plasticity for both Spike Timing Dependent Plasticity (STDP) and Spike Timing Dependent Delay Plasticity (STDDP). The proposed mixed-signal implementation consists of an a VLSI time window generator and a digital adaptor. The weight and delay values are stored in a digital memory, and the adaptor will send these values to the time window generator using a digital spike of which the duration is modulated according to these values. The analogue time window generator will then generate a time window, which is required for the implementation of STDP and STDDP. The digital adaptor will carry out the weight/delay adaption using this time window. The aVLSI time window generator is compact (50 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in IBM 130nm process) and we use a time multiplexing approach to achieve up to 65536 (64k) virtual digital adaptors with one physical adaptor, consuming only a fraction of the hardware resource on a Virtex 6 FPGA. Since the digital adaptor has been implemented on an FPGA, it can be easily reconfigured for different adaptation algorithms, which leaves it open for future development. Our mixed-signal implementation is therefore practical for implementing the synaptic plasticity in large-scale spiking neural networks running in real time. We show circuit simulation results illustrating both weight and delay adaptation.

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.

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.

A reconfigurable 4096-neuron, 1M-synapse chip in 10-nm FinFET CMOS is developed to accelerate inference and learning for many classes of spiking neural networks (SNNs). The SNN features digital circuits for leaky integrate and fire neuron models, on-chip spike-timing-dependent plasticity (STDP) learning, and high-fan-out multicast spike communication. Structured fine-grained weight sparsity reduces synapse memory by up to 16 $\times $ with less than 2% overhead for storing connections. Approximate computing co-optimizes the dropping flow control and benefits from algorithmic noise to process spatiotemporal spike patterns with up to 9.4 $\times $ lower energy. The SNN achieves a peak throughput of 25.2 GSOP/s at 0.9 V, peak energy efficiency of 3.8 pJ/SOP at 525 mV, and 2.3- $\mu \text{W}$ /neuron operation at 450 mV. On-chip unsupervised STDP trains a spiking restricted Boltzmann machine to de-noise Modified National Institute of Standards and Technology (MNIST) digits and to reconstruct natural scene images with RMSE of 0.036. Near-threshold operation, in conjunction with temporal and spatial sparsity, reduces energy by $17.4\times $ to 1.0- $\mu \text{J}$ /classification in a $236 \times 20$ feed-forward network that is trained to classify MNIST digits using supervised STDP. A binary-activation multilayer perceptron with 50% sparse weights is trained offline with error backpropagation to classify MNIST digits with 97.9% accuracy at 1.7- $\mu \text{J}$ /classification.

Predictive coding can be regarded as a function which reduces the error between an input signal and a top-down prediction. If reducing the error is equivalent to reducing the influence of stimuli from the environment, predictive coding can be regarded as stimulation avoidance by prediction. Our previous studies showed that action and selection for stimulation avoidance emerge in spiking neural networks through spike-timing dependent plasticity (STDP). In this study, we demonstrate that spiking neural networks with random structure spontaneously learn to predict temporal sequences of stimuli based solely on STDP.

The human brain is a dynamic system that is constantly learning. It employs a combination of various learning strategies to facilitate complex learning processes. However, implementing biological learning mechanisms into Spiking Neural Networks (SNNs) remains challenging; thus, most SNNs are trained with only a single learning strategy such as spike timing dependent plasticity (STDP). Moreover, conventional neural networks are first trained on one dataset and subsequently evaluated on unseen data. In this traditional approach, the weights and structure of the model remain fixed once the training step concludes. In this research, we aim to modify this traditional approach and hypothesize that adding short-term plasticity (STP) to a trained SNN enables the model to learn post-training without changing synaptic weights. In particular, by combining triplet STDP for long-term learning during initial training and STP for short-term learning after training (post-training), we employ multiple learning rules to enhance the biological plausibility and computational abilities of SNNs. In this way, two unsupervised learning pipelines are designed for image classification as a proof of concept, in which the dynamic synapse model, driven by neurotransmitter release and synaptic strength, is integrated into the trained network. The proposed method outperforms traditional training by achieving higher classification accuracy and a faster convergence rate. Consequently, our results show that the concept of post-training learning can be realized by incorporating STP in SNNs. Future studies should extend this concept to other challenges and explore its applicability to new datasets.