Supervised learning in spiking neural networks with synaptic delay-weight plasticity

Trainable Reference Spikes Improve Temporal Information Processing of SNNs With Supervised Learning

Spiking neural networks (SNNs) are the next-generation neural networks composed of biologically plausible neurons that communicate through trains of spikes. By modifying the plastic parameters of SNNs, including weights and time delays, SNNs can be trained to perform various AI tasks, although in general not at the same level of performance as typical artificial neural networks (ANNs). One possible solution to improve the performance of SNNs is to consider plastic parameters other than just weights and time delays drawn from the inherent complexity of the neural system of the brain, which may help SNNs improve their information processing ability and achieve brainlike functions. Here, we propose reference spikes as a new type of plastic parameters in a supervised learning scheme in SNNs. A neuron receives reference spikes through synapses providing reference information independent of input to help during learning, whose number of spikes and timings are trainable by error backpropagation. Theoretically, reference spikes improve the temporal information processing of SNNs by modulating the integration of incoming spikes at a detailed level. Through comparative computational experiments, we demonstrate using supervised learning that reference spikes improve the memory capacity of SNNs to map input spike patterns to target output spike patterns and increase classification accuracy on the MNIST, Fashion-MNIST, and SHD data sets, where both input and target output are temporally encoded. Our results demonstrate that applying reference spikes improves the performance of SNNs by enhancing their temporal information processing ability.

Delay learning based on temporal coding in Spiking Neural Networks

Spiking Neural Networks (SNNs) hold great potential for mimicking the brain's efficient processing of information. Although biological evidence suggests that precise spike timing is crucial for effective information encoding, contemporary SNN research mainly concentrates on adjusting connection weights. In this work, we introduce Delay Learning based on Temporal Coding (DLTC), an innovative approach that integrates delay learning with a temporal coding strategy to optimize spike timing in SNNs. DLTC utilizes a learnable delay shift, which assigns varying levels of importance to different informational elements. This is complemented by an adjustable threshold that regulates firing times, allowing for earlier or later neuron activation as needed. We have tested DLTC's effectiveness in various contexts, including vision and auditory classification tasks, where it consistently outperformed traditional weight-only SNNs. The results indicate that DLTC achieves remarkable improvements in accuracy and computational efficiency, marking a step forward in advancing SNNs towards real-world applications. Our codes are accessible at https://github.com/sunpengfei1122/DLTC.

Bioplausible Unsupervised Delay Learning for Extracting Spatiotemporal Features in Spiking Neural Networks

The plasticity of the conduction delay between neurons plays a fundamental role in learning temporal features that are essential for processing videos, speech, and many high-level functions. However, the exact underlying mechanisms in the brain for this modulation are still under investigation. Devising a rule for precisely adjusting the synaptic delays could eventually help in developing more efficient and powerful brain-inspired computational models. In this article, we propose an unsupervised bioplausible learning rule for adjusting the synaptic delays in spiking neural networks. We also provide the mathematical proofs to show the convergence of our rule in learning spatiotemporal patterns. Furthermore, to show the effectiveness of our learning rule, we conducted several experiments on random dot kinematogram and a subset of DVS128 Gesture data sets. The experimental results indicate the efficiency of applying our proposed delay learning rule in extracting spatiotemporal features in an STDP-based spiking neural network.

Minicolumn-Based Episodic Memory Model With Spiking Neurons, Dendrites and Delays

Episodic memory is fundamental to the brain's cognitive function, but how neuronal activity is temporally organized during its encoding and retrieval is still unknown. In this article, combining hippocampus structure with a spiking neural network (SNN), a new bionic spiking temporal memory (BSTM) model is proposed to explore the encoding, formation, and retrieval of episodic memory. For encoding episodic memory, the spike-timing-dependent-plasticity (STDP) learning algorithm and a proposed minicolumn selection algorithm are used to encode each input item into several active minicolumns. For the formation of episodic memory, a sequential memory algorithm is proposed to store the contexts between items. For retrieval of episodic memory, the local retrieval algorithm and the global retrieval algorithm are proposed to retrieve sequence information, achieving multisentence prediction and multitime step prediction. All functions of BSTM are based on bionic spiking neurons, which have biological characteristics including columnar and dendritic structures, firing and receiving spikes, and delaying transmission. To test the performance of the BSTM model, the Children's Book Test (CBT) data set was used to conduct a series of experiments under different settings, including changing the number of minicolumns, neurons and sequences, modifying sequence items, etc. Compared to other sequence memory algorithms, the experimental results show that the proposed BSTM achieves higher accuracy and better robustness.

Co-learning synaptic delays, weights and adaptation in spiking neural networks

Spiking neural network (SNN) distinguish themselves from artificial neural network (ANN) because of their inherent temporal processing and spike-based computations, enabling a power-efficient implementation in neuromorphic hardware. In this study, we demonstrate that data processing with spiking neurons can be enhanced by co-learning the synaptic weights with two other biologically inspired neuronal features: (1) a set of parameters describing neuronal adaptation processes and (2) synaptic propagation delays. The former allows a spiking neuron to learn how to specifically react to incoming spikes based on its past. The trained adaptation parameters result in neuronal heterogeneity, which leads to a greater variety in available spike patterns and is also found in the brain. The latter enables to learn to explicitly correlate spike trains that are temporally distanced. Synaptic delays reflect the time an action potential requires to travel from one neuron to another. We show that each of the co-learned features separately leads to an improvement over the baseline SNN and that the combination of both leads to state-of-the-art SNN results on all speech recognition datasets investigated with a simple 2-hidden layer feed-forward network. Our SNN outperforms the benchmark ANN on the neuromorphic datasets (Spiking Heidelberg Digits and Spiking Speech Commands), even with fewer trainable parameters. On the 35-class Google Speech Commands dataset, our SNN also outperforms a GRU of similar size. Our study presents brain-inspired improvements in SNN that enable them to excel over an equivalent ANN of similar size on tasks with rich temporal dynamics.

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.

Improving Multispike Learning With Plastic Synaptic Delays

Emulating the spike-based processing in the brain, spiking neural networks (SNNs) are developed and act as a promising candidate for the new generation of artificial neural networks that aim to produce efficient cognitions as the brain. Due to the complex dynamics and nonlinearity of SNNs, designing efficient learning algorithms has remained a major difficulty, which attracts great research attention. Most existing ones focus on the adjustment of synaptic weights. However, other components, such as synaptic delays, are found to be adaptive and important in modulating neural behavior. How could plasticity on different components cooperate to improve the learning of SNNs remains as an interesting question. Advancing our previous multispike learning, we propose a new joint weight-delay plasticity rule, named TDP-DL, in this article. Plastic delays are integrated into the learning framework, and as a result, the performance of multispike learning is significantly improved. Simulation results highlight the effectiveness and efficiency of our TDP-DL rule compared to baseline ones. Moreover, we reveal the underlying principle of how synaptic weights and delays cooperate with each other through a synthetic task of interval selectivity and show that plastic delays can enhance the selectivity and flexibility of neurons by shifting information across time. Due to this capability, useful information distributed away in the time domain can be effectively integrated for a better accuracy performance, as highlighted in our generalization tasks of the image, speech, and event-based object recognitions. Our work is thus valuable and significant to improve the performance of spike-based neuromorphic computing.

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.

Learnable axonal delay in spiking neural networks improves spoken word recognition

Spiking neural networks (SNNs), which are composed of biologically plausible spiking neurons, and combined with bio-physically realistic auditory periphery models, offer a means to explore and understand human auditory processing-especially in tasks where precise timing is essential. However, because of the inherent temporal complexity in spike sequences, the performance of SNNs has remained less competitive compared to artificial neural networks (ANNs). To tackle this challenge, a fundamental research topic is the configuration of spike-timing and the exploration of more intricate architectures. In this work, we demonstrate a learnable axonal delay combined with local skip-connections yields state-of-the-art performance on challenging benchmarks for spoken word recognition. Additionally, we introduce an auxiliary loss term to further enhance accuracy and stability. Experiments on the neuromorphic speech benchmark datasets, NTIDIDIGITS and SHD, show improvements in performance when incorporating our delay module in comparison to vanilla feedforward SNNs. Specifically, with the integration of our delay module, the performance on NTIDIDIGITS and SHD improves by 14% and 18%, respectively. When paired with local skip-connections and the auxiliary loss, our approach surpasses both recurrent and convolutional neural networks, yet uses 10 × fewer parameters for NTIDIDIGITS and 7 × fewer for SHD.

Learning heterogeneous delays in a layer of spiking neurons for fast motion detection

The precise timing of spikes emitted by neurons plays a crucial role in shaping the response of efferent biological neurons. This temporal dimension of neural activity holds significant importance in understanding information processing in neurobiology, especially for the performance of neuromorphic hardware, such as event-based cameras. Nonetheless, many artificial neural models disregard this critical temporal dimension of neural activity. In this study, we present a model designed to efficiently detect temporal spiking motifs using a layer of spiking neurons equipped with heterogeneous synaptic delays. Our model capitalizes on the diverse synaptic delays present on the dendritic tree, enabling specific arrangements of temporally precise synaptic inputs to synchronize upon reaching the basal dendritic tree. We formalize this process as a time-invariant logistic regression, which can be trained using labeled data. To demonstrate its practical efficacy, we apply the model to naturalistic videos transformed into event streams, simulating the output of the biological retina or event-based cameras. To evaluate the robustness of the model in detecting visual motion, we conduct experiments by selectively pruning weights and demonstrate that the model remains efficient even under significantly reduced workloads. In conclusion, by providing a comprehensive, event-driven computational building block, the incorporation of heterogeneous delays has the potential to greatly improve the performance of future spiking neural network algorithms, particularly in the context of neuromorphic chips.

Direct learning-based deep spiking neural networks: a review

The spiking neural network (SNN), as a promising brain-inspired computational model with binary spike information transmission mechanism, rich spatially-temporal dynamics, and event-driven characteristics, has received extensive attention. However, its intricately discontinuous spike mechanism brings difficulty to the optimization of the deep SNN. Since the surrogate gradient method can greatly mitigate the optimization difficulty and shows great potential in directly training deep SNNs, a variety of direct learning-based deep SNN works have been proposed and achieved satisfying progress in recent years. In this paper, we present a comprehensive survey of these direct learning-based deep SNN works, mainly categorized into accuracy improvement methods, efficiency improvement methods, and temporal dynamics utilization methods. In addition, we also divide these categorizations into finer granularities further to better organize and introduce them. Finally, the challenges and trends that may be faced in future research are prospected.

Deep Spike Learning With Local Classifiers

Backpropagation has been successfully generalized to optimize deep spiking neural networks (SNNs), where, nevertheless, gradients need to be propagated back through all layers, resulting in a massive consumption of computing resources and an obstacle to the parallelization of training. A biologically motivated scheme of local learning provides an alternative to efficiently train deep networks but often suffers a low performance of accuracy on practical tasks. Thus, how to train deep SNNs with the local learning scheme to achieve both efficient and accurate performance still remains an important challenge. In this study, we focus on a supervised local learning scheme where each layer is independently optimized with an auxiliary classifier. Accordingly, we first propose a spike-based efficient local learning rule by only considering the direct dependencies in the current time. We then propose two variants that additionally incorporate temporal dependencies through a backward and forward process, respectively. The effectiveness and performance of our proposed methods are extensively evaluated with six mainstream datasets. Experimental results show that our methods can successfully scale up to large networks and substantially outperform the spike-based local learning baselines on all studied benchmarks. Our results also reveal that gradients with temporal dependencies are essential for high performance on temporal tasks, while they have negligible effects on rate-based tasks. Our work is significant as it brings the performance of spike-based local learning to a new level with the computational benefits being retained.

Precise Spiking Motifs in Neurobiological and Neuromorphic Data

Why do neurons communicate through spikes? By definition, spikes are all-or-none neural events which occur at continuous times. In other words, spikes are on one side binary, existing or not without further details, and on the other, can occur at any asynchronous time, without the need for a centralized clock. This stands in stark contrast to the analog representation of values and the discretized timing classically used in digital processing and at the base of modern-day neural networks. As neural systems almost systematically use this so-called event-based representation in the living world, a better understanding of this phenomenon remains a fundamental challenge in neurobiology in order to better interpret the profusion of recorded data. With the growing need for intelligent embedded systems, it also emerges as a new computing paradigm to enable the efficient operation of a new class of sensors and event-based computers, called neuromorphic, which could enable significant gains in computation time and energy consumption-a major societal issue in the era of the digital economy and global warming. In this review paper, we provide evidence from biology, theory and engineering that the precise timing of spikes plays a crucial role in our understanding of the efficiency of neural networks.

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.

Synaptic delay plasticity based on frequency-switched VCSELs for optical delay-weight spiking neural networks

In this Letter, we propose an optical delay-weight spiking neural network (SNN) architecture constructed by cascaded frequency and intensity-switched vertical-cavity surface emitting lasers (VCSELs). The synaptic delay plasticity of frequency-switched VCSELs is deeply studied by numerical analysis and simulations. The principal factors related to the delay manipulation are investigated with the tunable spiking delay up to 60 ns. Moreover, a two-layer spiking neural network based on the delay-weight supervised learning algorithm is applied to a spiking sequence pattern training task and then a classification task of the Iris dataset. The proposed optical SNN provides a compact and cost-efficient solution for delay weighted computing architecture without considerations of extra programmable optical delay lines.

Biophysical Model: A Promising Method in the Study of the Mechanism of Propofol: A Narrative Review

The physiological and neuroregulatory mechanism of propofol is largely based on very limited knowledge. It is one of the important puzzling issues in anesthesiology and is of great value in both scientific and clinical fields. It is acknowledged that neural networks which are comprised of a number of neural circuits might be involved in the anesthetic mechanism. However, the mechanism of this hypothesis needs to be further elucidated. With the progress of artificial intelligence, it is more likely to solve this problem through using artificial neural networks to perform temporal waveform data analysis and to construct biophysical computational models. This review focuses on current knowledge regarding the anesthetic mechanism of propofol, an intravenous general anesthetic, by constructing biophysical computational models.