Determining the similarity between dynamical systems remains a long-standing challenge in both machine learning and neuroscience. Recent works based on Koopman operator theory have proven effective in analyzing dynamical similarity by examining discrepancies in the Koopman spectrum. Nevertheless, existing similarity metrics can be severely constrained when systems exhibit complex nonlinear behaviors across multiple temporal scales. In this work, we propose KoopSTD, a dynamical similarity measurement framework that precisely characterizes the underlying dynamics by approximating the Koopman spectrum with explicit timescale decoupling and spectral residual control. We show that KoopSTD maintains invariance under several common representation-space transformations, which ensures robust measurements across different coordinate systems. Our extensive experiments on physical and neural systems validate the effectiveness, scalability, and robustness of KoopSTD compared to existing similarity metrics. We also apply KoopSTD to explore two open-ended research questions in neuroscience and large language models, highlighting its potential to facilitate future scientific and engineering discoveries. Code is available at link.

Temporal processing is vital for extracting meaningful information from time-varying signals. Recent advancements in Spiking Neural Networks (SNNs) have shown immense promise in efficiently processing these signals. However, progress in this field has been impeded by the lack of effective and standardized benchmarks, which complicates the consistent measurement of technological advancements and limits the practical applicability of SNNs. To bridge this gap, we introduce the Neuromorphic Sequential Arena (NSA), a comprehensive benchmark that offers an effective, versatile, and application-oriented evaluation framework for neuromorphic temporal processing. The NSA includes seven real-world temporal processing tasks from a diverse range of application scenarios, each capturing rich temporal dynamics across multiple timescales. Utilizing NSA, we conduct extensive comparisons of recently introduced spiking neuron models and neural architectures, presenting comprehensive baselines in terms of task performance, training speed, memory usage, and energy efficiency. Our findings emphasize an urgent need for efficient SNN designs that can consistently deliver high performance across tasks with varying temporal complexities while maintaining low computational costs. NSA enables systematic tracking of advancements in neuromorphic algorithm research and paves the way for developing effective and efficient neuromorphic temporal processing systems.

Despite the rapid progress of neuromorphic computing, inadequate capacity and insufficient representation power of spiking neural networks (SNNs) severely restrict their application scope in practice. Residual learning and shortcuts have been evidenced as an important approach for training deep neural networks, but rarely did previous work assessed their applicability to the specifics of SNNs. In this article, we first identify that this negligence leads to impeded information flow and the accompanying degradation problem in a spiking version of vanilla ResNet. To address this issue, we propose a novel SNN-oriented residual architecture termed MS-ResNet, which establishes membrane-based shortcut pathways, and further proves that the gradient norm equality can be achieved in MS-ResNet by introducing block dynamical isometry theory, which ensures the network can be well-behaved in a depth-insensitive way. Thus, we are able to significantly extend the depth of directly trained SNNs, e.g., up to 482 layers on CIFAR-10 and 104 layers on ImageNet, without observing any slight degradation problem. To validate the effectiveness of MS-ResNet, experiments on both frame-based and neuromorphic datasets are conducted. MS-ResNet104 achieves a superior result of 76.02% accuracy on ImageNet, which is the highest to the best of our knowledge in the domain of directly trained SNNs. Great energy efficiency is also observed, with an average of only one spike per neuron needed to classify an input sample. We believe our powerful and scalable models will provide strong support for further exploration of SNNs.

As well known, the huge memory and compute costs of both artificial neural networks (ANNs) and spiking neural networks (SNNs) greatly hinder their deployment on edge devices with high efficiency. Model compression has been proposed as a promising technique to improve the running efficiency via parameter and operation reduction, whereas this technique is mainly practiced in ANNs rather than SNNs. It is interesting to answer how much an SNN model can be compressed without compromising its functionality, where two challenges should be addressed: 1) the accuracy of SNNs is usually sensitive to model compression, which requires an accurate compression methodology and 2) the computation of SNNs is event-driven rather than static, which produces an extra compression dimension on dynamic spikes. To this end, we realize a comprehensive SNN compression through three steps. First, we formulate the connection pruning and weight quantization as a constrained optimization problem. Second, we combine spatiotemporal backpropagation (STBP) and alternating direction method of multipliers (ADMMs) to solve the problem with minimum accuracy loss. Third, we further propose activity regularization to reduce the spike events for fewer active operations. These methods can be applied in either a single way for moderate compression or a joint way for aggressive compression. We define several quantitative metrics to evaluate the compression performance for SNNs. Our methodology is validated in pattern recognition tasks over MNIST, N-MNIST, CIFAR10, and CIFAR100 datasets, where extensive comparisons, analyses, and insights are provided. To the best of our knowledge, this is the first work that studies SNN compression in a comprehensive manner by exploiting all compressible components and achieves better results.

Spiking neural network (SNN) is broadly deployed in neuromorphic devices to emulate brain function. In this context, SNN security becomes important while lacking in-depth investigation. To this end, we target the adversarial attack against SNNs and identify several challenges distinct from the artificial neural network (ANN) attack: 1) current adversarial attack is mainly based on gradient information that presents in a spatiotemporal pattern in SNNs, hard to obtain with conventional backpropagation algorithms; 2) the continuous gradient of the input is incompatible with the binary spiking input during gradient accumulation, hindering the generation of spike-based adversarial examples; and 3) the input gradient can be all-zeros (i.e., vanishing) sometimes due to the zero-dominant derivative of the firing function. Recently, backpropagation through time (BPTT)-inspired learning algorithms are widely introduced into SNNs to improve the performance, which brings the possibility to attack the models accurately given spatiotemporal gradient maps. We propose two approaches to address the above challenges of gradient-input incompatibility and gradient vanishing. Specifically, we design a gradient-to-spike (G2S) converter to convert continuous gradients to ternary ones compatible with spike inputs. Then, we design a restricted spike flipper (RSF) to construct ternary gradients that can randomly flip the spike inputs with a controllable turnover rate, when meeting all-zero gradients. Putting these methods together, we build an adversarial attack methodology for SNNs. Moreover, we analyze the influence of the training loss function and the firing threshold of the penultimate layer on the attack effectiveness. Extensive experiments are conducted to validate our solution. Besides the quantitative analysis of the influence factors, we also compare SNNs and ANNs against adversarial attacks under different attack methods. This work can help reveal what happens in SNN attacks and might stimulate more research on the security of SNN models and neuromorphic devices.

Although spiking neural networks (SNNs) take benefits from the bioplausible neural modeling, the low accuracy under the common local synaptic plasticity learning rules limits their application in many practical tasks. Recently, an emerging SNN supervised learning algorithm inspired by backpropagation through time (BPTT) from the domain of artificial neural networks (ANNs) has successfully boosted the accuracy of SNNs, and helped improve the practicability of SNNs. However, current general-purpose processors suffer from low efficiency when performing BPTT for SNNs due to the ANN-tailored optimization. On the other hand, current neuromorphic chips cannot support BPTT because they mainly adopt local synaptic plasticity rules for simplified implementation. In this work, we propose H2Learn, a novel architecture that can achieve high efficiency for BPTT-based SNN learning, which ensures high accuracy of SNNs. At the beginning, we characterized the behaviors of BPTT-based SNN learning. Benefited from the binary spike-based computation in the forward pass and weight update, we first design look-up table (LUT)-based processing elements in the forward engine and weight update engine to make accumulations implicit and to fuse the computations of multiple input points. Second, benefited from the rich sparsity in the backward pass, we design a dual-sparsity-aware backward engine, which exploits both input and output sparsity. Finally, we apply a pipeline optimization between different engines to build an end-to-end solution for the BPTT-based SNN learning. Compared with the modern NVIDIA V100 GPU, H2Learn achieves$7.38\times $area saving,$5.74-10.20\times $speedup, and$5.25-7.12\times $energy saving on several benchmark datasets.

Spiking neural networks (SNNs) are promising in a bio-plausible coding for spatio-temporal information and event-driven signal processing, which is very suited for energy-efficient implementation in neuromorphic hardware. However, the unique working mode of SNNs makes them more difficult to train than traditional networks. Currently, there are two main routes to explore the training of deep SNNs with high performance. The first is to convert a pre-trained ANN model to its SNN version, which usually requires a long coding window for convergence and cannot exploit the spatio-temporal features during training for solving temporal tasks. The other is to directly train SNNs in the spatio-temporal domain. But due to the binary spike activity of the firing function and the problem of gradient vanishing or explosion, current methods are restricted to shallow architectures and thereby difficult in harnessing large-scale datasets (e.g. ImageNet). To this end, we propose a threshold-dependent batch normalization (tdBN) method based on the emerging spatio-temporal backpropagation, termed “STBP-tdBN”, enabling direct training of a very deep SNN and the efficient implementation of its inference on neuromorphic hardware. With the proposed method and elaborated shortcut connection, we significantly extend directly-trained SNNs from a shallow structure (

Biological spiking neurons with intrinsic dynamics underlie the powerful representation and learning capabilities of the brain for processing multimodal information in complex environments. Despite recent tremendous progress in spiking neural networks (SNNs) for handling Euclidean-space tasks, it still remains challenging to exploit SNNs in processing non-Euclidean-space data represented by graph data, mainly due to the lack of effective modeling framework and useful training techniques. Here we present a general spike-based modeling framework that enables the direct training of SNNs for graph learning. Through spatial-temporal unfolding for spiking data flows of node features, we incorporate graph convolution filters into spiking dynamics and formalize a synergistic learning paradigm. Considering the unique features of spike representation and spiking dynamics, we propose a spatial-temporal feature normalization (STFN) technique suitable for SNN to accelerate convergence. We instantiate our methods into two spiking graph models, including graph convolution SNNs and graph attention SNNs, and validate their performance on three node-classification benchmarks, including Cora, Citeseer, and Pubmed. Our model can achieve comparable performance with the state-of-the-art graph neural network (GNN) models with much lower computation costs, demonstrating great benefits for the execution on neuromorphic hardware and prompting neuromorphic applications in graphical scenarios.

Spiking neural networks (SNNs) that enables energy efficient implementation on emerging neuromorphic hardware are gaining more attention. Yet now, SNNs have not shown competitive performance compared with artificial neural networks (ANNs), due to the lack of effective learning algorithms and efficient programming frameworks. We address this issue from two aspects: (1) We propose a neuron normalization technique to adjust the neural selectivity and develop a direct learning algorithm for deep SNNs. (2) Via narrowing the rate coding window and converting the leaky integrate-and-fire (LIF) model into an explicitly iterative version, we present a Pytorch-based implementation method towards the training of large-scale SNNs. In this way, we are able to train deep SNNs with tens of times speedup. As a result, we achieve significantly better accuracy than the reported works on neuromorphic datasets (N-MNIST and DVSCIFAR10), and comparable accuracy as existing ANNs and pre-trained SNNs on non-spiking datasets (CIFAR10). To our best knowledge, this is the first work that demonstrates direct training of deep SNNs with high performance on CIFAR10, and the efficient implementation provides a new way to explore the potential of SNNs.