Daily Papers

Artificial Neural Networks (ANN) have gained significant popularity thanks to their ability to learn using the well-known backpropagation algorithm. Conversely, Spiking Neural Networks (SNNs), despite having broader capabilities than ANNs, have always posed challenges in the training phase. This paper shows a new method to perform supervised learning on SNNs, using Spike Timing Dependent Plasticity (STDP) and homeostasis, aiming at training the network to identify spatial patterns. Spatial patterns refer to spike patterns without a time component, where all spike events occur simultaneously. The method is tested using the SpiNNaker digital architecture. A SNN is trained to recognise one or multiple patterns and performance metrics are extracted to measure the performance of the network. Some considerations are drawn from the results showing that, in the case of a single trained pattern, the network behaves as the ideal detector, with 100% accuracy in detecting the trained pattern. However, as the number of trained patterns on a single network increases, the accuracy of identification is linked to the similarities between these patterns. This method of training an SNN to detect spatial patterns may be applied to pattern recognition in static images or traffic analysis in computer networks, where each network packet represents a spatial pattern. It will be stipulated that the homeostatic factor may enable the network to detect patterns with some degree of similarity, rather than only perfectly matching patterns.The principles outlined in this article serve as the fundamental building blocks for more complex systems that utilise both spatial and temporal patterns by converting specific features of input signals into spikes.One example of such a system is a computer network packet classifier, tasked with real-time identification of packet streams based on features within the packet content

Spiking Neural Networks (SNNs) have been widely praised for their high energy efficiency and immense potential. However, comprehensive research that critically contrasts and correlates SNNs with quantized Artificial Neural Networks (ANNs) remains scant, often leading to skewed comparisons lacking fairness towards ANNs. This paper introduces a unified perspective, illustrating that the time steps in SNNs and quantized bit-widths of activation values present analogous representations. Building on this, we present a more pragmatic and rational approach to estimating the energy consumption of SNNs. Diverging from the conventional Synaptic Operations (SynOps), we champion the "Bit Budget" concept. This notion permits an intricate discourse on strategically allocating computational and storage resources between weights, activation values, and temporal steps under stringent hardware constraints. Guided by the Bit Budget paradigm, we discern that pivoting efforts towards spike patterns and weight quantization, rather than temporal attributes, elicits profound implications for model performance. Utilizing the Bit Budget for holistic design consideration of SNNs elevates model performance across diverse data types, encompassing static imagery and neuromorphic datasets. Our revelations bridge the theoretical chasm between SNNs and quantized ANNs and illuminate a pragmatic trajectory for future endeavors in energy-efficient neural computations.

Edge AI applications increasingly require ultra-low-power, low-latency inference. Neuromorphic computing based on event-driven spiking neural networks (SNNs) offers an attractive path, but practical deployment on resource-constrained devices is limited by training difficulty, hardware-mapping overheads, and sensitivity to temporal dynamics. We present NeuEdge, a framework that combines adaptive SNN models with hardware-aware optimization for edge deployment. NeuEdge uses a temporal coding scheme that blends rate and spike-timing patterns to reduce spike activity while preserving accuracy, and a hardware-aware training procedure that co-optimizes network structure and on-chip placement to improve utilization on neuromorphic processors. An adaptive threshold mechanism adjusts neuron excitability from input statistics, reducing energy consumption without degrading performance. Across standard vision and audio benchmarks, NeuEdge achieves 91-96% accuracy with up to 2.3 ms inference latency on edge hardware and an estimated 847 GOp/s/W energy efficiency. A case study on an autonomous-drone workload shows up to 312x energy savings relative to conventional deep neural networks while maintaining real-time operation.

The current article introduces a supervised learning algorithm for multilayer spiking neural networks. The algorithm presented here overcomes some limitations of existing learning algorithms as it can be applied to neurons firing multiple spikes and it can in principle be applied to any linearisable neuron model. The algorithm is applied successfully to various benchmarks, such as the XOR problem and the Iris data set, as well as complex classifications problems. The simulations also show the flexibility of this supervised learning algorithm which permits different encodings of the spike timing patterns, including precise spike trains encoding.

Modeling invasive neural spike data is fundamental to advancing high-performance brain-computer interfaces (BCIs). However, existing approaches face critical challenges, including limited-scale heterogeneous data, cross-domain distribution shift, and the intrinsic spatiotemporal complexity of invasive neural signals. In this work, we propose UniBCI, a unified pretrained model for invasive Brain-Computer Interfaces. The model integrates three key components: (1) a context-conditioned spatio-temporal tokenization (CST) scheme that embeds neural signals together with metadata into a shared representation space; (2) a hierarchical Interval-Area Attention (IAA) mechanism that captures patterns of spike dynamics in slots via linear attention and locality dependencies via sliding-window attention; and (3) a scalable self-supervised masked signals reconstruction objective for learning generalizable neural representations from large-scale unlabeled data. We construct a pretraining corpus spanning multiple species, subjects, brain regions, and behavioral experiment paradigms. These heterogeneous recordings are standardize via our proposed unified normalization and tokenization. Comprehensive experiments demonstrate that UniBCI achieves SOTA performance across diverse downstream tasks while improving generalization. Moreover, the model achieves a strong balance between accuracy and efficiency, with fewer trainable parameters and lower inference latency. These results suggest that UniBCI provides a practical step toward general-purpose neural foundation models, enabling robust, scalable, and transferable representation learning for invasive neural data. The code for this paper is available at: https://anonymous.4open.science/r/UniBCI-C805.

Few algorithms for supervised training of spiking neural networks exist that can deal with patterns of multiple spikes, and their computational properties are largely unexplored. We demonstrate in a set of simulations that the ReSuMe learning algorithm can be successfully applied to layered neural networks. Input and output patterns are encoded as spike trains of multiple precisely timed spikes, and the network learns to transform the input trains into target output trains. This is done by combining the ReSuMe learning algorithm with multiplicative scaling of the connections of downstream neurons. We show in particular that layered networks with one hidden layer can learn the basic logical operations, including Exclusive-Or, while networks without hidden layer cannot, mirroring an analogous result for layered networks of rate neurons. While supervised learning in spiking neural networks is not yet fit for technical purposes, exploring computational properties of spiking neural networks advances our understanding of how computations can be done with spike trains.

Neurons encode information in a binary manner and process complex signals. However, predicting or generating diverse neural activity patterns remains challenging. In vitro and in vivo studies provide distinct advantages, yet no robust computational framework seamlessly integrates both data types. We address this by applying the Transformer model, widely used in large-scale language models, to neural data. To handle binary data, we introduced Dice loss, enabling accurate cross-domain neural activity generation. Structural analysis revealed how Dice loss enhances learning and identified key brain regions facilitating high-precision data generation. Our findings support the 3Rs principle in animal research, particularly Replacement, and establish a mathematical framework bridging animal experiments and human clinical studies. This work advances data-driven neuroscience and neural activity modeling, paving the way for more ethical and effective experimental methodologies.

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.

Recently, interest has grown in exploring the hypothesis that neural activity conveys information through precise spiking motifs. To investigate this phenomenon, various algorithms have been proposed to detect such motifs in Single Unit Activity (SUA) recorded from populations of neurons. In this study, we present a novel detection model based on the inversion of a generative model of raster plot synthesis. Using this generative model, we derive an optimal detection procedure that takes the form of logistic regression combined with temporal convolution. A key advantage of this model is its differentiability, which allows us to formulate a supervised learning approach using a gradient descent on the binary cross-entropy loss. To assess the model's ability to detect spiking motifs in synthetic data, we first perform numerical evaluations. This analysis highlights the advantages of using spiking motifs over traditional firing rate based population codes. We then successfully demonstrate that our learning method can recover synthetically generated spiking motifs, indicating its potential for further applications. In the future, we aim to extend this method to real neurobiological data, where the ground truth is unknown, to explore and detect spiking motifs in a more natural and biologically relevant context.

Spiking neural networks (SNNs) represent a promising approach to developing artificial neural networks that are both energy-efficient and biologically plausible. However, applying SNNs to sequential tasks, such as text classification and time-series forecasting, has been hindered by the challenge of creating an effective and hardware-friendly spike-form positional encoding (PE) strategy. Drawing inspiration from the central pattern generators (CPGs) in the human brain, which produce rhythmic patterned outputs without requiring rhythmic inputs, we propose a novel PE technique for SNNs, termed CPG-PE. We demonstrate that the commonly used sinusoidal PE is mathematically a specific solution to the membrane potential dynamics of a particular CPG. Moreover, extensive experiments across various domains, including time-series forecasting, natural language processing, and image classification, show that SNNs with CPG-PE outperform their conventional counterparts. Additionally, we perform analysis experiments to elucidate the mechanism through which SNNs encode positional information and to explore the function of CPGs in the human brain. This investigation may offer valuable insights into the fundamental principles of neural computation. Our code is available at https://github.com/microsoft/SeqSNN.

Legged locomotion is a challenging task in the field of robotics but a rather simple one in nature. This motivates the use of biological methodologies as solutions to this problem. Central pattern generators are neural networks that are thought to be responsible for locomotion in humans and some animal species. As for robotics, many attempts were made to reproduce such systems and use them for a similar goal. One interesting design model is based on spiking neural networks. This model is the main focus of this work, as its contribution is not limited to engineering but also applicable to neuroscience. This paper introduces a new general framework for building central pattern generators that are task-independent, biologically plausible, and rely on learning methods. The abilities and properties of the presented approach are not only evaluated in simulation but also in a robotic experiment. The results are very promising as the used robot was able to perform stable walking at different speeds and to change speed within the same gait cycle.

Coronaviruses are membrane-enveloped, non-segmented positive-strand RNA viruses belonging to the Coronaviridae family. Various animal species, mainly mammalian and avian, are severely infected by various coronaviruses, causing serious concerns like the recent pandemic (COVID-19). Therefore, building a deeper understanding of these viruses is essential to devise prevention and mitigation mechanisms. In the Coronavirus genome, an essential structural region is the spike region, and it's responsible for attaching the virus to the host cell membrane. Therefore, the usage of only the spike protein, instead of the full genome, provides most of the essential information for performing analyses such as host classification. In this paper, we propose a novel method for predicting the host specificity of coronaviruses by analyzing spike protein sequences from different viral subgenera and species. Our method involves using the Poisson correction distance to generate a distance matrix, followed by using a radial basis function (RBF) kernel and kernel principal component analysis (PCA) to generate a low-dimensional embedding. Finally, we apply classification algorithms to the low-dimensional embedding to generate the resulting predictions of the host specificity of coronaviruses. We provide theoretical proofs for the non-negativity, symmetry, and triangle inequality properties of the Poisson correction distance metric, which are important properties in a machine-learning setting. By encoding the spike protein structure and sequences using this comprehensive approach, we aim to uncover hidden patterns in the biological sequences to make accurate predictions about host specificity. Finally, our classification results illustrate that our method can achieve higher predictive accuracy and improve performance over existing baselines.

Brain-computer interfaces (BCIs), transform neural signals in the brain into in-structions to control external devices. However, obtaining sufficient training data is difficult as well as limited. With the advent of advanced machine learning methods, the capability of brain-computer interfaces has been enhanced like never before, however, these methods require a large amount of data for training and thus require data augmentation of the limited data available. Here, we use spiking neural networks (SNN) as data generators. It is touted as the next-generation neu-ral network and is considered as one of the algorithms oriented to general artifi-cial intelligence because it borrows the neural information processing from bio-logical neurons. We use the SNN to generate neural spike information that is bio-interpretable and conforms to the intrinsic patterns in the original neural data. Ex-periments show that the model can directly synthesize new spike trains, which in turn improves the generalization ability of the BCI decoder. Both the input and output of the spiking neural model are spike information, which is a brain-inspired intelligence approach that can be better integrated with BCI in the future.

Spiking Neural Networks (SNNs) are highly efficient due to their spike-based activation, which inherently produces bit-sparse computation patterns. Existing hardware implementations of SNNs leverage this sparsity pattern to avoid wasteful zero-value computations, yet this approach fails to fully capitalize on the potential efficiency of SNNs. This study introduces a novel sparsity paradigm called Product Sparsity, which leverages combinatorial similarities within matrix multiplication operations to reuse the inner product result and reduce redundant computations. Product Sparsity significantly enhances sparsity in SNNs without compromising the original computation results compared to traditional bit sparsity methods. For instance, in the SpikeBERT SNN model, Product Sparsity achieves a density of only 1.23% and reduces computation by 11times, compared to bit sparsity, which has a density of 13.19%. To efficiently implement Product Sparsity, we propose Prosperity, an architecture that addresses the challenges of identifying and eliminating redundant computations in real-time. Compared to prior SNN accelerator PTB and the A100 GPU, Prosperity achieves an average speedup of 7.4times and 1.8times, respectively, along with energy efficiency improvements of 8.0times and 193times, respectively. The code for Prosperity is available at https://github.com/dubcyfor3/Prosperity.

Across many scientific fields, measurements often represent the number of times an event occurs. For example, a document can be represented by word occurrence counts, neural activity by spike counts per time window, or online communication by daily email counts. These measurements yield high-dimensional count data that often approximate a Poisson distribution, frequently with low rates that produce substantial sparsity and complicate downstream analysis. A useful approach is to embed the data into a low-dimensional space that preserves meaningful structure, commonly termed dimensionality reduction. Yet existing dimensionality reduction methods, including both linear (e.g., PCA) and nonlinear approaches (e.g., t-SNE), often assume continuous Euclidean geometry, thereby misaligning with the discrete, sparse nature of low-rate count data. Here, we propose p-SNE (Poisson Stochastic Neighbor Embedding), a nonlinear neighbor embedding method designed around the Poisson structure of count data, using KL divergence between Poisson distributions to measure pairwise dissimilarity and Hellinger distance to optimize the embedding. We test p-SNE on synthetic Poisson data and demonstrate its ability to recover meaningful structure in real-world count datasets, including weekday patterns in email communication, research area clusters in OpenReview papers, and temporal drift and stimulus gradients in neural spike recordings.

Learning synaptic weights of spiking neural network (SNN) models that can reproduce target spike trains from provided neural firing data is a central problem in computational neuroscience and spike-based computing. The discovery of the optimal weight values can be posed as a supervised learning task wherein the weights of the model network are chosen to maximize the similarity between the target spike trains and the model outputs. It is still largely unknown whether optimizing spike train similarity of highly recurrent SNNs produces weight matrices similar to those of the ground truth model. To this end, we propose flexible heuristic supervised learning rules, termed Pre-Synaptic Pool Modification (PSPM), that rely on stochastic weight updates in order to produce spikes within a short window of the desired times and eliminate spikes outside of this window. PSPM improves spike train similarity for all-to-all SNNs and makes no assumption about the post-synaptic potential of the neurons or the structure of the network since no gradients are required. We test whether optimizing for spike train similarity entails the discovery of accurate weights and explore the relative contributions of local and homeostatic weight updates. Although PSPM improves similarity between spike trains, the learned weights often differ from the weights of the ground truth model, implying that connectome inference from spike data may require additional constraints on connectivity statistics. We also find that spike train similarity is sensitive to local updates, but other measures of network activity such as avalanche distributions, can be learned through synaptic homeostasis.

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g. naturalistic) stimulus distribution, we review several inference methods, focussing in particular on two information-theory-based approaches (maximization of stimulus energy or of noise entropy) and a likelihood-based approach (Bayesian spike-triggered covariance, extensions of generalized linear models). We analyze the formal connection between the likelihood-based and information-based approaches to show how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

The brain is the perfect place to look for inspiration to develop more efficient neural networks. The inner workings of our synapses and neurons provide a glimpse at what the future of deep learning might look like. This paper serves as a tutorial and perspective showing how to apply the lessons learnt from several decades of research in deep learning, gradient descent, backpropagation and neuroscience to biologically plausible spiking neural neural networks. We also explore the delicate interplay between encoding data as spikes and the learning process; the challenges and solutions of applying gradient-based learning to spiking neural networks (SNNs); the subtle link between temporal backpropagation and spike timing dependent plasticity, and how deep learning might move towards biologically plausible online learning. Some ideas are well accepted and commonly used amongst the neuromorphic engineering community, while others are presented or justified for the first time here. The fields of deep learning and spiking neural networks evolve very rapidly. We endeavour to treat this document as a 'dynamic' manuscript that will continue to be updated as the common practices in training SNNs also change. A series of companion interactive tutorials complementary to this paper using our Python package, snnTorch, are also made available. See https://snntorch.readthedocs.io/en/latest/tutorials/index.html .

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.

Spiking neural networks (SNNs) possess energy-efficient potential due to event-based computation. However, supervised training of SNNs remains a challenge as spike activities are non-differentiable. Previous SNNs training methods can be generally categorized into two basic classes, i.e., backpropagation-like training methods and plasticity-based learning methods. The former methods are dependent on energy-inefficient real-valued computation and non-local transmission, as also required in artificial neural networks (ANNs), whereas the latter are either considered to be biologically implausible or exhibit poor performance. Hence, biologically plausible (bio-plausible) high-performance supervised learning (SL) methods for SNNs remain deficient. In this paper, we proposed a novel bio-plausible SNN model for SL based on the symmetric spike-timing dependent plasticity (sym-STDP) rule found in neuroscience. By combining the sym-STDP rule with bio-plausible synaptic scaling and intrinsic plasticity of the dynamic threshold, our SNN model implemented SL well and achieved good performance in the benchmark recognition task (MNIST dataset). To reveal the underlying mechanism of our SL model, we visualized both layer-based activities and synaptic weights using the t-distributed stochastic neighbor embedding (t-SNE) method after training and found that they were well clustered, thereby demonstrating excellent classification ability. Furthermore, to verify the robustness of our model, we trained it on another more realistic dataset (Fashion-MNIST), which also showed good performance. As the learning rules were bio-plausible and based purely on local spike events, our model could be easily applied to neuromorphic hardware for online training and may be helpful for understanding SL information processing at the synaptic level in biological neural systems.

Spiking Neural Networks (SNNs) are a promising research direction for building power-efficient information processing systems, especially for temporal tasks such as speech recognition. In SNNs, delays refer to the time needed for one spike to travel from one neuron to another. These delays matter because they influence the spike arrival times, and it is well-known that spiking neurons respond more strongly to coincident input spikes. More formally, it has been shown theoretically that plastic delays greatly increase the expressivity in SNNs. Yet, efficient algorithms to learn these delays have been lacking. Here, we propose a new discrete-time algorithm that addresses this issue in deep feedforward SNNs using backpropagation, in an offline manner. To simulate delays between consecutive layers, we use 1D convolutions across time. The kernels contain only a few non-zero weights - one per synapse - whose positions correspond to the delays. These positions are learned together with the weights using the recently proposed Dilated Convolution with Learnable Spacings (DCLS). We evaluated our method on three datasets: the Spiking Heidelberg Dataset (SHD), the Spiking Speech Commands (SSC) and its non-spiking version Google Speech Commands v0.02 (GSC) benchmarks, which require detecting temporal patterns. We used feedforward SNNs with two or three hidden fully connected layers, and vanilla leaky integrate-and-fire neurons. We showed that fixed random delays help and that learning them helps even more. Furthermore, our method outperformed the state-of-the-art in the three datasets without using recurrent connections and with substantially fewer parameters. Our work demonstrates the potential of delay learning in developing accurate and precise models for temporal data processing. Our code is based on PyTorch / SpikingJelly and available at: https://github.com/Thvnvtos/SNN-delays

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least 1-δ, where δ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

Spiking neural networks (SNNs), inspired by the spiking behavior of biological neurons, provide a unique pathway for capturing the intricacies of temporal data. However, applying SNNs to time-series forecasting is challenging due to difficulties in effective temporal alignment, complexities in encoding processes, and the absence of standardized guidelines for model selection. In this paper, we propose a framework for SNNs in time-series forecasting tasks, leveraging the efficiency of spiking neurons in processing temporal information. Through a series of experiments, we demonstrate that our proposed SNN-based approaches achieve comparable or superior results to traditional time-series forecasting methods on diverse benchmarks with much less energy consumption. Furthermore, we conduct detailed analysis experiments to assess the SNN's capacity to capture temporal dependencies within time-series data, offering valuable insights into its nuanced strengths and effectiveness in modeling the intricate dynamics of temporal data. Our study contributes to the expanding field of SNNs and offers a promising alternative for time-series forecasting tasks, presenting a pathway for the development of more biologically inspired and temporally aware forecasting models. Our code is available at https://github.com/microsoft/SeqSNN.

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

Nowadays, neural networks act as a synonym for artificial intelligence. Present neural network models, although remarkably powerful, are inefficient both in terms of data and energy. Several alternative forms of neural networks have been proposed to address some of these problems. Specifically, spiking neural networks are suitable for efficient hardware implementations. However, effective learning algorithms for spiking networks remain elusive, although it is suspected that effective plasticity mechanisms could alleviate the problem of data efficiency. Here, we present a new framework for spiking neural networks - Spark - built upon the idea of modular design, from simple components to entire models. The aim of this framework is to provide an efficient and streamlined pipeline for spiking neural networks. We showcase this framework by solving the sparse-reward cartpole problem with simple plasticity mechanisms. We hope that a framework compatible with traditional ML pipelines may accelerate research in the area, specifically for continuous and unbatched learning, akin to the one animals exhibit.

Spiking Neural Networks (SNNs) have emerged as an energy-efficient alternative to conventional neural networks, demonstrating strong performance in computer vision and robotics. More recently, SNNs have been applied to time series forecasting (TSF), with methods exploring spiking temporal backbones, spike-compatible positional encodings, Fourier-domain processing, and redesigned neuron dynamics. However, existing SNN forecasting approaches process variables independently, lacking explicit mechanisms for modeling inter-variable dependencies. This is a critical limitation in multivariate settings, where cross-variable correlations carry substantial predictive information. We propose Spiking Fourier Graph Operators (SpikF-GO), which addresses this gap by combining a hypervariate graph formulation in which every scalar observation becomes a graph node with spike-driven spectral processing. SpikF-GO introduces a Hard Concrete frequency gate for learnable sparse frequency selection and a Complex LIF gate that applies independent spiking neurons to real and imaginary Fourier components, preserving binary, event-driven computation throughout the spectral domain. We further present a variant incorporating Central Pattern Generator-based positional encodings for stronger long-range temporal modeling. Evaluated on eight benchmarks under a unified experimental protocol, SpikF-GO achieves the best average rank among all SNN methods and outperforms its ANN counterpart, FourierGNN, at reduced energy cost. SpikF-GO maintains competitive accuracy even at substantially smaller embedding dimensions, thereby achieving significant energy reductions. To our knowledge, this is among the first works to bring graph-based multivariate modeling into the spiking domain for TSF and the first to provide a unified comparison across SNN forecasting architectures under a common experimental protocol.

This study examines the integration of Contrastive Predictive Coding (CPC) with Spiking Neural Networks (SNN). While CPC learns the predictive structure of data to generate meaningful representations, SNN mimics the computational processes of biological neural systems over time. In this study, the goal is to develop a predictive coding model with greater biological plausibility by processing inputs and outputs in a spike-based system. The proposed model was tested on the MNIST dataset and achieved a high classification rate in distinguishing positive sequential samples from non-sequential negative samples. The study demonstrates that CPC can be effectively combined with SNN, showing that an SNN trained for classification tasks can also function as an encoding mechanism. Project codes and detailed results can be accessed on our GitHub page: https://github.com/vnd-ogrenme/ongorusel-kodlama/tree/main/CPC_SNN

Spiking Neural Networks (SNNs) are well known as a promising energy-efficient alternative to conventional artificial neural networks. Subject to the preconceived impression that SNNs are sparse firing, the analysis and optimization of inherent redundancy in SNNs have been largely overlooked, thus the potential advantages of spike-based neuromorphic computing in accuracy and energy efficiency are interfered. In this work, we pose and focus on three key questions regarding the inherent redundancy in SNNs. We argue that the redundancy is induced by the spatio-temporal invariance of SNNs, which enhances the efficiency of parameter utilization but also invites lots of noise spikes. Further, we analyze the effect of spatio-temporal invariance on the spatio-temporal dynamics and spike firing of SNNs. Then, motivated by these analyses, we propose an Advance Spatial Attention (ASA) module to harness SNNs' redundancy, which can adaptively optimize their membrane potential distribution by a pair of individual spatial attention sub-modules. In this way, noise spike features are accurately regulated. Experimental results demonstrate that the proposed method can significantly drop the spike firing with better performance than state-of-the-art SNN baselines. Our code is available in https://github.com/BICLab/ASA-SNN.

Extracellular recordings are transient voltage fluctuations in the vicinity of neurons, serving as a fundamental modality in neuroscience for decoding brain activity at single-neuron resolution. Spike sorting, the process of attributing each detected spike to its corresponding neuron, is a pivotal step in brain sensing pipelines. However, it remains challenging under low signal-to-noise ratio (SNR), electrode drift and cross-session variability. In this paper, we propose HuiduRep, a robust self-supervised representation learning framework that extracts discriminative and generalizable features from extracellular recordings. By integrating contrastive learning with a denoising autoencoder, HuiduRep learns latent representations that are robust to noise and drift. With HuiduRep, we develop a spike sorting pipeline that clusters spike representations without ground truth labels. Experiments on hybrid and real-world datasets demonstrate that HuiduRep achieves strong robustness. Furthermore, the pipeline outperforms state-of-the-art tools such as KiloSort4 and MountainSort5. These findings demonstrate the potential of self-supervised spike representation learning as a foundational tool for robust and generalizable processing of extracellular recordings. Code is available at: https://github.com/IgarashiAkatuki/HuiduRep

Spiking neural networks (SNN) are a biologically inspired model of neural networks with certain brain-like properties. In the past few decades, this model has received increasing attention in computer science community, owing also to the successful phenomenon of deep learning. In SNN, communication between neurons takes place through the spikes and spike trains. This differentiates these models from the ``standard'' artificial neural networks (ANN) where the frequency of spikes is replaced by real-valued signals. Spiking neural P systems (SNPS) can be considered a branch of SNN based more on the principles of formal automata, with many variants developed within the framework of the membrane computing theory. In this paper, we first briefly compare structure and function, advantages and drawbacks of SNN and SNPS. A key part of the article is a survey of recent results and applications of machine learning and deep learning models of both SNN and SNPS formalisms.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

Spiking Neural Networks (SNNs) are computational models inspired by the structure and dynamics of biological neuronal networks. Their event-driven nature enables them to achieve high energy efficiency, particularly when deployed on neuromorphic hardware platforms. Unlike conventional Artificial Neural Networks (ANNs), which primarily rely on layered architectures, SNNs naturally support a wide range of connectivity patterns, from traditional layered structures to small-world graphs characterized by locally dense and globally sparse connections. In this work, we introduce NeuroCoreX, an FPGA-based emulator designed for the flexible co-design and testing of SNNs. NeuroCoreX supports all-to-all connectivity, providing the capability to implement diverse network topologies without architectural restrictions. It features a biologically motivated local learning mechanism based on Spike-Timing-Dependent Plasticity (STDP). The neuron model implemented within NeuroCoreX is the Leaky Integrate-and-Fire (LIF) model, with current-based synapses facilitating spike integration and transmission . A Universal Asynchronous Receiver-Transmitter (UART) interface is provided for programming and configuring the network parameters, including neuron, synapse, and learning rule settings. Users interact with the emulator through a simple Python-based interface, streamlining SNN deployment from model design to hardware execution. NeuroCoreX is released as an open-source framework, aiming to accelerate research and development in energy-efficient, biologically inspired computing.

Loss spikes commonly emerge during neural network training with the Adam optimizer across diverse architectures and scales, yet their underlying mechanism remains elusive. While previous explanations attribute these phenomena to sharper loss landscapes at lower loss, we show that landscape geometry alone is insufficient to explain the phenomenon. In this work, we pinpoint the root cause in the internal dynamics of Adam's second moment estimator. We identify a critical ``decoupling'' mechanism where the adaptive preconditioner v_t fails to track the instantaneous squared gradients g_t^2, causing the adaptive mechanism to effectively fail. This decoupling allows the preconditioner to decay autonomously despite rising gradients, which pushes the maximum eigenvalue of the preconditioned Hessian beyond the stability threshold 2/η for sustained periods, manifesting as dramatic loss spikes. Through a quadratic approximation analysis, we theoretically and experimentally characterize five distinct stages of spike evolution and propose a predictor for anticipating spikes based on gradient-directional curvature. We empirically find that the proposed loss spike mechanism, although derived from simplified models, generalizes well to practical scenarios ranging from small neural networks to large-scale Transformers.

Modern neural recording techniques allow neuroscientists to obtain spiking activity of multiple neurons from different brain regions over long time periods, which requires new statistical methods to be developed for understanding structure of the large-scale data. In this paper, we develop a bi-clustering method to cluster the neural spiking activity spatially and temporally, according to their low-dimensional latent structures. The spatial (neuron) clusters are defined by the latent trajectories within each neural population, while the temporal (state) clusters are defined by (populationally) synchronous local linear dynamics shared with different periods. To flexibly extract the bi-clustering structure, we build the model non-parametrically, and develop an efficient Markov chain Monte Carlo (MCMC) algorithm to sample the posterior distributions of model parameters. Validating our proposed MCMC algorithm through simulations, we find the method can recover unknown parameters and true bi-clustering structures successfully. We then apply the proposed bi-clustering method to multi-regional neural recordings under different experiment settings, where we find that simultaneously considering latent trajectories and spatial-temporal clustering structures can provide us with a more accurate and interpretable result. Overall, the proposed method provides scientific insights for large-scale (counting) time series with elongated recording periods, and it can potentially have application beyond neuroscience.

Emergence of deep neural networks (DNNs) has raised enormous attention towards artificial neural networks (ANNs) once again. They have become the state-of-the-art models and have won different machine learning challenges. Although these networks are inspired by the brain, they lack biological plausibility, and they have structural differences compared to the brain. Spiking neural networks (SNNs) have been around for a long time, and they have been investigated to understand the dynamics of the brain. However, their application in real-world and complicated machine learning tasks were limited. Recently, they have shown great potential in solving such tasks. Due to their energy efficiency and temporal dynamics there are many promises in their future development. In this work, we reviewed the structures and performances of SNNs on image classification tasks. The comparisons illustrate that these networks show great capabilities for more complicated problems. Furthermore, the simple learning rules developed for SNNs, such as STDP and R-STDP, can be a potential alternative to replace the backpropagation algorithm used in DNNs.

This study introduces a novel approach by replacing the traditional perceptron neuron model with a biologically inspired probabilistic meta neuron, where the internal neuron parameters are jointly learned, leading to improved classification accuracy of spiking neural networks (SNNs). To validate this innovation, we implement and compare two SNN architectures: one based on standard leaky integrate-and-fire (LIF) neurons and another utilizing the proposed probabilistic meta neuron model. As a second key contribution, we present a new biologically inspired classification framework that uniquely integrates SNNs with Lempel-Ziv complexity (LZC) a measure closely related to entropy rate. By combining the temporal precision and biological plausibility of SNNs with the capacity of LZC to capture structural regularity, the proposed approach enables efficient and interpretable classification of spatiotemporal neural data, an aspect not addressed in existing works. We consider learning algorithms such as backpropagation, spike-timing-dependent plasticity (STDP), and the Tempotron learning rule. To explore neural dynamics, we use Poisson processes to model neuronal spike trains, a well-established method for simulating the stochastic firing behavior of biological neurons. Our results reveal that depending on the training method, the classifier's efficiency can improve by up to 11.00%, highlighting the advantage of learning additional neuron parameters beyond the traditional focus on weighted inputs alone.

Spiking Neural Networks (SNNs) offer a promising, biologically inspired approach for processing spatiotemporal data, particularly for time series forecasting. However, conventional neuron models like the Leaky Integrate-and-Fire (LIF) struggle to capture long-term dependencies and effectively process multi-scale temporal dynamics. To overcome these limitations, we introduce the Temporal Segment Leaky Integrate-and-Fire (TS-LIF) model, featuring a novel dual-compartment architecture. The dendritic and somatic compartments specialize in capturing distinct frequency components, providing functional heterogeneity that enhances the neuron's ability to process both low- and high-frequency information. Furthermore, the newly introduced direct somatic current injection reduces information loss during intra-neuronal transmission, while dendritic spike generation improves multi-scale information extraction. We provide a theoretical stability analysis of the TS-LIF model and explain how each compartment contributes to distinct frequency response characteristics. Experimental results show that TS-LIF outperforms traditional SNNs in time series forecasting, demonstrating better accuracy and robustness, even with missing data. TS-LIF advances the application of SNNs in time-series forecasting, providing a biologically inspired approach that captures complex temporal dynamics and offers potential for practical implementation in diverse forecasting scenarios. The source code is available at https://github.com/kkking-kk/TS-LIF.

Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. We model streams of discrete events in continuous time, by constructing a neurally self-modulating multivariate point process in which the intensities of multiple event types evolve according to a novel continuous-time LSTM. This generative model allows past events to influence the future in complex and realistic ways, by conditioning future event intensities on the hidden state of a recurrent neural network that has consumed the stream of past events. Our model has desirable qualitative properties. It achieves competitive likelihood and predictive accuracy on real and synthetic datasets, including under missing-data conditions.

We introduce a mathematically rigorous framework based on rough path theory to model stochastic spiking neural networks (SSNNs) as stochastic differential equations with event discontinuities (Event SDEs) and driven by c\`adl\`ag rough paths. Our formalism is general enough to allow for potential jumps to be present both in the solution trajectories as well as in the driving noise. We then identify a set of sufficient conditions ensuring the existence of pathwise gradients of solution trajectories and event times with respect to the network's parameters and show how these gradients satisfy a recursive relation. Furthermore, we introduce a general-purpose loss function defined by means of a new class of signature kernels indexed on c\`adl\`ag rough paths and use it to train SSNNs as generative models. We provide an end-to-end autodifferentiable solver for Event SDEs and make its implementation available as part of the diffrax library. Our framework is, to our knowledge, the first enabling gradient-based training of SSNNs with noise affecting both the spike timing and the network's dynamics.

As the prevalence of Alzheimer's disease (AD) rises, improving mechanistic insight from non-invasive biomarkers is increasingly critical. Recent work suggests that circuit-level brain alterations manifest as changes in electroencephalography (EEG) spectral features detectable by machine learning. However, conventional deep learning approaches for EEG-based AD detection are computationally intensive and mechanistically opaque. Spiking neural networks (SNNs) offer a biologically plausible and energy-efficient alternative, yet their application to AD diagnosis remains largely unexplored. We propose a neuro-bridge framework that links data-driven learning with minimal, biophysically grounded simulations, enabling bidirectional interpretation between machine learning signatures and circuit-level mechanisms in AD. Using resting-state clinical EEG, we train an SNN classifier that achieves competitive performance (AUC = 0.839) and identifies the aperiodic 1/f slope as a key discriminative marker. The 1/f slope reflects excitation-inhibition balance. To interpret this mechanistically, we construct spiking network simulations in which inhibitory-to-excitatory synaptic ratios are systematically varied to emulate healthy, mild cognitive impairment, and AD-like states. Using both membrane potential-based and synaptic current-based EEG proxies, we reproduce empirical spectral slowing and altered alpha organization. Incorporating empirical functional connectivity priors into multi-subnetwork simulations further enhances spectral differentiation, demonstrating that large-scale network topology constrains EEG signatures more strongly than excitation-inhibition balance alone. Overall, this neuro-bridge approach connects SNN-based classification with interpretable circuit simulations, advancing mechanistic understanding of EEG biomarkers while enabling scalable, explainable AD detection.

Motivated by the celebrated discrete-time model of nervous activity outlined by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the McCulloch-Pitts network (MPN), for sequence learning in spiking neural networks. Our model has a local learning rule, such that the synaptic weight updates depend only on the information directly accessible by the synapse. By exploiting asymmetry in the connections between binary neurons, we show that MPN can be trained to robustly memorize multiple spatiotemporal patterns of binary vectors, generalizing the ability of the symmetric Hopfield network to memorize static spatial patterns. In addition, we demonstrate that the model can efficiently learn sequences of binary pictures as well as generative models for experimental neural spike-train data. Our learning rule is consistent with spike-timing-dependent plasticity (STDP), thus providing a theoretical ground for the systematic design of biologically inspired networks with large and robust long-range sequence storage capacity.

This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability, the descendant patterns exponentially drift away from ancestral patterns, even when the automaton is deterministic. While this is far from being the first instance of evolutionary dynamics in a cellular automaton, it is the first to do so by exploiting the power and convenience of Neural Cellular Automata, arguably increasing the space of variations and the opportunity for Open Ended Evolution.

The Backpropagation algorithm has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, the recently introduced Forward-Forward algorithm replaces the forward and backward passes of Backpropagation with two forward passes. In this work, we show that the internal representations obtained by the Forward-Forward algorithm can organise into category-specific ensembles exhibiting high sparsity -- composed of a low number of active units. This situation is reminiscent of what has been observed in cortical sensory areas, where neuronal ensembles are suggested to serve as the functional building blocks for perception and action. Interestingly, while this sparse pattern does not typically arise in models trained with standard Backpropagation, it can emerge in networks trained with Backpropagation on the same objective proposed for the Forward-Forward algorithm.

Spiking neural networks (SNNs) are brain-inspired machine learning algorithms with merits such as biological plausibility and unsupervised learning capability. Previous works have shown that converting Artificial Neural Networks (ANNs) into SNNs is a practical and efficient approach for implementing an SNN. However, the basic principle and theoretical groundwork are lacking for training a non-accuracy-loss SNN. This paper establishes a precise mathematical mapping between the biological parameters of the Linear Leaky-Integrate-and-Fire model (LIF)/SNNs and the parameters of ReLU-AN/Deep Neural Networks (DNNs). Such mapping relationship is analytically proven under certain conditions and demonstrated by simulation and real data experiments. It can serve as the theoretical basis for the potential combination of the respective merits of the two categories of neural networks.

Spiking Neural Networks (SNNs) provide an energy-efficient way to extract 3D spatio-temporal features. Point clouds are sparse 3D spatial data, which suggests that SNNs should be well-suited for processing them. However, when applying SNNs to point clouds, they often exhibit limited performance and fewer application scenarios. We attribute this to inappropriate preprocessing and feature extraction methods. To address this issue, we first introduce the Spike Voxel Coding (SVC) scheme, which encodes the 3D point clouds into a sparse spike train space, reducing the storage requirements and saving time on point cloud preprocessing. Then, we propose a Spike Sparse Convolution (SSC) model for efficiently extracting 3D sparse point cloud features. Combining SVC and SSC, we design an efficient 3D SNN backbone (E-3DSNN), which is friendly with neuromorphic hardware. For instance, SSC can be implemented on neuromorphic chips with only minor modifications to the addressing function of vanilla spike convolution. Experiments on ModelNet40, KITTI, and Semantic KITTI datasets demonstrate that E-3DSNN achieves state-of-the-art (SOTA) results with remarkable efficiency. Notably, our E-3DSNN (1.87M) obtained 91.7\% top-1 accuracy on ModelNet40, surpassing the current best SNN baselines (14.3M) by 3.0\%. To our best knowledge, it is the first direct training 3D SNN backbone that can simultaneously handle various 3D computer vision tasks (e.g., classification, detection, and segmentation) with an event-driven nature. Code is available: https://github.com/bollossom/E-3DSNN/.

Compared with rate-based artificial neural networks, Spiking Neural Networks (SNN) provide a more biological plausible model for the brain. But how they perform supervised learning remains elusive. Inspired by recent works of Bengio et al., we propose a supervised learning algorithm based on Spike-Timing Dependent Plasticity (STDP) for a hierarchical SNN consisting of Leaky Integrate-and-fire (LIF) neurons. A time window is designed for the presynaptic neuron and only the spikes in this window take part in the STDP updating process. The model is trained on the MNIST dataset. The classification accuracy approach that of a Multilayer Perceptron (MLP) with similar architecture trained by the standard back-propagation algorithm.

In recent years, deep learning has been a revolution in the field of machine learning, for computer vision in particular. In this approach, a deep (multilayer) artificial neural network (ANN) is trained in a supervised manner using backpropagation. Huge amounts of labeled examples are required, but the resulting classification accuracy is truly impressive, sometimes outperforming humans. Neurons in an ANN are characterized by a single, static, continuous-valued activation. Yet biological neurons use discrete spikes to compute and transmit information, and the spike times, in addition to the spike rates, matter. Spiking neural networks (SNNs) are thus more biologically realistic than ANNs, and arguably the only viable option if one wants to understand how the brain computes. SNNs are also more hardware friendly and energy-efficient than ANNs, and are thus appealing for technology, especially for portable devices. However, training deep SNNs remains a challenge. Spiking neurons' transfer function is usually non-differentiable, which prevents using backpropagation. Here we review recent supervised and unsupervised methods to train deep SNNs, and compare them in terms of accuracy, but also computational cost and hardware friendliness. The emerging picture is that SNNs still lag behind ANNs in terms of accuracy, but the gap is decreasing, and can even vanish on some tasks, while the SNNs typically require much fewer operations.

Spiking neural networks (SNNs) are well suited for spatio-temporal learning and implementations on energy-efficient event-driven neuromorphic processors. However, existing SNN error backpropagation (BP) methods lack proper handling of spiking discontinuities and suffer from low performance compared with the BP methods for traditional artificial neural networks. In addition, a large number of time steps are typically required to achieve decent performance, leading to high latency and rendering spike-based computation unscalable to deep architectures. We present a novel Temporal Spike Sequence Learning Backpropagation (TSSL-BP) method for training deep SNNs, which breaks down error backpropagation across two types of inter-neuron and intra-neuron dependencies and leads to improved temporal learning precision. It captures inter-neuron dependencies through presynaptic firing times by considering the all-or-none characteristics of firing activities and captures intra-neuron dependencies by handling the internal evolution of each neuronal state in time. TSSL-BP efficiently trains deep SNNs within a much shortened temporal window of a few steps while improving the accuracy for various image classification datasets including CIFAR10.

Spiking neural networks (SNNs) are rich in spatio-temporal dynamics and are suitable for processing event-based neuromorphic data. However, event-based datasets are usually less annotated than static datasets. This small data scale makes SNNs prone to overfitting and limits their performance. In order to improve the generalization ability of SNNs on event-based datasets, we use static images to assist SNN training on event data. In this paper, we first discuss the domain mismatch problem encountered when directly transferring networks trained on static datasets to event data. We argue that the inconsistency of feature distributions becomes a major factor hindering the effective transfer of knowledge from static images to event data. To address this problem, we propose solutions in terms of two aspects: feature distribution and training strategy. Firstly, we propose a knowledge transfer loss, which consists of domain alignment loss and spatio-temporal regularization. The domain alignment loss learns domain-invariant spatial features by reducing the marginal distribution distance between the static image and the event data. Spatio-temporal regularization provides dynamically learnable coefficients for domain alignment loss by using the output features of the event data at each time step as a regularization term. In addition, we propose a sliding training strategy, which gradually replaces static image inputs probabilistically with event data, resulting in a smoother and more stable training for the network. We validate our method on neuromorphic datasets, including N-Caltech101, CEP-DVS, and N-Omniglot. The experimental results show that our proposed method achieves better performance on all datasets compared to the current state-of-the-art methods. Code is available at https://github.com/Brain-Cog-Lab/Transfer-for-DVS.

The Spiking Neural Network (SNN) has attracted more and more attention recently. It adopts binary spike signals to transmit information. Benefitting from the information passing paradigm of SNNs, the multiplications of activations and weights can be replaced by additions, which are more energy-efficient. However, its ``Hard Reset" mechanism for the firing activity would ignore the difference among membrane potentials when the membrane potential is above the firing threshold, causing information loss. Meanwhile, quantifying the membrane potential to 0/1 spikes at the firing instants will inevitably introduce the quantization error thus bringing about information loss too. To address these problems, we propose to use the ``Soft Reset" mechanism for the supervised training-based SNNs, which will drive the membrane potential to a dynamic reset potential according to its magnitude, and Membrane Potential Rectifier (MPR) to reduce the quantization error via redistributing the membrane potential to a range close to the spikes. Results show that the SNNs with the ``Soft Reset" mechanism and MPR outperform their vanilla counterparts on both static and dynamic datasets.

All embodied agents are fundamentally patterns in physiological or other excitable media, blurring the distinction between objects and processes. Emergent patterns with complex behaviors, such as Gliders in the Game of Life and virtual patterns in Lenia, are powerful model systems in which to understand the properties and origins of behavioral traits in novel agents. To evaluate the behavior of patterns in Lenia, we introduce regions into their environment from which no sensory information is available - in effect, making creatures blind to parts of their surroundings. Complementing the conventional concept of infotaxis, we find that creatures tend to avoid these regions, a behavior we term agnosiophobia. To explain this behavior, we map each test creature's sensitivity to targeted occlusions and interpret the results in the language of dynamical systems. We observe Lenia creatures taking advantage of their freedom to change heading in order to achieve what appears to be a more fundamental goal: the preservation of their morphology. This work illustrates the beginning of an important roadmap to understand how emergent agents' behavioral propensities interact with the informational, not only tangible, topography of their world.

Parkinsons disease (PD) alters cortical neural dynamics, yet reliable non-invasive electrophysiological biomarkers remain elusive. This study examined whether interpretable EEG features capturing complementary aspects of neural dynamics can discriminate Parkinsonian neural states. A comprehensive set of interpretable features was extracted and grouped into Standard descriptors (spectral power, phase synchronization, time-domain statistics) and Dynamical descriptors (aperiodic activity, cross-frequency coupling, scale-free dynamics, neuronal avalanche statistics, and instantaneous frequency measures). A multi-head attention transformer classifier was trained using strict LOSO validation. Group-level comparisons were performed to identify electrophysiological differences associated with disease and medication state. Standard feature sets achieved strongest performance in discriminating medication states (PDoff vs PDon), whereas Dynamical performed competitively in contrasts between PD patients and healthy controls. Random feature ablation analyses indicated that Dynamical descriptors provide complementary information distributed across features while correlation analysis revealed low redundancy within both feature sets. Group-level comparisons revealed medication-sensitive reductions in delta power and voltage variance, modulation of neuronal avalanche statistics, persistent increases in theta phase synchronization in PD patients, and disease-related alterations in cross-frequency interactions. Traditional spectral and synchronization features primarily reflect medication-related neural modulation, whereas dynamical descriptors reveal broader alterations in cortical network organization associated with disease but also with medication. These findings support multivariate EEG representations as a promising framework for developing non-invasive biomarkers of PD.

Diagnosing epilepsy is challenging when routine EEGs lack interictal epileptiform discharges (IEDs). Intermittent photic stimulation (IPS) and hyperventilation (HV) can increase diagnostic yield, but their interpretation is subjective. We propose a reproducible pipeline that classifies EEG recordings acquired during stimulation procedures, using machine-learning features spanning temporal, spectral, wavelet, and connectivity domains, and a stacked ensemble to combine complementary feature sets. Performance is evaluated with leave-one-subject-out (LOSO) cross-validation on the TUH Epilepsy Corpus and a clinical Erasmus MC (EMC) cohort, including IED-free analyses on TUH. On TUH, ensembles achieve up to 97.8\% AUC / 93.1\% BAC on IED-free resting-state EEG and 94.1\% AUC / 86.8\% BAC on IED-free IPS. On EMC, IPS provides the strongest discrimination (79.4\% AUC / 73.9\% BAC), while HV performance benefits from stratifying subjects by responsiveness. These results indicate that stimulation-evoked activity, particularly IPS, contains meaningful discriminative information for IED-free epilepsy classification and that multi-domain ensembling improves robustness.

State-of-the-art systems neuroscience experiments yield large-scale multimodal data, and these data sets require new tools for analysis. Inspired by the success of large pretrained models in vision and language domains, we reframe the analysis of large-scale, cellular-resolution neuronal spiking data into an autoregressive spatiotemporal generation problem. Neuroformer is a multimodal, multitask generative pretrained transformer (GPT) model that is specifically designed to handle the intricacies of data in systems neuroscience. It scales linearly with feature size, can process an arbitrary number of modalities, and is adaptable to downstream tasks, such as predicting behavior. We first trained Neuroformer on simulated datasets, and found that it both accurately predicted simulated neuronal circuit activity, and also intrinsically inferred the underlying neural circuit connectivity, including direction. When pretrained to decode neural responses, the model predicted the behavior of a mouse with only few-shot fine-tuning, suggesting that the model begins learning how to do so directly from the neural representations themselves, without any explicit supervision. We used an ablation study to show that joint training on neuronal responses and behavior boosted performance, highlighting the model's ability to associate behavioral and neural representations in an unsupervised manner. These findings show that Neuroformer can analyze neural datasets and their emergent properties, informing the development of models and hypotheses associated with the brain.

Recent breakthroughs in synaptic-resolution network connectomics have revealed that brain circuits feature fine-scale structural connectivity, such as pairs of correlated synaptic couplings known as second-order motifs. Large-scale recordings of neuronal activity in networks containing nonlinear neurons reveal macroscopic heterogeneous population dynamics throughout the brain. These findings rekindle the inquiry into this intriguing question: Can microscale synaptic structures contribute to macroscopic heterogeneous dynamics and computations in ways that canonical brain circuit models cannot? To answer this question, we create random RNNs with various cell types, nonlinear non-negative neural responses, and arbitrary marginal and second-order correlated synaptic statistics. We derive mean-field low-rank equations for P-population networks in which the pre- and postsynaptic neuronal population identities determine the synaptic and motif strengths. Our framework requires 2P latent dynamic variables with P variables describing mean population activity and P variables capturing within-population variability. Theoretical and simulational results demonstrate that chain motifs induce correlations in synaptic variability, enabling microscopic fluctuations to be integrated and influence mesoscopic mean population dynamics. We apply this framework to reverse engineer network connectivity that recapitulates the heterogeneous activity across the population in the mouse primary visual cortex. By bridging the gap between synaptic organization and nonlinear heterogeneous population dynamics, our results offer a principled approach and testable predictions regarding the relationship between fine-scale connectivity, heterogeneous dynamics, and functional computations.

The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors at different times. We introduce an unsupervised approach to learn the dynamic affinities between neurons in live, behaving animals, and to reveal which communities form among neurons at different times. The inference occurs in two major steps. First, pairwise non-linear affinities between neuronal traces from brain-wide calcium activity are organized by non-negative tensor factorization (NTF). Each factor specifies which groups of neurons are most likely interacting for an inferred interval in time, and for which animals. Finally, a generative model that allows for weighted community detection is applied to the functional motifs produced by NTF to reveal a dynamic functional connectome. Since time codes the different experimental variables (e.g., application of chemical stimuli), this provides an atlas of neural motifs active during separate stages of an experiment (e.g., stimulus application or spontaneous behaviors). Results from our analysis are experimentally validated, confirming that our method is able to robustly predict causal interactions between neurons to generate behavior. Code is available at https://github.com/dyballa/dynamic-connectomes.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

Spike-based Transformer presents a compelling and energy-efficient alternative to traditional Artificial Neural Network (ANN)-based Transformers, achieving impressive results through sparse binary computations. However, existing spike-based transformers predominantly focus on spatial attention while neglecting crucial temporal dependencies inherent in spike-based processing, leading to suboptimal feature representation and limited performance. To address this limitation, we propose Spiking Transformer with Spatial-Temporal Attention (STAtten), a simple and straightforward architecture that efficiently integrates both spatial and temporal information in the self-attention mechanism. STAtten introduces a block-wise computation strategy that processes information in spatial-temporal chunks, enabling comprehensive feature capture while maintaining the same computational complexity as previous spatial-only approaches. Our method can be seamlessly integrated into existing spike-based transformers without architectural overhaul. Extensive experiments demonstrate that STAtten significantly improves the performance of existing spike-based transformers across both static and neuromorphic datasets, including CIFAR10/100, ImageNet, CIFAR10-DVS, and N-Caltech101. The code is available at https://github.com/Intelligent-Computing-Lab-Yale/STAtten

We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural field model with a simple functional form that still able to predict or reproduce empirical findings. Each neural unit was modelled using a neural mass and the accompanying field theory was derived in the continuum limit. The field theory comprised coupled (real) Klein-Gordon fields, where predictions of the model fall within the range of experimental findings. These predictions included the frequency spectrum of electric activity measured from the cortex, which was derived using an equipartition of energy over eigenfunctions of the neural fields. Moreover, the neural field model was invariant, within a set of parameters, to the dynamical system used to model each neuronal mass. Specifically, topologically equivalent dynamical systems resulted in the same neural field model when connected in a lattice; indicating that the fields derived could be read as a canonical cortical field theory. We specifically investigated non-dispersive fields that provide a structure for the coding (or representation) of afferent information. Further elaboration of the ensuing neural field theory, including the effect of dispersive forces, could be of importance in the understanding of the cortical processing of information.

As the size of large language models continue to scale, so does the computational resources required to run it. Spiking Neural Networks (SNNs) have emerged as an energy-efficient approach to deep learning that leverage sparse and event-driven activations to reduce the computational overhead associated with model inference. While they have become competitive with non-spiking models on many computer vision tasks, SNNs have also proven to be more challenging to train. As a result, their performance lags behind modern deep learning, and we are yet to see the effectiveness of SNNs in language generation. In this paper, inspired by the Receptance Weighted Key Value (RWKV) language model, we successfully implement `SpikeGPT', a generative language model with binary, event-driven spiking activation units. We train the proposed model on two model variants: 45M and 216M parameters. To the best of our knowledge, SpikeGPT is the largest backpropagation-trained SNN model to date, rendering it suitable for both the generation and comprehension of natural language. We achieve this by modifying the transformer block to replace multi-head self attention to reduce quadratic computational complexity O(N^2) to linear complexity O(N) with increasing sequence length. Input tokens are instead streamed in sequentially to our attention mechanism (as with typical SNNs). Our preliminary experiments show that SpikeGPT remains competitive with non-spiking models on tested benchmarks, while maintaining 20x fewer operations when processed on neuromorphic hardware that can leverage sparse, event-driven activations. Our code implementation is available at https://github.com/ridgerchu/SpikeGPT.

Spiking Neural Networks (SNNs) promise energy-efficient vision, but applying them to RGB visual tracking remains difficult: Existing SNN tracking frameworks either do not fully align with spike-driven computation or do not fully leverage neurons' spatiotemporal dynamics, leading to a trade-off between efficiency and accuracy. To address this, we introduce SpikeTrack, a spike-driven framework for energy-efficient RGB object tracking. SpikeTrack employs a novel asymmetric design that uses asymmetric timestep expansion and unidirectional information flow, harnessing spatiotemporal dynamics while cutting computation. To ensure effective unidirectional information transfer between branches, we design a memory-retrieval module inspired by neural inference mechanisms. This module recurrently queries a compact memory initialized by the template to retrieve target cues and sharpen target perception over time. Extensive experiments demonstrate that SpikeTrack achieves the state-of-the-art among SNN-based trackers and remains competitive with advanced ANN trackers. Notably, it surpasses TransT on LaSOT dataset while consuming only 1/26 of its energy. To our knowledge, SpikeTrack is the first spike-driven framework to make RGB tracking both accurate and energy efficient. The code and models are available at https://github.com/faicaiwawa/SpikeTrack.

Regarded as the third generation of neural networks, Spiking Neural Networks (SNNs) have garnered significant traction due to their biological plausibility and energy efficiency. Recent advancements in large models necessitate spiking neurons capable of high performance, adaptability, and training efficiency. In this work, we first propose a novel functional perspective that provides general guidance for designing the new generation of spiking neurons. Following the insightful guidelines, we propose the Adaptive Spiking Neuron (ASN), which incorporates trainable parameters to learn membrane potential dynamics and enable adaptive firing. ASN adopts an integer training and spike inference paradigm, facilitating efficient SNN training. To further enhance robustness, we propose a specialized variant of ASN, the Normalized Adaptive Spiking Neuron (NASN), which integrates normalization to stabilize training. We evaluate our neuron model on 19 datasets spanning five distinct tasks in both vision and language modalities, demonstrating the effectiveness and versatility of the ASN family. Our ASN family is expected to become the new generation of general-purpose spiking neurons.

The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal physiological data presents many analytic challenges: the data is noisy, contains many missing values, and each series has a different length. Most methods proposed for time series analysis and classification do not handle datasets with these characteristics nor do they offer interpretability and explainability, a critical requirement in the health domain. We propose an unsupervised method for learning representations of time series based on common patterns identified within them. The patterns are, interpretable, variable in length, and extracted using Byte Pair Encoding compression technique. In this way the method can capture both long-term and short-term dependencies present in the data. We show that this method applies to both univariate and multivariate time series and beats state-of-the-art approaches on a real world dataset collected from wearable sensors.

Understanding and decoding brain activity from electroencephalography (EEG) signals is a fundamental challenge in neuroscience and AI, with applications in cognition, emotion recognition, diagnosis, and brain-computer interfaces. While recent EEG foundation models advance generalized decoding via unified architectures and large-scale pretraining, they adopt a scale-agnostic dense modeling paradigm inherited from NLP and vision. This design neglects a core property of neural activity: cross-scale spatiotemporal structure. EEG task patterns span a wide range of temporal and spatial scales, from short bursts to slow rhythms, and from localized cortical responses to distributed interactions. Ignoring this diversity leads to suboptimal representations and weak generalization. We propose CSBrain, a Cross-scale Spatiotemporal Brain foundation model for generalized EEG decoding. CSBrain introduces: (i) Cross-scale Spatiotemporal Tokenization (CST), which aggregates multi-scale features from localized temporal windows and anatomical brain regions into compact scale-aware tokens; and (ii) Structured Sparse Attention (SSA), which captures cross-window and cross-region dependencies, enhancing scale diversity while removing spurious correlations. CST and SSA are alternately stacked to progressively integrate multi-scale dependencies. Experiments on 11 EEG tasks across 16 datasets show that CSBrain consistently outperforms task-specific and foundation model baselines. These results establish cross-scale modeling as a key inductive bias and position CSBrain as a robust backbone for future brain-AI research.

This paper presents the first application of spiking neural networks (SNNs) for the classification of chronic lower back pain (CLBP) using the EmoPain dataset. Our work has two main contributions. We introduce Spike Threshold Adaptive Learning (STAL), a trainable encoder that effectively converts continuous biosignals into spike trains. Additionally, we propose an ensemble of Spiking Recurrent Neural Network (SRNN) classifiers for the multi-stream processing of sEMG and IMU data. To tackle the challenges of small sample size and class imbalance, we implement minority over-sampling with weighted sample replacement during batch creation. Our method achieves outstanding performance with an accuracy of 80.43%, AUC of 67.90%, F1 score of 52.60%, and Matthews Correlation Coefficient (MCC) of 0.437, surpassing traditional rate-based and latency-based encoding methods. The STAL encoder shows superior performance in preserving temporal dynamics and adapting to signal characteristics. Importantly, our approach (STAL-SRNN) outperforms the best deep learning method in terms of MCC, indicating better balanced class prediction. This research contributes to the development of neuromorphic computing for biosignal analysis. It holds promise for energy-efficient, wearable solutions in chronic pain management.

Vital to primary visual processing, retinal circuitry shows many similar structures across a very broad array of species, both vertebrate and non-vertebrate, especially functional components such as lateral inhibition. This surprisingly conservative pattern raises a question of how evolution leads to it, and whether there is any alternative that can also prompt helpful preprocessing. Here we design a method using genetic algorithm that, with many degrees of freedom, leads to architectures whose functions are similar to biological retina, as well as effective alternatives that are different in structures and functions. We compare this model to natural evolution and discuss how our framework can come into goal-driven search and sustainable enhancement of neural network models in machine learning.

Recent advancements in large language models (LLMs) with billions of parameters have improved performance in various applications, but their inference processes demand significant energy and computational resources. In contrast, the human brain, with approximately 86 billion neurons, is much more energy-efficient than LLMs with similar parameters. Inspired by this, we redesign 7sim70 billion parameter LLMs using bio-plausible spiking mechanisms, emulating the efficient behavior of the human brain. We propose the first spiking large language model, SpikeLLM. Coupled with the proposed model, two essential approaches are proposed to improve spike training efficiency: Generalized Integrate-and-Fire (GIF) neurons to compress spike length from T to T{L} log_2 L bits, and an Optimal Brain Spiking framework to divide outlier channels and allocate different T for GIF neurons, which further compresses spike length to approximate log_2T bits. The necessity of spike-driven LLM is proved by comparison with quantized LLMs with similar operations. In the OmniQuant pipeline, SpikeLLM reduces 11.01% WikiText2 perplexity and improves 2.55% accuracy of common scene reasoning on a LLAMA-7B W4A4 model. In the GPTQ pipeline, SpikeLLM achieves direct additive in linear layers, significantly exceeding PB-LLMs.

Deep Spiking Neural Networks (SNNs) present optimization difficulties for gradient-based approaches due to discrete binary activation and complex spatial-temporal dynamics. Considering the huge success of ResNet in deep learning, it would be natural to train deep SNNs with residual learning. Previous Spiking ResNet mimics the standard residual block in ANNs and simply replaces ReLU activation layers with spiking neurons, which suffers the degradation problem and can hardly implement residual learning. In this paper, we propose the spike-element-wise (SEW) ResNet to realize residual learning in deep SNNs. We prove that the SEW ResNet can easily implement identity mapping and overcome the vanishing/exploding gradient problems of Spiking ResNet. We evaluate our SEW ResNet on ImageNet, DVS Gesture, and CIFAR10-DVS datasets, and show that SEW ResNet outperforms the state-of-the-art directly trained SNNs in both accuracy and time-steps. Moreover, SEW ResNet can achieve higher performance by simply adding more layers, providing a simple method to train deep SNNs. To our best knowledge, this is the first time that directly training deep SNNs with more than 100 layers becomes possible. Our codes are available at https://github.com/fangwei123456/Spike-Element-Wise-ResNet.

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point, or stationary distribution) towards a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged towards their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal 'back-propagated' during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not.

Epilepsy is a common disease of the nervous system. Timely prediction of seizures and intervention treatment can significantly reduce the accidental injury of patients and protect the life and health of patients. This paper presents a neuromorphic Spiking Convolutional Transformer, named Spiking Conformer, to detect and predict epileptic seizure segments from scalped long-term electroencephalogram (EEG) recordings. We report evaluation results from the Spiking Conformer model using the Boston Children's Hospital-MIT (CHB-MIT) EEG dataset. By leveraging spike-based addition operations, the Spiking Conformer significantly reduces the classification computational cost compared to the non-spiking model. Additionally, we introduce an approximate spiking neuron layer to further reduce spike-triggered neuron updates by nearly 38% without sacrificing accuracy. Using raw EEG data as input, the proposed Spiking Conformer achieved an average sensitivity rate of 94.9% and a specificity rate of 99.3% for the seizure detection task, and 96.8%, 89.5% for the seizure prediction task, and needs >10x fewer operations compared to the non-spiking equivalent model.

We investigate Josephson arrays consisting of a dice-lattice network of superconducting weak links surrounding rhombic plaquettes of proximitized semiconductor. Josephson coupling of the weak links and electron density in the plaquettes are independently controlled by separate electrostatic gates. Applied magnetic flux results in an intricate pattern of switching currents associated with frustration, f. For depleted plaquettes, the switching current is nearly periodic in f, expected for a phase-only description, while occupied plaquettes yield a decreasing envelope of switching currents with increasing f. A model of flux dependence based on ballistic small-area junctions and diffusive large-area plaquettes yields excellent agreement with experiment.

We introduce a novel mathematical framework that unifies neural population dynamics, hippocampal sharp wave-ripple (SpWR) generation, and cognitive consistency constraints inspired by Heider's theory. Our model leverages low-dimensional manifold representations to capture structured neural drift and incorporates a balance energy function to enforce coherent synaptic interactions, effectively simulating the memory consolidation processes observed in biological systems. Simulation results demonstrate that our approach not only reproduces key features of SpWR events but also enhances network interpretability. This work paves the way for scalable neuromorphic architectures that bridge neuroscience and artificial intelligence, offering more robust and adaptive learning mechanisms for future intelligent systems.

We develop a dynamical mean-field theory for random recurrent networks with low-rank structure and firing-rate-driven adaptation. When the random connectivity is strong enough to generate chaos, increasing adaptation strength drives the network through four regimes: a static coherent state, noise-sustained oscillations that progress from regular to irregular, stochastic switching between symmetric wells, and a global limit cycle. The theory identifies two instability mechanisms, chaos onset from the random connectivity and a Hopf bifurcation of the coherent mode, and shows how adaptation shapes both through the frequency-dependent single-neuron transfer function. A reduced three-dimensional model captures the bifurcation structure of the full network. Above the chaos threshold, coherent population-level oscillations coexist with heterogeneous firing rates and network-generated stochasticity at the single-neuron level. The interaction of adaptation with random and low-rank connectivity produces a rich oscillatory repertoire, including waxing-and-waning rhythmic episodes, persistent state switching, and slow Up-Down alternations, dynamics that have been observed during wakefulness, sleep, and anesthesia.

Spiking Transformers have recently emerged as promising architectures for combining the efficiency of spiking neural networks with the representational power of self-attention. However, the lack of standardized implementations, evaluation pipelines, and consistent design choices has hindered fair comparison and principled analysis. In this paper, we introduce STEP, a unified benchmark framework for Spiking Transformers that supports a wide range of tasks, including classification, segmentation, and detection across static, event-based, and sequential datasets. STEP provides modular support for diverse components such as spiking neurons, input encodings, surrogate gradients, and multiple backends (e.g., SpikingJelly, BrainCog). Using STEP, we reproduce and evaluate several representative models, and conduct systematic ablation studies on attention design, neuron types, encoding schemes, and temporal modeling capabilities. We also propose a unified analytical model for energy estimation, accounting for spike sparsity, bitwidth, and memory access, and show that quantized ANNs may offer comparable or better energy efficiency. Our results suggest that current Spiking Transformers rely heavily on convolutional frontends and lack strong temporal modeling, underscoring the need for spike-native architectural innovations. The full code is available at: https://github.com/Fancyssc/STEP

Spiking neural networks offer low energy consumption due to their event-driven nature. Beyond binary spike outputs, their intrinsic floating-point dynamics merit greater attention. Neuronal threshold levels and reset modes critically determine spike count and timing. Hard reset cause information loss, while soft reset apply uniform treatment to neurons. To address these issues, we design an adaptive reset neuron that establishes relationships between inputs, outputs, and reset, while integrating a simple yet effective threshold adjustment strategy. Experimental results demonstrate that our method achieves excellent performance while maintaining lower energy consumption. In particular, it attains state-of-the-art accuracy on Tiny-ImageNet and CIFAR10-DVS. Codes are available at https://github.com/2ephyrus/AR-LIF.

The human brain is autonomously active, being characterized by a self-sustained neural activity which would be present even in the absence of external sensory stimuli. Here we study the interrelation between the self-sustained activity in autonomously active recurrent neural nets and external sensory stimuli. There is no a priori semantical relation between the influx of external stimuli and the patterns generated internally by the autonomous and ongoing brain dynamics. The question then arises when and how are semantic correlations between internal and external dynamical processes learned and built up? We study this problem within the paradigm of transient state dynamics for the neural activity in recurrent neural nets, i.e. for an autonomous neural activity characterized by an infinite time-series of transiently stable attractor states. We propose that external stimuli will be relevant during the sensitive periods, {\it viz} the transition period between one transient state and the subsequent semi-stable attractor. A diffusive learning signal is generated unsupervised whenever the stimulus influences the internal dynamics qualitatively. For testing we have presented to the model system stimuli corresponding to the bars and stripes problem. We found that the system performs a non-linear independent component analysis on its own, being continuously and autonomously active. This emergent cognitive capability results here from a general principle for the neural dynamics, the competition between neural ensembles.

Spiking Neural Networks (SNNs) as one of the biology-inspired models have received much attention recently. It can significantly reduce energy consumption since they quantize the real-valued membrane potentials to 0/1 spikes to transmit information thus the multiplications of activations and weights can be replaced by additions when implemented on hardware. However, this quantization mechanism will inevitably introduce quantization error, thus causing catastrophic information loss. To address the quantization error problem, we propose a regularizing membrane potential loss (RMP-Loss) to adjust the distribution which is directly related to quantization error to a range close to the spikes. Our method is extremely simple to implement and straightforward to train an SNN. Furthermore, it is shown to consistently outperform previous state-of-the-art methods over different network architectures and datasets.

In the present research, we delve into the intricate realm of electroencephalogram (EEG) data analysis, focusing on sequence-to-sequence prediction of data across 32 EEG channels. The study harmoniously fuses the principles of applied chaos theory and dynamical systems theory to engender a novel feature set, enriching the representational capacity of our deep learning model. The endeavour's cornerstone is a transformer-based sequence-to-sequence architecture, calibrated meticulously to capture the non-linear and high-dimensional temporal dependencies inherent in EEG sequences. Through judicious architecture design, parameter initialisation strategies, and optimisation techniques, we have navigated the intricate balance between computational expediency and predictive performance. Our model stands as a vanguard in EEG data sequence prediction, demonstrating remarkable generalisability and robustness. The findings not only extend our understanding of EEG data dynamics but also unveil a potent analytical framework that can be adapted to diverse temporal sequence prediction tasks in neuroscience and beyond.

Spiking neural networks (SNNs) can be used in low-power and embedded systems (such as emerging neuromorphic chips) due to their event-based nature. Also, they have the advantage of low computation cost in contrast to conventional artificial neural networks (ANNs), while preserving ANN's properties. However, temporal coding in layers of convolutional spiking neural networks and other types of SNNs has yet to be studied. In this paper, we provide insight into spatio-temporal feature extraction of convolutional SNNs in experiments designed to exploit this property. The shallow convolutional SNN outperforms state-of-the-art spatio-temporal feature extractor methods such as C3D, ConvLstm, and similar networks. Furthermore, we present a new deep spiking architecture to tackle real-world problems (in particular classification tasks) which achieved superior performance compared to other SNN methods on NMNIST (99.6%), DVS-CIFAR10 (69.2%) and DVS-Gesture (96.7%) and ANN methods on UCF-101 (42.1%) and HMDB-51 (21.5%) datasets. It is also worth noting that the training process is implemented based on variation of spatio-temporal backpropagation explained in the paper.

In this paper, we study the flow of signals through linear paths with the nonlinear condition that a node emits a signal when it receives external stimuli or when two incoming signals from other nodes arrive coincidentally with a combined amplitude above a fixed threshold. Sets of such nodes form a polychrony group and can sometimes lead to cascades. In the context of this work, cascades are polychrony groups in which the number of nodes activated as a consequence of other nodes is greater than the number of externally activated nodes. The difference between these two numbers is the so-called profit. Given the initial conditions, we predict the conditions for a vertex to activate at a prescribed time and provide an algorithm to efficiently reconstruct a cascade. We develop a dictionary between polychrony groups and graph theory. We call the graph corresponding to a cascade a chinampa. This link leads to a topological classification of chinampas. We enumerate the chinampas of profits zero and one and the description of a family of chinampas isomorphic to a family of partially ordered sets, which implies that the enumeration problem of this family is equivalent to computing the Stanley-order polynomials of those partially ordered sets.

Attention Deficit Hyperactive Disorder (ADHD) is a common behavioral problem affecting children. In this work, we investigate the automatic classification of ADHD subjects using the resting state Functional Magnetic Resonance Imaging (fMRI) sequences of the brain. We show that the brain can be modeled as a functional network, and certain properties of the networks differ in ADHD subjects from control subjects. We compute the pairwise correlation of brain voxels' activity over the time frame of the experimental protocol which helps to model the function of a brain as a network. Different network features are computed for each of the voxels constructing the network. The concatenation of the network features of all the voxels in a brain serves as the feature vector. Feature vectors from a set of subjects are then used to train a PCA-LDA (principal component analysis-linear discriminant analysis) based classifier. We hypothesized that ADHD-related differences lie in some specific regions of the brain and using features only from those regions is sufficient to discriminate ADHD and control subjects. We propose a method to create a brain mask that includes the useful regions only and demonstrate that using the feature from the masked regions improves classification accuracy on the test data set. We train our classifier with 776 subjects and test on 171 subjects provided by The Neuro Bureau for the ADHD-200 challenge. We demonstrate the utility of graph-motif features, specifically the maps that represent the frequency of participation of voxels in network cycles of length 3. The best classification performance (69.59%) is achieved using 3-cycle map features with masking. Our proposed approach holds promise in being able to diagnose and understand the disorder.

Exact firing rate models, also known as next-generation neural mass models (NG-NMMs), provide a rigorous description of the dynamics of neural populations. While in its simplest form a single population only displays fixed-point activity, multi-population models may display a range of different behaviors. In this work, we study the dynamics of all-excitatory or all-inhibitory NG-NMMs coupled through sparse random networks with row-normalized network topology. Linear stability analysis of the homogeneous states of the system, representing asynchronous neural activity, provides a dispersion relation linking the emergence of spatiotemporal dynamics to the spectra of the connectivity matrix. Using bounds from random matrix theory, we identify the parameter regions where instabilities occur. In undirected networks, only inhibitory systems produce heterogeneous stationary patterns, corresponding to a winner-takes-all mechanism. In directed networks, exotic rhythmic states with high frequencies emerge in both, excitatory and inhibitory systems. Numerical simulations reveal that these hectic oscillatory states correspond to high-dimensional chaos with extensive properties.

Spiking Neural Networks (SNN) are a class of bio-inspired neural networks that promise to bring low-power and low-latency inference to edge devices through asynchronous and sparse processing. However, being temporal models, SNNs depend heavily on expressive states to generate predictions on par with classical artificial neural networks (ANNs). These states converge only after long transient periods, and quickly decay without input data, leading to higher latency, power consumption, and lower accuracy. This work addresses this issue by initializing the state with an auxiliary ANN running at a low rate. The SNN then uses the state to generate predictions with high temporal resolution until the next initialization phase. Our hybrid ANN-SNN model thus combines the best of both worlds: It does not suffer from long state transients and state decay thanks to the ANN, and can generate predictions with high temporal resolution, low latency, and low power thanks to the SNN. We show for the task of event-based 2D and 3D human pose estimation that our method consumes 88% less power with only a 4% decrease in performance compared to its fully ANN counterparts when run at the same inference rate. Moreover, when compared to SNNs, our method achieves a 74% lower error. This research thus provides a new understanding of how ANNs and SNNs can be used to maximize their respective benefits.

Traveling waves of neural activity have been observed throughout the brain at a diversity of regions and scales; however, their precise computational role is still debated. One physically inspired hypothesis suggests that the cortical sheet may act like a wave-propagating system capable of invertibly storing a short-term memory of sequential stimuli through induced waves traveling across the cortical surface, and indeed many experimental results from neuroscience correlate wave activity with memory tasks. To date, however, the computational implications of this idea have remained hypothetical due to the lack of a simple recurrent neural network architecture capable of exhibiting such waves. In this work, we introduce a model to fill this gap, which we denote the Wave-RNN (wRNN), and demonstrate how such an architecture indeed efficiently encodes the recent past through a suite of synthetic memory tasks where wRNNs learn faster and reach significantly lower error than wave-free counterparts. We further explore the implications of this memory storage system on more complex sequence modeling tasks such as sequential image classification and find that wave-based models not only again outperform comparable wave-free RNNs while using significantly fewer parameters, but additionally perform comparably to more complex gated architectures such as LSTMs and GRUs.

Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers (SCS) showed that random recurrent networks undergo a transition from quiescence to asynchronous chaos, establishing a paradigmatic link between random connectivity, dynamical instability, and internally generated fluctuations in neural circuits. Here, we extend this framework to two-population firing-rate networks with segregated excitatory and inhibitory neurons and target-specific inhibitory couplings that break excitation--inhibition balance. Using dynamical mean-field theory, we derive self-consistent equations for the macroscopic mean activities and autocorrelations, together with stability criteria distinguishing mean-driven and fluctuation-driven instabilities. We show that target-specific inhibition organizes the phase diagram into three qualitative classes: inhibition-dominated or strictly balanced networks display only quiescent activity and asynchronous chaos; excitation-dominated networks display persistent activity together with either synchronous chaos with non-vanishing mean activity or coherent oscillations, depending on the stability-matrix eigenvalues. Crucially, coherent oscillations do not coexist with chaotic fluctuations around the periodic mean trajectory; rather, their onset suppresses the chaotic component, reminiscent of input-induced suppression of chaos. These results generalize SCS theory to recurrent networks with explicit excitatory--inhibitory structure and identify target-specific inhibition as a key control parameter for large-scale neural dynamics.

Recurrent Neural Networks (RNNs) are popular models of brain function. The typical training strategy is to adjust their input-output behavior so that it matches that of the biological circuit of interest. Even though this strategy ensures that the biological and artificial networks perform the same computational task, it does not guarantee that their internal activity dynamics match. This suggests that the trained RNNs might end up performing the task employing a different internal computational mechanism, which would make them a suboptimal model of the biological circuit. In this work, we introduce a novel training strategy that allows learning not only the input-output behavior of an RNN but also its internal network dynamics, based on sparse neural recordings. We test the proposed method by training an RNN to simultaneously reproduce internal dynamics and output signals of a physiologically-inspired neural model. Specifically, this model generates the multiphasic muscle-like activity patterns typically observed during the execution of reaching movements, based on the oscillatory activation patterns concurrently observed in the motor cortex. Remarkably, we show that the reproduction of the internal dynamics is successful even when the training algorithm relies on the activities of a small subset of neurons sampled from the biological network. Furthermore, we show that training the RNNs with this method significantly improves their generalization performance. Overall, our results suggest that the proposed method is suitable for building powerful functional RNN models, which automatically capture important computational properties of the biological circuit of interest from sparse neural recordings.

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ell_2 gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.

Event-based cameras are attracting significant interest as they provide rich edge information, high dynamic range, and high temporal resolution. Many state-of-the-art event-based algorithms rely on splitting the events into fixed groups, resulting in the omission of crucial temporal information, particularly when dealing with diverse motion scenarios (\eg, high/low speed).In this work, we propose SpikeSlicer, a novel-designed plug-and-play event processing method capable of splitting events stream adaptively.SpikeSlicer utilizes a low-energy spiking neural network (SNN) to trigger event slicing. To guide the SNN to fire spikes at optimal time steps, we propose the Spiking Position-aware Loss (SPA-Loss) to modulate the neuron's state. Additionally, we develop a Feedback-Update training strategy that refines the slicing decisions using feedback from the downstream artificial neural network (ANN). Extensive experiments demonstrate that our method yields significant performance improvements in event-based object tracking and recognition. Notably, SpikeSlicer provides a brand-new SNN-ANN cooperation paradigm, where the SNN acts as an efficient, low-energy data processor to assist the ANN in improving downstream performance, injecting new perspectives and potential avenues of exploration.

Event cameras are bio-inspired sensors that respond to local changes in light intensity and feature low latency, high energy efficiency, and high dynamic range. Meanwhile, Spiking Neural Networks (SNNs) have gained significant attention due to their remarkable efficiency and fault tolerance. By synergistically harnessing the energy efficiency inherent in event cameras and the spike-based processing capabilities of SNNs, their integration could enable ultra-low-power application scenarios, such as action recognition tasks. However, existing approaches often entail converting asynchronous events into conventional frames, leading to additional data mapping efforts and a loss of sparsity, contradicting the design concept of SNNs and event cameras. To address this challenge, we propose SpikePoint, a novel end-to-end point-based SNN architecture. SpikePoint excels at processing sparse event cloud data, effectively extracting both global and local features through a singular-stage structure. Leveraging the surrogate training method, SpikePoint achieves high accuracy with few parameters and maintains low power consumption, specifically employing the identity mapping feature extractor on diverse datasets. SpikePoint achieves state-of-the-art (SOTA) performance on four event-based action recognition datasets using only 16 timesteps, surpassing other SNN methods. Moreover, it also achieves SOTA performance across all methods on three datasets, utilizing approximately 0.3\% of the parameters and 0.5\% of power consumption employed by artificial neural networks (ANNs). These results emphasize the significance of Point Cloud and pave the way for many ultra-low-power event-based data processing applications.

Human cognition emerges from coordinated spiking dynamics in distributed neural circuits, where information is encoded via both firing rates and precise spike timing determined by brain rhythms. Inspired by this notion, we propose a brain-inspired learning primitive in which cognition-level neural synchrony emerges through iterative bottom-up and top-down interactions between micro-scale dynamics of spiking neurons and a macro-scale mechanism of oscillatory synchronization. Specifically, we model each parcel (e.g., a cortical region or an image pixel) in the target system as a spiking neuron embedded in a predefined connectivity scaffold. Low-level information is encoded in a spatiotemporal domain, where neurons are selectively grouped and fire spontaneously over time through self-organized dynamics. In the bottom-up route, oscillatory synchronization is formed from past spiking activity accumulated over a finite memory window. Since brain dynamics operate in a regime of partial and transient synchronization rather than global phase locking, we model oscillatory coordination using a time-delayed synchronization formulation, which enables a top-down modulation of heterogeneous neural spiking for a large-scale distributed system. Together, we devise a spiking-by-synchronization neural network (S2-Net) that uses rhythmic timing as a control mechanism for efficient information processing. Promising results have been achieved across a broad range of tasks, including neural activity decoding, energy-efficient signal processing, temporal binding and semantic reasoning.

Spiking neural networks (SNNs) are known as a typical kind of brain-inspired models with their unique features of rich neuronal dynamics, diverse coding schemes and low power consumption properties. How to obtain a high-accuracy model has always been the main challenge in the field of SNN. Currently, there are two mainstream methods, i.e., obtaining a converted SNN through converting a well-trained Artificial Neural Network (ANN) to its SNN counterpart or training an SNN directly. However, the inference time of a converted SNN is too long, while SNN training is generally very costly and inefficient. In this work, a new SNN training paradigm is proposed by combining the concepts of the two different training methods with the help of the pretrain technique and BP-based deep SNN training mechanism. We believe that the proposed paradigm is a more efficient pipeline for training SNNs. The pipeline includes pipeS for static data transfer tasks and pipeD for dynamic data transfer tasks. SOTA results are obtained in a large-scale event-driven dataset ES-ImageNet. For training acceleration, we achieve the same (or higher) best accuracy as similar LIF-SNNs using 1/10 training time on ImageNet-1K and 2/5 training time on ES-ImageNet and also provide a time-accuracy benchmark for a new dataset ES-UCF101. These experimental results reveal the similarity of the functions of parameters between ANNs and SNNs and also demonstrate the various potential applications of this SNN training pipeline.

Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task, and, then, pruning neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning a large randomly initialized model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from a randomly initialized RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and temporal prediction. We experimentally show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.

Spiking Neural Networks (SNNs), the third generation NNs, have come under the spotlight for machine learning based applications due to their biological plausibility and reduced complexity compared to traditional artificial Deep Neural Networks (DNNs). These SNNs can be implemented with extreme energy efficiency on neuromorphic processors like the Intel Loihi research chip, and fed by event-based sensors, such as DVS cameras. However, DNNs with many layers can achieve relatively high accuracy on image classification and recognition tasks, as the research on learning rules for SNNs for real-world applications is still not mature. The accuracy results for SNNs are typically obtained either by converting the trained DNNs into SNNs, or by directly designing and training SNNs in the spiking domain. Towards the conversion from a DNN to an SNN, we perform a comprehensive analysis of such process, specifically designed for Intel Loihi, showing our methodology for the design of an SNN that achieves nearly the same accuracy results as its corresponding DNN. Towards the usage of the event-based sensors, we design a pre-processing method, evaluated for the DvsGesture dataset, which makes it possible to be used in the DNN domain. Hence, based on the outcome of the first analysis, we train a DNN for the pre-processed DvsGesture dataset, and convert it into the spike domain for its deployment on Intel Loihi, which enables real-time gesture recognition. The results show that our SNN achieves 89.64% classification accuracy and occupies only 37 Loihi cores. The source code for generating our experiments is available online at https://github.com/albertomarchisio/EfficientSNN.

The realization that complex systems such as ecological communities can collapse or shift regimes suddenly and without rapid external forcing poses a serious challenge to our understanding and management of the natural world. The potential to identify early warning signals that would allow researchers and managers to predict such events before they happen has therefore been an invaluable discovery that offers a way forward in spite of such seemingly unpredictable behavior. Research into early warning signals has demonstrated that it is possible to define and detect such early warning signals in advance of a transition in certain contexts. Here we describe the pattern emerging as research continues to explore just how far we can generalize these results. A core of examples emerges that shares three properties: the phenomenon of rapid regime shifts, a pattern of 'critical slowing down' that can be used to detect the approaching shift, and a mechanism of bifurcation driving the sudden change. As research has expanded beyond these core examples, it is becoming clear that not all systems that show regime shifts exhibit critical slowing down, or vice versa. Even when systems exhibit critical slowing down, statistical detection is a challenge. We review the literature that explores these edge cases and highlight the need for (a) new early warning behaviors that can be used in cases where rapid shifts do not exhibit critical slowing down, (b) the development of methods to identify which behavior might be an appropriate signal when encountering a novel system; bearing in mind that a positive indication for some systems is a negative indication in others, and (c) statistical methods that can distinguish between signatures of early warning behaviors and noise.

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.

Automotive telemetry data exhibits slow drifts and fast spikes, often within the same sequence, making reliable anomaly detection challenging. Standard reconstruction-based methods, including sequence variational autoencoders (VAEs), use a single latent process and therefore mix heterogeneous time scales, which can smooth out spikes or inflate variances and weaken anomaly separation. In this paper, we present STREAM-VAE, a variational autoencoder for anomaly detection in automotive telemetry time-series data. Our model uses a dual-path encoder to separate slow drift and fast spike signal dynamics, and a decoder that represents transient deviations separately from the normal operating pattern. STREAM-VAE is designed for deployment, producing stable anomaly scores across operating modes for both in-vehicle monitors and backend fleet analytics. Experiments on an automotive telemetry dataset and the public SMD benchmark show that explicitly separating drift and spike dynamics improves robustness compared to strong forecasting, attention, graph, and VAE baselines.

Loss spikes often occur during pre-training of large language models. The spikes degrade the performance of large language models and sometimes ruin the pre-training. Since the pre-training needs a vast computational budget, we should avoid such spikes. To investigate the cause of loss spikes, we focus on gradients of internal layers. Through theoretical analyses, we reveal two causes of the exploding gradients, and provide requirements to prevent the explosion. In addition, we propose a method to satisfy the requirements by combining the initialization method and a simple modification to embeddings. We conduct various experiments to verify our theoretical analyses empirically. Experimental results indicate that the combination is effective in preventing spikes during pre-training.

Time series foundation models (TSFMs) pretrained on data from multiple domains have shown strong performance on diverse modeling tasks. Various efforts have been made to develop foundation models specific to electroencephalography (EEG) data, which records brain electrical activity as time series. However, no comparative analysis of EEG-specific foundation models (EEGFMs) versus general TSFMs has been performed on EEG-specific tasks. We introduce a novel Spatial-Temporal Adapter with Multi-Head Pooling (STAMP), which leverages univariate embeddings produced by a general TSFM, implicitly models spatial-temporal characteristics of EEG data, and achieves performance comparable to state-of-the-art EEGFMs. A comprehensive analysis is performed on 8 benchmark datasets of clinical tasks using EEG for classification, along with ablation studies. Our proposed adapter is lightweight in trainable parameters and flexible in the inputs it can accommodate, supporting easy modeling of EEG data using TSFMs.

We study the scaling properties of avalanche activity in the two-dimensional Abelian sandpile model. Instead of the conventional avalanche size distribution, we analyze the site activity distribution, which measures how often a site participates in avalanches when grains are added across the lattice. Using numerical simulations for system sizes up to \(L = 160\), averaged over \(10^4\) configurations, we determine the probability distribution \(P(A, L)\) of site activities. The results show that \(P(A, L)\) follows a finite-size scaling form \[ P(A, L) \sim L^{-2} F\Big(A{L^2}\Big). \] For small values \(A \ll L^2\) the scaling function behaves as \[ F(u) \sim u^{-1/2}, \quad corresponding to \quad P(A) \sim 1{L}, \] while for large activities \(A \sim O(L^2)\) the distribution decays as \[ F(u) \sim \exp\big(-c_3 u - c_4 u^2\big). \] The crossover between these two regimes occurs at \[ A^* \sim 0.1 \, L^2, \] marking the threshold between typical and highly excitable sites. This characterization of local avalanche activity provides complementary information to the usual avalanche size statistics, highlighting how local regions serve as frequent conduits for critical dynamics. These results may help connect sandpile models to real-world self-organized critical systems where only partial local activity can be observed.

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking Hebbian Network (a variation on theme of the Hopfield model working on sparse data-sets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) amount of patterns, mirroring the low-storage level of standard associative neural networks at work with pattern recognition. For mild dilution in the patterns, the network handles them hierarchically, distributing the amplitudes of their signals as power-laws w.r.t. their information content (hierarchical regime), while, for strong dilution, all the signals pertaining to all the patterns are raised with the same strength (parallel regime). Further, confined to the low-storage setting (i.e., far from the spin glass limit), the presence of a teacher neither alters the multitasking performances nor changes the thresholds for learning: the latter are the same whatever the training protocol is supervised or unsupervised. Results obtained through statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting insights on multiple learning at once: for instance, whenever the cost-function of the model is minimized in parallel on several patterns (in its description via Statistical Mechanics), the same happens to the standard sum-squared error Loss function (typically used in Machine Learning).

Speech patterns have been identified as potential diagnostic markers for neuropsychiatric conditions. However, most studies only compare a single clinical group to healthy controls, whereas clinical practice often requires differentiating between multiple potential diagnoses (multiclass settings). To address this, we assembled a dataset of repeated recordings from 420 participants (67 with major depressive disorder, 106 with schizophrenia and 46 with autism, as well as matched controls), and tested the performance of a range of conventional machine learning models and advanced Transformer models on both binary and multiclass classification, based on voice and text features. While binary models performed comparably to previous research (F1 scores between 0.54-0.75 for autism spectrum disorder, ASD; 0.67-0.92 for major depressive disorder, MDD; and 0.71-0.83 for schizophrenia); when differentiating between multiple diagnostic groups performance decreased markedly (F1 scores between 0.35-0.44 for ASD, 0.57-0.75 for MDD, 0.15-0.66 for schizophrenia, and 0.38-0.52 macro F1). Combining voice and text-based models yielded increased performance, suggesting that they capture complementary diagnostic information. Our results indicate that models trained on binary classification may learn to rely on markers of generic differences between clinical and non-clinical populations, or markers of clinical features that overlap across conditions, rather than identifying markers specific to individual conditions. We provide recommendations for future research in the field, suggesting increased focus on developing larger transdiagnostic datasets that include more fine-grained clinical features, and that can support the development of models that better capture the complexity of neuropsychiatric conditions and naturalistic diagnostic assessment.

A network-based approach is presented to investigate the cerebrovascular flow patterns during atrial fibrillation (AF) with respect to normal sinus rhythm (NSR). AF, the most common cardiac arrhythmia with faster and irregular beating, has been recently and independently associated with the increased risk of dementia. However, the underlying hemodynamic mechanisms relating the two pathologies remain mainly undetermined so far; thus the contribution of modeling and refined statistical tools is valuable. Pressure and flow rate temporal series in NSR and AF are here evaluated along representative cerebral sites (from carotid arteries to capillary brain circulation), exploiting reliable artificially built signals recently obtained from an in silico approach. The complex network analysis evidences, in a synthetic and original way, a dramatic signal variation towards the distal/capillary cerebral regions during AF, which has no counterpart in NSR conditions. At the large artery level, networks obtained from both AF and NSR hemodynamic signals exhibit elongated and chained features, which are typical of pseudo-periodic series. These aspects are almost completely lost towards the microcirculation during AF, where the networks are topologically more circular and present random-like characteristics. As a consequence, all the physiological phenomena at microcerebral level ruled by periodicity - such as regular perfusion, mean pressure per beat, and average nutrient supply at cellular level - can be strongly compromised, since the AF hemodynamic signals assume irregular behaviour and random-like features. Through a powerful approach which is complementary to the classical statistical tools, the present findings further strengthen the potential link between AF hemodynamic and cognitive decline.

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

Unsupervised feature extraction algorithms form one of the most important building blocks in machine learning systems. These algorithms are often adapted to the event-based domain to perform online learning in neuromorphic hardware. However, not designed for the purpose, such algorithms typically require significant simplification during implementation to meet hardware constraints, creating trade offs with performance. Furthermore, conventional feature extraction algorithms are not designed to generate useful intermediary signals which are valuable only in the context of neuromorphic hardware limitations. In this work a novel event-based feature extraction method is proposed that focuses on these issues. The algorithm operates via simple adaptive selection thresholds which allow a simpler implementation of network homeostasis than previous works by trading off a small amount of information loss in the form of missed events that fall outside the selection thresholds. The behavior of the selection thresholds and the output of the network as a whole are shown to provide uniquely useful signals indicating network weight convergence without the need to access network weights. A novel heuristic method for network size selection is proposed which makes use of noise events and their feature representations. The use of selection thresholds is shown to produce network activation patterns that predict classification accuracy allowing rapid evaluation and optimization of system parameters without the need to run back-end classifiers. The feature extraction method is tested on both the N-MNIST benchmarking dataset and a dataset of airplanes passing through the field of view. Multiple configurations with different classifiers are tested with the results quantifying the resultant performance gains at each processing stage.

The spectral behaviour of the synaptic matrix, representing the neuronal connection strengths, is an important tool to analyze the stability and transient dynamics of a typical brain as well as its learning process and memory capacity. The complexity of the brain due to large number of neurons as well as underlying transient mechanisms e.g. homeostasis, seizure or synaptic plasticity can lead to networks with time-varying degree and type of sparsity. This renders an exact determination of the synaptic matrix not only technically difficult but also meaningless, leaving its statistical analysis as the best available theoretical approach. This motivates us to pursue a spectral analysis of the synaptic matrix models with different type of sparsity and thereby analyze latter's role on various aspects of network dynamics and stability. Our results have potential relevance for detemining the type of synaptic sparsity required to induce a specific brain function or desired transient mechanism e.g for pharmacological effects or physiological modulators.

The Forward-Forward (FF) algorithm trains networks layer-by-layer using a local "goodness function," yet sum-of-squares (SoS) has remained the only choice studied. We systematically explore the goodness-function design space and identify a unifying principle: the goodness function must be sensitive to the shape of neural activity, not its total energy. This principle is motivated by the observation that deep network activations follow heavy-tailed distributions and that discriminative information is often concentrated in peak activities. We propose two complementary families: selective functions (top-k, entmax-weighted energy) that measure only peak activity, and shape-sensitive functions (excess kurtosis / "burstiness" and higher-order moments) that reward heavy-tailed distributions via scale-invariant statistics. Combined with separate label-feature forwarding (FFCL), controlled experiments across 13 goodness functions, 5 activations, 6 datasets, and three continuous sweeps, each tracing a characteristic inverted-U, yield 89.0% on Fashion-MNIST and 98.2+-0.1% on MNIST (4x2000), a +32.6pp gain over SoS, with consistent improvements across all benchmarks (+72pp USPS, +52pp SVHN). The scale-invariant nature of burstiness makes it particularly robust to magnitude shifts across layers and datasets.

Infectious diseases remain among the top contributors to human illness and death worldwide, among which many diseases produce epidemic waves of infection. The unavailability of specific drugs and ready-to-use vaccines to prevent most of these epidemics makes the situation worse. These force public health officials and policymakers to rely on early warning systems generated by reliable and accurate forecasts of epidemics. Accurate forecasts of epidemics can assist stakeholders in tailoring countermeasures, such as vaccination campaigns, staff scheduling, and resource allocation, to the situation at hand, which could translate to reductions in the impact of a disease. Unfortunately, most of these past epidemics exhibit nonlinear and non-stationary characteristics due to their spreading fluctuations based on seasonal-dependent variability and the nature of these epidemics. We analyse a wide variety of epidemic time series datasets using a maximal overlap discrete wavelet transform (MODWT) based autoregressive neural network and call it EWNet model. MODWT techniques effectively characterize non-stationary behavior and seasonal dependencies in the epidemic time series and improve the nonlinear forecasting scheme of the autoregressive neural network in the proposed ensemble wavelet network framework. From a nonlinear time series viewpoint, we explore the asymptotic stationarity of the proposed EWNet model to show the asymptotic behavior of the associated Markov Chain. We also theoretically investigate the effect of learning stability and the choice of hidden neurons in the proposal. From a practical perspective, we compare our proposed EWNet framework with several statistical, machine learning, and deep learning models. Experimental results show that the proposed EWNet is highly competitive compared to the state-of-the-art epidemic forecasting methods.

Spiking neural networks (SNNs) exhibit superior energy efficiency but suffer from limited performance. In this paper, we consider SNNs as ensembles of temporal subnetworks that share architectures and weights, and highlight a crucial issue that affects their performance: excessive differences in initial states (neuronal membrane potentials) across timesteps lead to unstable subnetwork outputs, resulting in degraded performance. To mitigate this, we promote the consistency of the initial membrane potential distribution and output through membrane potential smoothing and temporally adjacent subnetwork guidance, respectively, to improve overall stability and performance. Moreover, membrane potential smoothing facilitates forward propagation of information and backward propagation of gradients, mitigating the notorious temporal gradient vanishing problem. Our method requires only minimal modification of the spiking neurons without adapting the network structure, making our method generalizable and showing consistent performance gains in 1D speech, 2D object, and 3D point cloud recognition tasks. In particular, on the challenging CIFAR10-DVS dataset, we achieved 83.20\% accuracy with only four timesteps. This provides valuable insights into unleashing the potential of SNNs.

Spiking neural networks (SNNs) are brain-inspired energy-efficient models that encode information in spatiotemporal dynamics. Recently, deep SNNs trained directly have shown great success in achieving high performance on classification tasks with very few time steps. However, how to design a directly-trained SNN for the regression task of object detection still remains a challenging problem. To address this problem, we propose EMS-YOLO, a novel directly-trained SNN framework for object detection, which is the first trial to train a deep SNN with surrogate gradients for object detection rather than ANN-SNN conversion strategies. Specifically, we design a full-spike residual block, EMS-ResNet, which can effectively extend the depth of the directly-trained SNN with low power consumption. Furthermore, we theoretically analyze and prove the EMS-ResNet could avoid gradient vanishing or exploding. The results demonstrate that our approach outperforms the state-of-the-art ANN-SNN conversion methods (at least 500 time steps) in extremely fewer time steps (only 4 time steps). It is shown that our model could achieve comparable performance to the ANN with the same architecture while consuming 5.83 times less energy on the frame-based COCO Dataset and the event-based Gen1 Dataset.

Neuromorphic computing, which exploits Spiking Neural Networks (SNNs) on neuromorphic chips, is a promising energy-efficient alternative to traditional AI. CNN-based SNNs are the current mainstream of neuromorphic computing. By contrast, no neuromorphic chips are designed especially for Transformer-based SNNs, which have just emerged, and their performance is only on par with CNN-based SNNs, offering no distinct advantage. In this work, we propose a general Transformer-based SNN architecture, termed as ``Meta-SpikeFormer", whose goals are: 1) Lower-power, supports the spike-driven paradigm that there is only sparse addition in the network; 2) Versatility, handles various vision tasks; 3) High-performance, shows overwhelming performance advantages over CNN-based SNNs; 4) Meta-architecture, provides inspiration for future next-generation Transformer-based neuromorphic chip designs. Specifically, we extend the Spike-driven Transformer in yao2023spike into a meta architecture, and explore the impact of structure, spike-driven self-attention, and skip connection on its performance. On ImageNet-1K, Meta-SpikeFormer achieves 80.0\% top-1 accuracy (55M), surpassing the current state-of-the-art (SOTA) SNN baselines (66M) by 3.7\%. This is the first direct training SNN backbone that can simultaneously supports classification, detection, and segmentation, obtaining SOTA results in SNNs. Finally, we discuss the inspiration of the meta SNN architecture for neuromorphic chip design. Source code and models are available at https://github.com/BICLab/Spike-Driven-Transformer-V2.

Spiking Neural networks (SNN) have emerged as an attractive spatio-temporal computing paradigm for a wide range of low-power vision tasks. However, state-of-the-art (SOTA) SNN models either incur multiple time steps which hinder their deployment in real-time use cases or increase the training complexity significantly. To mitigate this concern, we present a training framework (from scratch) for one-time-step SNNs that uses a novel variant of the recently proposed Hoyer regularizer. We estimate the threshold of each SNN layer as the Hoyer extremum of a clipped version of its activation map, where the clipping threshold is trained using gradient descent with our Hoyer regularizer. This approach not only downscales the value of the trainable threshold, thereby emitting a large number of spikes for weight update with a limited number of iterations (due to only one time step) but also shifts the membrane potential values away from the threshold, thereby mitigating the effect of noise that can degrade the SNN accuracy. Our approach outperforms existing spiking, binary, and adder neural networks in terms of the accuracy-FLOPs trade-off for complex image recognition tasks. Downstream experiments on object detection also demonstrate the efficacy of our approach.

Time-series forecasting in domains like traffic management and industrial monitoring often requires real-time, energy-efficient processing on edge devices with limited resources. Spiking neural networks (SNNs) offer event-driven computation and ultra-low power and have been proposed for use in this space. Unfortunately, existing SNN-based time-series forecasters often use complex transformer blocks. To address this issue, we propose SpikySpace, a spiking state-space model (SSM) that reduces the quadratic cost in the attention block to linear time via spiking selective scanning. Further, we introduce PTsoftplus and PTSiLU, two efficient approximations of SiLU and Softplus that replace costly exponential and division operations with simple bit-shifts. Evaluated on four multivariate time-series benchmarks, SpikySpace outperforms the leading SNN in terms of accuracy by up to 3.0% while reducing energy consumption by over 96.1%. As the first fully spiking state-space model, SpikySpace bridges neuromorphic efficiency with modern sequence modeling, opening a practical path toward efficient time series forecasting systems. Our code is available at https://anonymous.4open.science/r/SpikySpace.

Graph Convolutional Networks (GCNs) achieve an impressive performance due to the remarkable representation ability in learning the graph information. However, GCNs, when implemented on a deep network, require expensive computation power, making them difficult to be deployed on battery-powered devices. In contrast, Spiking Neural Networks (SNNs), which perform a bio-fidelity inference process, offer an energy-efficient neural architecture. In this work, we propose SpikingGCN, an end-to-end framework that aims to integrate the embedding of GCNs with the biofidelity characteristics of SNNs. The original graph data are encoded into spike trains based on the incorporation of graph convolution. We further model biological information processing by utilizing a fully connected layer combined with neuron nodes. In a wide range of scenarios (e.g. citation networks, image graph classification, and recommender systems), our experimental results show that the proposed method could gain competitive performance against state-of-the-art approaches. Furthermore, we show that SpikingGCN on a neuromorphic chip can bring a clear advantage of energy efficiency into graph data analysis, which demonstrates its great potential to construct environment-friendly machine learning models.

The ability to connect visual patterns with the processes that form them represents one of the deepest forms of visual understanding. Textures of clouds and waves, the growth of cities and forests, or the formation of materials and landscapes are all examples of patterns emerging from underlying mechanisms. We present the Scitextures dataset, a large-scale collection of textures and visual patterns from all domains of science, tech, and art, along with the models and code that generate these images. Covering over 1,200 different models and 100,000 images of patterns and textures from physics, chemistry, biology, sociology, technology, mathematics, and art, this dataset offers a way to explore the connection between the visual patterns that shape our world and the mechanisms that produce them. Created by an agentic AI pipeline that autonomously collects and implements models in standardized form, we use SciTextures to evaluate the ability of leading AI models to link visual patterns to the models and code that generate them, and to identify different patterns that emerged from the same process. We also test AIs ability to infer and recreate the mechanisms behind visual patterns by providing a natural image of a real-world pattern and asking the AI to identify, model, and code the mechanism that formed the pattern, then run this code to generate a simulated image that is compared to the real image. These benchmarks show that vision-language models (VLMs) can understand and simulate the physical system beyond a visual pattern. The dataset and code are available at: https://zenodo.org/records/17485502

Sequence learning reduces to similarity-based retrieval over a temporally indexed representation space, a constraint on any sequence model, not a property of a specific architecture. We show that a spiking Sparse Distributed Memory sequence machine (2007) and the transformer (2017) independently instantiate the same five functional operations (encoding, context maintenance, associative retrieval, storage, and decoding), with cosine similarity as the shared retrieval primitive in both. We formalise a Phase-Latency Isomorphism showing that sinusoidal positional phase and spike timing are linearly related, and prove that dot product attention is invariant to this mapping up to a global scale factor on the positional component (Lemma 1). Empirically, frequency-compressed positional encoding fails to converge on a positionally demanding copy task, while a learned rank-based embedding matches or exceeds sinusoidal encoding, indicating that the critical property for positional representation is distance discriminability under dot-product similarity, not sinusoidal form. Time, phase, and rank are three instantiations of the same computational primitive, an ordered index whose structure survives similarity-based retrieval.

Recent years have seen significant progress in developing spiking neural networks (SNNs) as a potential solution to the energy challenges posed by conventional artificial neural networks (ANNs). However, our theoretical understanding of SNNs remains relatively limited compared to the ever-growing body of literature on ANNs. In this paper, we study a discrete-time model of SNNs based on leaky integrate-and-fire (LIF) neurons, referred to as discrete-time LIF-SNNs, a widely used framework that still lacks solid theoretical foundations. We demonstrate that discrete-time LIF-SNNs with static inputs and outputs realize piecewise constant functions defined on polyhedral regions, and more importantly, we quantify the network size required to approximate continuous functions. Moreover, we investigate the impact of latency (number of time steps) and depth (number of layers) on the complexity of the input space partitioning induced by discrete-time LIF-SNNs. Our analysis highlights the importance of latency and contrasts these networks with ANNs employing piecewise linear activation functions. Finally, we present numerical experiments to support our theoretical findings.

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of neural networks that are shift invariant and preserve smoothness of the data: functional neural networks (FNNs). For this, we use methods from functional data analysis (FDA) to extend multi-layer perceptrons and convolutional neural networks to functional data. We propose different model architectures, show that the models outperform a benchmark model from FDA in terms of accuracy and successfully use FNNs to classify electroencephalography (EEG) data.

Epidemic forecasting has become an integral part of real-time infectious disease outbreak response. While collaborative ensembles composed of statistical and machine learning models have become the norm for real-time forecasting, standardized benchmark datasets for evaluating such methods are lacking. Further, there is limited understanding on performance of these methods for novel outbreaks with limited historical data. In this paper, we propose IDOBE, a curated collection of epidemiological time series focused on outbreak forecasting. IDOBE compiles from multiple data repositories spanning over a century of surveillance and across U.S. states and global locations. We perform derivative-based segmentation to generate over 10,000 outbreaks covering multiple outcomes such as cases and hospitalizations for 13 diseases. We consider a variety of information-theoretic and distributional measures to quantify the epidemiological diversity of the dataset. Finally, we perform multi-horizon short-term forecasting (1- to 4-week-ahead) through the progression of the outbreak using 11 baseline models and report on their performance. In addition to standard metrics such as NMSE and MAPE for point forecasts, we include probabilistic scoring rules such as Normalized Weighted Interval Score (NWIS) to quantify the performance. We find that MLP-based methods have the most robust performance, with statistical methods having a slight edge during the pre-peak phase. IDOBE dataset along with baselines are released publicly on https://github.com/NSSAC/IDOBE to enable standardized, reproducible benchmarking of outbreak forecasting methods.

Time series forecasting has played the key role in different industrial, including finance, traffic, energy, and healthcare domains. While existing literatures have designed many sophisticated architectures based on RNNs, GNNs, or Transformers, another kind of approaches based on multi-layer perceptrons (MLPs) are proposed with simple structure, low complexity, and {superior performance}. However, most MLP-based forecasting methods suffer from the point-wise mappings and information bottleneck, which largely hinders the forecasting performance. To overcome this problem, we explore a novel direction of applying MLPs in the frequency domain for time series forecasting. We investigate the learned patterns of frequency-domain MLPs and discover their two inherent characteristic benefiting forecasting, (i) global view: frequency spectrum makes MLPs own a complete view for signals and learn global dependencies more easily, and (ii) energy compaction: frequency-domain MLPs concentrate on smaller key part of frequency components with compact signal energy. Then, we propose FreTS, a simple yet effective architecture built upon Frequency-domain MLPs for Time Series forecasting. FreTS mainly involves two stages, (i) Domain Conversion, that transforms time-domain signals into complex numbers of frequency domain; (ii) Frequency Learning, that performs our redesigned MLPs for the learning of real and imaginary part of frequency components. The above stages operated on both inter-series and intra-series scales further contribute to channel-wise and time-wise dependency learning. Extensive experiments on 13 real-world benchmarks (including 7 benchmarks for short-term forecasting and 6 benchmarks for long-term forecasting) demonstrate our consistent superiority over state-of-the-art methods.