Binary Spikes

Spike-based encodings are sparse and energy-efficient, but have largely been formulated probabilistically, disconnected from most signal processing literature. We recast spike encoders as time-causal wavelet frames with quantitative bandwidths and reconstruction error bounds. The proposed wavelets preserve the sparsity and locality of spiking representations, with reconstruction up to spike quantization and time discretization. We demonstrate reconstruction on ECG and audio datasets, achieving a normalized RMSE comparable to continuous wavelet transforms. The spiking wavelets map directly to neuromorphic hardware.

Underwater image enhancement (UIE) is a practically important yet underexplored application of spiking neural networks (SNNs), where the dominant degradations are large-scale and low-frequency, such as wavelength-dependent colour casts and scattering-induced veiling. Existing SNN restoration designs rely on locally bounded spiking perception, which can limit global correction and lead to saturated or inconsistent representations. To address these challenges, we propose a scale-aware SNN framework for UIE named UIESNN. At its core is a Multi-scale Pooling LIF Block (MPLB) that injects hierarchical multi-scale pooling responses into membrane dynamics, thereby enlarging the effective receptive field while preserving fine-grained details and inducing heterogeneous scale-dependent activations. Building on MPLB, we design a spiking residual architecture that integrates frequency decomposition and attention-based refinement in a fully spike-driven pipeline. Extensive experiments on the EUVP and LSUI benchmarks demonstrate that UIESNN achieves state-of-the-art performance among SNN-based methods, delivering improved colour fidelity and spatial coherence with competitive energy cost.

The Hessian spectrum of trained deep networks exhibits a characteristic structure: a continuous bulk of near-zero eigenvalues and a small number of large outlier eigenvalues (spikes), confirming the relevance of Random Matrix Theory in deep learning. The spike count matches the number of classes minus one. While prior work has described this structure, no method has exploited it operationally to improve classification performance. We propose Hessian Surgery, a post-hoc optimization method that directly perturbs model weights along spike eigenvectors to rebalance per-class accuracy without retraining. We introduce (i) a spike-class sensitivity matrix that quantifies the directional derivative of each class's accuracy along each spike eigenvector, (ii) a constrained optimization of perturbation coefficients that targets weak classes while preserving strong ones, and (iii) an adaptive amplitude control that raises or lowers the perturbation budget based on iteration-level improvement signals. We obtain encouraging results on CIFAR-10 and ISIC-2019 on both balanced accuracy and standard deviation.

Evaluating fairness in Spiking Neural Networks (SNNs) demands rigorous benchmarks that reflect real-world complexities, yet existing assessments remain limited by superficial dataset diversity and idealized hardware assumptions. This work introduces the first systematic fairness benchmark for SNNs, addressing three critical dimensions of realism: (1) demographic coverage gaps in training data, (2) spurious feature leakage (e.g., skin tone as a proxy for class labels), and (3) deployment-environment mismatches (e.g., edge devices with constrained spike encoding). Our framework integrates four cross-demographic datasets with controlled bias injections and three neuromorphic hardware simulators (Loihi 2, SpiNNaker), enabling isolated analysis of fairness-performance trade-offs under resource constraints. Standardized evaluations of 12 state-of-the-art SNNs reveal stark disparities: models trained on biased data exhibit 23% higher false positive rates for underrepresented groups, while hardware limitations (e.g., reduced spike precision) further amplify accuracy gaps by up to 41% in edge deployments. Critically, bias mitigation strategies developed for cloud-based SNNs often degrade under resource constraints, highlighting the need for co-design principles that jointly optimize fairness and hardware efficiency. By bridging algorithmic fairness research with neuromorphic engineering, our benchmark provides a foundation for trustworthy SNNs in socially critical applications such as healthcare and autonomous systems. Our code is available at: https://anonymous.4open.science/r/SNN-Benchmarks-8017.

Modern AI-generated videos are photorealistic at the single-frame level, leaving inter-frame dynamics as the main remaining axis for detection. Existing detectors typically handle this temporal evidence in three ways: feeding the full frame sequence to a generic temporal backbone, reducing one dominant temporal cue to fixed video-level descriptors, or comparing temporal features to real-video statistics through a detection metric. These strategies degrade sharply under cross-generator evaluation, where artifact type and timescale vary across generators. On caption-paired benchmark, GenVidBench, we identify two signatures that prior detectors do not jointly exploit: AI-generated videos exhibit smoother frame-to-frame temporal residuals at the pixel level, and more compact trajectories in the semantic feature space, indicating a temporal smoothness gap at both levels. We further observe that, when raw video is fed into a Spiking Neural Networks (SNNs), fake clips elicit firing predominantly at object and motion boundaries, unlike real clips, suggesting that the SNN responds to temporal artifacts localized at edges. These cues are sparse, asynchronous, and concentrated at moments of change, which makes SNNs a natural choice for this task: their event-driven, sparsely-activated dynamics align with the structure of the residual signal in a way that dense ANN backbones do not. Building on this observation, we propose MAST, a detector that processes multi-channel temporal residuals with a spike-driven temporal branch alongside a frozen semantic encoder for cross-generator generalization. On the GenVideo benchmark, MAST achieves 93.14% mean accuracy across 10 unseen generators under strict cross-generator evaluation, matching or surpassing the strongest ANN-based detectors and demonstrating the practical applicability of SNNs to AI-generated video detection.

Biological neural systems achieve remarkable robustness and adaptability in uncertain environments through sparse, event-driven spike-based information processing and adaptive regulation. Inspired by this paradigm, this paper develops a neuromorhpic disturbance observer (NDO) and control framework that replaces conventional continuous-time signal representations with spike-timing encoding. Both disturbance estimates and control inputs are constructed via integrate-and-fire (IF) neuron dynamics from discrete spike events, yielding intrinsically event-driven updates. An adaptive-threshold triggering mechanism is inspired by spike-frequency adaptation (SFA), enabling history-dependent regulation of spike generation. Simulation results demonstrate that the proposed framework achieves neurally inspired robustness and adaptability, while the adaptive-threshold spiking scheme reduces spike events to 42.6% of the fixed-threshold case under noisy conditions.

Spiking neural networks (SNNs) are promising for edge sensing due to their event-driven computation and temporal filtering capability. However, standard leaky integrate-and-fire (LIF) neurons communicate only through binary spikes, which severely limit representational capacity. Existing multi-level spiking neurons improve information transmission, but often rely on uniform quantization that mismatches membrane-potential distributions or introduces costly synaptic multiplications. In this paper, we propose ShiftLIF, a multi-level spiking neuron that maps membrane potentials to a logarithmically spaced power-of-two spike set. This design provides finer representation in the small-amplitude regime, where membrane potentials are densely concentrated, while enabling multiplier-free synaptic computation through bit-shift and accumulation operations. As a result, ShiftLIF improves spike-level expressiveness without sacrificing the hardware-friendly nature of standard SNN computation. We evaluate ShiftLIF on 10 datasets spanning wireless, acoustic, motion, and visual sensing tasks. Results show that ShiftLIF consistently matches or exceeds the accuracy of existing multi-level spiking neurons while maintaining synaptic energy consumption close to standard binary LIF. These results indicate that ShiftLIF provides a favorable accuracy-efficiency trade-off for cross-modal edge sensing.

Spiking Neural Networks (SNNs) are widely regarded as an energy-efficient paradigm for modeling and processing temporal and event-driven information. Incorporating delays in SNNs has been proven to be an effective mechanism for improving spike alignment in event-driven tasks. However, existing delay learning approaches predominantly assign static delays to individual synapses, resulting in a large number of delay parameters and limited adaptability to input-dependent activity dynamics. To this end, we propose a Congestion-Aware Dynamic Axonal Delay (CADAD) mechanism, which decomposes the delay into a channel-wise static base delay for temporal structuring and a global, activity-conditioned shift that dynamically regulates the state update rate under varying spike intensities. The delay parameters are learned using differentiable linear interpolation and discretized at inference time, preserving the benefits of dynamic delay modulation while incurring only minimal additional cost. Experiments on speech benchmarks, including the Spiking Heidelberg Dataset, Spiking Speech Commands, and Google Speech Commands, demonstrate that introducing congestion-aware delays into synaptic signal transmission effectively improves accuracy on temporal tasks, notably achieving 93.75% accuracy on SHD, 80.69% accuracy on SSC, and 95.58% on GSC-35, while reducing the parameter count by approximately 50% compared to state-of-the-art delay-based methods with the same architecture.

We propose EdgeSpike, a co-designed spiking neural network (SNN) framework for autonomous low-power sensing in edge Internet of Things (IoT) architectures. EdgeSpike unifies (i) a hybrid surrogate-gradient and direct-encoding training pipeline, (ii) a hardware-aware neural architecture search (NAS) bounded by per-inference energy and memory budgets, (iii) an event-driven runtime targeting Intel Loihi 2, SpiNNaker 2, and commodity ARM Cortex-M microcontrollers with custom spike-sparse SIMD kernels, and (iv) a lightweight local plasticity rule enabling continual on-device adaptation without backpropagation. The framework is evaluated across five sensing tasks (keyword spotting, vibration-based machine fault detection, surface electromyography gesture recognition, 77 GHz radar human-activity classification, and structural-health acoustic-emission monitoring) on three hardware targets. EdgeSpike achieves a mean classification accuracy of 91.4%, within 1.2 percentage points (pp) of strong INT8 convolutional neural network (CNN) baselines (mean 92.6%), while reducing energy per inference by 18x to 47x on neuromorphic hardware (mean 31x) and by 4.6x to 7.9x on Cortex-M (mean 6.1x). End-to-end latency remains at or below 9.4 ms across all 15 task-hardware configurations. A seven-month, 64-node wireless field deployment confirms a 6.3x extension in projected battery lifetime (from 312 to 1978 days at 2 Wh per node) and bounded accuracy degradation under seasonal drift (0.7 pp with on-device adaptation versus 2.1 pp without). Hardware-aware NAS evaluates 8400 candidates and yields a 12-point Pareto front. EdgeSpike will be released as open source with reproducible training pipelines, hardware-portable runtimes, and benchmark suites.

Binary spike coding enables sparse and event-driven computation in spiking neural networks (SNNs), yet its 1-bit-per-timestep representation fundamentally limits information throughput. This bottleneck becomes increasingly restrictive in deep architectures under short simulation horizons. We propose the Quantized Burst-LIF (QB-LIF) neuron, which reformulates burst spiking as a saturated uniform quantization of membrane potentials with a learnable scale. Instead of relying on predefined multi-threshold structures, QB-LIF treats the quantization scale as a trainable parameter, allowing each layer to autonomously adapt its spiking resolution to the underlying membrane-potential statistics. To preserve hardware efficiency, we introduce an absorbable scale strategy that folds the learned quantized scale into synaptic weights during inference, maintaining a strict accumulate-only (AC) execution paradigm. To enable stable optimization in the discrete multi-level space, we further design ReLSG-ET, a rectified-linear surrogate gradient with exponential tails that sustains gradient flow across burst intervals. Extensive experiments on static (CIFAR-10/100, ImageNet) and event-driven (CIFAR10-DVS, DVS128-Gesture) benchmarks demonstrate that QB-LIF consistently outperforms binary and fixed-burst SNNs, achieving higher accuracy under ultra-low latency while preserving neuromorphic compatibility.

Spiking Neural Networks (SNNs) offer a biologically inspired foundation for low-power, event-driven intelligence, yet their direct on-chip supervised training remains a key hardware challenge. This paper presents a multiplication-free, spike-time-based learning algorithm specifically designed for efficient FPGA realization. The proposed approach eliminates floating-point arithmetic and explicit gradient storage, enabling a fully event-driven, digital training pipeline. Implemented on a Xilinx Artix-7 FPGA, the architecture achieves high operating speed and minimal resource usage while maintaining competitive accuracy. These results demonstrate that the learning algorithm effectively maps onto reconfigurable hardware, achieving both computational and energy efficiency. Software simulations further validate scalability, with 96.5% and 84.8% accuracy on MNIST and Fashion-MNIST. With its spike-driven and multiplier-free operation, the proposed framework delivers a practical and scalable hardware solution for real-time, on-chip SNN learning in edge environments.

Spiking Vision Transformers (S-ViTs) offer a promising framework for energy-efficient visual learning. However, existing designs remain limited by two fundamental issues: the restricted information capacity of binary spike coding and the dense token interactions introduced by global self-attention. To address these challenges, this work proposes BSViT, a burst spiking-driven Vision Transformer featuring a Dual-Channel Burst Spiking Self-Attention (DBSSA) mechanism. DBSSA encodes queries with binary spikes and keys with burst spikes to enhance representational capacity. The value pathway adopts dual excitatory and inhibitory binary channels, enabling signed modulation and richer spike interactions. Importantly, the entire attention operation preserves addition-only computation, ensuring compatibility with energy-efficient neuromorphic hardware. To further reduce spike activity and incorporate spatial priors, a patch adjacency masking strategy is introduced to restrict attention to local neighborhoods, resulting in structure-aware sparsity and reduced computational overhead. In addition, burst spike coding is systematically integrated across the network to increase spike-level representational capacity beyond conventional binary spiking. Extensive experiments on both static and event-based vision benchmarks demonstrate that BSViT consistently outperforms existing spiking Transformers in accuracy while maintaining competitive energy efficiency.

Pre-trained vision models have found widespread application across diverse domains. Prompt tuning-based methods have emerged as a parameter-efficient paradigm for adapting pre-trained vision models. While effective on standard benchmarks, the continuous and dense nature of learned prompts can lead to sensitivity against input noise, as the high-capacity prompts tend to overfit task-irrelevant details. To address this trade-off, we propose Spike-NVPT, a noise-robust visual prompt tuning method. Specifically, we design a Signal Filtering Layer based on spiking neurons, which uses the integrate-and-fire (IF) mechanism to accumulate task-relevant signals over time and filter transient noise fluctuations. A subsequent Spike Discretization Unit converts filtered signals into sparse binary prompts. This discretization acts as a strong regularizer, forcing the model to anchor decision boundaries on the most discriminative and robust features. Notably, the resulting binary prompts remain static during deployment, ensuring zero additional computational overhead during inference. Experimental results demonstrate that Spike-NVPT achieves superior robustness performance, with a maximum improvement of 11.2% over conventional methods, and retains competitive accuracy on clean datasets. To the best of our knowledge, this is the first attempt to leverage spiking neurons for fine-tuning traditional artificial neural network (ANN)-based visual models.

When do transformers commit to a decision, and what prevents them from correcting it? We introduce \textbf{prolepsis}: a transformer commits early, task-specific attention heads sustain the commitment, and no layer corrects it. Replicating \citeauthor{lindsey2025biology}'s (\citeyear{lindsey2025biology}) planning-site finding on open models (Gemma2 2B, Llama3.2 1B), we ask five questions. (Q1)~Planning is invisible to six residual-stream methods; CLTs are necessary. (Q2)~The planning-site spike replicates with identical geometry. (Q3)~Specific attention heads route the decision to the output, filling a gap flagged as invisible to attribution graphs. (Q4)~Search requires ${\leq}16$ layers; commitment requires more. (Q5)~Factual recall shows the same motif at a different network depth, with zero overlap between recurring planning heads and the factual top-10. Prolepsis is architectural: the template is shared, the routing substrates differ. All experiments run on a single consumer GPU (16,GB VRAM).

Conventional RGB-based high dynamic range (HDR) imaging faces a fundamental trade-off between motion artifacts in multi-exposure captures and irreversible information loss in single-shot techniques. Modulo sensors offer a promising alternative by encoding theoretically unbounded dynamic range into wrapped measurements. However, existing modulo solutions remain bottlenecked by iterative unwrapping overhead and hardware constraints limiting them to low-speed, grayscale capture. In this work, we present a complete modulo-based HDR imaging system that enables high-speed, full-color HDR acquisition by synergistically advancing both the sensing formulation and the unwrapping algorithm. At the core of our approach is an exposure-decoupled formulation of modulo imaging that allows multiple measurements to be interleaved in time, preserving a clean, observation-wise measurement model. Building upon this, we introduce an iteration-free unwrapping algorithm that integrates diffusion-based generative priors with the physical least absolute remainder property of modulo images, supporting highly efficient, physics-consistent HDR reconstruction. Finally, to validate the practical viability of our system, we demonstrate a proof-of-concept hardware implementation based on modulo-encoded spike streams. This setup preserves the native high temporal resolution of spike cameras, achieving 1000 FPS full-color imaging while reducing output data bandwidth from approximately 20 Gbps to 6 Gbps. Extensive evaluations indicate that our coordinated approach successfully overcomes key systemic bottlenecks, demonstrating the feasibility of deploying modulo imaging in dynamic scenarios.

Spiking neural networks (SNNs) offer a biologically inspired computing paradigm with significant potential for energy-efficient neural processing. Among neural coding schemes of SNNs, Time-To-First-Spike (TTFS) coding, which encodes information through the precise timing of a neuron's first spike, provides exceptional activity sparsity and energy efficiency. However, existing TTFS models lack efficient training methods, suffering from high inference latency and limited performance, limiting their practicality on neuromorphic hardware. In this work, we propose latency coding, an extension of TTFS coding, and present a compatible framework that enables the efficient training of deep latency-coded SNNs by leveraging backpropagation through time (BPTT) algorithm. The framework includes: (1) a latency encoding (LE) module with feature extraction and straight-through estimators to address severe information loss in direct intensity-to-latency mapping; (2) relaxation of the strict single-spike constraint in intermediate layers to improve information propagation and gradient flow; and (3) a temporal adaptive decision (TAD) loss function that dynamically weights supervision signals based on the model's confidence, balancing the trade-off between speed and accuracy. Experimental results demonstrate that our method achieves competitive or superior accuracy compared with existing TTFS-coded SNNs with ultra-low inference latency and high energy efficiency. Latency-coded SNNs also demonstrate improved robustness against input perturbations. These findings highlight latency coding as a practical and hardware-friendly approach for fast and energy-efficient neuromorphic processing.

Spectral gradient methods, such as the Muon optimizer, modify gradient updates by preserving directional information while discarding scale, and have shown strong empirical performance in deep learning. We investigate the mechanisms underlying these gains through a dynamical analysis of a nonlinear phase retrieval model with anisotropic Gaussian inputs, equivalent to training a two-layer neural network with the quadratic activation and fixed second-layer weights. Focusing on a spiked covariance setting where the dominant variance direction is orthogonal to the signal, we show that gradient descent (GD) suffers from a variance-induced misalignment: during the early escaping stage, the high-variance but uninformative spike direction is multiplicatively amplified, degrading alignment with the true signal under strong anisotropy. In contrast, spectral gradient descent (SpecGD) removes this spike amplification effect, leading to stable alignment and accelerated noise contraction. Numerical experiments confirm the theory and show that these phenomena persist under broader anisotropic covariances.

Supervised learning in spiking neural networks (SNNs) typically requires either gradient-based backpropagation, which sacrifices the Hebbian, spike-driven character of biological plasticity, or reward-modulated Spike-Timing-Dependent Plasticity (STDP), in which class supervision enters only as a scalar gate on an otherwise class-agnostic correlation signal. We propose Supervised Spike Agreement-Dependent Plasticity (Supervised SADP), a gradient-free supervised Hebbian learning algorithm in which class information is embedded directly into the Hebbian plasticity computation rather than introduced through reward modulation. SADP trains the output layer via a supervised Hebbian rule that encodes class labels into output spike patterns, then trains the hidden layer by measuring each hidden neuron's chance-corrected temporal agreement, Cohen's kappa, with the correct-class output spike train produced by the forward pass without gradient computation or external reward. A K-shift extension aggregates agreement over temporal offsets, providing robustness to spike-timing jitter at linear computational cost. We evaluate Supervised SADP against reward-modulated STDP across six benchmark and medical imaging datasets, four input encoding strategies, K_shift in {5,25}, and three reward modes (none, binary, margin). Supervised SADP outperforms STDP in a significant majority of comparisons. Under Poisson encoding, SADP achieves 86.46% on MNIST and 76.62% on Fashion-MNIST, outperforming the best STDP configurations by 23.66 and 23.29 percentage points, respectively. Across the encodings tested, including CNN-extracted features, SADP outperforms STDP in the large majority of cells and trains 1.47x faster on average, with up to 2.86x speedup under Poisson inputs. These results position Supervised SADP as a stable, efficient, gradient-free alternative to reward-modulated STDP for supervised SNN learning.

Spiking neural networks (SNNs), central to computational neuroscience and neuromorphic machine learning (ML), require efficient simulation and gradient-based training. While AI accelerators offer promising speedups, gradient-based SNNs typically implement sparse spike events using dense, memory-heavy data-structures. Existing exact gradient methods lack generality, and current simulators often omit or inefficiently handle delayed spikes. We address this by deriving gradient computation through spike event queues, including delays, and implementing this into memory-efficient, autodifferentiable spike event queues (ADSEQ). These are benchmarked across CPU, GPU, TPU, and LPU platforms. We find that queue design strongly shapes performance. CPUs, as expected, perform well with traditional tree-based or FIFO implementations, while GPUs excel with ring buffers for smaller simulations, yet under higher memory pressure prefer more sparse data-structures. TPUs seem to favor an implementation based on sorting intrinsics. Selective spike dropping provides a simple performance-accuracy trade-off, which could be enhanced by future autograd frameworks adapting diverging primal/tangent data-structures.

Neuromorphic and quantum computing have recently emerged as promising paradigms for advancing artificial intelligence, each offering complementary strengths. Neuromorphic systems built on spiking neurons excel at processing time series data efficiently through sparse, event-driven computation, consuming energy only upon input events. Quantum computing, on the other hand, operates on state spaces that grow exponentially in dimension with the number of qubits -- as a consequence of tensor-product composition -- with quantum states admitting superposition across basis states and entanglement between subsystems. Hybrid approaches combining these paradigms have begun to show potential, but existing quantum spiking models have important limitations. Notably, they implement classical memory mechanisms on single qubits, requiring repeated measurements to estimate firing probabilities, while relying on conventional backpropagation for training. In this paper, we propose a novel stochastic quantum spiking (SQS) neuron model that addresses these challenges. The SQS neuron uses multi-qubit quantum circuits to realize a spiking unit with internal quantum memory, enabling event-driven probabilistic spike generation in a single shot during inference. Furthermore, we study networks of SQS neurons, dubbed SQS neural networks (SQSNN), and demonstrate that they can be trained via a hardware-friendly local learning rule, eliminating the need for global classical backpropagation. The proposed SQSNN model is shown via experiments with both conventional and neuromorphic datasets to improve over previous quantum spiking neural networks, as well as over classical counterparts, when fixing the overall number of trainable parameters, highlighting its potential for event-driven applications such as neuromorphic integrated sensing and communications (N-ISAC).

Neuromorphic computing aims to improve the efficiency of artificial neural networks by taking inspiration from biological neurons and leveraging temporal sparsity, spatial sparsity, and compute near/in memory. Although these approaches have shown efficiency gains, training these spiking neural networks (SNN) remains difficult. The original attempts at converting trained conventional analog neural networks (ANN) to SNNs used the rate of binary spikes to represent neuron activations. This required many simulation time steps per inference, which degraded efficiency. Intel's Loihi 2 is a neuromorphic platform that supports graded spikes which can be used to represent changes in neuron activation. In this work, we use Loihi 2's graded spikes to develop a method for converting ANN networks to spiking networks, which exploits temporal and spatial sparsity. We evaluated the performance of this network on Loihi 2 and compared it to NVIDIA's Jetson Xavier edge AI platform. The results show that neuromorphic approaches achieve significant improvements in efficiency and latency (energy-delay product) over existing solutions.

AI is rapidly advancing neuroscience, yet many laboratories fail to fully unleash its potential due to significant interdisciplinary barriers. While pre-trained neural models for physiological data are progressing quickly, their heterogeneous architectures and modality-specific constraints hinder systematic integration, selection, and evaluation. Despite recent advances in large language model (LLM)-based agent systems for intelligent scientific applications, existing approaches often still lack the domain expertise required to effectively select and coordinate diverse neuroscience pre-trained models and handle unique data types in this domain. We present NS-Copilot, an LLM-driven multi-agent system for neuroscience analysis that autonomously supports end-to-end workflows for diverse professional tasks. It unifies domain-specific pre-trained models and supports key neuroscience modalities, including EEG and extracellular spike data, through a natural-language interface. Given raw data and a task description, NS-Copilot orchestrates agents with specialized roles for planning, adaptive control, code generation, and result synthesis, enabling analysis without dataset-specific heuristics. We evaluate NS-Copilot on neuroscience benchmarks spanning Alzheimer's disease, Parkinson's disease, and working memory spike decoding. Across 8 trials per task, the system consistently outperforms strong baselines on the primary metric, demonstrating the ability of NS-Copilot for effective and scalable neuroscience analysis. Our code is publicly available at https://github.com/FrankLiu1102/ns-copilot.

The brain uses discrete spikes for dynamic computation, yet, how neural microcircuits (NMCs) solve temporal credit assignment using local spike timing remains a fundamental open question. Dominant spiking neural network (SNN) approaches circumvent this by approximating backpropagation through surrogate gradients, decoupling learning from biological spike timing. Here, we reformulate temporal credit assignment as a state separation problem: extracting task-required components induced by historical perturbations directly from the current neural state. This enables an online feedback learning framework for NMCs through a gradient tunneling (GT) algorithm and the lead-lag expansion technique that derives credit assignment from local synaptic spike timing, while remaining compatible with ANN-SNN hybrid architectures. Experimentally, GT-trained NMCs excel at long-timescale evidence integration and noise-robust memory retention, and perform comparably to leading SNN online learning methods on real-world benchmarks with far fewer parameters. The proposed framework addresses the two-decade-old NMC feedback learning problem and suggests a computationally plausible explanation for the brain's learning mechanisms.