Frequency Domain

Machine fault diagnosis from vibration requires learning from scarce labelled fault recordings while meeting the computational constraints of edge devices for local inference. We introduce DualRes, a compact oscillatory state-space model that combines two complementary spectral views of vibration, capturing rapid changes and fine frequency structure. Time-aligned views are processed by selective oscillatory memory, which learns how long to retain temporal patterns. The encoder contains 39,528 parameters. We evaluate supervised learning across six bearing datasets and a gearbox benchmark, with an additional gearbox pilot. Recording-level splits and explicit accounting of labelled duration distinguish data efficiency from repeated exposure to correlated samples. On the main gearbox benchmark, DualRes achieves state-of-the-art performance among the nine evaluated methods at six of seven label budgets. With about six labelled seconds per class, it improves macro-F1 by 16.1 percentage points over the next strongest comparator. On the same benchmark, DualRes achieves a 1.44-fold recording-level speedup and a 24.8-fold reduction in checkpoint storage relative to a selective state-space baseline under matched hardware and runtime conditions. Bearing results reveal task-dependent trade-offs. These findings support oscillatory memory as a compact approach to vibration diagnosis under limited labelled exposure.

Modeling spatiotemporal dynamical systems governed by partial differential equations (PDEs) poses two major challenges: it either requires expensive physics-based simulators that entail iterative numerical solving at high computational cost, or it depends on abundant training data, yet purely data-driven models often generalize poorly to downstream dynamic operating conditions. We propose DEFT, a frequency-domain data sampling method that identifies the dominant Fourier modes of a physical system and systematically varies the corresponding amplitudes and phases to generate physically consistent training data via the inverse discrete Fourier transform. In addition, we derive a generalization bound of this method. We note that it also provides a theoretically principled criterion for selecting $K$. We evaluate the proposed method through three sets of experiments, each targeting a distinct aspect of its utility. First, we validate the framework on canonical PDEs solving demonstrating that it outperforms traditional methods when the system is dominated by a few prominent frequency components. Second, we employ DEFT as a data-value filter on the diffusion--sorption and Burgers equations of PDEBench, showing that it reduces data requirements by $40\%$ while sacrificing less than $2\%$ in predictive accuracy. Third, to evaluate DEFT for more challenging and practically relevant problems, we validate it in the battery degradation PDE system, achieving consistently high predictive accuracy across various test datasets with $R^2$ values exceeding $0.99$. Moreover, the learned frequency-domain features transfer to other battery chemistries with only $20\%$ of the fine-tuning data. These results demonstrate that DEFT is an effective data-sampling method for efficient operator learning.

To address the degradation of bearing fault diagnosis accuracy under strong noise, this paper proposes a time-frequency dual-domain multi-scale convolutional neural network. The time-domain branch employs three parallel convolutional kernels to capture multi-scale impulse features, while the frequency-domain branch applies the Fast Fourier Transform to extract noise-robust spectral structure information. Features from both branches are fused for fault classification, yielding a compact model of 110,122 parameters. Experiments on the CWRU bearing dataset across seven signal-to-noise ratio levels demonstrate that the proposed method achieves 99.75% accuracy under clean conditions and maintains 92.50% at -4 dB SNR, representing a 7.25 percentage-point improvement over the single-domain baseline with monotonically increasing gains under stronger noise. Ablation experiments validate the independent performance contributions of the time-domain multi-scale branch and the frequency-domain branch. Comparative experiments against WDCNN, DRSN-CW, MCNN, and 1D-LeNet confirm the superiority of the proposed method under strong noise conditions.

Deep learning is a new way for machinery fault diagnosis but requires extensive labeled data, a scarce resource in industrial settings. We propose Spectral Aliasing Pretext (SAP), a self-supervised learning method that pretrains models on unlabeled vibration data by exploiting spectral aliasing. We deliberately undersample signals to create folded spectrum, then train a Transformer to reconstruct the original unfolded spectrum. This pretext task forces the model to learn frequency-domain invariants characteristic of mechanical faults, without potentially destructive augmentations. Experiments on the CWRU dataset show that SAP learns stable and highly discriminative representations. In a linear probing setting, SAP quickly achieves very high classification performance with only a small fraction of labeled data and low variance. In contrast, full fine-tuning, including fully supervised training, does not lead to more stable or better results. Overall, these findings suggest that SAP combined with linear probing can be more effective and reliable than fully supervised training for fault diagnosis with limited labeled data.

Low-light image enhancement (LLIE) aims to improve image quality and clarity in diverse and demanding low-illumination environments. However, existing deep learning-based LLIE methods struggle to accurately capture real-world illumination and restore texture details, largely because their algorithmic strengths remain underutilized. To address these issues, we present a supervised frequency domain deep learning network for LLIE, named multi-scale attention combined with the Fourier transform (MSFT) which adopts a U-shaped, one-stage architecture that infuses guidance from low-light images into the network by channeling it through multi-scale attention. We further fuse the amplitude information from priori channels with that of the low-light image in MSFT's self-created module, and carry out multi-scale guidance along with the network. Subsequently, to better enhance the faint feature, such as fine content and textures, and to better fuse global context confidence in the decoding stage, we separately introduce a multi-shape synergistic attention and a lightweight network that effectively integrate information in high-dimensional space to embed into the superlative feature space channel containing rich texture information. Extensive experiments conducted on LOL, SID, SMID, and SDSD datasets demonstrate that MSFT significantly outperforms state-of-the-art competitors. For example, compared with Retinexformer, our method achieves a peak signal-to-noise ratio of up to 41.76 decibels on the SDSD-outdoor dataset with an increase of 11.92 decibels and a structural similarity index of 0.988 with a 13.80% improvement.

Existing Large Vision-Language Models (LVLMs) struggle with long-form video understanding due to the quadratic computational cost of visual tokens. While recent efficient methods attempt to compress tokens via hard pruning or uniform merging, they operate strictly in the spatial feature domain, where robust structural context and discriminative semantic details are inherently entangled. In this work, we propose WaveZip, a joint signal-frequency-domain framework for efficient video inference. Driven by the insight that temporal redundancy resides in low-pass approximation scales while spatial saliency strongly correlates with high-frequency components, WaveZip leverages Discrete Wavelet Transforms (DWT) to disentangle these signals. Temporally, it employs 1D DWT to analyze query-frame relevance, and the resulting high-frequency coefficients are further gated by inter-frame differences, with both signals jointly driving the dynamic allocation of a precise frame-level token budget. Spatially, a 2D DWT decomposes features into low-frequency approximations and high-frequency detail components, where the high-frequency coefficients are modulated within query-salient regions to regulate spatial reconstruction. Importantly, WaveZip requires no task-specific training and can be seamlessly integrated into off-the-shelf LVLMs to boost inference efficiency. Extensive experiments on long video understanding benchmarks demonstrate that WaveZip retains 99.6% of the full performance under an extreme 10x compression ratio, consistently outperforming state-of-the-art methods.

The dynamics of communication environments induce significant distribution shifts across domains, challenging the generalization of deep learning-based automatic modulation classification (AMC) models. While existing UDA methods alleviate this problem by aligning source and target features, they give limited consideration to modulation-specific structures that remain informative across domain conditions. In this paper, we consider signal prior knowledge, grounded in communication protocols and physical principles, as a potential way to enhance cross-domain representation learning. Given that different priors may vary in modulation discriminability, domain stability, and complementarity, this paper first analyzes five commonly adopted signal representations that instantiate different signal priors. From them, in-phase/quadrature (IQ), amplitude--phase (AP), and autocorrelation function (ACF) are selected as compact prior-guided inputs. Based on that, a dual knowledge and data-driven network (DKDNet) is proposed for cross-domain AMC. The multi-representation feature encoder (MRFE) and dynamic lightweight fusion unit (DLFU) are designed to achieve unified representation learning and adaptive feature fusion, and the resulting fused features are optimized with modulation classification and adversarial domain alignment objectives. Experiments on both simulated and public datasets validate the rationality of the prior selection and demonstrate the superiority of the proposed method.

Generalizing sleep staging models to unseen datasets is challenging, and typical domain generalization (DG) methods often rely on multiple source domains or domain labels that are rarely available in practice. We tackle the stricter and more practical setting of single-source domain generalization: training on a single labeled source dataset, without domain labels or access to target data. We present SleepBand, a physiology-guided framework that embeds oscillatory priors via a learnable Morlet filter bank and a structured integration-and-recalibration pipeline. This anchors representations to domain-invariant sleep rhythms (e.g., slow waves, spindles), reducing reliance on dataset-specific artefacts. On five public datasets, SleepBand achieves state-of-the-art SDG performance and remains competitive under leave-one-domain-out (multi-source) DG. Analyses show that the learned filters align with canonical neurophysiology and that robustness stems from focusing on narrowband, physiologically meaningful cues. Our results suggest that principled, physiology-aware inductive biases are a promising path for robust single-domain sleep staging. Code is available at https://github.com/lzcn/sleep-band

Federated Learning (FL) is fundamentally challenged by statistical heterogeneity, where non-identically distributed (non-IID) data induces client drift that severely hampers global convergence. While existing approaches attempt to mitigate this drift through spatial-domain gradient correction or regularization, they overlook the intrinsic spectral structure of optimization signals. In this work, we revisit client drift from a novel frequency-domain perspective and uncover a critical Spectral Bias of Drift: inter-client gradient divergence is predominantly concentrated in low-frequency components which encode client-specific distributional shifts, while high-frequency components representing fine-grained features remain relatively consistent. Motivated by this, we propose SpecGradFilter, a unified Spectral Gradient Filtering Framework that tames heterogeneity by suppressing discordant low-frequency signals. Crucially, we demonstrate that SpecGradFilter is a generalizable principle, effective not only via precise FFT-based truncation but also through spatial approximations like Gaussian detrending. Extensive experiments on benchmarks such as CIFAR-10/100 and Tiny-ImageNet demonstrate that SpecGradFilter significantly performs better performance in highly Non-IID settings with negligible communication overhead, establishing a new paradigm for robust federated optimization.

Federated Learning (FL) enables decentralized training without data sharing, but suffers from statistical heterogeneity across clients, leading to client drift, poor generalization, and sharp minima compared to centralized training. Sharpness-Aware Minimization (SAM) has emerged as a promising approach to improve generalization, yet its application in federated learning still suffers from divergence problems, since perturbations are computed locally and reflect client-specific loss geometries. To better understand this issue, we provide experimental evidence from a new perspective, the frequency domain, for SAM perturbations in federated settings, revealing that inter-client perturbation inconsistencies are predominantly concentrated in the low-frequency spectrum. Motivated by this insight, we propose Federated learning with Frequency-domain Filtering of SAM perturbations (FedFFT). It is a lightweight and plug-and-play method that filters out low-frequency components of SAM perturbations without requiring additional communication, thereby suppressing inconsistent components in client updates while preserving consistent learning signals. Extensive experiments across multiple benchmarks and diverse backbones demonstrate that FedFFT consistently outperforms SAM-based FL methods, particularly under severe non-IID distributions. These results highlight the effectiveness, scalability, and general applicability of our frequency-domain perspective for sharpness-aware federated optimization.

Object detection under adverse weather remains challenging due to severe visual degradations and domain shifts. Existing enhancer-based approaches attempt to improve detection by cascading an enhancer with a detector, but they introduce redundant feature extraction and incur high computational cost with limited accuracy gains when paired with SOTA detectors. We propose FR-DETR, a detector-centric framework that refines features rather than images, focusing enhancement on regions of interest and leveraging frequency-domain cues. Specifically, we design (I) a Frequency Refinement Module that dynamically separates and reweights low- and high-frequency components to improve foreground-background discrimination, and (II) a Recurrent Focus Refinement Module (RFRM) that iteratively refines features using coarse predictions as guidance. Extensive experiments demonstrate that FR-DETR achieves superior detection accuracy under adverse weather while being significantly more computationally efficient than enhancer-based methods. Our implementation is available at https://github.com/ducnt1210/FR-DETR.

In next-generation wireless networks, the growing density of devices and limited spectrum resources pose severe jamming challenges to fragile legitimate communication links in the wireless electromagnetic environment. Crucially, when jamming overlaps with pilot and data symbols in both time and frequency domains, it inflicts a severe bottleneck on receiver-side joint estimation and detection. Existing schemes often lack an effective framework to combat such jamming contamination, thereby failing to guarantee reliable transmission. To address this issue, we propose a Brownian bridge diffusion-based joint channel estimation and data detection framework (BBD-JCED) for jamming-resilient receivers. Specifically, the proposed framework comprises two core modules: the first extracts jamming features in the short-time Fourier transform (STFT) domain and suppresses jamming samples, thereby improving the signal-to-jamming-plus-noise ratio (SJNR) of the received signal; the second introduces a Brownian bridge diffusion (BBD) process to model the evolution of the suppressed signal and the encoded bits in the presence of channel estimation errors, thereby enabling enhanced joint channel estimation and data detection. To alleviate the computational burden of the BBD process in the second module, we further derive a fast ordinary differential equation (ODE) solver that enables its low-complexity iterative evolution. Finally, we design a multi-module training algorithm to improve the data recovery capability of the proposed framework. Simulation results demonstrate that the proposed framework achieves superior bit recovery performance compared with baseline schemes while maintaining a lower number of model parameters and competitive computational complexity.

Diffusion prior-based methods have shown impressive results in real-world image super-resolution (ISR), yet two key challenges persist: balancing pixel-level fidelity with semantic quality, and adapting to diverse degradations. Existing dual-branch approaches freeze the pixel module during semantic training, but the semantic branch can still expand capacity within the pixel subspace, precluding genuine perceptual improvement. Moreover, using a single static adapter cannot generalize across heterogeneous real-world corruptions. To address both issues, we propose FreqOrtho-SR, which comprises: $\textbf{Freq}$uency-guided Mixture of LoRA Experts (FreqMoE), it routes inputs to specialized experts via a non-parametric FFT-based degradation-feature extractor that encodes frequency-domain signatures, enabling stable and interpretable specialization across corruption types; and $\textbf{Ortho}$gonal Gradient Projection (OGP), which reframes the dual-objective optimization as a subspace-constrained problem: by extracting the pixel-fidelity subspace via SVD on combined expert weight deltas and projecting semantic gradients onto its null space, OGP guarantees orthogonality between the two objectives, enabling genuinely complementary learning without mutual interference. Experiments show that FreqOrtho-SR achieves competitive overall performance and a strong fidelity-perception trade-off across multiple benchmarks with efficient single-step inference. The source code of our method can be found at $\href{https://github.com/sonhm3029/FreqOrtho-SR}{\texttt{sonhm3029/FreqOrtho-SR}}$.

Heart Rate Variability (HRV) analysis is a key indicator of cardiac physiological state and aids in disease diagnosis. However, research on HRV parameters in healthy individuals remains limited, and no gold standard exists. This study evaluates HRV indices in 40 healthy adults (20 men, 20 women, aged 30-50) to improve HRV's clinical utility. Using computational methods for signal processing and data analysis, time, frequency, and nonlinear indices were analyzed to address five questions: (1) normality, (2) stability, (3) correlation, (4) reproducibility, and (5) consistency. Key findings: (1) Time-domain and nonlinear indices, particularly global and LF (low frequency), follow normal distributions, with gender differences noted. (2) Most indices are stable except HF (high frequency)-related ones. (3) High correlations in HF-related indices suggest redundancy, indicating only one is necessary in studies. (4) Comparisons with the Fantasia database revealed less than 10% error for most indices, except SD2 and SDNN in women (greater than 15%). (5) Time-domain and nonlinear indices show low inter-study variability, while frequency-domain indices exhibit high variability, limiting cross-study comparisons. The selected indices-ApEn and IRRR (global variability), HRVi and SD2 (LF), and MADRR or rMSSD (HF)-are best suited for accurately representing HRV components and enhancing its clinical and research relevance.

While the quadratic sequence-length bottleneck of transformers has fueled a resurgence in recurrent models, effectively capturing complex dynamics requires architectures that balance efficient training with highly expressive latent states. Echo State Networks (ESNs) offer a compelling approach by utilizing fixed recurrent weights to circumvent backpropagation through time, enabling a closed-form training solution. However, achieving the expressivity needed for complex tasks demands large reservoirs, exposing an $\mathcal{O}(N^2)$ state-update bottleneck that prevents ESNs from matching the scale of contemporary recurrent models. To address this limitation, we introduce Frequency Domain Reservoir Computing (FRESCO), an ESN architecture operating entirely in the frequency domain while avoiding domain-shift overheads to achieve $\mathcal{O}(N)$ complexity for dense, non-linear recurrent updates. By employing a novel dimensional zero-padding input embedding, a packed \FDh readout, and a natively applied frequency-domain non-linearity, FRESCO drastically reduces computational costs and energy consumption of training and inference. Furthermore, FRESCO matches the state-of-the-art predictive performance on memory benchmarks, sequential classification, and multivariate long-horizon forecasting, offering a scalable path forward for dense recurrent architectures.

Operator learning is an emerging field at the intersection of machine learning and scientific computing. By learning mappings between function spaces, neural operators provide data-driven surrogate models for families of partial differential equations (PDEs). Once trained, these models can evaluate solution operators efficiently, making them suitable for many-query applications such as real-time prediction and parameter sweeps. However, maintaining high approximation accuracy and stable long-term predictions remains challenging for complex forward and inverse problems. To address these challenges, we propose the Starter-Iterator Neural Operator (SINO), which incorporates the initialization and residual-correction structures of classical iterative solvers into neural operator learning. The frequency-domain Starter captures dominant global spectral features and provides an informed initial approximation, while the latent-space Iterator applies successive residual-based corrections to refine local and multiscale solution structures. Experiments on representative time-dependent PDEs, including the Navier-Stokes and acoustic wave equations, together with applications to image super-resolution and weather forecasting, show that SINO achieves competitive accuracy and stable performance across the benchmarks considered in this work.

Radar SLAM is attractive for autonomous ground vehicles operating in visually degraded environments, however, scanning radars are noisy, have low scanning rates, and their measurements are challenging to match reliably over long trajectories. This paper presents FD-SLAM, a fast dense radar-inertial SLAM system that extends dense radar-inertial odometry with frequency-domain loop closure and pose graph optimization. The proposed method preserves an image-like structure of scanning radar measurements by using a compact frequency-domain polar descriptor for loop-candidate retrieval and a multi-stage verification pipeline based on temporal filtering, phase-correlation screening, scan-alignment similarity, and geometric consistency checks. Verified loop closures are added as non-sequential constraints in an SE(2) pose graph together with radar-inertial odometry factors. FD-SLAM is evaluated on a publicly available dataset using standard KITTI evaluation metrics. The results show that FD-SLAM improves FD-RIO baseline, achieves competitive performance against current state-of-the-art radar SLAM methods, and provides favorable rotational accuracy across multiple evaluated driving trajectories. Runtime analysis further indicates that the radar-inertial front-end operates above the radar sampling rate on a CPU-only setup, while loop closure detection and graph optimization remain suitable for parallel background execution.

Hearing aids impose strict latency and power constraints that current DNN-based speech enhancement systems struggle to meet on embedded hardware. We characterize this gap by deploying both speech separation and denoising using the lightweight SuDoRM-RF++ architecture on the AMD-Xilinx Kria KV260, evaluated at FP32 and 16-bit fixed-point precision for each task. Across these configurations, first-sample latency tracks with on-chip parameter caching rather than arithmetic throughput, identifying data movement as the primary bottleneck. Precision reduction halves the model memory footprint without compromising objective speech quality. The fixed-point denoising accelerator achieves a first-sample latency of 9.7ms, meeting the 10ms clinical threshold, while speech separation reaches 16.0~ms. These measurements establish concrete resource requirements for embedded DNN-based speech enhancement and quantify the remaining gap to hearing aid deployment.

Tremor is a common movement disorder associated with conditions like Parkinson's disease and Essential tremor, traditionally diagnosed through expert clinician assessment. Current automated detection methods rely on frequency-domain features informed by clinical expertise. In this work, we present an explainable, two-stage hierarchical framework for tremor detection in the time domain that learns tremor patterns directly from 3D kinematic marker time-series data across entire tremor-provoking trials. Our framework combined a deep convolutional and long short-term memory network to learn tremor representations from short, discrete, non-overlapping time segments of kinematic time series data from trials, which are then processed by a vision transformer that models their long-term temporal dynamics of time segment features for trial (session) level classification. Evaluated across nine body parts, the framework achieved F1-scores of 0.594 - 0.947 depending on body parts (average: 0.765), falling short of the frequency-domain state-of-the-art performance (0.909) while requiring minimal preprocessing. Attention weights and gradient-based class activation maps (Grad-CAM) identified time-domain features of tremor across body parts. This proof of concept demonstrated the feasibility of data-driven time-domain modeling for tremor detection across anatomically diverse body parts, while reducing reliance on expert-engineered spectral features and providing posthoc interpretability of temporal and anatomical patterns of tremor.

Electroencephalograph (EEG) timeseries signals are characterized by significant noise and coarse spatial resolution, which complicates the classification of neurodegenerative diseases. Even SOTA deep learning architectures struggle to distinguish between healthy controls and diseased subjects, or between different disease types, due to high intergroup similarity. In this paper, we show that a spectrally selective approach to feature construction enhances class separability. By isolating signal strengths within the primary brainwave bands, we transform high dimensional raw data into high value spectral features. Our results demonstrate that in small datasets a) features derived from frequency and time frequency domain allow traditional machine learning models to match or exceed the performance of SOTA deep learning models, b) Attention mechanism is unable to distill the stable feature signatures that characterize healthy neural activity in both resting and task EEGs, and c) the limitations of attention based models in finding relevant spectral features appear to be robust in that providing frequency selective time domain input do not appreciably improve their performance. We validate our methodology across three open source resting EEG datasets and one task EEG dataset, providing robust empirical evidence for our claims.

Event-based cameras (EBCs) are an attractive sensing modality for surveillance due to their reporting of pixel-level radiance changes with microsecond resolution and high dynamic range, enabling motion extraction while suppressing background. Their asynchronous, sparse output, however, necessitate algorithms that identify targets in event-space without processing full frames. We introduce Frequency Rate Information for Event Space (FRIES), a neuromorphic processing framework that detects periodicity in events, such as rotor rotation and mechanical vibrations, to discriminate and monitor man-made objects. FRIES first applies a time gate to suppress background and noise, then aggregates events into a pixel-wise activity (e.g., density) map and clusters pixels into regions-of-interest (ROIs). A localized spectral analysis is applied to each ROI to extract dominant frequencies used to distinguish structured object signatures from unstructured background and noise. Discriminated targets are visualized using a Resonant Time Surface (RTS), a frequency-selective method that weights events by their phase coherence with the extracted frequencies, rewarding in-sync content and suppressing out-of-sync clutter. We demonstrate FRIES and RTS in a controlled indoor experiment to recover the rotational frequency of a mechanical chopper and drone rotors against a moving background. We further test these methods on an outdoor data to detect a hovering drone against a realistic treeline. These preliminary results establish frequency-domain event processing as a promising front-end for selective surveillance in neuromorphic pipelines and a complementary surveillance modality, leveraging the high temporal resolution to enable spectral discrimination.

Despite extensive research on computed tomography (CT) denoising, few studies exploit projection-domain data characteristics to mitigate noise correlation. To bridge this gap, this work proposes FrequencyCT, the first zero-shot self-supervised method for pseudo-sample generation in the frequency domain for low-dose CT denoising. Specifically, by exploiting the distinct frequency-domain distributions of noise and true signal, a regional low-frequency anchoring technique is proposed. Applying phase-preserving noise and mask perturbations to the high-frequency region generates pseudo-samples for self-supervision. Driven by the exponential correlation between noise variance of noisy projections and the underlying true signal, consistent data truncation is applied to the generated samples to stabilize optimization gradients. Evaluation results on multiple public and real datasets confirm the clinical application potential of this research, which provides an innovative perspective for the field of denoising. The code is available at: https://github.com/yqx7150/FrequencyCT.

This paper presents a preliminary analysis of the ability of Chronos foundation model to process and internally represent frequency domain information. Foundation models that process time-series data offer practitioners a unified architecture capable of learning generic temporal representations across diverse tasks and domains, reducing the need for task-specific feature engineering and enabling transfer across signal modalities. Despite their growing adoption, the extent to which such models encode fundamental signal properties remains insufficiently characterised. We address this gap by analysing Chronos under controlled conditions, starting from the simplest class of signals: discrete sinusoids generated at fixed frequencies. Using lightweight online minimum description length probes applied to the decoder architecture, we test for the presence and separability of frequency information in the model's internal representations. The results provide insight into how frequential content is captured across the frequency spectrum and highlight regimes in which representation quality may degrade or require particular care. These findings offer practical guidance for users of Chronos in signal processing and information fusion contexts, and contribute to ongoing efforts to improve the interpretability and evaluation of foundation models for temporal data.

Diffusion-based visuomotor policies perform well in robotic manipulation, yet current methods still inherit image-generation-style decoders and multi-step sampling. We revisit this design from a frequency-domain perspective. Robot action trajectories are highly smooth, with most energy concentrated in a few low-frequency discrete cosine transform modes. Under this structure, we show that the error of the optimal denoiser is bounded by the low-frequency subspace dimension and residual high-frequency energy, implying that denoising error saturates after very few reverse steps. This also suggests that action denoising requires a much simpler denoising model than image generation. Motivated by this insight, we propose Hyper-DP3 (HDP3), a pocket-scale 3D diffusion policy with a lightweight Diffusion Mixer decoder that supports two-step DDIM inference. Our synthetic experiments validate the theory and support the sufficiency of two-step denoising. Futhermore, across RoboTwin2.0, Adroit, MetaWorld, and real-world tasks, HDP3 achieves state-of-the-art performance with fewer than 1% of the parameters of prior 3D diffusion-based policies and substantially lower inference latency.

Multivariate time series anomaly detection in ICS has attracted growing attention due to the increasing threat of cyber-physical attacks on critical infrastructure. State-of-the-art methods model inter-sensor relationships from raw time-domain amplitude values, using graph neural networks, Transformers. However, these methods discard the phase spectrum produced by time frequency transformations, We argue that phase information constitutes a complementary and previously overlooked detection modality for ICS anomaly detection. We present PhaseNet++, a frequency-domain autoencoder that operates on the Short-Time Fourier Transform (STFT) of sliding sensor windows, retaining both magnitude and phase spectra. A Phase Coherence Index (PCI), inspired by the Phase Locking Value from neuroscience, summarizes pairwise phase consistency across frequency bins into a continuous adjacency matrix. This matrix guides a graph attention network that propagates information preferentially among phase-synchronized sensors. A sensor-token Transformer encoder captures system-wide structure, and a dual-head decoder reconstructs magnitude and phase jointly via circular and coherence-aware objectives. Evaluated on the Secure Water Treatment (SWaT) benchmark, PhaseNet++ achieves an F1-score of 90.98%, ROC-AUC of 95.66%, and average precision of 91.51%. Ablation studies show that the phase-aware front-end and PCI graph module together add only 264,816 parameters, demonstrating that the phase inductive bias is lightweight. While the absolute F1-score is second best than that of all recent raw-value methods evaluated under different protocols, we position this work as the first systematic study of phase-domain anomaly detection for ICS.

Accurate long-term time series forecasting (LTSF) requires the capture of complex long-range dependencies and dynamic periodic patterns. Recent advances in frequency-domain analysis offer a global perspective for uncovering temporal characteristics. However, real-world time series often exhibit pronounced cross-domain heterogeneity where variables that appear synchronized in the time domain can differ substantially in the frequency domain. Existing frequency-based LTSF methods often rely on implicit assumptions of cross-domain homogeneity, which limits their ability to adapt to such intricate variability. To effectively integrate frequency-domain analysis with temporal dependency learning, we propose AdaMamba, a novel framework that endogenizes adaptive and context-aware frequency analysis within the Mamba state-space update process. Specifically, AdaMamba introduces an interactive patch encoding module to capture inter-variable interaction dynamics. Then, we develop an adaptive frequency-gated state-space module that generates input-dependent frequency bases, and generalizes the conventional temporal forgetting gate into a unified time-frequency forgetting gate. This allows dynamic calibration of state transitions based on learned frequency-domain importance, while preserving Mamba's capability in modeling long-range dependencies. Extensive experiments on seven public LTSF benchmarks and two domain-specific datasets demonstrate that AdaMamba consistently outperforms state-of-the-art methods in forecasting accu racy while maintaining competitive computational efficiency. The code of AdaMamba is available at https://github.com/XDjiang25/AdaMamba.

Diffusion models achieve remarkable success in time series generation. However, slow inference limits their practical deployment. We propose E$^2$-CRF (Error-Feedback Event-Driven Cumulative Residual Feature caching) to accelerate frequency domain diffusion models. Our method exploits two structural properties: (1) spectral localization, where signal energy concentrates in low frequencies, and (2) mirror symmetry, which halves the effective frequency dimension. E$^2$-CRF uses a closed-loop error-feedback system that adaptively caches transformer KV features across diffusion steps. We trigger recomputation using event-driven residual dynamics instead of fixed schedules. Our method selectively recomputes high-energy or rapidly-changing tokens while reusing cached features for stable high-frequency components. E$^2$-CRF achieves ~2.2 speedup while maintaining sample quality. We demonstrate effectiveness on 5 datasets. Our caching strategy naturally aligns with the diffusion process's structure-to-detail progression. We include sufficient-condition error and complexity bounds under standard regularity assumptions (Appendix), alongside empirical validation. Our code is available at https://github.com/NoakLiu/FastFourierDiffusion and is also integrated in https://github.com/NoakLiu/FastCache-xDiT.

Digital image watermarking has advanced rapidly for copyright protection of generative AI, yet the comparatively limited progress in watermark attack techniques has broken the attack-defense balance and hindered further advances in the field. In this paper, we propose FMDiffWA, a frequency-domain modulated diffusion framework for watermark attacks. Specifically, we introduce a frequency-domain watermark modulation (FWM) module and incorporate it into the sampling stages both the forward and reverse diffusion processes. This mechanism enables selective modulation of watermark-related frequency components, thereby allowing FMDiffWA to effectively neutralize the invisible watermark signals while preserving the perceptual quality of the attacked watermarked images. To achieve a better trade-off between attack efficacy and visual fidelity, we reformulate the training strategy of conventional diffusion models by augmenting the canonical noise estimation objective with an auxiliary refinement constraint. Comprehensive experiments demonstrate that FMDiffWA achieves superior visual fidelity compared to existing watermark attacks, while exhibiting strong generalization across diverse watermarking schemes.

Generalized Category Discovery (GCD) holds significant promise for the label-scarce Synthetic Aperture Radar (SAR) domain, yet its efficacy is severely constrained by the cross-modal incompatibility between the inherent optical prior of the Large Vision Models (LVMs) and SAR imagery. Existing domain adaptation methods often lack an inductive bias that reflects imaging characteristics, consequently failing to effectively transfer optical prior into the SAR domain. To address this issue, the Modal Discrepancy Curve (MDC) is introduced to model cross-modal discrepancy as a structured frequency-domain descriptor derived from spectral energy distributions. Leveraging this formulation, we propose the MDC-guided Cross-modal Prior Transfer (MCPT) framework, a pre-training paradigm that operates on paired optical-SAR data. Within this framework, Adaptive Frequency Tokenization (AFT) converts the MDC into learnable tokens, and Frequency-aware Expert Refinement (FER) performs band-wise discrepancy-aware feature refinement using these tokens. Based on the refined representations, contrastive learning aligns refined embeddings across modalities and internalizes the adaptation pattern. Ultimately, the superior SAR feature representation capability learned during paired pre-training is applied to downstream single-modal SAR-GCD tasks. Extensive experiments demonstrate state-of-the-art performance across multiple mainstream datasets, indicating that frequency-domain discrepancy modeling enables more effective adaptation of optical prior to SAR imagery.

The widespread use of sensors in modern power grids has led to the accumulation of large amounts of voltage and current waveform data, especially during fault events. However, the lack of labeled datasets poses a significant challenge for fault classification and analysis. This paper explores the application of unsupervised clustering techniques for fault diagnosis in high-voltage power systems. A dataset provided by the Réseau de Transport d'Électricité (RTE) is analyzed, with frequency domain features extracted using the Fast Fourier Transform (FFT). The K-Means algorithm is then applied to identify underlying patterns in the data, enabling automated fault categorization without the need for labeled training samples. The resulting clusters are evaluated in collaboration with power system experts to assess their alignment with real-world fault characteristics. The results demonstrate the potential of unsupervised learning for scalable and data-driven fault analysis by structuring large unlabeled waveform datasets and supporting targeted expert review.