Frequency-Domain Feature Learning

Time series, spatial data, and images are natural applications of Neural Processes. However, when such data exhibit strong periodicity and quasi-periodicity, existing methods often suffer from underfitting and generalise poorly beyond the training distribution. In this work, we propose Spectral Transformer Neural Processes (STNPs), a frequency-aware extension of Transformer Neural Processes (TNPs). STNPs introduce a Spectral Aggregator that estimates an empirical context spectrum, compresses it into a spectral mixture, samples task-adaptive spectral features, and concatenates them with time-domain embeddings, thereby injecting a spectral-mixture-kernel bias into TNPs. This design reshapes the similarity geometry, allowing inputs that are distant in Euclidean space to remain close in an induced periodic manifold while enhancing time-frequency interactions. Extensive experiments on synthetic regression tasks, real-world time-series datasets, and an image dataset demonstrate that STNPs consistently improve predictive performance over existing baselines, extending Neural Processes beyond translation equivariance towards effective modelling of periodicity and quasi-periodicity.

Graphs with heterophily, where adjacent nodes carry different labels, are prevalent in real-world applications, from social networks to molecular interactions. However, existing spectral Graph Neural Network (GNN) approaches tailored for heterophilous graph classification suffer from hub-dominated (node with large degree) aggregation and oversmoothing, as their suboptimal polynomial filters introduce approximation errors and blend distant signals. To address the degree-biased aggregation and suboptimal polynomial filtering, we introduce a Hierarchical Multi-view HAAR (HMH), a novel spectral graph-learning framework that scales in near-linear time . HMH first learns feature- and structure-aware signed affinities via a heterophily-aware encoder, then constructs a soft graph hierarchy guided by these embeddings. At each hierarchical level, HMH constructs a sparse, orthonormal, and locality-aware Haar basis to apply learnable spectral filters in the frequency domain. Finally, skip-connection unpooling layers combine outputs from all hierarchical levels back into the original graph, effectively preventing hub domination and long-range signal bottleneck (over-squashing). Experimentation shows that HMH outperforms state-of-the-art spectral baselines, achieving up to a 3% improvement on node classification and 7% points on graph classification datasets, all while maintaining linear scalability.

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.

Multi-rater medical image segmentation captures the inherent ambiguity of clinical interpretation, where diagnostic boundaries vary across experts and imaging devices. Existing approaches often reduce this diversity to consensus labels or treat rater differences as noise, resulting in overconfident and poorly calibrated models. We propose a harmonized probabilistic framework that disentangles acquisition artifacts from genuine annotator variability through adaptive feature conditioning and frequency-domain personalization. A lightweight Harmonizer Network implicitly models scanner-specific artifacts and performs dynamic feature modulation to standardize latent representations, ensuring that uncertainty reflects anatomy rather than noise. To represent rater-specific styles, we introduce a novel High-Frequency Prompt Modules that operate in the spectral domain to encode annotator-dependent boundary precision and textural sensitivity. These prompts adaptively modulate harmonized features to produce personalized yet anatomically consistent segmentations. Furthermore, a Generalized Energy Distance based regularization aligns the generative distribution with empirical annotation variability, promoting diversity where experts disagree and consensus where they converge. Experiments on LIDC-IDRI and NPC-170 show SOTA aggregated and individualized segmentation, with notable GED reductions and improved Dice scores, especially on noisy cases. Beyond accuracy, the model exhibits clinically meaningful uncertainty. Confidence rises in agreement regions and declines in ambiguous areas, supporting its use as a reliable and interpretable tool for multi-expert clinical workflows.

Existing prompt learning for VLMs exhibits a modality asymmetry, predominantly optimizing text tokens while still relying on frozen visual encoder as holistic extractor and neglecting the spectral granularity essential for fine-grained discrimination. To bridge this, we introduce Disentangling Spectral Granularity for Prompt Learning (SpecPL), which approaches prompt learning from a novel spectral perspective via Counterfactual Granule Supervision. Specifically, we leverage a frozen VAE to decompose visual signals into semantic low-frequency bands and granular high-frequency details. A frozen Visual Semantic Bank anchors text representations to universal low-frequency invariants, mitigating overfitting. Crucially, fine-grained discrimination is driven by counterfactual granule training: by permuting high-frequency signals, we compel the model to explicitly distinguish visual granularity from semantic invariance. Uniquely, SpecPL serves as a universal plug-and-play booster, revitalizing text-oriented baselines like CoOp and MaPLe via visual-side guidance. Experiments on 11 benchmarks demonstrate competitive state-of-the-art performance, achieving a new performance ceiling of 81.51% harmonic-mean accuracy. These results validate that spectral disentanglement with counterfactual supervision effectively bridges the gap in the stability-generalization trade-off. Code is released at https://github.com/Mlrac1e/SpecPL-Prompt-Learning.

The field of sensor-based human activity recognition (HAR) mainly uses posture, motion and context data of Inertial Measurement Units (IMUs) to identify daily activities. Despite the advancements in learning-based methods, it is challenging to perform information fusion from the temporal perspective due to the complexities in fusing heterogeneous sensor data and establishing long-term context correlations. This paper proposes a novel triple spectral fusion framework tailored for HAR. First, we develop an adaptive complementary filtering technique for noise suppression and organize each IMU's sensors into posture and motion modality nodes. Given that IMU nodes form a dynamic heterogeneous graph, we then apply adaptive filtering within the graph Fourier domain to merge both homogeneous and heterogeneous node information. Furthermore, an adaptive wavelet frequency selection approach is implemented to suppress context redundancy and shorten the length of features. This approach enhances both timestamp-based graph aggregation and the correlation of long-term contexts. Our framework uses adaptive filtering in the Fourier, graph Fourier, and wavelet domains, enabling effective multi-sensor fusion and context correlation. Extensive experiments on ten benchmark datasets demonstrate the superior performance of our framework. Project page: https://github.com/crocodilegogogo/TSF-TPAMI2026.

Pansharpening aims to generate high-resolution multispectral (HRMS) images by fusing low-resolution multispectral (LRMS) and high-resolution panchromatic (PAN) images. Although deep learning has advanced this field, mainstream frequency-based methods relying on standard scaled dot-product attention suffer from quadratic computational complexity and fail to exploit the inherent regional sparsity of remote sensing imagery. Furthermore, existing spatial enhancement strategies typically employ static convolution kernels, which struggle to adapt to the complex frequency and regional variations of PAN and MS images. To address these bottlenecks, we propose a Region-Aware Fusion (RAFNet) Network that synergistically models spatial and frequency information. Specifically, we design a Spatial Adaptive Refinement (SAR) module that leverages the discrete wavelet transform (DWT) for directional frequency separation and K-means clustering for regional partitioning, which enables the dynamic construction of region-specific adaptive convolution kernels, achieving spatially and frequency-adaptive feature enhancement. Moreover, we introduce a Clustered Frequency Aggregation (CFA) module based on a sparse attention mechanism guided by the semantic clusters, which executes a region-aware sparse attention strategy that drastically reduces computational redundancy while ensuring high-quality frequency feature extraction. In addition we integrated these modules into a progressive, multi-level spatial-frequency network architecture to facilitate robust interaction and accurate image reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that the proposed RAFNet significantly outperforms state-of-the-art pansharpening methods in both reduced- and full-resolution assessments. The code is available at https://github.com/PatrickNod/RAFNet.

Network traffic anomaly detection represents a critical cybersecurity task, yet widespread encryption makes this task increasingly challenging. In response, image-based methods that model traffic as visual patterns have emerged as the dominant approach. However, this work pioneers the identification of a pervasive full-frequency'' characteristic and an associated limitation termed spectral mismatch'' within this paradigm. Specifically, while encrypted traffic exhibits prominent high-frequency components, mainstream reconstruction methods demonstrate an inherent bias toward learning low-frequency information. This fundamental mismatch results in incomplete representations that consequently degrade anomaly detection performance. To address this challenge, we propose FreeUp, a novel frequency-decoupled framework designed explicitly for encrypted traffic analysis. FreeUp decomposes traffic data into distinct low- and high-frequency bands, processing them through separate, dedicated branches along with a customized training strategy that ensures stable and independent frequency-specific learning. Furthermore, recognizing that simple reconstruction error proves inadequate for evaluating dual-branch architectures, we introduce an uncertainty-inspired fusion scoring mechanism. This mechanism quantifies the reconstruction uncertainty of the frequency-specific branches and dynamically integrates their outputs, yielding a more comprehensive and reliable anomaly score. Extensive experiments across multiple benchmarks demonstrate that FreeUp consistently outperforms state-of-the-art baselines. The code is available at https://github.com/ikun0124/FreeUp.

Sequential recommendation models often struggle to capture latent periodic patterns in user interests, primarily due to the noise inherent in time-domain behavioral data. While frequency-domain analysis offers a global perspective to address this, existing approaches typically treat user sequences in isolation, overlooking the crucial context of the target item. In this work, we present a novel empirical observation: user attention scores exhibit distinct spectral entropy distributions when conditioned on positive versus negative target items. Specifically, true user interests manifest as highly concentrated spectral patterns with lower entropy in the frequency domain, whereas irrelevant behaviors appear as high-entropy noise. Leveraging this insight, we propose the Frequency-Enhanced Deep Interest Network (FEDIN). FEDIN introduces a frequency-domain branch that utilizes a target-aware spectrum filtering mechanism to isolate these periodic interest signals. Extensive experiments on three public datasets demonstrate that FEDIN consistently outperforms state-of-the-art sequential recommendation baselines, demonstrating superior robustness against noise. We have released our code at: https://github.com/otokoneko/FEDIN.

Pansharpening aims to generate high-resolution multispectral (HRMS) images by fusing low-resolution multispectral (LRMS) images with high-resolution panchromatic (PAN) images. However, the current mainstream frequency-based pansharpening methods employ fixed frequency filters, which cannot precisely adapt to complex and spatially diversified frequency distributions in PAN and MS images. Furthermore, existing denoising strategies insufficiently exploit frequency components for denoising and struggle to suppress various noise types accurately. To address these challenges, we propose CGFformer, a cluster-guidance frequency Transformer that focuses on varying frequency distribution and interactions between frequency and spatial components. Specifically, we design an adaptive separation module that integrates local features and non-local information through K-means clustering, enabling more precise separation of high- and low-frequency components. Subsequently, we introduce a dual-stream refinement module combined with Transformer-based cross-attention to remove various noise, allowing the network to jointly suppress frequency-relevant and irrelevant disturbances. In addition, we develop a frequency-spatial fusion module designed to enhance detail and facilitate spatial-frequency interaction, ensuring more effective reconstruction of spatial structures in the fused results. Extensive experiments on multiple benchmark datasets demonstrate that the proposed CGFformer achieves notable improvements over existing pansharpening approaches.

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.

Animals hear and vocalize across frequency ranges that differ substantially from humans, often extending into the ultrasonic domain. Yet most computational bioacoustics systems rely on audio models pre-trained at 16 kHz, restricting their usable bandwidth to the 0-8 kHz baseband and discarding higher-frequency information present in many bioacoustic recordings. We investigate a multi-band encoding framework that decomposes the full spectrum of animal calls into band features and fuses them into a unified representation. Similarity analyses on models show that certain encoders produce decorrelated band embeddings that improve class separation after fusion. Classification experiments on three bioacoustic datasets using eight pre-trained models and five fusion strategies show that fused representations consistently outperform the baseband and time-expansion baselines on two datasets, showing the potential of multi-band methods for full-spectrum encoding of animal calls.

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.

State space models (SSMs) achieve linear-time complexity but struggle with multi-channel physiological signals due to three limitations: fixed kernels cannot capture multi-scale temporal dynamics (motor preparation over hundreds of milliseconds vs. execution transients in tens of milliseconds), Markovian state updates restrict global context for periodic oscillations, and channel-independent processing ignores spatial electrode topology. We introduce NAKUL, extending SSMs for medical signal analysis through three contributions: (1) Dynamic Kernel Generation-parallel SSM branches with varying kernel sizes (3, 5, 7, 11 timesteps) are weighted by a meta-network that analyzes input statistics, enabling adaptive temporal scale selection; (2) Spectral Context Modeling-FFT-based operations with learnable Gaussian frequency band filters capture global periodic patterns in $O(N \log N)$ complexity; (3) Graph-Guided Spatial Attention-fixed electrode topology provides spatial biases to multi-head attention for principled cross-channel interaction. On BCI Competition IV-2a motor imagery (our primary benchmark), NAKUL achieves 91.7$\pm$0.6% accuracy, matching EEG-Conformer (92.1$\pm$0.7%) while using 28% fewer parameters (2.5M vs 3.5M) and 2.0$\times$ faster inference (4.3ms vs 8.7ms). The model generalizes to EEG emotion recognition (83.6%), multimodal EEG-fMRI (91.4%), and medical imaging (92.8% on ultrasound), demonstrating architectural versatility. Ablations show dynamic kernels contribute +2.6% and exhibit interpretable scale selection patterns correlated with known neural dynamics.

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.

Language models trained on natural text learn to represent numbers using periodic features with dominant periods at $T=2, 5, 10$. In this paper, we identify a two-tiered hierarchy of these features: while Transformers, Linear RNNs, LSTMs, and classical word embeddings trained in different ways all learn features that have period-$T$ spikes in the Fourier domain, only some learn geometrically separable features that can be used to linearly classify a number mod-$T$. To explain this incongruity, we prove that Fourier domain sparsity is necessary but not sufficient for mod-$T$ geometric separability. Empirically, we investigate when model training yields geometrically separable features, finding that the data, architecture, optimizer, and tokenizer all play key roles. In particular, we identify two different routes through which models can acquire geometrically separable features: they can learn them from complementary co-occurrence signals in general language data, including text-number co-occurrence and cross-number interaction, or from multi-token (but not single-token) addition problems. Overall, our results highlight the phenomenon of convergent evolution in feature learning: A diverse range of models learn similar features from different training signals.

We introduce the Latent Fourier Transform (LatentFT), a framework that provides novel frequency-domain controls for generative music models. LatentFT combines a diffusion autoencoder with a latent-space Fourier transform to separate musical patterns by timescale. By masking latents in the frequency domain during training, our method yields representations that can be manipulated coherently at inference. This allows us to generate musical variations and blends from reference examples while preserving characteristics at desired timescales, which are specified as frequencies in the latent space. LatentFT parallels the role of the equalizer in music production: while traditional equalizers operates on audible frequencies to shape timbre, LatentFT operates on latent-space frequencies to shape musical structure. Experiments and listening tests show that LatentFT improves condition adherence and quality compared to baselines. We also present a technique for hearing frequencies in the latent space in isolation, and show different musical attributes reside in different regions of the latent spectrum. Our results show how frequency-domain control in latent space provides an intuitive, continuous frequency axis for conditioning and blending, advancing us toward more interpretable and interactive generative music models.

Camouflaged Object Detection is challenging due to the high degree of similarity between camouflaged objects and their surrounding backgrounds. Current COD methods mainly rely on edge extraction in the spatial domain and local pixel-level information, neglecting the importance of global structural features. Additionally, they fail to effectively leverage the importance of phase spectrum information within frequency domain features. To this end, we propose a COD framework BASFNet based on boundary-aware frequency domain and spatial domain fusion.This method uses dual guided integration of frequency domain and spatial domain features. A phase-spectrum-based frequency-enhanced edge exploration module (FEEM) and a spatial core segmentation module (SCSM) are introduced to jointly capture the boundary and object features of camouflaged objects. These features are then effectively integrated through a spatial-frequency fusion interaction module (SFFIM). Furthermore, the boundary detection is further optimized through an boundary-aware training strategy. BASFNet outperforms existing state-of-the-art methods on three benchmark datasets, validating the effectiveness of the fusion of frequency and spatial domain information in COD tasks.

Advanced deepfake technologies are blurring the lines between real and fake, presenting both revolutionary opportunities and alarming threats. While it unlocks novel applications in fields like entertainment and education, its malicious use has sparked urgent ethical and societal concerns ranging from identity theft to the dissemination of misinformation. To tackle these challenges, feature analysis using frequency features has emergedas a promising direction for deepfake detection. However, oneaspect that has been overlooked so far is that existing methodstend to concentrate on one or a few specific frequency domains,which risks overfitting to particular artifacts and significantlyundermines their robustness when facing diverse forgery patterns. Another underexplored aspect we observe is that different features often attend to the same forged region, resulting in redundant feature representations and limiting the diversity of the extracted clues. This may undermine the ability of a model to capture complementary information across different facets, thereby compromising its generalization capability to diverse manipulations. In this paper, we seek to tackle these challenges from two aspects: (1) we propose a triple-branch network that jointly captures spatial and frequency features by learning from both original image and image reconstructed by different frequency channels, and (2) we mathematically derive feature decoupling and fusion losses grounded in the mutual information theory, which enhances the model to focus on task-relevant features across the original image and the image reconstructed by different frequency channels. Extensive experiments on six large-scale benchmark datasets demonstrate that our method consistently achieves state-of-the-art performance. Our code is released at https://github.com/injooker/Unveiling Deepfake.

Feature reconstruction techniques are widely applied for few-shot fine-grained image classification (FSFGIC). Our research indicates that one of the main challenges facing existing feature-based FSFGIC methods is how to choose the size of the receptive field to extract feature descriptors (including spatial and frequency feature descriptors) from different category input images, thereby better performing the FSFGIC tasks. To address this, an adaptive receptive field-based spatial-frequency feature reconstruction network (ARF-SFR-Net) is proposed. The designed ARF-SFR-Net has the capability to adaptively determine receptive field sizes for obtaining spatial and frequency features, and effectively fuse them for reconstruction and FSFGIC tasks. The designed ARF-SFR-Net can be easily embedded into a given episodic training mechanism for end-to-end training from scratch. Extensive experiments on multiple FSFGIC benchmarks demonstrate the effectiveness and superiority of the proposed ARF-SFR-Net over state-of-the-art approaches. The code is available at: https://github.com/ICL-SUST/ARF-SFR-Net.git.

Structural health monitoring plays a critical role in ensuring structural safety by analyzing vibration responses from engineering systems. This paper proposes a Spectro-Temporal Alignment framework and a Hybrid Spectro-Temporal Fusion framework that integrate arrival-time interval descriptors with spectral features to capture both fine-scale and coarse-scale vibration dynamics. Experiments conducted on data collected from an LDS V406 electrodynamic shaker demonstrate that the proposed spectro-temporal representations significantly outperform conventional input formulations. The results indicate that a temporal resolution (Δτ) of 0.008 of 0.02 favors traditional machine learning models, whereas a finer resolution (Δτ) of 0.008 effectively unlocks the performance potential of deep learning architectures. Beyond classification accuracy, a comprehensive stability analysis based on condensed indices, including mean performance, standard deviation, coefficient of variation, and balanced score, shows that the proposed hybrid framework consistently achieves higher accuracy with substantially lower variability compared to baseline and alignment-only approaches. Overall, these results demonstrate that the proposed framework provides a robust, accurate, and reliable solution for vibration-based structural health monitoring.

Graph self-supervised learning can reduce the need for labeled graph data and has been widely used in recommendation, social networks, and other web applications. However, existing methods often underuse high-frequency signals and may overfit to specific local patterns, which limits representation quality and generalization. We propose Frequency-Corrupt Based Graph Self-Supervised Learning (FC-GSSL), a method that builds corrupted graphs biased toward high-frequency information by corrupting nodes and edges according to their low-frequency contributions. These corrupted graphs are used as inputs to an autoencoder, while low-frequency and general features are reconstructed as supervision targets, forcing the model to fuse information from multiple frequency bands. We further design multiple sampling strategies and generate diverse corrupted graphs from the intersections and unions of the sampling results. By aligning node representations from these views, the model can discover useful frequency combinations, reduce reliance on specific high-frequency components, and improve robustness. Experiments on 14 datasets across node classification, graph prediction, and transfer learning show that FC-GSSL consistently improves performance and generalization.

Few-shot fine-grained image classification aims to recognize subcategories with high visual similarity using only a limited number of annotated samples. Existing metric learning-based methods typically rely solely on spatial domain features. Confined to this single perspective, models inevitably suffer from inherent texture biases, entangling essential structural details with high-frequency background noise. Furthermore, lacking cross-view geometric constraints, single-view metrics tend to overfit this noise, resulting in structural instability under few-shot conditions. To address these issues, this paper proposes the Frequency-Enhanced Dual-Subspace Network (FEDSNet). Specifically, FEDSNet utilizes the Discrete Cosine Transform (DCT) and a low-pass filtering mechanism to explicitly isolate low-frequency global structural components from spatial features, thereby suppressing background interference. Truncated Singular Value Decomposition (SVD) is employed to construct independent, low-rank linear subspaces for both spatial texture and frequency structural features. An adaptive gating mechanism is designed to dynamically fuse the projection distances from these dual views. This strategy leverages the structural stability of the frequency subspace to prevent the spatial subspace from overfitting to background features. Extensive experiments on four benchmark datasets - CUB-200-2011, Stanford Cars, Stanford Dogs, and FGVC-Aircraft - demonstrate that FEDSNet exhibits excellent classification performance and robustness, achieving highly competitive results compared to existing metric learning algorithms. Complexity analysis further confirms that the proposed network achieves a favorable balance between high accuracy and computational efficiency, providing an effective new paradigm for few-shot fine-grained visual recognition.

Small object detection remains a significant challenge due to feature degradation from downsampling, mutual occlusion in dense clusters, and complex background interference. To address these issues, this paper proposes FSDETR, a frequency-spatial feature enhancement framework built upon the RT-DETR baseline. By establishing a collaborative modeling mechanism, the method effectively leverages complementary structural information. Specifically, a Spatial Hierarchical Attention Block (SHAB) captures both local details and global dependencies to strengthen semantic representation. Furthermore, to mitigate occlusion in dense scenes, the Deformable Attention-based Intra-scale Feature Interaction (DA-AIFI) focuses on informative regions via dynamic sampling. Finally, the Frequency-Spatial Feature Pyramid Network (FSFPN) integrates frequency filtering with spatial edge extraction via the Cross-domain Frequency-Spatial Block (CFSB) to preserve fine-grained details. Experimental results show that with only 14.7M parameters, FSDETR achieves 13.9% APS on VisDrone 2019 and 48.95% AP50 tiny on TinyPerson, showing strong performance on small-object benchmarks. The code and models are available at https://github.com/YT3DVision/FSDETR.

Vision State Space Models (SSMs) like Vim, VMamba, and SiMBA rely on complex scanning strategies to adapt sequential SSMs to process 2D images, introducing computational overhead and architectural complexity. We propose HAMSA, a scanning-free SSM operating directly in the spectral domain. HAMSA introduces three key innovations: (1) simplified kernel parameterization-a single Gaussian-initialized complex kernel replacing traditional (A, B, C) matrices, eliminating discretization instabilities; (2) SpectralPulseNet (SPN)-an input-dependent frequency gating mechanism enabling adaptive spectral modulation; and (3) Spectral Adaptive Gating Unit (SAGU)-magnitude-based gating for stable gradient flow in the frequency domain. By leveraging FFT-based convolution, HAMSA eliminates sequential scanning while achieving O(L log L) complexity with superior simplicity and efficiency. On ImageNet-1K, HAMSA reaches 85.7% top-1 accuracy (state-of-the-art among SSMs), with 2.2 X faster inference than transformers (4.2ms vs 9.2ms for DeiT-S) and 1.4-1.9X speedup over scanning-based SSMs, while using less memory (2.1GB vs 3.2-4.5GB) and energy (12.5J vs 18-25J). HAMSA demonstrates strong generalization across transfer learning and dense prediction tasks.

Existing single-modal RGB trackers often face performance bottlenecks in complex dynamic scenes, while the introduction of event sensors offers new potential for enhancing tracking capabilities. However, most current RGB-event fusion methods, primarily designed in the spatial domain using convolutional, Transformer, or Mamba architectures, fail to fully exploit the unique temporal response and high-frequency characteristics of event data. To address this, we1 propose FreqTrack, a frequency-aware RGBE tracking framework that establishes complementary inter-modal correlations through frequency-domain transformations for more robust feature fusion. We design a Spectral Enhancement Transformer (SET) layer that incorporates multi-head dynamic Fourier filtering to adaptively enhance and select frequency-domain features. Additionally, we develop a Wavelet Edge Refinement (WER) module, which leverages learnable wavelet transforms to explicitly extract multi-scale edge structures from event data, effectively improving modeling capability in high-speed and low-light scenarios. Extensive experiments on the COESOT and FE108 datasets demonstrate that FreqTrack achieves highly competitive performance, particularly attaining leading precision of 76.6% on the COESOT benchmark, validating the effectiveness of frequency-domain modeling for RGBE tracking.

Force and torque (F/T) sensors enable contact-aware control by providing reactive feedback, but they are often fragile and expensive. To overcome these limitations, sensorless methods estimate F/T or wrench solely from robot proprioception, and have shown success in slow interaction tasks such as grasping. However, their low-pass characteristics limit the estimation of high-frequency signals, which are critical in rapid-contact tasks such as grinding. Communication delays can also make their estimates outdated during deployment, but few methods address this directly. To bridge these gaps, we propose a Frequency-aware Decomposition Network (FDN) to estimate vibration-rich wrench in a sensorless, multi-step-ahead manner. Considering higher-frequency stochasticity, FDN spectrally decomposes the wrench horizon into a low-frequency trend and a high-frequency residual, and estimates each by pointwise regression and a learned conditional distribution, respectively. The frequency-aware layers impose band decomposition priors on the outputs and adaptively enhance frequency amplitudes of the inputs. FDN requires neither an identified robot model nor an F/T sensor during estimation. On real-world grinding data from our 6-DoF hydraulic manipulator, FDN reduces high-frequency amplitude error by up to 47% over the baselines under assumed time delays and maintains competitive low-frequency pointwise accuracy, while the baselines fail to balance these two. We also find multi-step-ahead estimation feasible, with FDN estimating a 1,000 ms horizon within 11 ms on a single CPU thread. Ablation studies further support our design choices. In an exploratory study, transferring wrench dynamics learned from an open-source everyday manipulation dataset reduces low-frequency error by 8%, while high-frequency dynamics appear domain-specific.

Existing camouflage object detection (COD) methods typically rely on fully-supervised learning guided by mask annotations. However, obtaining mask annotations is time-consuming and labor-intensive. Compared to fully-supervised methods, existing weakly-supervised COD methods exhibit significantly poorer performance. Even for the Segment Anything Model (SAM), there are still challenges in handling weakly-supervised camouflage object detection (WSCOD), such as: a. non-camouflage target responses, b. local responses, c. extreme responses, and d. lack of refined boundary awareness, which leads to unsatisfactory results in camouflage scenes. To alleviate these issues, we propose a frequency-aware and contrastive learning-based WSCOD framework in this paper, named FCL-COD. To mitigate the problem of non-camouflaged object responses, we propose the Frequency-aware Low-rank Adaptation (FoRA) method, which incorporates frequency-aware camouflage scene knowledge into SAM. To overcome the challenges of local and extreme responses, we introduce a gradient-aware contrastive learning approach that effectively delineates precise foreground-background boundaries. Additionally, to address the lack of refined boundary perception, we present a multi-scale frequency-aware representation learning strategy that facilitates the modeling of more refined boundaries. We validate the effectiveness of our approach through extensive empirical experiments on three widely recognized COD benchmarks. The results confirm that our method surpasses both state-of-the-art weakly supervised and even fully supervised techniques.

Synthetic aperture radar automatic target recognition (SAR ATR) is severely challenged by coherent speckle noise, whose interference can be progressively amplified by hierarchical nonlinear transformations and eventually damage high-level semantic representations. To address this issue, we propose a Target-Aware Frequency-Spatial Collaborative Enhancement (FSCE) framework for noise-resilient SAR ATR, which integrates frequency-spatial modeling for early feature stabilization with semantic regularization. Specifically, we design a Frequency-Spatial Early-stage Adaptive Enhancement (FS-EAE) module at the network entrance to suppress noise propagation and preserve target structures through collaborative spatial-frequency modeling. Building upon stabilized shallow representation, we further introduce an Adaptive Policy-driven Semantic Alignment (APSA) mechanism, which uses an online teacher policy to impose top-down semantic constraints on the student and feeds semantic guidance back to the enhanced early features during training. Experiments on MSTAR, OpenSARShip, and FUSARShip demonstrate the effectiveness of this synergy. Moreover, the competitive performance of our lightweight impletation $\text{FSCE-Net}_μ$ with only 0.17M parameters suggests that the proposed framework is applicable to both high-capacity and lightweight architectures.

Infrared small targets are typically tiny and locally salient, which belong to high-frequency components (HFCs) in images. Single-frame infrared small target (SIRST) detection is challenging, since there are many HFCs along with targets, such as bright corners, broken clouds, and other clutters. Current learning-based methods rely on the powerful capabilities of deep networks, but neglect explicit modeling and discriminative representation learning of various HFCs, which is important to distinguish targets from other HFCs. To address the aforementioned issues, we propose a dynamic high-frequency convolution (DHiF) to translate the discriminative modeling process into the generation of a dynamic local filter bank. Especially, DHiF is sensitive to HFCs, owing to the dynamic parameters of its generated filters being symmetrically adjusted within a zero-centered range according to Fourier transformation properties. Combining with standard convolution operations, DHiF can adaptively and dynamically process different HFC regions and capture their distinctive grayscale variation characteristics for discriminative representation learning. DHiF functions as a drop-in replacement for standard convolution and can be used in arbitrary SIRST detection networks without significant decrease in computational efficiency. To validate the effectiveness of our DHiF, we conducted extensive experiments across different SIRST detection networks on real-scene datasets. Compared to other state-of-the-art convolution operations, DHiF exhibits superior detection performance with promising improvement. Codes are available at https://github.com/TinaLRJ/DHiF.