Frequency-Domain Feature Learning

Follow this topic Ask about this topic

Momentum

6 papers in the last four weeks, up 20% on the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 126

Jul 9, 2026cs.SD

Structural Bottlenecks on Frequency Representation in End-to-End Audio Models

End-to-end neural audio models achieve high-fidelity compression and generation. We might read that performance as evidence they directly represent interpretable features such as pitch and timbre, but a model can produce plausible outputs without doing so. A model may encode these features in any reachable basis, but regardless of which, the features are well described as compositions of time-frequency-localized primitives. Whether state-of-the-art encoders preserve access to these primitives, and thus to compositions of them, remains unclear. Through theoretical analysis and controlled experiments, we show that several state-of-the-art strided convolutional encoders impose two structural bottlenecks, both predictable from architecture and signal structure, on access to these primitives: (1) they collapse primitives into alias equivalence classes, establishing a bound on representational capacity, and (2) they limit the frequency resolution available to learned filters, restricting separability. For well structured data, we find collapse rates of 31-35% and filter bandwidths 10-35x above the theoretical resolution bound, confirming that both bottlenecks arise under realistic signal conditions. We then introduce Gabor Latent Refactorization (GLRF), a lightweight post-hoc intervention that re-expresses encoder latents in a frequency-localized basis, reducing filter bandwidths from 10-35x to 1.5-3x of the theoretical resolution bound while preserving reconstruction fidelity and improving control over attributes like pitch. These results show that the encoders in question predictably degrade access to frequency-localized primitives, entangling the features that depend on them, and that a lightweight, retraining-free intervention can recover much of that access, improving steerability and interpretability.

Nicole Cosme-Clifford

Yale University New Haven, CT

Audio Representation Learning Neural Audio Codecs Frequency-Domain Feature Learning Neural Network Interpretability

Jul 8, 2026cs.LG

FourierQK: Spectral Preprocessing of Query-Key Projections Improves Transformer Attention

FFT-based spectral preprocessing of learned query-key (Q/K) projections substantially improves transformer attention on character-level language modelling. On TinyShakespeare: a fixed random spectral filter achieves val=1.031 (Delta=+0.443); a single learned frequency at paragraph scale achieves val=0.608 (Delta=+0.867); and four learned frequencies spanning paragraph to word scale achieve val=0.309 (Delta=+1.166), a 79% reduction over standard dot-product attention. The single-frequency result is confirmed across three random seeds (mean val=0.236, std=0.019). The four frequencies converge to a near-geometric multi-scale ordering (49, 27, 10, 6 tokens/cycle) corresponding to paragraph, sub-paragraph, phrase, and word scales. The gain is specific to spectral preprocessing: random orthogonal and non-orthogonal projections of Q/K produce no measurable improvement, suggesting the benefit comes from global frequency-domain mixing rather than metric distortion. All results are verified by a shuffled-validation diagnostic against positional leakage. Causal filters (Gaussian, Mexican Hat, Morlet) do not improve over standard attention at character-level tokenisation: the bilateral FFT kernel is structurally non-causal, coupling every position to future tokens. This defines an architectural boundary between bilateral spectral attention (this paper) and genuinely causal spectral attention at word-scale tokenisation (companion paper MorletQK). This work is architecturally distinct from FNet (Lee-Thorp et al., 2021), which replaces attention with Fourier mixing of token embeddings. Here, spectral preprocessing applies only to Q/K projections while the full attention score structure is preserved.

Athanasios Zeris

Independent Researcher, Athens, Greece.

Frequency-Domain Feature Learning Transformer Attention Language Modeling

Jul 8, 2026cs.CV

A Theory of Contrastive Learning with Natural Images

Why does contrastive learning with simple images and augmentations yield useful representations for downstream tasks? We address this question by analytically computing the optimal representation in terms of a contrastive loss for a range of basic augmentations and any image dataset with stationary statistics. We show that for certain augmentations the optimum can be attained by a CNN whose first layer filters are sinusoids, followed by a pointwise nonlinearity, global average pooling, and a final linear layer that performs partial whitening. We also show that the optimal weights in such CNNs for more complicated augmentations are still sinusoids. The frequencies of the sinusoids and their weights can be computed using a simple waterfilling algorithm given the dataset's expected power spectrum. Experiments with different image datasets and augmentations show that such CNNs trained with SGD empirically learn sinusoids in their first layer and to perform partial whitening

Antonio Torralba, Yair Weiss

CSAIL, MIT · School of Computer Science and Engineering, Hebrew University of Jerusalem

Contrastive Learning Frequency-Domain Feature Learning Convolutional Neural Networks

Jul 6, 2026cs.MM

SleepBand: Single-Source Domain Generalization for Sleep Staging via Physiologically Structured Spectral Modeling

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

Zhi Lu, Yang Hu, Yan Chen

Laboratory of Intelligent Collaborative Computing, University of Electronic Science and Technology of China, Chengdu 611731, China · School of Information Science and Technology, University of Science and Technology of China, Hefei 230026, China · School of Cyber Science and Technology, University of Science and Technology of China, Hefei 230026, China

Sleep Stage Classification EEG Decoding Frequency-Domain Feature Learning Domain Generalization Cross-Dataset Generalization

Jul 5, 2026cs.CV

UniSkip-Mamba: A Frequency-Aware State Space Model for Audio-Visual Temporal Forgery Localization

With the proliferation of AI-generated content, sophisticated multimedia manipulation has raised critical concerns about malicious applications such as opinion manipulation and evidence fabrication, making Audio-Visual Temporal Forgery Localization (AV-TFL) an urgent research frontier. Existing TFL methods have progressed along two main paradigms: Transformer-based temporal modeling and channel-wise multimodal fusion. While these approaches capture temporal dependencies and cross-modal correlations, they process all frequency components indiscriminately, leading to overfitting on high-frequency noise and limited robustness under real-world data degradation. Through systematic frequency domain analysis, we find that forgery-discriminative patterns concentrate in the low/mid-frequency range (normalized frequency 0-0.15), while high-frequency components primarily introduce noise, removing them even improves detection performance by +1.4%. Based on this phenomenon, we propose UniSkip-Mamba, a frequency-aware State Space Model framework that incorporates Unified Multimodal Sequence Fusion to preserve cross-modal phase relationships, and Skip-Scanning Mamba Blocks that implement frequency-aware regularization through a novel Group-Scan-Merge mechanism, naturally biasing learning toward discriminative low/mid-frequency patterns (0-0.15) while maintaining representational completeness. We achieve state-of-the-art (SOTA) performance: 63.4% [email protected] on LAV-DF (+9.8% improvement) and 63.58% mAP on AV-Deepfake1M (+14.32% improvement), with 6x faster inference. Our frequency-domain analysis provides theoretical justification from a signal processing perspective for why skip-scanning inherently improves both accuracy and robustness.

Cangjin Qiu, Quan Zhang, Dan Jiang +1

Cangjin Qiu and Ke Zhang are with Soochow University, Suzhou, China. · Quan Zhang and Dan Jiang are with Tsinghua University, Beijing, China.

Frequency-Domain Feature Learning Deepfake Detection State Space Models

Jul 2, 2026eess.SP

Fourier Preconditioning for Neural Feature Learning

Mutual information (MI)-inspired feature learning techniques are capable of generating low-dimensional embeddings that retain nonlinear dependence structures, but direct estimations of MI suffer from noisy probability distribution estimates in the low-data regime. The H-Score objective, computed from second-order statistics, provides a practical proxy metric for training feature extraction networks. We prove that H-Score is invariant to invertible transformations in the unrestricted functional setting, but becomes sensitive to input basis rotations under constrained approximation classes. Consequently, we study unitary preconditioning for H-Score networks and show that selecting an appropriate basis rotation reduces finite-width truncation error by concentrating predictive dependence into fewer dominant modes. We identify the fast Fourier transform (FFT) as an effective data-independent, low-cost preconditioner for approximately stationary processes, where spectral structure induces concentration of the cross-covariance singular value spectrum. We introduce training-free metrics based on spectral entropy and cumulative dependence energy to quantify basis suitability and predict downstream inference gains prior to network training. Experiments across eight multivariate datasets demonstrate that FFT preconditioning is particularly useful in resource-constrained regimes, achieving up to 50% normalized mean squared error (NMSE) reduction, while the proposed metrics correlate with observed performance gains and correctly identify cases where spectral preconditioning is detrimental.

Preston Pitzer, Anish Pradhan, Harpreet S. Dhillon

Frequency-Domain Feature Learning Predictive Representation Learning Invariant Representation Learning

Jul 2, 2026cs.LG

Frequency Shift Physics-Informed Extreme Learning Machine for Solving High-Frequency Partial Differential Equations

Solving partial differential equations (PDEs) with high-frequency solutions remains a central challenge in physics-informed machine learning due to spectral bias -- the tendency of neural networks to learn low-frequency components preferentially. This paper proposes a Frequency Shift Physics-Informed Extreme Learning Machine (FS-PIELM) framework that addresses this limitation through an additive mechanism for weight initialization. Rather than multiplying random weights by a scaling factor, the method translates the mean of the Gaussian weight distribution while keeping the variance fixed at unity, thereby avoiding the variance amplification inherent in scaling-based methods. Two variants are developed: FS-PIELM-L assigns independent frequency magnitudes to individual neurons, while FS-PIELM-G groups neurons for improved robustness. Theoretical analysis shows that the frequency variance under the proposed framework remains bounded and approaches unity regardless of target frequency, in contrast to the quadratic growth of conventional approaches. The method preserves the computational efficiency of extreme learning machines, requiring only a single linear solve. Experiments on seven benchmark problems spanning six equation types -- Helmholtz, wave, Poisson, Klein-Gordon, heat, and advection-diffusion -- on both regular and complex geometries show that the linear variant achieves the best accuracy in six of seven cases, with improvements of one to nearly five orders of magnitude over existing PIELM variants. The code and data accompanying this manuscript will be made publicly available at https://github.com/xgxgnpu/Physics-informed-vibe-coding/tree/main/FS-PIELM.

Xiong Xiong, Ruonan Zhai, Zheng Zeng +3

School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710072, China · MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an, 710072, China · College of Science, Shijiazhuang University, Shijiazhuang, 050035, China +2

PDE Solving Frequency-Domain Feature Learning Spectral Bias Physics-Informed ML

Jul 1, 2026cs.LG

I\textsuperscript{2}RiMA: Spectral Riemannian Representation with Temporal Attention for Mental Stress Detection based on EEG Signals

Cross-subject EEG stress detection remains challenging because discriminative stress-related patterns are both subject-dependent and frequency-specific. Conventional Riemannian methods model spatial covariance mainly in the time domain, overlooking neural oscillations that are critical for high-level cognitive state decoding, while standard temporal tokenization often fragments inter-slice temporal coherence. To address these limitations, we propose \method{}, an Intra-Inter Riemannian Manifold Attention Network for EEG-based stress detection. \method{} constructs spatial covariance matrices independently at each frequency point and maps them to the SPD tangent space, preserving channel-wise geometry together with frequency-specific discriminative cues. It further introduces frequency cluster aggregation to select informative spectral components and reduce redundancy by forming compact, data-driven frequency clusters aligned with EEG rhythms. Finally, an intra-inter slice attention module adaptively integrates local slice-level spectral dynamics and global temporal context across EEG sequences. Experiments on three datasets show that \method{} consistently outperforms five state-of-the-art baselines, achieving up to 82.78% balanced accuracy while remaining efficient with only 1.60M parameters and 31.95M FLOPs.

Cheng He, Kunyu Peng, Shangen Han +3

Laboratory of Neural Computing and Intelligent Perception, College of Information Engineering, Capital Normal University, Beijing, China · Karlsruhe Institute of Technology, Germany · School of Psychology, Capital Normal University, Beijing, China

Cross-Subject EEG Decoding Electroencephalography Frequency-Domain Feature Learning Geometric Representation Learning

Jun 29, 2026cs.CV

FR-DETR: Frequency and Recurrent Feature Refinement for Robust Object Detection under Adverse Weather

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.

Tuan-Duc Nguyen, Duc-Trong Le

FPT Software AI Center · VNU University of Engineering and Technology

Frequency-Domain Feature Learning Detection Transformer Object Detection

Jun 26, 2026cs.CV

ScaLe-INR: Scale and Learn Implicit Neural Representations

Implicit Neural Representations (INRs) parameterized by multilayer perceptrons excel at modeling continuous signals. However, a key challenge persists as INRs fundamentally suffer from spectral bias and information cross-talk. When a single network attempts to capture multi-scale phenomena, high-frequency weight updates destructively interfere with the underlying low-frequency structural approximation. We introduce Scale and Learn INR (ScaLe-INR), a novel multi-branch architecture that resolves these limitations by explicitly matching the signal's frequency spectrum with the optimal operating region of the INR. Drawing upon the Fourier inverse scaling theorem we demonstrate that applying directional coordinate scaling expands a network's representational bandwidth along specific spatial axes. To mathematically enforce functional disentanglement and minimize task-specific information leakage between branches, we propose a Directional Edge Guidance Loss, a spatially-conditioned sparsity prior derived from ground-truth gradients. By constraining the high-frequency branches to act as strict, localized edge-filters, ScaLe-INR eliminates spectral cross-talk, accelerates convergence, and achieves high-fidelity signal reconstruction on complex multi-scale topologies. We evaluate ScaLe-INR across diverse reconstruction and inverse tasks, demonstrating substantial performance gains over existing state-of-the-art (SOTA) methods. The proposed architecture improves upon the nearest baselines by +5.16 dB in image reconstruction and +0.65 dB in image denoising. Furthermore, it achieve an impressive figure of 50.02 dB on audio reconstruction and 0.999 IOU(Intersection Over Union) on 3D reconstruction which beats the all SOTA models.

Buwaneka Epakanda, Athulya Ratnayake, Pandula Thennakoon +4

Implicit Neural Representations Frequency-Domain Feature Learning Spectral Bias

Jun 24, 2026cs.SD

Frequency-Aware Self-Supervised Music Representation Learning

Self-supervised learning (SSL) has emerged as an essential paradigm for music information retrieval (MIR). While current SSL models achieve state-of-the-art performance across various MIR tasks, they typically treat audio as 1D sequences, either operating on time-domain waveforms or on flattened time-frequency-domain spectrograms. This discards the rich spatial and structural information in time-frequency representations and overlooks a fundamental intuition in music production. In particular, music is naturally represented as time-frequency grids in MIDI-based workflows, a structure that tightly corresponds to 2D spectrograms and inherently makes many MIR tasks trivial. Motivated by this intuition, we propose PupuM2D, a musical Masked Modeling Duo (M2D) model that is trained directly on 2D music spectrograms. Instead of applying masked language modeling (MLM) to 1D sequences, PupuM2D learns robust representations by predicting the latent embeddings of masked 2D music spectrogram patches from unmasked contexts. To optimally adapt such a framework to music signals, we also apply domain-specific modifications to model architecture, training scheme, and inference paradigm, with comprehensive ablation studies showing their effectiveness. Evaluations on the MARBLEv2 benchmark show that PupuM2D outperforms the sequence-based SSL models across multiple MIR tasks in linear probing. Additionally, case studies of the attention maps also confirm that PupuM2D captures musically meaningful patterns within the 2D time-frequency domain. Codes and checkpoints are available at: https://www.yichenggu.com/PupuM2D/.

Yicheng Gu, Junan Zhang, Jerry Li +2

Spellbrush, Akihabara, Tokyo 101-0021, Japan · Acoustic Lab, Department of Information and Communications Engineering (DICE), Aalto University, Espoo 02150, Finland · School of Data Science, The Chinese University of Hong Kong, Shenzhen, Guangdong 518172, China

Audio Representation Learning Frequency-Domain Feature Learning Music Information Retrieval

Jun 22, 2026cs.CV

From Spatial to Spectral: An Efficient, Frequency-Guided Feature Representation Learner for Small Object Detection

Efficient small object detection is bottlenecked by the inherent feature scarcity of tiny targets, which is further aggravated by operations of spatial-domain detectors that indiscriminately discard critical high-frequency details. Recovering these fragile cues within the spatial domain is notoriously difficult, as it often requires computationally expensive architectural upscaling that inadvertently amplifies background noise. To bridge this gap, we propose a paradigm \textbf{shift from spatial to spectral} feature processing, introducing a holistic solution with the following novelty: (1) A versatile \textbf{Frequency-Guided Feature Representation framework} that generalizes across diverse detector architectures (both CNN and Transformer-based), offering a robust alternative to spatial-only feature extraction; (2) The unified \textbf{Decompose--Enhance--Reconstruct (DER)} operator, instantiated via three \textbf{lightweight, plug-and-play} modules -- Wavelet-Difference Gate (WDG), Log-Gabor Enhancer (LGE), and Frequency-Driven Head (FDHead) -- to systematically inject frequency-aware modulation into the backbone, neck, and head. This mechanism decouples feature modeling from resolution reduction, capturing discriminative high-frequency components to enable accurate localization with significantly reduced parameter redundancy; (3) Extensive validation on multi-domain benchmarks (VisDrone2019, UAVDT, TinyPerson, DOTAv1) demonstrating consistent gains. Notably, our proposed \textbf{DERNet} series outperforms YOLOv11 models under the same scale while requiring \textbf{only 1/6 of the parameters}, backed by rigorous spectral diagnostics and error decomposition analysis.

Yuhan Rui, Shihan Qiao, Yibin Lou +7

Southern University of Science and Technology, Shenzhen, China · University of Pennsylvania

Frequency-Domain Feature Learning Small Object Detection Efficient Object Detection Object Detection Aerial Object Detection

Jun 22, 2026cs.CV

Spectral Gating via Damped Oscillations for Adaptive Implicit Neural Representations

Implicit Neural Representations (INRs) have been proven successful in encoding continuous signals through coordinate-based networks, yet facing a spectral dilemma: periodic activations capture fine details but act as all-pass filters that memorise noise, while spatially compact activations regularise effectively but suffer from low-frequency bias. Existing attempts to resolve this trade-off introduce computational overhead or tuning frailty. We propose to model each neuron's activation as the steady-state response of a sinusoidally-forced damped harmonic oscillator, whose amplitude naturally governs the network's spectral selectivity during training. By jointly optimising the oscillator parameters alongside the network weights, our method adapts to the target signal's spectral content without explicit regularisation. Initialised in the stopband, the network exhibits a coarse-to-fine learning curriculum that progressively expands its spectral gate, capturing low-frequency structures first and high-frequency details only when justified by the reconstruction objective. Comprehensive experiments show that our approach consistently achieves state-of-the-art or competitive results against established INRs, while requiring no task-specific tuning of any hyperparameters.

Alex Costanzino, Pierluigi Zama Ramirez, Giuseppe Lisanti +1

CVLab, University of Bologna · Ca’ Foscari University of Venice

Implicit Neural Representations Frequency-Domain Feature Learning Spectral Bias

Jun 22, 2026cs.LG

Temporal-Spectral Alignment with Frequency Adaptation for Source-Free Time-Series Adaptation

The goal of source-free domain adaptation (SFDA) for time-series data is to transfer knowledge from a pre-trained source model to an unlabeled target domain without requiring access to source data, while addressing feature shift and temporal drift inherent in the signals. Although existing approaches have explored temporal dynamics in unsupervised source-free adaptation, they largely overlook spectral shifts in time-series data. Towards this end, we propose a novel approach termed temporal-Spectral Alignment with Frequency Adaptation (SAFA) for source-free time-series domain adaptation. Specifically, we first model the source domain at multiple scales by jointly capturing temporal dependencies and spectral characteristics. To adapt time-series data in the target domain, we introduce a trainable frequency adaptation module that modulates the phase and amplitude of target signals in the frequency domain to align them with the source distribution. Extensive experiments on multiple benchmark datasets demonstrate the efficacy and robustness of SAFA.

Shichang Meng, Linquan Wu, Xuan Ai +1

City University of Hong Kong Hong Kong, China

Source-Free Domain Adaptation Domain Adaptation Frequency-Domain Feature Learning

Jun 21, 2026cs.CV

Efficient Document Tampering Localization with Multi-Level Discrepancy Features and Unified DCT-Quantization Embedding

Localizing document tampering is extremely challenging, as manipulations are crafted to appear visually consistent and often leave only subtle traces that are nearly invisible to the human eye. In prior work, evaluation has been largely dominated by synthetic benchmarks that closely match the training distribution, and methods have shown steady progress under this setting. However, these gains often translate poorly to human-made forgeries and to cross-domain evaluation, where both the source documents and the tampering pipeline can change, leading to a distribution shift. In addition, since the introduction of the Frequency Perception Head for the discrete cosine transform (DCT) modality, it has become a standard choice, and subsequent work has largely focused on downstream modules and fusion strategies rather than revisiting the backbone itself. To help close this gap in cross-domain performance and improve the DCT backbone design, we propose \textbf{DiffNet}, a relatively simple yet effective RGB--DCT early-fusion architecture driven by two key design choices. First, to ensure that the decoder aggregates multi-scale inconsistency evidence rather than operating on raw, content-heavy activations, we apply a lightweight multi-level discrepancy transformation at the output of each backbone stage, replacing features with magnitude-only responses to learned zero-sum filters. Second, we design an efficient DCT-domain backbone that relies on a lightweight frequency-index-aware DCT--quantization joint embedding. Our approach achieves state-of-the-art performance on cross-domain and human-made document tampering localization, outperforming prior methods by around 30%, with up to

7\times

higher throughput than the previous best model.

Mohamed Dhouib, Ye Zhu, Sonia Vanier +1

LIX, École Polytechnique, IP Paris, France · DataLab Groupe, Crédit Agricole S.A., France

Digital Image Forensics Frequency-Domain Feature Learning Image Forgery Localization

Jun 20, 2026cs.LG

Frequency-Domain Neural ODEs for Modeling Non-Linear Dynamical Systems

Standard continuous-depth models, such as Neural Ordinary Differential Equations (NODEs), offer significant advantages in modeling physical systems by learning continuous vector fields rather than discrete temporal steps. However, when applied to complex dynamical systems, standard NODEs frequently struggle with highly nonlinear dynamics. This paper investigates the Frequency-domain Neural ODE (FNODE), an architecture that projects continuous temporal dynamics into the frequency domain using the Fast Fourier Transform (FFT). By operating in the frequency domain, the model provides better generalization to the dynamical system. The architecture is empirically evaluated against discrete models, specifically Gated Recurrent Units (GRUs) and Long Short-Term Memory (LSTMs), and other continuous-depth variants, including Augmented Neural ODE (ANODE), across four distinct dynamical systems: the Lotka-Volterra model, the forced Duffing oscillator, the Van der Pol oscillator, and the Lorenz system. To rigorously assess generalization and robustness, curriculum and ensemble learning are used to evaluate the model's convergence by estimating confidence intervals across different ensemble models. The empirical results demonstrate that the FNODE architecture achieves better generalization while exhibiting remarkable convergence stability.

Mohammed Ashraf, Ayman A. El-Badawy

Department of Mechatronics Engineering, German University in Cairo, Cairo, Egypt

Frequency-Domain Feature Learning Nonlinear System Identification Neural ODEs

Jun 18, 2026cs.CV

FUSE: Frequency-domain Unification and Spectral Energy Alignment for Multi-modal Object Re-Identification

Despite significant progress in multi-modal Re-Identification (ReID), existing methods tend to emphasize low-frequency cues. Consequently, they focus on attributes such as color, illumination, and coarse appearance, while overlooking mid and high-frequency structures that encode geometric, textural, and identity-discriminative details. This imbalance leads to incomplete spectral representations and unstable cross-modal alignment. To overcome these limitations, we introduce FUSE, a frequency-domain framework that reformulates multi-modal ReID as a two-stage process of spectral disentanglement and energy alignment. The proposed Spectral Decomposition Module (SDM) adaptively partitions features into low, mid, and high-frequency subspaces, enabling hierarchical spectral modeling. The Cross-Modal Alignment Module (CAM) further enforces energy alignment and subspace complementarity across modalities via frequency-consistency regularization. In addition, FUSE incorporates learnable frequency modulation to enhance robustness under varying illumination and heterogeneous sensor conditions. Extensive experiments on RGBNT201, RGBNT100, and MSVR310 show that FUSE achieves 9.1% mAP and 9.5% Rank-1 improvements, establishing an interpretable frequency-domain paradigm for multi-modal representation learning.

Xuanhao Qi, Tom H. Luan, Yukang Zhang +4

School of Cyber Science and Engineering, Xi’an Jiaotong University, Xi’an, China · School of Informatics, Xiamen University, Xiamen, China · National University of Singapore, Singapore

Cross-Modal Representation Learning Multimodal Robustness Frequency-Domain Feature Learning Cross-Modal Alignment Person Re-Identification

Jun 16, 2026cs.CV

Neural Phase Correlation

Correspondence is fundamentally relational: it seeks the unknown transformation between two observations of a common scene, not the content of either. Yet the dominant learning-based methods do not represent the transformation as a first-class object in the architecture. They encode each image independently and let a learned similarity function or a deep decoder discover the mapping implicitly. Phase correlation is the canonical exception, measuring the inter-image relationship directly in the Fourier domain, but the rigidity of its fixed basis confines it to global translation. We introduce a learned generalization of phase correlation that lifts this restriction by learning the basis on which the transformation decomposes. The same algebraic primitive extends to dense non-rigid deformations and to unitary dynamics. On the ACDC cardiac-MRI benchmark the framework matches or exceeds prior published baselines on both registration directions. On CAMUS echocardiography it matches state-of-the-art without auxiliary scoring or adaptive-smoothness mechanisms. Applied to time-evolved wavefunction pairs of the 1-D quantum harmonic oscillator, the same framework recovers the Hermite-function eigenstates and the quantized energy levels of the unknown Hamiltonian from observation pairs alone.

Cole Reynolds

Weyl Labs

Quantum System Identification Frequency-Domain Feature Learning Medical Image Registration Deformable Image Registration

Jun 16, 2026cs.CV

TaFD: Threat-Aware Frequency Decoupling for Adversarial Robustness against Heterogeneous Attacks

Multi-threat robustness remains a fundamental challenge in deep learning. Although joint adversarial training (JAT) is widely adopted, it suffers from negative transfer under heterogeneous threats, particularly between

\ell_p

-bounded and semantic attacks. Through first-order gradient analysis, we formalize this as gradient incompatibility and theoretically establish the necessity of decoupled optimization. We further reveal that these conflicting threats exhibit separable spectral characteristics in the frequency domain. Motivated by this observation, we propose Threat-aware Frequency Decoupling (TaFD), a two-stage defense framework that reformulates JAT as a frequency-domain divide-and-conquer paradigm. TaFD first discovers latent threat domains via unsupervised clustering of attack spectral prototypes and trains a lightweight classifier for inference-time threat domain identification. Conditioned on the prediction, TaFD employs a Frequency-Conditional Convolution that learns threat-domain-specific spectral masks and routes each sample to the corresponding expert, enforcing structural parameter separation and alleviating optimization conflicts. We validate TaFD on three representative image-classification benchmarks (CIFAR-10, CIFAR-100, and Tiny-ImageNet) and on two representative architectures (the convolutional ResNet and the hybrid-transformer MobileViT). Extensive results demonstrate that TaFD achieves more balanced robustness against heterogeneous attacks than existing JAT and frequency-domain baselines, improving average robust accuracy by approximately 11% over the strongest baseline while maintaining leading clean accuracy.

Mengda Xie, Yiling He, Meie Fang

School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou, Guangdong, China · Information Security Research Group, University College London, London, United Kingdom

Adversarial Training Frequency-Domain Feature Learning Neural Network Robustness Adversarial Robustness

Jun 16, 2026cs.CV

Bridging Spatial And Frequency Views For Disaster Assessment: Benefits And Limitations

Rapid assessment of building damage from satellite imagery is essential for effective disaster response and recovery. While most deep learning methods rely on spatial-domain features, frequency-domain representations can capture complementary structural cues such as debris patterns and collapse-induced textures. This study presents a controlled comparison of spatial-domain, frequency-domain, and dual-domain deep learning approaches for multi-class building damage classification using post-disaster imagery from the xView2 (xBD) dataset. To ensure fairness, all models are built on an EfficientNet-B0 backbone and trained under identical settings, differing only in their input representations and fusion strategies. Performance is evaluated using accuracy, macro F1-score, per-class metrics, and confusion matrices. Results show that dual-domain models provide measurable improvements over single-domain approaches. The dual spatial configuration achieves the highest test accuracy (0.4688) and lowest loss, while the spatial-only model attains the best macro F1-score (0.4254), indicating more balanced class performance. In contrast, frequency-only models perform worst and exhibit overfitting, suggesting limited generalization. Despite these gains, all models struggle to detect subtle damage levels, particularly the Minor class, due to class imbalance and fine-grained visual ambiguity. While dual-domain approaches improve detection of severe damage, challenges remain. These findings highlight the benefits and limitations of hybrid representations and motivate future work on data balancing, advanced fusion, and regularization.

Shikha V. Chandel, Yadav Raj Ghimire, Timothy Agboada +1

College of Science and Technology North Carolina A&T State University Greensboro, NC · Computational Data Science and Engineering North Carolina A&T State University Greensboro, NC

Remote Sensing Image Understanding Building Damage Assessment Frequency-Domain Feature Learning Disaster Response

Jun 16, 2026cs.LG

The Discrete-Log Clock: How a Transformer Learns Modular Multiplication

When small transformers grok modular multiplication, prior work reports that the learned embedding has a "dense" Fourier spectrum requiring all frequencies. This contrasts with modular addition, where only a sparse set of key frequencies suffices. We show this density is an artifact of analyzing in the wrong basis. The natural Fourier transform for multiplication is not the standard additive DFT but the multiplicative character transform, which decomposes functions on the multiplicative group

(\mathbb{Z}/p\mathbb{Z})^*

into its irreducible representations. Applying this transform to a grokked transformer trained on

a \cdot b \bmod 113

, we find the embedding spectrum becomes highly sparse (Gini coefficient 0.58 vs. 0.07 in the additive basis) with only 4 key frequencies carrying significant energy. Furthermore, 96.9% of MLP neurons are cleanly tuned to a single multiplicative frequency, and neuron activation heatmaps reveal 2D-periodic structure when reordered by the discrete logarithm. These results demonstrate the transformer reduces multiplication to addition in discrete-log space, implementing a "Discrete-Log Clock" algorithm analogous to Nanda et al.'s Clock algorithm for addition. The methodology generalizes: matching the analysis basis to the algebraic structure of the task reveals interpretable structure where standard tools see noise.

Huu Danh Nguyen

Stanford University

Transformer Interpretability Frequency-Domain Feature Learning Spectral Methods Modular Arithmetic LLM Mathematical Reasoning

Jun 15, 2026cs.CV

FATE: Pillar Encoding and Frequency-Aware Training for Event-Based Object Detection

Event cameras are bio-inspired sensors that asynchronously capture logarithmic intensity changes, offering inherent advantages in high-speed and high-dynamic-range scenarios. However, the sparse and asynchronous nature of event streams poses a fundamental challenge for modern deep learning architectures. To enable compatibility with standard models, most existing approaches partition the accumulation window into fixed temporal sub-bins. While effective for spatial processing, this internal discretization discards fine-grained temporal structure and constrains inference to the low temporal frequencies imposed by training supervision. To address this limitation, we propose FATE, a unified framework built upon a novel Pillar Encoding (PE). While operating over discrete macro-accumulation windows dictated by the target frequency, PE avoids internal temporal sub-binning. It organizes events into spatial pillars and approximates their intra-window evolution via projection onto a continuous-time orthogonal polynomial basis. This formulation yields an L2-optimal representation that retains rich temporal dynamics in a dense pseudo-image, mitigating information loss under sparse event conditions. To fully leverage this representation, we introduce Frequency-Aware Training (FAT), a soft mean-teacher curriculum that generates temporally dense pseudo-labels, effectively bridging the mismatch between low-frequency supervision and high-frequency inference. Extensive experiments demonstrate that FATE generalizes across architectural paradigms and consistently outperforms strong baselines. It enables robust object detection at high temporal resolutions up to 200 Hz, while incurring minimal overhead in parameter count and inference latency

Md Tawheedul Islam Bhuian, Kyoung-Don Kang

School of Computing State University of New York at Binghamton

Event-Based Vision Frequency-Domain Feature Learning Event-Based Object Detection

Jun 15, 2026cs.CV

The Importance of Phase in Neural Representations: An Internal Oppenheim-Lim Test of Image Classifiers

Oppenheim and Lim (1981) showed that natural images stay recognizable when reconstructed from their Fourier phase alone, while the magnitude carries little of their identity. We ask whether trained image classifiers reproduce this asymmetry inside their hidden layers, and we test it causally: given two images, we transplant the phase of one onto the magnitude of the other at a chosen layer and record which image the prediction follows. In PRISM2D, GFNet, and ViT-B/16 the prediction follows the phase or sign donor, and deleting all image-specific magnitude barely moves accuracy, so identity rides on phase while image-specific magnitude is largely dispensable to the readout. ResNet-50 at first seems to break the pattern, because transplanting sign after its ReLUs does nothing; a fair intervention before the ReLU reveals a strong latent sign code in the late blocks, and a DC-only control shows the readout consumes a channel-wise spatial average. Controls rule out the trivial case in which magnitude simply stops depending on the image. The architectures therefore share a phase/sign identity code but expose it in different bases, set by rectification and readout geometry, which gives a mechanistic account of the texture--shape gap between CNNs and attention models.

Alper Yıldırım

Visual Representation Learning Frequency-Domain Feature Learning Image Classification

Jun 12, 2026eess.SP

FAConformer: Frequency-Aware Convolutional Transformer for Auditory Attention Decoding

Auditory attention decoding (AAD) aims to infer the attended speaker from neural responses in multi-speaker acoustic environments and is a key problem for neuro-steered hearing systems. Although recent studies have achieved encouraging progress, existing AAD models still do not fully exploit frequency domain electroencephalography (EEG) information. In particular, most approaches introduce multi-band information through handcrafted feature extraction or direct cross-band feature concatenation, which mainly exploit frequency information at a shallow level and may overlook band-specific patterns and cross-band interactions. To address these limitations, this paper proposes FAConformer, a frequency-aware CNN-Transformer framework for AAD that explicitly integrates band-specific encoding and adaptive cross-band interaction. Specifically, FAConformer first decomposes EEG signals into multiple frequency bands and assigns each band to an independent CNN-Transformer encoder for band-specific modeling. The resulting band-wise features are then adaptively fused by a carefully designed frequency-aware attention (FAA) module that models cross-band dependencies by treating band-wise features as tokens. Further, band-wise auxiliary supervision (BAS) is introduced to prevent weakly contributing branches from being under-optimized during joint training. In this way, FAConformer performs frequency-aware modeling that more effectively exploits frequency domain information. Extensive experiments on two public AAD datasets with three decision-window lengths demonstrated that FAConformer consistently outperformed 12 competitive baselines, surpassing the current state-of-the-art model by 4.9%. Further analyses of band importance, ablation, and parameter sensitivity verify the effectiveness, robustness, and interpretability of the proposed framework. Code is available at https://github.com/wzwvv/FAConformer.

Ziwei Wang, Xingyi He, Tianwang Jia +2

Hubei Key Laboratory of Brain-inspired Intelligent Systems, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China

Hybrid CNN-Transformer Architectures Neural Decoding EEG Decoding Frequency-Domain Feature Learning Transformer Attention

Jun 11, 2026cs.LG

Circuit Synchronization Precedes Generalization: A Causal Precursor to Grokking

Grokking is the delayed generalisation phenomenon where a transformer trained on modular arithmetic abruptly transitions from near-chance to near-perfect validation accuracy. It has been attributed to a Fourier-based algorithmic circuit, but its timing, causal structure, and controllability remain poorly understood. We introduce the Frequency Synchronization Degree (FSD), a normalised, permutation-tested metric for Fourier circuit synchronisation requiring no prior knowledge of the circuit. Across nine modular addition configurations (five primes, three seeds), FSD reaches its post-grokking level 500 to 3000 steps before grokking (mean lead 1722 steps, every configuration positive, sign-test p approx 0.004), and synchronises before a restricted-logit loss baseline in all nine cases, making it the earliest available predictor. We give direct causal evidence that the inter-phase gap is a regularisation phenomenon: forking training at the FSD-ceiling step and varying weight decay lambda produces monotonically earlier grokking, with delta-t proportional to 1/lambda. This law replicates across three primes (R-squared 0.89 to 0.99 on seed-averaged delta-t); per-run R-squared is unstable due to the chaotic transition, so we report error bars rather than single runs. Grokking occurs at a near-constant memorisation norm across lambda, grounding the constant in a threshold mechanism. This is not an artefact of applying a Fourier detector to a Fourier circuit: on the non-abelian group S5, a basis-faithful generalisation of FSD precedes grokking on all six seeds, while the original Fourier FSD does not. Using the FSD ceiling to schedule a weight-decay increase also accelerates grokking over a fixed schedule without destabilising training. An attention-only variant groks with a strong FSD precursor while an MLP-only model never groks.

Achyuthan Sivasankar

New York University

Weight Decay Frequency-Domain Feature Learning Neural Network Training Dynamics Grokking

Jun 10, 2026cs.SD

BASENet: Band-Adapted Speech Enhancement Network with Cross-Band Attention

Speech enhancement models typically apply uniform capacity across all frequencies, disregarding the non-uniform spectral resolution of human hearing. We propose BASENet, a frequency-adapted architecture that partitions the spectrum into Bark-scale bands and assigns each a scaled-capacity encoder derived from critical-band density, automatically granting deeper branches to perceptually dense low frequencies and lighter ones to high frequencies. A cross-band attention module captures harmonic dependencies across bands through compact frequency-pooled representations at linear complexity. Built on inverted residual blocks with dense connectivity and a convolutional recurrent network, BASENet achieves 3.55 PESQ and STOI~~96% on VoiceBank+DEMAND with only 0.83M parameters and 7.3 G~~MACs, the fewest parameters among all methods with PESQ > 3.50. A causal variant (3.44 PESQ) surpasses several non-causal baselines, confirming suitability for real-time streaming on resource-constrained devices.

Damien Martins Gomes, François Capman

Thales SIX GTS, FRANCE

Frequency-Domain Feature Learning Speech Enhancement

Jun 10, 2026cs.CV

MFEN:Multi-Frequency Expert Network for Visible-Infrared Person Re-ID

Visible-infrared person re-identification (VI-ReID) is challenging due to the large modality discrepancy between visible and infrared images. We contend that this discrepancy is largely related to differing lighting conditions, including differences in light wavelength and light source type. Recently, frequency-based VI-ReID approaches have achieved notable success because frequency information can better extract identity-relevant contours and details while excluding irrelevant lighting and color. However, existing methods either do not distinguish different frequency bands or focus on only one band, which is insufficient under diverse lighting conditions. To perform comprehensive frequency domain learning, we propose a Multi-Frequency Expert Network (MFEN) that enables multi-frequency modulation and adaptively combines different bands through a mixture-of-experts design. We further introduce Random Frequency Augmentation (RFA) and Frequency Auxiliary Optimization (FAO) to better train MFEN. The three modules are complementary and jointly capture critical frequency-domain details for robust representation learning. Extensive experiments on three VI-ReID datasets demonstrate the effectiveness of our approach.

Xulin Li, Yan Lu, Bin Liu +4

University of Science and Technology of China, China · Anhui Province Key Laboratory of Digital Security, China · The Chinese University of Hong Kong, China

Frequency-Domain Feature Learning Person Re-Identification

Jun 10, 2026cs.CV

FreqKD: Frequency-Decoupled Cross-Modal Knowledge Distillation for Infrared Object Detection

Transfer learning from large-scale RGB foundation models to infrared (IR) imagery through knowledge distillation (KD) remains challenging due to fundamental differences in image formation physics. We investigate the spectral structure of the RGB--IR modality gap and observe that feature divergence is not uniform across spatial frequencies: low-frequency components (shape, layout) show greater cross-modal alignment than high-frequency components (texture, fine edges), which reflect modality-specific characteristics. Based on this analysis, we propose FreqKD, a frequency-decoupled distillation framework that applies asymmetric supervision adapted to each band's cross-modal consistency. The method employs strict mean squared error (MSE) on the low-frequency band to preserve shared structural information and a relaxed log-MSE loss (weighted at 0.1) on the high-frequency band to provide edge guidance while tolerating texture differences. Spectral divergence analysis on 500 paired samples shows that high-frequency divergence exceeds low-frequency divergence by a factor of 2.4x on average across all analysed transformer layers. On KAIST multispectral pedestrian detection, FreqKD achieves 64.1 mAP50, improving 2.4 points over the DINOv2 baseline. The learned representation transfers across datasets (FLIR ADAS, +2.1 mAP50), tasks (MFNet segmentation, +1.85 mean intersection-over-union), and architectures (ResNet-50, +1.0 mAP50). Code is available at: https://anonymous.4open.science/r/freq_decoupled_kd-5E5A

Keval Thaker, Venkatraman Narayanan, Abdalmalek Aburaddaha +1

University of Michigan-Dearborn 4901 Evergreen Rd Dearborn, MI 48128, USA

Cross-Modal Knowledge Distillation Multispectral Object Detection Frequency-Domain Feature Learning Infrared Object Detection Knowledge Distillation

Jun 9, 2026cs.CV

PF-Trans: Physics-Embedded Frequency-Aware Transformer for Spectral Reconstruction

Snapshot Broadband Filter Array (BFA) imaging provides high light throughput for spectral reconstruction but introduces severe spectral aliasing due to complex modulation. Current deep learning approaches, limited to spatial denoising, often fail to address the global frequency-specific degradations caused by the mask structure. To address this, we propose a Physics-embedded Frequency-aware Transformer (PF-Trans) for high-fidelity remote sensing spectral reconstruction. Our method explicitly integrates the physical sensing model through mask injection and a gray-scale consistency loss to ensure physical fidelity. Furthermore, we introduce a Dual-domain Block with a parallel Fast Fourier Transform (FFT) branch, enabling the network to perceive and suppress aliasing artifacts in the frequency domain. Extensive experiments on multiple datasets demonstrate that PF-Trans achieves state-of-the-art performance, achieving a Peak Signal-to-Noise Ratio (PSNR) of up to 48.50 dB on the GF-5 Shanghai dataset, significantly outperforming comparison methods.

Yuzhe Gui, Tianzhu Liu, Yanfeng Gu +1

Harbin Institute of Technology 150001 Harbin, China

Frequency-Domain Feature Learning Hyperspectral Imaging Physics-Informed ML

Jun 8, 2026cs.CV

Frequency Decoupled Framework for Screen Content Image Super-Resolution

Methods based on implicit neural representations have demonstrated superior performance in Screen Content Image Super-Resolution (SCISR) . However, they overlooked the inherent frequency characteristics, leading to suboptimal performance. We propose a frequency decoupled framework (FDF) that rethinks SCISR from a phasor perspective by capturing structured energy in amplitude and relational continuity in phase, and jointly exploiting them with bespoke implicit representations to faithfully recover the regular textures and global configuration of Screen Content Image (SCI). Amplitude-Phase Factorization Network (APFN) first separates images into amplitude and phase streams, where Amplitude Clustering Module (ACM) organizes sparse yet high-energy amplitude responses into representative prototypes for periodic pattern extraction, while Phase Consistency Self-Attention (PCSA) progressively reinforces configuration through continuous consistency propagation. And Oscillation-Anharmonic Implicit Fitting Network (OAIF-Net) integrates periodic and coherent implicit representations for efficient exploitation of the periodic patterns and coherent context embedded in SCI. Experimental results show FDF achieves state-of-the-art SCISR performance at multiple scales across four public SCI datasets. Ablation experiments further demonstrate the effectiveness of each component in extracting and exploiting periodic patterns and coherent context.

Xufei Wang, Qicheng Zhang, Qi Wu +2

School of Electronic and Information Engineering, Anhui University, Hefei 230039, China

Implicit Neural Representations Frequency-Domain Feature Learning Image Super-Resolution