Daily Papers

Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict g_1 star g_2 for elements of a finite group G. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient ascent on a representation-theoretic energy functional. We prove that, under random initialization, this flow drives each neuron to converge almost surely toward a single irreducible representation, while the cross-layer Fourier coefficients achieve a rotational rank-one alignment. This framework provides a representation-theoretic account of feature learning and characterizes a novel low-rank compression phenomenon for matrix-valued group representations. Moreover, for Abelian groups, we provide a complete population-level description: random initialization promotes uniform diversification across nontrivial representations and induces Haar-uniform phases, jointly approximating the indicator via a majority-vote mechanism. We further prove that both phase alignment and representation competition emerge with exponential convergence rates.

Spectral imaging offers promising applications across diverse domains, including medicine and urban scene understanding, and is already established as a critical modality in remote sensing. However, variability in channel dimensionality and captured wavelengths among spectral cameras impede the development of AI-driven methodologies, leading to camera-specific models with limited generalizability and inadequate cross-camera applicability. To address this bottleneck, we introduce CARL, a model for Camera-Agnostic Representation Learning across RGB, multispectral, and hyperspectral imaging modalities. To enable the conversion of a spectral image with any channel dimensionality to a camera-agnostic representation, we introduce a novel spectral encoder, featuring a self-attention-cross-attention mechanism, to distill salient spectral information into learned spectral representations. Spatio-spectral pre-training is achieved with a novel feature-based self-supervision strategy tailored to CARL. Large-scale experiments across the domains of medical imaging, autonomous driving, and satellite imaging demonstrate our model's unique robustness to spectral heterogeneity, outperforming on datasets with simulated and real-world cross-camera spectral variations. The scalability and versatility of the proposed approach position our model as a backbone for future spectral foundation models. Code and model weights are publicly available at https://github.com/IMSY-DKFZ/CARL.

We present GB-LSR (Global-Bandwidth Local Spectral Representation), a fixed-grid local spectral representation for continuous image reconstruction. The image domain is partitioned into non-overlapping square patches, each carrying coefficients for a truncated Fourier basis predicted from shared convolutional-encoder features. A single trainable scalar bandwidth is shared globally across all patches and images, and reconstruction at any continuous coordinate is a fixed-size basis contraction whose cost is independent of image size. We study three bandwidth-handling variants: a trainable global scalar (main), a fixed global scalar, and a per-patch bandwidth field. On a standardized native-reconstruction benchmark across Kodak, Set14, and Urban100, the main variant outperforms matched-budget amortized LIIF / LTE / WIRE re-implementations by 2.8-3.6 dB PSNR and 0.11-0.15 LPIPS, while running at roughly one-quarter of the slowest baseline's inference cost. The single global scalar suffices empirically: per-patch adaptive-bandwidth alternatives do not improve over it on either a closed-form locality diagnostic or an end-to-end ablation. In a separate arbitrary-scale super-resolution (ASR) extension, GB-LSR achieves competitive PSNR-Y under a canonical-style SR protocol and runs 1.44x faster than LIIF-RDN and 3.25x faster than LTE-SwinIR at x4; within the same extension, a variant trained and evaluated without 4-corner local-ensemble averaging gives a 1.77x speedup with 35% lower peak memory and negligible PSNR change, while additionally widening the RDN encoder from 64 to 96 channels gives a small positive PSNR shift with a 1.58x speedup and 31% lower peak memory. Native-reconstruction claims are scoped to the matched-budget amortized protocol, and ASR claims are scoped to a separate canonical-style SR protocol.

Vision-language foundation models (VLFMs) promise zero-shot and retrieval understanding for Earth observation. While operational satellite systems often lack full multi-spectral coverage, making RGB-only inference highly desirable for scalable deployment, the adoption of VLFMs for satellite imagery remains hindered by two factors: (1) multi-spectral inputs are informative but difficult to exploit consistently due to band redundancy and misalignment; and (2) CLIP-style text encoders limit semantic expressiveness and weaken fine-grained alignment. We present SATtxt, a spectrum-aware VLFM that operates with RGB inputs only at inference while retaining spectral cues learned during training. Our framework comprises two stages. First, Spectral Representation Distillation transfers spectral priors from a frozen multi-spectral teacher to an RGB student via a lightweight projector. Second, Spectrally Grounded Alignment with Instruction-Augmented LLMs bridges the distilled visual space and an expressive LLM embedding space. Across EuroSAT, BigEarthNet, and ForestNet, SATtxt improves zero-shot classification on average by 4.2%, retrieval by 5.9%, and linear probing by 2.7% over baselines, showing an efficient path toward spectrum-aware vision-language learning for Earth observation. Project page: https://ikhado.github.io/sattxt/

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, standard MLP-based PINNs often fail to converge when dealing with complex initial value problems, leading to solutions that violate causality and suffer from a spectral bias towards low-frequency components. To address these issues, we introduce NeuSA (Neuro-Spectral Architectures), a novel class of PINNs inspired by classical spectral methods, designed to solve linear and nonlinear PDEs with variable coefficients. NeuSA learns a projection of the underlying PDE onto a spectral basis, leading to a finite-dimensional representation of the dynamics which is then integrated with an adapted Neural ODE (NODE). This allows us to overcome spectral bias, by leveraging the high-frequency components enabled by the spectral representation; to enforce causality, by inheriting the causal structure of NODEs, and to start training near the target solution, by means of an initialization scheme based on classical methods. We validate NeuSA on canonical benchmarks for linear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models are available in https://github.com/arthur-bizzi/neusa.

Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in the resulting representations. As a result, most GNNs rely on local approximations such as polynomial Laplacian filters or message passing, which limit their ability to model long-range dependencies. In this paper, we introduce an exact factorization of the GFT into operators acting on subgraphs, which are then combined via a sequence of Cauchy matrices. Building on this factorization, we propose a new class of spectral GNNs, termed L2G-Net (Local to Global Net). Unlike existing spectral methods, which are either fully global (when using the GFT) or local (when using polynomial filters), L2G-Net operates by processing the spectral representations of subgraphs and then combining them via structured matrices. Our algorithm avoids full eigendecompositions, exploiting graph topology to construct the factorization with quadratic complexity in the number of nodes, scaled by the maximum cut size between subgraphs. Experiments stressing long-range dependencies on large graphs show that L2G-Net scales to regimes out of reach for the standard GFT, and is competitive with state-of-the-art methods with orders of magnitude fewer learnable parameters.

One of the decisions that arise when designing a neural network for any application is how the data should be represented in order to be presented to, and possibly generated by, a neural network. For audio, the choice is less obvious than it seems to be for visual images, and a variety of representations have been used for different applications including the raw digitized sample stream, hand-crafted features, machine discovered features, MFCCs and variants that include deltas, and a variety of spectral representations. This paper reviews some of these representations and issues that arise, focusing particularly on spectrograms for generating audio using neural networks for style transfer.

Accurate remote sensing-based crop yield prediction remains a fundamental challenging task due to complex spatial patterns, heterogeneous spectral characteristics, and dynamic agricultural conditions. Existing methods often suffer from limited spatial modeling capacity, weak generalization across crop types and years. To address these challenges, we propose DFYP, a novel Dynamic Fusion framework for crop Yield Prediction, which combines spectral channel attention, edge-adaptive spatial modeling and a learnable fusion mechanism to improve robustness across diverse agricultural scenarios. Specifically, DFYP introduces three key components: (1) a Resolution-aware Channel Attention (RCA) module that enhances spectral representation by adaptively reweighting input channels based on resolution-specific characteristics; (2) an Adaptive Operator Learning Network (AOL-Net) that dynamically selects operators for convolutional kernels to improve edge-sensitive spatial feature extraction under varying crop and temporal conditions; and (3) a dual-branch architecture with a learnable fusion mechanism, which jointly models local spatial details and global contextual information to support cross-resolution and cross-crop generalization. Extensive experiments on multi-year datasets MODIS and multi-crop dataset Sentinel-2 demonstrate that DFYP consistently outperforms current state-of-the-art baselines in RMSE, MAE, and R2 across different spatial resolutions, crop types, and time periods, showcasing its effectiveness and robustness for real-world agricultural monitoring.

Detecting the tiny Doppler shifts induced by Earth-mass planets in stellar radial-velocity measurements remains extremely challenging due to stellar activity. Many deep-learning methods performing well on simulated data remain difficult to apply reliably on real stellar spectra. The aim of this work is to develop a deep-learning framework that generalizes to real, unseen spectra and improves the detectability of Earth-mass planets in radial-velocity data. We train artificial neural networks on HARPS-N solar spectra with injected planetary signals, using physics-motivated spectral representations based on flux and line-formation temperature, together with their velocity gradients. Two training strategies are explored: hold-out testing and cross-validation. Model robustness is enhanced through genetic-algorithm-based hyperparameter optimization, and predictive uncertainty is quantified using Monte Carlo dropout. Our most precise neural network model reliably retrieves, under the cross-validation strategy, the amplitudes, phases, and orbital periods of planetary signals with amplitudes greater than or equal to 25 cm/s and periods between 10 and 550 days. In addition, in all cases tested here, the successfully recovered signals correspond to the most significant peaks in the periodograms of the Doppler-shift predictions. Temperature-based spectral-shell representations consistently outperform flux-based shells. We also release doppleriann, a Python package implementing the proposed framework. Our results demonstrate that combining physically motivated spectral representations with deep learning provides a promising pathway toward the detection of Earth-mass planets in radial-velocity data from real observations, supported by a modeling framework that is both physically grounded and statistically rigorous, incorporating uncertainty quantification and optimized training strategies.

Plant traits such as leaf carbon content and leaf mass are essential variables in the study of biodiversity and climate change. However, conventional field sampling cannot feasibly cover trait variation at ecologically meaningful spatial scales. Machine learning represents a valuable solution for plant trait prediction across ecosystems, leveraging hyperspectral data from remote sensing. Nevertheless, trait prediction from hyperspectral data is challenged by label scarcity and substantial domain shifts (\eg across sensors, ecological distributions), requiring robust cross-domain methods. Here, we present GreenHyperSpectra, a pretraining dataset encompassing real-world cross-sensor and cross-ecosystem samples designed to benchmark trait prediction with semi- and self-supervised methods. We adopt an evaluation framework encompassing in-distribution and out-of-distribution scenarios. We successfully leverage GreenHyperSpectra to pretrain label-efficient multi-output regression models that outperform the state-of-the-art supervised baseline. Our empirical analyses demonstrate substantial improvements in learning spectral representations for trait prediction, establishing a comprehensive methodological framework to catalyze research at the intersection of representation learning and plant functional traits assessment. All code and data are available at: https://github.com/echerif18/HyspectraSSL.

Smoke segmentation is critical for wildfire management and industrial safety applications. Traditional visible-light-based methods face limitations due to insufficient spectral information, particularly struggling with cloud interference and semi-transparent smoke regions. To address these challenges, we introduce hyperspectral imaging for smoke segmentation and present the first hyperspectral smoke segmentation dataset (HSSDataset) with carefully annotated samples collected from over 18,000 frames across 20 real-world scenarios using a Many-to-One annotations protocol. However, different spectral bands exhibit varying discriminative capabilities across spatial regions, necessitating adaptive band weighting strategies. We decompose this into three technical challenges: spectral interaction contamination, limited spectral pattern modeling, and complex weighting router problems. We propose a mixture of prototypes (MoP) network with: (1) Band split for spectral isolation, (2) Prototype-based spectral representation for diverse patterns, and (3) Dual-level router for adaptive spatial-aware band weighting. We further construct a multispectral dataset (MSSDataset) with RGB-infrared images. Extensive experiments validate superior performance across both hyperspectral and multispectral modalities, establishing a new paradigm for spectral-based smoke segmentation.

Although Kolmogorov-Arnold based interpretable networks (KAN) have strong theoretical expressiveness, they face significant parameter explosion and high-frequency feature capture challenges in high-dimensional tasks. To address this issue, we propose the Kolmogorov-Arnold-Fourier Network (KAF), which effectively integrates trainable Random Fourier Features (RFF) and a novel hybrid GELU-Fourier activation mechanism to balance parameter efficiency and spectral representation capabilities. Our key technical contributions include: (1) merging KAN's dual-matrix structure through matrix association properties to substantially reduce parameters; (2) introducing learnable RFF initialization strategies to eliminate spectral distortion in high-dimensional approximation tasks; (3) implementing an adaptive hybrid activation function that progressively enhances frequency representation during the training process. Comprehensive experiments demonstrate the superiority of our KAF across various domains including vision, NLP, audio processing, and differential equation-solving tasks, effectively combining theoretical interpretability with practical utility and computational efficiency.

Long short-term memory (LSTM) models are a particular type of recurrent neural networks (RNNs) that are central to sequential modeling tasks in domains such as urban telecommunication forecasting, where temporal correlations and nonlinear dependencies dominate. However, conventional LSTMs suffer from high parameter redundancy and limited nonlinear expressivity. In this work, we propose the Quantum-inspired Kolmogorov-Arnold Long Short-Term Memory (QKAN-LSTM), which integrates Data Re-Uploading Activation (DARUAN) modules into the gating structure of LSTMs. Each DARUAN acts as a quantum variational activation function (QVAF), enhancing frequency adaptability and enabling an exponentially enriched spectral representation without multi-qubit entanglement. The resulting architecture preserves quantum-level expressivity while remaining fully executable on classical hardware. Empirical evaluations on three datasets, Damped Simple Harmonic Motion, Bessel Function, and Urban Telecommunication, demonstrate that QKAN-LSTM achieves superior predictive accuracy and generalization with a 79% reduction in trainable parameters compared to classical LSTMs. We extend the framework to the Jiang-Huang-Chen-Goan Network (JHCG Net), which generalizes KAN to encoder-decoder structures, and then further use QKAN to realize the latent KAN, thereby creating a Hybrid QKAN (HQKAN) for hierarchical representation learning. The proposed HQKAN-LSTM thus provides a scalable and interpretable pathway toward quantum-inspired sequential modeling in real-world data environments.

Neural audio autoencoders create compact latent representations that preserve perceptually important information, serving as the foundation for both modern audio compression systems and generation approaches like next-token prediction and latent diffusion. Despite their prevalence, most audio processing operations, such as spatial and spectral up-sampling, still inefficiently operate on raw waveforms or spectral representations rather than directly on these compressed representations. We propose a framework that performs audio processing operations entirely within an autoencoder's latent space, eliminating the need to decode to raw audio formats. Our approach dramatically simplifies training by operating solely in the latent domain, with a latent L1 reconstruction term, augmented by a single latent adversarial discriminator. This contrasts sharply with raw-audio methods that typically require complex combinations of multi-scale losses and discriminators. Through experiments in bandwidth extension and mono-to-stereo up-mixing, we demonstrate computational efficiency gains of up to 100x while maintaining quality comparable to post-processing on raw audio. This work establishes a more efficient paradigm for audio processing pipelines that already incorporate autoencoders, enabling significantly faster and more resource-efficient workflows across various audio tasks.

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool for molecular structure analysis, and spectral artificial intelligence offers great potential for its rapid and automated interpretation. However, the scarcity of experimental NMR datasets has constrained deep learning in this domain to narrow, task-specific applications that lack broad generalization. Here, we introduce UltraNMR, a large-scale foundation model for NMR that leverages the intrinsic properties of NMR spectra to learn generalizable spectral representations. We collected 158 million paired simulated ^{1}H and ^{13}C NMR spectra to train UltraNMR, employing multiple domain-specific pre-training objectives. UltraNMR captures both intra-spectral and inter-spectral dependencies, enabling seamless simulation-to-real adaptation. We demonstrate that adapting UltraNMR to a range of molecular structure analysis tasks on experimental NMR spectra consistently yields state-of-the-art performance and clearly outperforms UltraNMR variants trained directly on downstream data without simulation pre-training. We also construct a large-scale NMR spectral vector library by encoding simulated NMR spectra using UltraNMR, covering 94 million unique molecules and enabling effective structure-aware retrieval. In real-world applications, UltraNMR facilitates the structural elucidation of two previously unknown natural products from Chinese herbal medicines recorded in the Chinese Pharmacopoeia. These results suggest that large-scale simulation pre-training can effectively bridge the simulation-to-real gap, enabling robust and generalizable molecular structure analysis of real-world NMR spectra.

One-dimensional nuclear magnetic resonance (NMR) spectroscopy is essential for molecular structure elucidation in organic synthesis, drug discovery, natural product characterization, and metabolomics, yet its interpretation remains heavily dependent on expert knowledge and difficult to scale. Although machine learning has been applied to NMR spectrum prediction, library retrieval, and structure generation, these tasks have evolved in isolation using simulated data and incompatible spectral representations, limiting their utility under real experimental scenarios. Here we present NMRPeak, a unified cross-modal learning system that integrates these three tasks through experimentally grounded design. We curate approximately 1.8 million experimental and simulated spectra to construct the largest benchmark for NMR-based structure elucidation and systematically quantify the distribution shift between these domains. We introduce a chemically-aware adaptive tokenizer that dynamically balances discretization granularity to preserve spectral semantics while controlling vocabulary size, and an assignment-free peak-aware similarity metric that enables direct comparison between predicted and experimental spectra. Through a unified molecule-to-spectrum paradigm and synergistic coupling of prediction, retrieval, and generation modules, NMRPeak achieves transformative performance on experimental benchmarks: it overcomes the longstanding simulation-to-experiment gap in spectrum prediction while delivering over 95% top-1 accuracy in molecular retrieval and approximately 75% top-1 accuracy in stereochemistry-aware de novo structure generation. These capabilities establish a foundation for automated, high-throughput molecular structure elucidation in organic synthesis, drug discovery, and chemical biology.

We demonstrate that the unitarity of quantum field theory, through the positivity of spectral functions, underlies thermodynamic irreversibility for a subsystem separated by a horizon, in direct analogy with the irreversibility of renormalization-group flows. To this end, we explicitly find the shear and bulk viscosities -- the entanglement viscosities -- for thermal radiation in Rindler space using the universal spectral representation. A direct consequence of the obtained general formulas is the relationship between the acceleration-induced shear viscosity in flat space and the conformal quantum anomaly in curved space, pointing to a possible novel probe of the conformal anomaly in systems with extreme acceleration. Moreover, for conformal field theories, we explicitly show that globally entanglement viscosity saturates the Kovtun-Son-Starinets bound.

The delayed access to specialized psychiatric assessments and care for patients at risk of suicidal tendencies in emergency departments creates a notable gap in timely intervention, hindering the provision of adequate mental health support during critical situations. To address this, we present a non-invasive, speech-based approach for automatic suicide risk assessment. For our study, we have collected a novel dataset of speech recordings from 20 patients from which we extract three sets of features, including wav2vec, interpretable speech and acoustic features, and deep learning-based spectral representations. We proceed by conducting a binary classification to assess suicide risk in a leave-one-subject-out fashion. Our most effective speech model achieves a balanced accuracy of 66.2,%. Moreover, we show that integrating our speech model with a series of patients' metadata, such as the history of suicide attempts or access to firearms, improves the overall result. The metadata integration yields a balanced accuracy of 94.4,%, marking an absolute improvement of 28.2,%, demonstrating the efficacy of our proposed approaches for automatic suicide risk assessment in emergency medicine.

Sound event localization and detection consists of two subtasks which are sound event detection and direction-of-arrival estimation. While sound event detection mainly relies on time-frequency patterns to distinguish different sound classes, direction-of-arrival estimation uses magnitude or phase differences between microphones to estimate source directions. Therefore, it is often difficult to jointly train these two subtasks simultaneously. We propose a novel feature called spatial cue-augmented log-spectrogram (SALSA) with exact time-frequency mapping between the signal power and the source direction-of-arrival. The feature includes multichannel log-spectrograms stacked along with the estimated direct-to-reverberant ratio and a normalized version of the principal eigenvector of the spatial covariance matrix at each time-frequency bin on the spectrograms. Experimental results on the DCASE 2021 dataset for sound event localization and detection with directional interference showed that the deep learning-based models trained on this new feature outperformed the DCASE challenge baseline by a large margin. We combined several models with slightly different architectures that were trained on the new feature to further improve the system performances for the DCASE sound event localization and detection challenge.

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, audio, and 3D scenes. However, existing INR frameworks -- including MLPs with Fourier features, SIREN, and multiresolution hash grids -- implicitly assume a global and stationary spectral basis. This assumption is fundamentally misaligned with real-world signals whose frequency characteristics vary significantly across space, exhibiting local high-frequency textures, smooth regions, and frequency drift phenomena. We propose Neural Spectral Transport Representation (NSTR), the first INR framework that explicitly models a spatially varying local frequency field. NSTR introduces a learnable frequency transport equation, a PDE that governs how local spectral compositions evolve across space. Given a learnable local spectrum field S(x) and a frequency transport network F_θ enforcing nabla S(x) approx F_θ(x, S(x)), NSTR reconstructs signals by spatially modulating a compact set of global sinusoidal bases. This formulation enables strong local adaptivity and offers a new level of interpretability via visualizing frequency flows. Experiments on 2D image regression, audio reconstruction, and implicit 3D geometry show that NSTR achieves significantly better accuracy-parameter trade-offs than SIREN, Fourier-feature MLPs, and Instant-NGP. NSTR requires fewer global frequencies, converges faster, and naturally explains signal structure through spectral transport fields. We believe NSTR opens a new direction in INR research by introducing explicit modeling of space-varying spectrum.

With the growing volume of CT examinations, there is an increasing demand for automated tools such as organ segmentation, abnormality detection, and report generation to support radiologists in managing their clinical workload. Multi-label classification of 3D Chest CT scans remains a critical yet challenging problem due to the complex spatial relationships inherent in volumetric data and the wide variability of abnormalities. Existing methods based on 3D convolutional neural networks struggle to capture long-range dependencies, while Vision Transformers often require extensive pre-training on large-scale, domain-specific datasets to perform competitively. In this work of academic research, we propose a 2.5D alternative by introducing a new graph-based framework that represents 3D CT volumes as structured graphs, where axial slice triplets serve as nodes processed through spectral graph convolution, enabling the model to reason over inter-slice dependencies while maintaining complexity compatible with clinical deployment. Our method, trained and evaluated on 3 datasets from independent institutions, achieves strong cross-dataset generalization, and shows competitive performance compared to state-of-the-art visual encoders. We further conduct comprehensive ablation studies to evaluate the impact of various aggregation strategies, edge-weighting schemes, and graph connectivity patterns. Additionally, we demonstrate the broader applicability of our approach through transfer experiments on automated radiology report generation and abdominal CT data.

Dense light field depth estimation remains challenging due to sparse angular sampling, occlusion boundaries, textureless regions, and the cost of exhaustive multi-view matching. We propose Deep Spectral Epipolar Representation (DSER), a geometry-aware framework that introduces spectral regularization in the epipolar domain for dense disparity reconstruction. DSER models frequency-consistent EPI structure to constrain correspondence estimation and couples this prior with a hybrid inference pipeline that combines least squares gradient initialization, plane-sweeping cost aggregation, and multiscale EPI refinement. An occlusion-aware directed random walk further propagates reliable disparity along edge-consistent paths, improving boundary sharpness and weak-texture stability. Experiments on benchmark and real-world light field datasets show that DSER achieves a strong accuracy-efficiency trade-off, producing more structurally consistent depth maps than representative classical and hybrid baselines. These results establish spectral epipolar regularization as an effective inductive bias for scalable and noise-robust light field depth estimation.

Hyperspectral image (HSI) classification is widely used for the analysis of remotely sensed images. Hyperspectral imagery includes varying bands of images. Convolutional Neural Network (CNN) is one of the most frequently used deep learning based methods for visual data processing. The use of CNN for HSI classification is also visible in recent works. These approaches are mostly based on 2D CNN. Whereas, the HSI classification performance is highly dependent on both spatial and spectral information. Very few methods have utilized the 3D CNN because of increased computational complexity. This letter proposes a Hybrid Spectral Convolutional Neural Network (HybridSN) for HSI classification. Basically, the HybridSN is a spectral-spatial 3D-CNN followed by spatial 2D-CNN. The 3D-CNN facilitates the joint spatial-spectral feature representation from a stack of spectral bands. The 2D-CNN on top of the 3D-CNN further learns more abstract level spatial representation. Moreover, the use of hybrid CNNs reduces the complexity of the model compared to 3D-CNN alone. To test the performance of this hybrid approach, very rigorous HSI classification experiments are performed over Indian Pines, Pavia University and Salinas Scene remote sensing datasets. The results are compared with the state-of-the-art hand-crafted as well as end-to-end deep learning based methods. A very satisfactory performance is obtained using the proposed HybridSN for HSI classification. The source code can be found at https://github.com/gokriznastic/HybridSN.

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the performance gap between pure machine learning approaches to that of the best numerical or hybrid solvers. This is achieved with new representations - separable spectral layers and improved residual connections - and a combination of training strategies such as the Markov assumption, Gaussian noise, and cosine learning rate decay. On several challenging benchmark PDEs on regular grids, structured meshes, and point clouds, the F-FNO can scale to deeper networks and outperform both the FNO and the geo-FNO, reducing the error by 83% on the Navier-Stokes problem, 31% on the elasticity problem, 57% on the airfoil flow problem, and 60% on the plastic forging problem. Compared to the state-of-the-art pseudo-spectral method, the F-FNO can take a step size that is an order of magnitude larger in time and achieve an order of magnitude speedup to produce the same solution quality.

Existing audio forgery detection and localization (AFDL) methods often overfit dataset-specific low-level artifacts, limiting their generalization to subtle, localized, and unseen manipulations. Recent audio large language model (ALLM)-based approaches cast AFDL as question answering but still model forensic evidence implicitly, without linking manipulation cues to predictions. To bridge this gap, we propose ThinkOmni, a reasoning-driven omni-modal large language model that jointly performs explicit forensic reasoning, spoofing detection, and temporal manipulation localization. To enable explicit reasoning supervision, we construct Forensic-Aware Chain-of-Thought (FACoT), a 100K-sample dataset with structured forensic evidence and reasoning annotations. Leveraging FACoT, we introduce Forensic-Aware Modality-Incremental Learning (FMIL), which progressively aligns semantic, acoustic, and spectral-visual representations with the LLM backbone to capture complementary forensic cues. We further propose Forensic-Consistent Multi-task Loss (FCML), which combines weighted cross-entropy with an adaptive localization loss to coordinate reasoning generation, spoofing detection, and temporal localization. Extensive experiments show that ThinkOmni achieves strong cross-dataset generalization in both detection and localization. Code, models, data, and inference examples are available at https://beyond0814.github.io/ThinkOmni/.

In this study, we present a simple multi-channel framework for contrastive learning (MC-SimCLR) to encode 'what' and 'where' of spatial audios. MC-SimCLR learns joint spectral and spatial representations from unlabeled spatial audios, thereby enhancing both event classification and sound localization in downstream tasks. At its core, we propose a multi-level data augmentation pipeline that augments different levels of audio features, including waveforms, Mel spectrograms, and generalized cross-correlation (GCC) features. In addition, we introduce simple yet effective channel-wise augmentation methods to randomly swap the order of the microphones and mask Mel and GCC channels. By using these augmentations, we find that linear layers on top of the learned representation significantly outperform supervised models in terms of both event classification accuracy and localization error. We also perform a comprehensive analysis of the effect of each augmentation method and a comparison of the fine-tuning performance using different amounts of labeled data.

Large language model (LLM) unlearning aims to remove specific data influences from pre-trained model without costly retraining, addressing privacy, copyright, and safety concerns. However, recent studies reveal a critical vulnerability: unlearned models rapidly recover "forgotten" knowledge through relearning attacks. This fragility raises serious security concerns, especially for open-weight models. In this work, we investigate the fundamental mechanism underlying this fragility from a representation geometry perspective. We discover that existing unlearning methods predominantly optimize along dominant components, leaving minor components largely unchanged. Critically, during relearning attacks, the modifications in these dominant components are easily reversed, enabling rapid knowledge recovery, whereas minor components exhibit stronger resistance to such reversal. We further provide a theoretical analysis that explains both observations from the spectral structure of representations. Building on this insight, we propose Minor Component Unlearning (MCU), a novel unlearning approach that explicitly targets minor components in representations. By concentrating unlearning effects in these inherently robust directions, our method achieves substantially improved resistance to relearning attacks. Extensive experiments on three datasets validate our approach, demonstrating significant improvements over state-of-the-art methods including sharpness-aware minimization.

Respiratory diseases remain major global health challenges, and traditional auscultation is often limited by subjectivity, environmental noise, and inter-clinician variability. This study presents an explainable multimodal deep learning framework for automatic lung-disease detection using respiratory audio signals. The proposed system integrates two complementary representations: a spectral-temporal encoder based on a CNN-BiLSTM Attention architecture, and a handcrafted acoustic-feature encoder capturing physiologically meaningful descriptors such as MFCCs, spectral centroid, spectral bandwidth, and zero-crossing rate. These branches are combined through late-stage fusion to leverage both data-driven learning and domain-informed acoustic cues. The model is trained and evaluated on the Asthma Detection Dataset Version 2 using rigorous preprocessing, including resampling, normalization, noise filtering, data augmentation, and patient-level stratified partitioning. The study achieved strong generalization with 91.21% accuracy, 0.899 macro F1-score, and 0.9866 macro ROC-AUC, outperforming all ablated variants. An ablation study confirms the importance of temporal modeling, attention mechanisms, and multimodal fusion. The framework incorporates Grad-CAM, Integrated Gradients, and SHAP, generating interpretable spectral, temporal, and feature-level explanations aligned with known acoustic biomarkers to build clinical transparency. The findings demonstrate the framework's potential for telemedicine, point-of-care diagnostics, and real-world respiratory screening.

In this paper, we study the diffusability (learnability) of variational autoencoders (VAE) in latent diffusion. First, we show that pixel-space diffusion trained with an MSE objective is inherently biased toward learning low and mid spatial frequencies, and that the power-law power spectral density (PSD) of natural images makes this bias perceptually beneficial. Motivated by this result, we propose the Spectrum Matching Hypothesis: latents with superior diffusability should (i) follow a flattened power-law PSD (Encoding Spectrum Matching, ESM) and (ii) preserve frequency-to-frequency semantic correspondence through the decoder (Decoding Spectrum Matching, DSM). In practice, we apply ESM by matching the PSD between images and latents, and DSM via shared spectral masking with frequency-aligned reconstruction. Importantly, Spectrum Matching provides a unified view that clarifies prior observations of over-noisy or over-smoothed latents, and interprets several recent methods as special cases (e.g., VA-VAE, EQ-VAE). Experiments suggest that Spectrum Matching yields superior diffusion generation on CelebA and ImageNet datasets, and outperforms prior approaches. Finally, we extend the spectral view to representation alignment (REPA): we show that the directional spectral energy of the target representation is crucial for REPA, and propose a DoG-based method to further improve the performance of REPA. Our code is available https://github.com/forever208/SpectrumMatching.

Large language models are increasingly adapted to downstream tasks through fine-tuning. Full supervised fine-tuning (SFT) and parameter-efficient fine-tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), are two dominant approaches. While PEFT methods are widely used for their computational efficiency, the implications of their configurations (e.g., rank) remain under-explored in downstream Q&A tasks and generalisation. In this work, we perform a comprehensive evaluation across multiple reasoning and recall datasets, conducting a rank sweep to quantify the trade-off between SFT and PEFT. We also compare the accuracy of PEFT and SFT models across in-domain and out-of-domain adaptation, highlighting distinct generalisation behaviour and task-specific forgetting. We demonstrate that LoRA achieves competitive and in some cases superior performance compared to SFT, particularly on reasoning tasks at specific rank values. Additionally, we analyze the internal representations via spectral features and layer-wise attention structures, offering insights into representational drift and structural changes in attention patterns.

The main challenge in vision-and-language navigation (VLN) is how to understand natural-language instructions in an unseen environment. The main limitation of conventional VLN algorithms is that if an action is mistaken, the agent fails to follow the instructions or explores unnecessary regions, leading the agent to an irrecoverable path. To tackle this problem, we propose Meta-Explore, a hierarchical navigation method deploying an exploitation policy to correct misled recent actions. We show that an exploitation policy, which moves the agent toward a well-chosen local goal among unvisited but observable states, outperforms a method which moves the agent to a previously visited state. We also highlight the demand for imagining regretful explorations with semantically meaningful clues. The key to our approach is understanding the object placements around the agent in spectral-domain. Specifically, we present a novel visual representation, called scene object spectrum (SOS), which performs category-wise 2D Fourier transform of detected objects. Combining exploitation policy and SOS features, the agent can correct its path by choosing a promising local goal. We evaluate our method in three VLN benchmarks: R2R, SOON, and REVERIE. Meta-Explore outperforms other baselines and shows significant generalization performance. In addition, local goal search using the proposed spectral-domain SOS features significantly improves the success rate by 17.1% and SPL by 20.6% for the SOON benchmark.

Implicit Neural Representations (INRs), as a versatile representation paradigm, have achieved success in various computer vision tasks. Due to the spectral bias of the vanilla multi-layer perceptrons (MLPs), existing methods focus on designing MLPs with sophisticated architectures or repurposing training techniques for highly accurate INRs. In this paper, we delve into the linear dynamics model of MLPs and theoretically identify the empirical Neural Tangent Kernel (eNTK) matrix as a reliable link between spectral bias and training dynamics. Based on this insight, we propose a practical Inductive Gradient Adjustment (IGA) method, which could purposefully improve the spectral bias via inductive generalization of eNTK-based gradient transformation matrix. Theoretical and empirical analyses validate impacts of IGA on spectral bias. Further, we evaluate our method on different INRs tasks with various INR architectures and compare to existing training techniques. The superior and consistent improvements clearly validate the advantage of our IGA. Armed with our gradient adjustment method, better INRs with more enhanced texture details and sharpened edges can be learned from data by tailored impacts on spectral bias.

Hyperspectral unmixing (HU) plays a fundamental role in a wide range of hyperspectral applications. It is still challenging due to the common presence of outlier channels and the large solution space. To address the above two issues, we propose a novel model by emphasizing both robust representation and learning-based sparsity. Specifically, we apply the ell_{2,1}-norm to measure the representation error, preventing outlier channels from dominating our objective. In this way, the side effects of outlier channels are greatly relieved. Besides, we observe that the mixed level of each pixel varies over image grids. Based on this observation, we exploit a learning-based sparsity method to simultaneously learn the HU results and a sparse guidance map. Via this guidance map, the sparsity constraint in the ell_{p}!left(!0!<! p!leq!1right)-norm is adaptively imposed according to the learnt mixed level of each pixel. Compared with state-of-the-art methods, our model is better suited to the real situation, thus expected to achieve better HU results. The resulted objective is highly non-convex and non-smooth, and so it is hard to optimize. As a profound theoretical contribution, we propose an efficient algorithm to solve it. Meanwhile, the convergence proof and the computational complexity analysis are systematically provided. Extensive evaluations verify that our method is highly promising for the HU task---it achieves very accurate guidance maps and much better HU results compared with state-of-the-art methods.

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

Understanding how feature representations evolve across layers in large language models (LLMs) is key to improving their interpretability and robustness. While recent studies have identified critical layers linked to specific functions or behaviors, these efforts typically rely on data-dependent analyses of fine-tuned models, limiting their use to post-hoc settings. In contrast, we introduce a data-oblivious approach to identify intrinsic critical layers in pre-fine-tuned LLMs by analyzing representation dynamics via Centered Kernel Alignment(CKA). We show that layers with significant shifts in representation space are also those most affected during fine-tuning--a pattern that holds consistently across tasks for a given model. Our spectral analysis further reveals that these shifts are driven by changes in the top principal components, which encode semantic transitions from rationales to conclusions. We further apply these findings to two practical scenarios: efficient domain adaptation, where fine-tuning critical layers leads to greater loss reduction compared to non-critical layers; and backdoor defense, where freezing them reduces attack success rates by up to 40%.

Cross-spectral person re-identification, which aims to associate identities to pedestrians across different spectra, faces a main challenge of the modality discrepancy. In this paper, we address the problem from both image-level and feature-level in an end-to-end hybrid learning framework named robust feature mining network (RFM). In particular, we observe that the reflective intensity of the same surface in photos shot in different wavelengths could be transformed using a linear model. Besides, we show the variable linear factor across the different surfaces is the main culprit which initiates the modality discrepancy. We integrate such a reflection observation into an image-level data augmentation by proposing the linear transformation generator (LTG). Moreover, at the feature level, we introduce a cross-center loss to explore a more compact intra-class distribution and modality-aware spatial attention to take advantage of textured regions more efficiently. Experiment results on two standard cross-spectral person re-identification datasets, i.e., RegDB and SYSU-MM01, have demonstrated state-of-the-art performance.

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of decoder-only models adapted from the modded NanoGPT codebase, we introduce an empirical protocol based on activation covariance and per-sample gradient SVD spectra. This dual-view reveals three empirical findings and one mechanistic explanation. First, batch size acts as a latent determinant of representation geometry: runs that reach equal loss settle into systematically distinct activation spectra. Second, the activation covariance tail measured early in training reliably forecasts downstream token efficiency. Third, movement of the activation spectrum head (leading modes), together with gradient spectra, characterizes underlying learning-dynamics changes, separating learning-side architectural improvements from primarily execution-side gains. These predictive and diagnostic signals persist across the 12-, 36-, and 48-layer model tiers. Finally, a mechanistic model proves the main observations and explains how activation covariance spectra correlate with task-aligned feature learning.

Standard training metrics like loss fail to explain the emergence of complex capabilities in large language models. We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training, measuring effective rank (RankMe) and eigenspectrum decay (α-ReQ). With OLMo (1B-7B) and Pythia (160M-12B) models, we uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining. The initial "warmup" phase exhibits rapid representational collapse. This is followed by an "entropy-seeking" phase, where the manifold's dimensionality expands substantially, coinciding with peak n-gram memorization. Subsequently, a "compression-seeking" phase imposes anisotropic consolidation, selectively preserving variance along dominant eigendirections while contracting others, a transition marked with significant improvement in downstream task performance. We show these phases can emerge from a fundamental interplay of cross-entropy optimization under skewed token frequencies and representational bottlenecks (d ll |V|). Post-training further transforms geometry: SFT and DPO drive "entropy-seeking" dynamics to integrate specific instructional or preferential data, improving in-distribution performance while degrading out-of-distribution robustness. Conversely, RLVR induces "compression-seeking", enhancing reward alignment but reducing generation diversity.

Vocal feedback (e.g., `mhm', `yeah', `okay') is an important component of spoken dialogue and is crucial to ensuring common ground in conversational systems. The exact meaning of such feedback is conveyed through both lexical and prosodic form. In this work, we investigate the perceived prosodic similarity of vocal feedback with the same lexical form, and to what extent existing speech representations reflect such similarities. A triadic comparison task with recruited participants is used to measure perceived similarity of feedback responses taken from two different datasets. We find that spectral and self-supervised speech representations encode prosody better than extracted pitch features, especially in the case of feedback from the same speaker. We also find that it is possible to further condense and align the representations to human perception through contrastive learning.

Time series analysis is a fundamental task in various application domains, and deep learning approaches have demonstrated remarkable performance in this area. However, many real-world time series data exhibit significant periodic or quasi-periodic dynamics that are often not adequately captured by existing deep learning-based solutions. This results in an incomplete representation of the underlying dynamic behaviors of interest. To address this gap, we propose an unsupervised method called Floss that automatically regularizes learned representations in the frequency domain. The Floss method first automatically detects major periodicities from the time series. It then employs periodic shift and spectral density similarity measures to learn meaningful representations with periodic consistency. In addition, Floss can be easily incorporated into both supervised, semi-supervised, and unsupervised learning frameworks. We conduct extensive experiments on common time series classification, forecasting, and anomaly detection tasks to demonstrate the effectiveness of Floss. We incorporate Floss into several representative deep learning solutions to justify our design choices and demonstrate that it is capable of automatically discovering periodic dynamics and improving state-of-the-art deep learning models.

Deep neural networks are known to exhibit a spectral learning bias, wherein low-frequency components are learned early in training, while high-frequency modes emerge more gradually in later epochs. However, when the target signal lacks low-frequency components and is dominated by broadband high frequencies, training suffers from a 'spectral bottleneck', and the model fails to reconstruct the entire signal, including the frequency components that lie within the network's representational capacity. We examine such a scenario in the context of implicit neural representations (INRs) with sinusoidal representation networks (SIRENs), focusing on the challenge of fitting high-frequency-dominant signals that are susceptible to spectral bottleneck. To effectively fit any target signal irrespective of it's frequency content, we propose a generalized target-aware 'weight perturbation scheme' (WINNER - weight initialization with noise for neural representations) for network initialization. The scheme perturbs uniformly initialized weights with Gaussian noise, where the noise scales are adaptively determined by the spectral centroid of the target signal. We show that the noise scales can provide control over the spectra of network activations and the eigenbasis of the empirical neural tangent kernel. This method not only addresses the spectral bottleneck but also yields faster convergence and with improved representation accuracy, outperforming state-of-the-art approaches in audio fitting and achieving notable gains in image fitting and denoising tasks. Beyond signal reconstruction, our approach opens new directions for adaptive weight initialization strategies in computer vision and scientific machine learning.

In language models, what a representation encodes is determined by the geometry of its representation space: distances, not activations, carry meaning. Existing tools characterize the shape of this geometry but do not ask what that shape is organized for. We introduce Subspace PGA, a metric that tests whether a layer's distance structure aligns with the readout subspace of the unembedding matrix W_U more than with random subspaces of equal size. Across seven Pythia models (70M--6.9B) and three cross-family models, intermediate geometry is significantly organized for prediction (peak z = 9--24), but the degree is scale-dependent: small models (d leq 1024) progressively lose it at late layers during training -- even as loss keeps improving -- while large models (d geq 2048) preserve it throughout. We trace this to a capacity trade-off: a few dominant directions migrate away from W_U's readout, masking rather than destroying the predictive structure beneath, and removing them restores alignment. Neither spectral metrics nor loss curves capture this distinction. Scale thus determines not only how well a model predicts, but how its representation geometry is organized to do so.

Neuroscience employs diverse neuroimaging techniques, each offering distinct insights into brain activity, from electrophysiological recordings such as EEG, which have high temporal resolution, to hemodynamic modalities such as fMRI, which have increased spatial precision. However, integrating these heterogeneous data sources remains a challenge, which limits a comprehensive understanding of brain function. We present the Spatiotemporal Alignment of Multimodal Brain Activity (SAMBA) framework, which bridges the spatial and temporal resolution gaps across modalities by learning a unified latent space free of modality-specific biases. SAMBA introduces a novel attention-based wavelet decomposition for spectral filtering of electrophysiological recordings, graph attention networks to model functional connectivity between functional brain units, and recurrent layers to capture temporal autocorrelations in brain signal. We show that the training of SAMBA, aside from achieving translation, also learns a rich representation of brain information processing. We showcase this classify external stimuli driving brain activity from the representation learned in hidden layers of SAMBA, paving the way for broad downstream applications in neuroscience research and clinical contexts.

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a uniform physical grid suffer significant aliasing error and information loss. Moreover, signals can exist in different topological structures as, for example, points, lines, surfaces and volumes. It has been challenging to analyze signals with mixed topologies (for example, point cloud with surface mesh). To this end, we develop mathematical formulations for Non-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample nonuniform data signals of different topologies defined on a simplex mesh into the spectral domain with no spatial sampling error. The spectral transform is performed in the Euclidean space, which removes the translation ambiguity from works on the graph spectrum. Our representation has four distinct advantages: (1) the process causes no spatial sampling error during the initial sampling, (2) the generality of this approach provides a unified framework for using CNNs to analyze signals of mixed topologies, (3) it allows us to leverage state-of-the-art backbone CNN architectures for effective learning without having to design a particular architecture for a particular data structure in an ad-hoc fashion, and (4) the representation allows weighted meshes where each element has a different weight (i.e., texture) indicating local properties. We achieve results on par with the state-of-the-art for the 3D shape retrieval task, and a new state-of-the-art for the point cloud to surface reconstruction task.

Recent research in medical image analysis with deep learning almost exclusively focuses on grid- or voxel-based data representations. We challenge this common choice by introducing MedFuncta, a modality-agnostic continuous data representation based on neural fields. We demonstrate how to scale neural fields from single instances to large datasets by exploiting redundancy in medical signals and by applying an efficient meta-learning approach with a context reduction scheme. We further address the spectral bias in commonly used SIREN activations, by introducing an omega_0-schedule, improving reconstruction quality and convergence speed. We validate our proposed approach on a large variety of medical signals of different dimensions and modalities (1D: ECG; 2D: Chest X-ray, Retinal OCT, Fundus Camera, Dermatoscope, Colon Histopathology, Cell Microscopy; 3D: Brain MRI, Lung CT) and successfully demonstrate that we can solve relevant downstream tasks on these representations. We additionally release a large-scale dataset of > 550k annotated neural fields to promote research in this direction.

We introduce a Three-Dimensional Convolutional Variational Autoencoder (3D-CVAE) for automated anomaly detection in Electron Energy Loss Spectroscopy Spectrum Imaging (EELS-SI) data. Our approach leverages the full three-dimensional structure of EELS-SI data to detect subtle spectral anomalies while preserving both spatial and spectral correlations across the datacube. By employing negative log-likelihood loss and training on bulk spectra, the model learns to reconstruct bulk features characteristic of the defect-free material. In exploring methods for anomaly detection, we evaluated both our 3D-CVAE approach and Principal Component Analysis (PCA), testing their performance using Fe L-edge peak shifts designed to simulate material defects. Our results show that 3D-CVAE achieves superior anomaly detection and maintains consistent performance across various shift magnitudes. The method demonstrates clear bimodal separation between normal and anomalous spectra, enabling reliable classification. Further analysis verifies that lower dimensional representations are robust to anomalies in the data. While performance advantages over PCA diminish with decreasing anomaly concentration, our method maintains high reconstruction quality even in challenging, noise-dominated spectral regions. This approach provides a robust framework for unsupervised automated detection of spectral anomalies in EELS-SI data, particularly valuable for analyzing complex material systems.

Implicit neural representations (INR) suffer from worsening spectral bias, which results in overly smooth solutions to the inverse problem. To deal with this problem, we propose a universal framework for processing inverse problems called High-Order Implicit Neural Representations (HOIN). By refining the traditional cascade structure to foster high-order interactions among features, HOIN enhances the model's expressive power and mitigates spectral bias through its neural tangent kernel's (NTK) strong diagonal properties, accelerating and optimizing inverse problem resolution. By analyzing the model's expression space, high-order derivatives, and the NTK matrix, we theoretically validate the feasibility of HOIN. HOIN realizes 1 to 3 dB improvements in most inverse problems, establishing a new state-of-the-art recovery quality and training efficiency, thus providing a new general paradigm for INR and paving the way for it to solve the inverse problem.

Personalized federated learning (PFL) has been widely investigated to address the challenge of data heterogeneity, especially when a single generic model is inadequate in satisfying the diverse performance requirements of local clients simultaneously. Existing PFL methods are inherently based on the idea that the relations between the generic global and personalized local models are captured by the similarity of model weights. Such a similarity is primarily based on either partitioning the model architecture into generic versus personalized components, or modeling client relationships via model weights. To better capture similar (yet distinct) generic versus personalized model representations, we propose spectral distillation, a novel distillation method based on model spectrum information. Building upon spectral distillation, we also introduce a co-distillation framework that establishes a two-way bridge between generic and personalized model training. Moreover, to utilize the local idle time in conventional PFL, we propose a wait-free local training protocol. Through extensive experiments on multiple datasets over diverse heterogeneous data settings, we demonstrate the outperformance and efficacy of our proposed spectral co-distillation method, as well as our wait-free training protocol.

Differential privacy (DP)'s effect in medical imaging is typically evaluated only through end-to-end performance, leaving the mechanism of privacy-induced utility loss unclear. We introduce Differential Privacy Representation Geometry for Medical Imaging (DP-RGMI), a framework that interprets DP as a structured transformation of representation space and decomposes performance degradation into encoder geometry and task-head utilization. Geometry is quantified by representation displacement from initialization and spectral effective dimension, while utilization is measured as the gap between linear-probe and end-to-end utility. Across over 594,000 images from four chest X-ray datasets and multiple pretrained initializations, we show that DP is consistently associated with a utilization gap even when linear separability is largely preserved. At the same time, displacement and spectral dimension exhibit non-monotonic, initialization- and dataset-dependent reshaping, indicating that DP alters representation anisotropy rather than uniformly collapsing features. Correlation analysis reveals that the association between end-to-end performance and utilization is robust across datasets but can vary by initialization, while geometric quantities capture additional prior- and dataset-conditioned variation. These findings position DP-RGMI as a reproducible framework for diagnosing privacy-induced failure modes and informing privacy model selection.

Diffusion models are a strong backbone for visual generation, but their inherently sequential denoising process leads to slow inference. Previous methods accelerate sampling by caching and reusing intermediate outputs based on feature distances between adjacent timesteps. However, existing caching strategies typically rely on raw feature differences that entangle content and noise. This design overlooks spectral evolution, where low-frequency structure appears early and high-frequency detail is refined later. We introduce Spectral-Evolution-Aware Cache (SeaCache), a training-free cache schedule that bases reuse decisions on a spectrally aligned representation. Through theoretical and empirical analysis, we derive a Spectral-Evolution-Aware (SEA) filter that preserves content-relevant components while suppressing noise. Employing SEA-filtered input features to estimate redundancy leads to dynamic schedules that adapt to content while respecting the spectral priors underlying the diffusion model. Extensive experiments on diverse visual generative models and the baselines show that SeaCache achieves state-of-the-art latency-quality trade-offs.

Stem retrieval, the task of matching missing stems to a given audio submix, is a key challenge currently limited by models that discard temporal information. We introduce PHALAR, a contrastive framework achieving a relative accuracy increase of up to approx 70% over the state-of-the-art while requiring <50% of the parameters and a 7times training speedup. By utilizing a Learned Spectral Pooling layer and a complex-valued head, PHALAR enforces pitch-equivariant and phase-equivariant biases. PHALAR establishes new retrieval state-of-the-art across MoisesDB, Slakh, and ChocoChorales, correlating significantly higher with human coherence judgment than semantic baselines. Finally, zero-shot beat tracking and linear chord probing confirm that PHALAR captures robust musical structures beyond the retrieval task.

A triangular mesh is one of the most popular 3D data representations. As such, the deployment of deep neural networks for mesh processing is widely spread and is increasingly attracting more attention. However, neural networks are prone to adversarial attacks, where carefully crafted inputs impair the model's functionality. The need to explore these vulnerabilities is a fundamental factor in the future development of 3D-based applications. Recently, mesh attacks were studied on the semantic level, where classifiers are misled to produce wrong predictions. Nevertheless, mesh surfaces possess complex geometric attributes beyond their semantic meaning, and their analysis often includes the need to encode and reconstruct the geometry of the shape. We propose a novel framework for a geometric adversarial attack on a 3D mesh autoencoder. In this setting, an adversarial input mesh deceives the autoencoder by forcing it to reconstruct a different geometric shape at its output. The malicious input is produced by perturbing a clean shape in the spectral domain. Our method leverages the spectral decomposition of the mesh along with additional mesh-related properties to obtain visually credible results that consider the delicacy of surface distortions. Our code is publicly available at https://github.com/StolikTomer/SAGA.

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.

Hyperspectral object tracking using snapshot mosaic cameras is emerging as it provides enhanced spectral information alongside spatial data, contributing to a more comprehensive understanding of material properties. Using transformers, which have consistently outperformed convolutional neural networks (CNNs) in learning better feature representations, would be expected to be effective for Hyperspectral object tracking. However, training large transformers necessitates extensive datasets and prolonged training periods. This is particularly critical for complex tasks like object tracking, and the scarcity of large datasets in the hyperspectral domain acts as a bottleneck in achieving the full potential of powerful transformer models. This paper proposes an effective methodology that adapts large pretrained transformer-based foundation models for hyperspectral object tracking. We propose an adaptive, learnable spatial-spectral token fusion module that can be extended to any transformer-based backbone for learning inherent spatial-spectral features in hyperspectral data. Furthermore, our model incorporates a cross-modality training pipeline that facilitates effective learning across hyperspectral datasets collected with different sensor modalities. This enables the extraction of complementary knowledge from additional modalities, whether or not they are present during testing. Our proposed model also achieves superior performance with minimal training iterations.

We study sinusoidal recurrence as an iterative mechanism for harmonic spectral enrichment in implicit neural representations (INRs). Our analysis reveals that sinusoidal activations induce a harmonic line spectrum, providing a spectral account of how recurrent unrolling enriches the effective spectral support. We realize this principle with a shared sinusoidal block that iteratively refines the latent representation. We empirically validate the resulting spectral behavior against feed-forward INRs, non-sinusoidal recurrent variants, and equilibrium-style sinusoidal models. Complementing this analysis, we evaluate the proposed architecture across image and 3D representation tasks. On RGB image benchmarks, our method achieves higher fidelity than feed-forward baselines with fewer parameters and fewer optimization steps, and it further transfers favorably to super-resolution, NeRF, and SDF tasks.

Subspace clustering seeks to identify subspaces that segment a set of n data points into k (k<<n) groups, which has emerged as a powerful tool for analyzing data from various domains, especially images and videos. Recently, several studies have demonstrated the great potential of subspace clustering models for partitioning vertices in attributed graphs, referred to as SCAG. However, these works either demand significant computational overhead for constructing the nxn self-expressive matrix, or fail to incorporate graph topology and attribute data into the subspace clustering framework effectively, and thus, compromise result quality. Motivated by this, this paper presents two effective and efficient algorithms, S2CAG and M-S2CAG, for SCAG computation. Particularly, S2CAG obtains superb performance through three major contributions. First, we formulate a new objective function for SCAG with a refined representation model for vertices and two non-trivial constraints. On top of that, an efficient linear-time optimization solver is developed based on our theoretically grounded problem transformation and well-thought-out adaptive strategy. We then conduct an in-depth analysis to disclose the theoretical connection of S2CAG to conductance minimization, which further inspires the design of M-S2CAG that maximizes the modularity. Our extensive experiments, comparing S2CAG and M-S2CAG against 17 competitors over 8 benchmark datasets, exhibit that our solutions outperform all baselines in terms of clustering quality measured against the ground truth while delivering high efficiency

Historically, most speech models in machine-learning have used the mel-spectrogram as a speech representation. Recently, discrete audio tokens produced by neural audio codecs have become a popular alternate speech representation for speech synthesis tasks such as text-to-speech (TTS). However, the data distribution produced by such codecs is too complex for some TTS models to predict, hence requiring large autoregressive models to get reasonable quality. Typical audio codecs compress and reconstruct the time-domain audio signal. We propose a spectral codec which compresses the mel-spectrogram and reconstructs the time-domain audio signal. A study of objective audio quality metrics suggests that our spectral codec has comparable perceptual quality to equivalent audio codecs. Furthermore, non-autoregressive TTS models trained with the proposed spectral codec generate audio with significantly higher quality than when trained with mel-spectrograms or audio codecs.

Small-molecule identification from tandem mass spectrometry (MS/MS) remains a bottleneck in untargeted settings where spectral libraries are incomplete. While deep learning offers a solution, current approaches typically fall into two extremes: explicit generative models that construct molecular graphs atom-by-atom, or joint contrastive models that learn cross-modal subspaces from scratch. We introduce SpecBridge, a novel implicit alignment framework that treats structure identification as a geometric alignment problem. SpecBridge fine-tunes a self-supervised spectral encoder (DreaMS) to project directly into the latent space of a frozen molecular foundation model (ChemBERTa), and then performs retrieval by cosine similarity to a fixed bank of precomputed molecular embeddings. Across MassSpecGym, Spectraverse, and MSnLib benchmarks, SpecBridge improves top-1 retrieval accuracy by roughly 20-25% relative to strong neural baselines, while keeping the number of trainable parameters small. These results suggest that aligning to frozen foundation models is a practical, stable alternative to designing new architectures from scratch. The code for SpecBridge is released at https://github.com/HassounLab/SpecBridge.

The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all widths, a process known as feature learning. Here, we show that feature learning is achieved by scaling the spectral norm of weight matrices and their updates like texttt{fan-out/fan-in}, in contrast to widely used but heuristic scalings based on Frobenius norm and entry size. Our spectral scaling analysis also leads to an elementary derivation of maximal update parametrization. All in all, we aim to provide the reader with a solid conceptual understanding of feature learning in neural networks.

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training in which hierarchical feature learning becomes an explicit iterative spectral procedure. In this limit, the dynamics at each layer decouple: given the current representation, the next layer selects directions with maximal accessible low-degree correlation to the label. This yields a tractable surrogate mechanism for deep learning, together with a natural kernel-space interpretation. Neural LoFi provides a mathematically explicit framework for studying multi-layer feature learning beyond the lazy regime. It predicts how representations are selected layer by layer, explains how emergence of concepts arises with given sample complexity,and gives a concrete mechanism by which depth progressively constructs new features from old ones through low-degree compositionality. We complement the theory with mechanistic experiments on fully connected and convolutional architectures, showing that Neural LoFi improves over lazy random-feature baselines, recovers meaningful structured filters, and predicts representations aligned with early gradient-descent feature discovery with real datasets.

Loss explosions in training deep neural networks can nullify multi-million dollar training runs. Conventional monitoring metrics like weight and gradient norms are often lagging and ambiguous predictors, as their values vary dramatically across different models and even between layers of the same model, making it difficult to establish a unified standard for detecting impending failure. We introduce Spectral Alignment (SA), a novel, theoretically-grounded metric that monitors the distributional alignment between layer inputs and the principal singular vectors of weight matrices. We show that a collapse in the sign diversity of this alignment is a powerful early predictor of representational collapse and training divergence. Empirical results on language models demonstrate that monitoring the SA distribution provides a significantly earlier and clearer warning of loss explosions than traditional scalar metrics. SA's low computational overhead makes it a practical tool for safeguarding model training.

In this paper, we propose SPECTRUM, a temporal-frequency synergistic model that unlocks the untapped potential of multi-domain representation learning for online handwriting verification (OHV). SPECTRUM comprises three core components: (1) a multi-scale interactor that finely combines temporal and frequency features through dual-modal sequence interaction and multi-scale aggregation, (2) a self-gated fusion module that dynamically integrates global temporal and frequency features via self-driven balancing. These two components work synergistically to achieve micro-to-macro spectral-temporal integration. (3) A multi-domain distance-based verifier then utilizes both temporal and frequency representations to improve discrimination between genuine and forged handwriting, surpassing conventional temporal-only approaches. Extensive experiments demonstrate SPECTRUM's superior performance over existing OHV methods, underscoring the effectiveness of temporal-frequency multi-domain learning. Furthermore, we reveal that incorporating multiple handwritten biometrics fundamentally enhances the discriminative power of handwriting representations and facilitates verification. These findings not only validate the efficacy of multi-domain learning in OHV but also pave the way for future research in multi-domain approaches across both feature and biometric domains. Code is publicly available at https://github.com/NiceRingNode/SPECTRUM.

Graph Neural Network (GNN) research is rapidly advancing due to GNNs' capacity to learn distributed representations from graph-structured data. However, centralizing large volumes of real-world graph data for GNN training is often impractical due to privacy concerns, regulatory restrictions, and commercial competition. Federated learning (FL), a distributed learning paradigm, offers a solution by preserving data privacy with collaborative model training. Despite progress in training huge vision and language models, federated learning for GNNs remains underexplored. To address this challenge, we present a novel method for federated learning on GNNs based on spectral GNNs equipped with neural ordinary differential equations (ODE) for better information capture, showing promising results across both homophilic and heterophilic graphs. Our approach effectively handles non-Independent and Identically Distributed (non-IID) data, while also achieving performance comparable to existing methods that only operate on IID data. It is designed to be privacy-preserving and bandwidth-optimized, making it suitable for real-world applications such as social network analysis, recommendation systems, and fraud detection, which often involve complex, non-IID, and heterophilic graph structures. Our results in the area of federated learning on non-IID heterophilic graphs demonstrate significant improvements, while also achieving better performance on homophilic graphs. This work highlights the potential of federated learning in diverse and challenging graph settings. Open-source code available on GitHub (https://github.com/SpringWiz11/Fed-GNODEFormer).

Implicit Neural Representation (INR) as a mighty representation paradigm has achieved success in various computer vision tasks recently. Due to the low-frequency bias issue of vanilla multi-layer perceptron (MLP), existing methods have investigated advanced techniques, such as positional encoding and periodic activation function, to improve the accuracy of INR. In this paper, we connect the network training bias with the reparameterization technique and theoretically prove that weight reparameterization could provide us a chance to alleviate the spectral bias of MLP. Based on our theoretical analysis, we propose a Fourier reparameterization method which learns coefficient matrix of fixed Fourier bases to compose the weights of MLP. We evaluate the proposed Fourier reparameterization method on different INR tasks with various MLP architectures, including vanilla MLP, MLP with positional encoding and MLP with advanced activation function, etc. The superiority approximation results on different MLP architectures clearly validate the advantage of our proposed method. Armed with our Fourier reparameterization method, better INR with more textures and less artifacts can be learned from the training data.

The foundation model has recently garnered significant attention due to its potential to revolutionize the field of visual representation learning in a self-supervised manner. While most foundation models are tailored to effectively process RGB images for various visual tasks, there is a noticeable gap in research focused on spectral data, which offers valuable information for scene understanding, especially in remote sensing (RS) applications. To fill this gap, we created for the first time a universal RS foundation model, named SpectralGPT, which is purpose-built to handle spectral RS images using a novel 3D generative pretrained transformer (GPT). Compared to existing foundation models, SpectralGPT 1) accommodates input images with varying sizes, resolutions, time series, and regions in a progressive training fashion, enabling full utilization of extensive RS big data; 2) leverages 3D token generation for spatial-spectral coupling; 3) captures spectrally sequential patterns via multi-target reconstruction; 4) trains on one million spectral RS images, yielding models with over 600 million parameters. Our evaluation highlights significant performance improvements with pretrained SpectralGPT models, signifying substantial potential in advancing spectral RS big data applications within the field of geoscience across four downstream tasks: single/multi-label scene classification, semantic segmentation, and change detection.

Spectral bias is an important observation of neural network training, stating that the network will learn a low frequency representation of the target function before converging to higher frequency components. This property is interesting due to its link to good generalization in over-parameterized networks. However, in low dimensional settings, a severe spectral bias occurs that obstructs convergence to high frequency components entirely. In order to overcome this limitation, one can encode the inputs using a high frequency sinusoidal encoding. Previous works attempted to explain this phenomenon using Neural Tangent Kernel (NTK) and Fourier analysis. However, NTK does not capture real network dynamics, and Fourier analysis only offers a global perspective on the network properties that induce this bias. In this paper, we provide a novel approach towards understanding spectral bias by directly studying ReLU MLP training dynamics. Specifically, we focus on the connection between the computations of ReLU networks (activation regions), and the speed of gradient descent convergence. We study these dynamics in relation to the spatial information of the signal to understand how they influence spectral bias. We then use this formulation to study the severity of spectral bias in low dimensional settings, and how positional encoding overcomes this.

Current deep learning models for Multispectral and Hyperspectral Image Fusion (MS/HS fusion) are typically designed for fixed spectral bands and spatial scales, which limits their transferability across diverse sensors. To address this, we propose SSA, a universal framework for MS/HS fusion with spectral-band and fusion-scale agnosticism. Specifically, we introduce Matryoshka Kernel (MK), a novel operator that enables a single model to adapt to arbitrary numbers of spectral channels. Meanwhile, we build SSA upon an Implicit Neural Representation (INR) backbone that models the HS signal as a continuous function, enabling reconstruction at arbitrary spatial resolutions. Together, these two forms of agnosticism enable a single MS/HS fusion model that generalizes effectively to unseen sensors and spatial scales. Extensive experiments demonstrate that our single model achieves state-of-the-art performance while generalizing well to unseen sensors and scales, paving the way toward future HS foundation models.

Spectral clustering is a leading clustering method. Two of its major shortcomings are the disjoint optimization process and the limited representation capacity. To address these issues, we propose a deep spectral clustering model (named BootSC), which jointly learns all stages of spectral clustering -- affinity matrix construction, spectral embedding, and k-means clustering -- using a single network in an end-to-end manner. BootSC leverages effective and efficient optimal-transport-derived supervision to bootstrap the affinity matrix and the cluster assignment matrix. Moreover, a semantically-consistent orthogonal re-parameterization technique is introduced to orthogonalize spectral embeddings, significantly enhancing the discrimination capability. Experimental results indicate that BootSC achieves state-of-the-art clustering performance. For example, it accomplishes a notable 16\% NMI improvement over the runner-up method on the challenging ImageNet-Dogs dataset. Our code is available at https://github.com/spdj2271/BootSC.

Previous research has shown that the principal singular vectors of a pre-trained model's weight matrices capture critical knowledge. In contrast, those associated with small singular values may contain noise or less reliable information. As a result, the LoRA-based parameter-efficient fine-tuning (PEFT) approach, which does not constrain the use of the spectral space, may not be effective for tasks that demand high representation capacity. In this study, we enhance existing PEFT techniques by incorporating the spectral information of pre-trained weight matrices into the fine-tuning process. We investigate spectral adaptation strategies with a particular focus on the additive adjustment of top singular vectors. This is accomplished by applying singular value decomposition (SVD) to the pre-trained weight matrices and restricting the fine-tuning within the top spectral space. Extensive speaker verification experiments on VoxCeleb1 and CN-Celeb1 demonstrate enhanced tuning performance with the proposed approach. Code is released at https://github.com/lizhepolyu/SpectralFT.

Recent advancements in local Implicit Neural Representation (INR) demonstrate its exceptional capability in handling images at various resolutions. However, frequency discrepancies between high-resolution (HR) and ground-truth images, especially at larger scales, result in significant artifacts and blurring in HR images. This paper introduces Frequency Consistency for Implicit Neural Representation (FreqINR), an innovative Arbitrary-scale Super-resolution method aimed at enhancing detailed textures by ensuring spectral consistency throughout both training and inference. During training, we employ Adaptive Discrete Cosine Transform Frequency Loss (ADFL) to minimize the frequency gap between HR and ground-truth images, utilizing 2-Dimensional DCT bases and focusing dynamically on challenging frequencies. During inference, we extend the receptive field to preserve spectral coherence between low-resolution (LR) and ground-truth images, which is crucial for the model to generate high-frequency details from LR counterparts. Experimental results show that FreqINR, as a lightweight approach, achieves state-of-the-art performance compared to existing Arbitrary-scale Super-resolution methods and offers notable improvements in computational efficiency. The code for our method will be made publicly available.

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.

Block-sparse attention is promising for accelerating long-context LLM pre-filling, yet identifying relevant blocks efficiently remains a bottleneck. Existing methods typically employ coarse-grained attention as a proxy for block importance estimation, but often resort to expensive token-level searching or scoring, resulting in significant selection overhead. In this work, we trace the inaccuracy of standard coarse-grained attention via mean pooling to a theoretical root cause: the interaction between mean pooling and Rotary Positional Embeddings (RoPE). We prove that mean pooling acts as a low-pass filter that induces destructive interference in high-frequency dimensions, effectively creating a "blind spot" for local positional information (e.g., slash patterns). To address this, we introduce Prism, a training-free spectral-aware approach that decomposes block selection into high-frequency and low-frequency branches. By applying energy-based temperature calibration, Prism restores the attenuated positional signals directly from pooled representations, enabling block importance estimation using purely block-level operations, thereby improving efficiency. Extensive evaluations confirm that Prism maintains accuracy parity with full attention while delivering up to 5.1times speedup.

Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes representational capacity, while whitening enforces isotropy at the cost of amplifying noise in the heavy-tailed eigenspectrum of retrieval embeddings. Intermediate spectral scaling methods unify these extremes by reweighting dimensions with a power coefficient γ, but treat γ as a fixed hyperparameter that requires task-specific tuning. We show that the optimal scaling strength γ is not a global constant: it varies systematically with target dimensionality k and is governed by the signal-to-noise ratio (SNR) of the retained subspace. Based on this insight, we propose Spectral Tempering (SpecTemp), a learning-free method that derives an adaptive γ(k) directly from the corpus eigenspectrum using local SNR analysis and knee-point normalization, requiring no labeled data or validation-based search. Extensive experiments demonstrate that Spectral Tempering consistently achieves near-oracle performance relative to grid-searched γ^*(k) while remaining fully learning-free and model-agnostic. Our code is publicly available at https://anonymous.4open.science/r/SpecTemp-0D37.

Recent advancements in learning latent codes derived from high-dimensional shapes have demonstrated impressive outcomes in 3D generative modeling. Traditionally, these approaches employ a trained autoencoder to acquire a continuous implicit representation of source shapes, which can be computationally expensive. This paper introduces a novel framework, spectral-domain diffusion for high-quality shape generation SpoDify, that utilizes singular value decomposition (SVD) for shape encoding. The resulting eigenvectors can be stored for subsequent decoding, while generative modeling is performed on the eigenfeatures. This approach efficiently encodes complex meshes into continuous implicit representations, such as encoding a 15k-vertex mesh to a 512-dimensional latent code without learning. Our method exhibits significant advantages in scenarios with limited samples or GPU resources. In mesh generation tasks, our approach produces high-quality shapes that are comparable to state-of-the-art methods.

Compound identification and structure annotation from mass spectra is a well-established task widely applied in drug detection, criminal forensics, small molecule biomarker discovery and chemical engineering. We propose SpecTUS: Spectral Translator for Unknown Structures, a deep neural model that addresses the task of structural annotation of small molecules from low-resolution gas chromatography electron ionization mass spectra (GC-EI-MS). Our model analyzes the spectra in de novo manner -- a direct translation from the spectra into 2D-structural representation. Our approach is particularly useful for analyzing compounds unavailable in spectral libraries. In a rigorous evaluation of our model on the novel structure annotation task across different libraries, we outperformed standard database search techniques by a wide margin. On a held-out testing set, including 28267 spectra from the NIST database, we show that our model's single suggestion perfectly reconstructs 43\% of the subset's compounds. This single suggestion is strictly better than the candidate of the database hybrid search (common method among practitioners) in 76\% of cases. In a~still affordable scenario of~10 suggestions, perfect reconstruction is achieved in 65\%, and 84\% are better than the hybrid search.

Image datasets are essential not only in validating existing methods in computer vision but also in developing new methods. Most existing image datasets focus on trichromatic intensity images to mimic human vision. However, polarization and spectrum, the wave properties of light that animals in harsh environments and with limited brain capacity often rely on, remain underrepresented in existing datasets. Although spectro-polarimetric datasets exist, these datasets have insufficient object diversity, limited illumination conditions, linear-only polarization data, and inadequate image count. Here, we introduce two spectro-polarimetric datasets: trichromatic Stokes images and hyperspectral Stokes images. These novel datasets encompass both linear and circular polarization; they introduce multiple spectral channels; and they feature a broad selection of real-world scenes. With our dataset in hand, we analyze the spectro-polarimetric image statistics, develop efficient representations of such high-dimensional data, and evaluate spectral dependency of shape-from-polarization methods. As such, the proposed dataset promises a foundation for data-driven spectro-polarimetric imaging and vision research. Dataset and code will be publicly available.

Bootstrap-based Self-Supervised Learning (SSL) has achieved remarkable progress in audio understanding. However, existing methods typically operate at a single level of granularity, limiting their ability to model the diverse temporal and spectral structures inherent in complex audio signals. Furthermore, bootstrapping representations from scratch is computationally expensive, often requiring extensive training to converge. In this work, we propose the Convolutional Audio Transformer (CAT), a unified framework designed to address these challenges. First, to capture hierarchical audio features, CAT incorporates a Multi-resolution Block that aggregates information across varying granularities. Second, to enhance training efficiency, we introduce a Representation Regularization objective. Drawing inspiration from generative modeling, this auxiliary task guides the student model by aligning its predictions with high-quality semantic representations from frozen, pre-trained external encoders. Experimental results demonstrate that CAT significantly outperforms baselines on audio understanding benchmarks. Notably, it achieves competitive performance on the AudioSet 20k dataset with 5 times faster convergence than existing methods. Codes and checkpoints will be released soon at https://github.com/realzhouchushu/CAT.

Time series data, characterized by its intrinsic long and short-range dependencies, poses a unique challenge across analytical applications. While Transformer-based models excel at capturing long-range dependencies, they face limitations in noise sensitivity, computational efficiency, and overfitting with smaller datasets. In response, we introduce a novel Time Series Lightweight Adaptive Network (TSLANet), as a universal convolutional model for diverse time series tasks. Specifically, we propose an Adaptive Spectral Block, harnessing Fourier analysis to enhance feature representation and to capture both long-term and short-term interactions while mitigating noise via adaptive thresholding. Additionally, we introduce an Interactive Convolution Block and leverage self-supervised learning to refine the capacity of TSLANet for decoding complex temporal patterns and improve its robustness on different datasets. Our comprehensive experiments demonstrate that TSLANet outperforms state-of-the-art models in various tasks spanning classification, forecasting, and anomaly detection, showcasing its resilience and adaptability across a spectrum of noise levels and data sizes. The code is available at https://github.com/emadeldeen24/TSLANet

Recently, the usefulness of self-supervised representation learning (SSRL) methods has been confirmed in various downstream tasks. Many of these models, as exemplified by HuBERT and WavLM, use pseudo-labels generated from spectral features or the model's own representation features. From previous studies, it is known that the pseudo-labels contain semantic information. However, the masked prediction task, the learning criterion of HuBERT, focuses on local contextual information and may not make effective use of global semantic information such as speaker, theme of speech, and so on. In this paper, we propose a new approach to enrich the semantic representation of HuBERT. We apply topic model to pseudo-labels to generate a topic label for each utterance. An auxiliary topic classification task is added to HuBERT by using topic labels as teachers. This allows additional global semantic information to be incorporated in an unsupervised manner. Experimental results demonstrate that our method achieves comparable or better performance than the baseline in most tasks, including automatic speech recognition and five out of the eight SUPERB tasks. Moreover, we find that topic labels include various information about utterance, such as gender, speaker, and its theme. This highlights the effectiveness of our approach in capturing multifaceted semantic nuances.

Symmetries play a central role in quantum many-body physics, yet uncovering them systematically remains challenging. We introduce a bootstrap framework designed to reconstruct the representation theory of hidden finite group symmetries of quantum many-body lattice Hamiltonians, using only a known symmetry subgroup N and spectral correlations between its symmetry sectors. We introduce a novel variant of the spectral form factor, the cross spectral form factor (xSFF), which we compute via exact diagonalization to seed the bootstrap algorithm. By applying the constraints derived from these data alongside the algebraic conditions of the fusion rules, our bootstrap procedure sharply restricts the set of candidate groups G. Remarkably, without any prior assumptions regarding the full symmetry group G, our method can systematically recover its representation-theoretic data, including the number and dimensions of the irreducible representations, their branching rules with respect to N, the fusion algebra, and the full character table. This framework applies equally well to chaotic and integrable many-body systems and accommodates both unitary and anti-unitary symmetries. Through various examples, we demonstrate that the underlying group G can be uniquely identified. In particular, our bootstrap independently recovers the Z_4 symmetry at the self-dual point of the three-state quantum torus chain, detects signatures of projective representations in the effective Hamiltonian of the driven Bose-Hubbard model, and rediscovers the η-pairing SO(4) symmetry of the one-dimensional Fermi-Hubbard model. Our framework thus establishes a practical route to identify symmetries directly from dynamical spectral observables.

Multispectral satellite images play a vital role in agriculture, fisheries, and environmental monitoring. However, their high dimensionality, large data volumes, and diverse spatial resolutions across multiple channels pose significant challenges for data compression and analysis. This paper presents ImpliSat, a unified framework specifically designed to address these challenges through efficient compression and reconstruction of multispectral satellite data. ImpliSat leverages Implicit Neural Representations (INR) to model satellite images as continuous functions over coordinate space, capturing fine spatial details across varying spatial resolutions. Furthermore, we introduce a Fourier modulation algorithm that dynamically adjusts to the spectral and spatial characteristics of each band, ensuring optimal compression while preserving critical image details.

Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way that couples spatial and spectral features of the signal that is not obvious in the usual discrete representation, paving the way for continuous signal processing and machine learning approaches that were not previously possible. Although INRs using sinusoidal activation functions have been studied in terms of Fourier theory, recent works have shown the advantage of using wavelets instead of sinusoids as activation functions, due to their ability to simultaneously localize in both frequency and space. In this work, we approach such INRs and demonstrate how they resolve high-frequency features of signals from coarse approximations done in the first layer of the MLP. This leads to multiple prescriptions for the design of INR architectures, including the use of complex wavelets, decoupling of low and band-pass approximations, and initialization schemes based on the singularities of the desired signal.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

We present a neural network architecture designed to naturally learn a positional embedding and overcome the spectral bias towards lower frequencies faced by conventional implicit neural representation networks. Our proposed architecture, SPDER, is a simple MLP that uses an activation function composed of a sinusoidal multiplied by a sublinear function, called the damping function. The sinusoidal enables the network to automatically learn the positional embedding of an input coordinate while the damping passes on the actual coordinate value by preventing it from being projected down to within a finite range of values. Our results indicate that SPDERs speed up training by 10x and converge to losses 1,500-50,000x lower than that of the state-of-the-art for image representation. SPDER is also state-of-the-art in audio representation. The superior representation capability allows SPDER to also excel on multiple downstream tasks such as image super-resolution and video frame interpolation. We provide intuition as to why SPDER significantly improves fitting compared to that of other INR methods while requiring no hyperparameter tuning or preprocessing.

TD-learning is a foundation reinforcement learning (RL) algorithm for value prediction. Critical to the accuracy of value predictions is the quality of state representations. In this work, we consider the question: how does end-to-end TD-learning impact the representation over time? Complementary to prior work, we provide a set of analysis that sheds further light on the representation dynamics under TD-learning. We first show that when the environments are reversible, end-to-end TD-learning strictly decreases the value approximation error over time. Under further assumptions on the environments, we can connect the representation dynamics with spectral decomposition over the transition matrix. This latter finding establishes fitting multiple value functions from randomly generated rewards as a useful auxiliary task for representation learning, as we empirically validate on both tabular and Atari game suites.

Deep representations across modalities are inherently intertwined. In this paper, we systematically analyze the spectral characteristics of various semantic and pixel encoders. Interestingly, our study uncovers a highly inspiring and rarely explored correspondence between an encoder's feature spectrum and its functional role: semantic encoders primarily capture low-frequency components that encode abstract meaning, whereas pixel encoders additionally retain high-frequency information that conveys fine-grained detail. This heuristic finding offers a unifying perspective that ties encoder behavior to its underlying spectral structure. We define it as the Prism Hypothesis, where each data modality can be viewed as a projection of the natural world onto a shared feature spectrum, just like the prism. Building on this insight, we propose Unified Autoencoding (UAE), a model that harmonizes semantic structure and pixel details via an innovative frequency-band modulator, enabling their seamless coexistence. Extensive experiments on ImageNet and MS-COCO benchmarks validate that our UAE effectively unifies semantic abstraction and pixel-level fidelity into a single latent space with state-of-the-art performance.

The approximation of Partial Differential Equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and flexibility in implementing various PDEs, PINNs often suffer from limited accuracy due to the spectral bias of Multi-Layer Perceptrons (MLPs), which struggle to effectively learn high-frequency and non-linear components. Recently, parametric mesh representations in combination with neural networks have been investigated as a promising approach to eliminate the inductive biases of neural networks. However, they usually require very high-resolution grids and a large number of collocation points to achieve high accuracy while avoiding overfitting issues. In addition, the fixed positions of the mesh parameters restrict their flexibility, making it challenging to accurately approximate complex PDEs. To overcome these limitations, we propose Physics-Informed Gaussians (PIGs), which combine feature embeddings using Gaussian functions with a lightweight neural network. Our approach uses trainable parameters for the mean and variance of each Gaussian, allowing for dynamic adjustment of their positions and shapes during training. This adaptability enables our model to optimally approximate PDE solutions, unlike models with fixed parameter positions. Furthermore, the proposed approach maintains the same optimization framework used in PINNs, allowing us to benefit from their excellent properties. Experimental results show the competitive performance of our model across various PDEs, demonstrating its potential as a robust tool for solving complex PDEs. Our project page is available at https://namgyukang.github.io/Physics-Informed-Gaussians/

Scaling laws have made language-model performance predictable from model size, data, and compute, but they typically treat the optimizer as a fixed training detail. We show that this assumption misses a fundamental axis of representation scaling: how effectively the optimizer converts added FFN width into utilized spectral capacity. Using eigenspectra of feed-forward network representations, measured through soft and hard spectral-ranks, we find that the same Transformer architecture realizes markedly different spectral scaling laws when trained with different optimizers. Holding architecture and width schedule fixed, AdamW exhibits weak hard-rank scaling (β=0.44) on rare-token (TAIL) representations where learning is known to be hardest, whereas Muon achieves linear scaling (β=1.02) in the same regimes, a 2.3times increase in the scaling exponent. This difference is not reducible to validation loss: AdamW configurations can match low-rank Dion variants in perplexity, under extended training, while exhibiting sharply different spectral geometry, demonstrating that matched loss does not imply matched representation structure. Hard--soft rank asymmetry further reveals that optimizers differ not only in how much capacity is realized, but also in how that capacity is structured across eigenmodes. To disentangle optimizer effects from architectural ones, we compare against architectural interventions (e.g., attention rank and positional encoding), and find that optimizer-induced spectral shifts often exceed the architectural effects. These results suggest optimization as a first-class axis of representation scaling, motivating optimizer--architecture co-design.

Audio mixing style encompasses the artistic and technical decisions a mix engineer makes, including level balancing, spatialization, and the choice, ordering, and parameterization of audio effects (FX) on each stem. FX chains are a key determinant of this style, yet existing approaches to modeling them remain limited. Some operate on stereo mixtures without explicit per-stem FX chain modeling, others fix the number or type of effects per track, and many require differentiable effect implementations or scarce multitrack datasets. We present StemFX, a framework that learns mixing style representations by autoregressively predicting variable-length FX chains on source-separated stems. A Transformer decoder predicts tokenized FX chains autoregressively, while a band-split multi-band CNN encoder with FiLM conditioning captures per-stem spectral structure. To enable large-scale paired training, we extract pseudo-stems from about 105K songs via source separation and augment them using MultiAFx, a toolkit unifying 85 audio effects from 7 Python libraries. Evaluated on mixing style retrieval, StemFX outperforms all baseline models across all tested chain lengths. On paired mixing style transfer, StemFX achieves the best spectral fidelity and the highest listener preference, over 4000 times faster than iterative optimization.

Activation outliers in large-scale transformer models pose a fundamental challenge to model quantization, creating excessively large ranges that cause severe accuracy drops during quantization. We empirically observe that outlier severity intensifies with pre-training scale (e.g., progressing from CLIP to the more extensively trained SigLIP and SigLIP2). Through theoretical analysis as well as empirical correlation studies, we establish the direct link between these activation outliers and dominant singular values of the weights. Building on this insight, we propose Selective Spectral Decay (S^2D), a geometrically-principled conditioning method that surgically regularizes only the weight components corresponding to the largest singular values during fine-tuning. Through extensive experiments, we demonstrate that S^2D significantly reduces activation outliers and produces well-conditioned representations that are inherently quantization-friendly. Models trained with S^2D achieve up to 7% improved PTQ accuracy on ImageNet under W4A4 quantization and 4% gains when combined with QAT. These improvements also generalize across downstream tasks and vision-language models, enabling the scaling of increasingly large and rigorously trained models without sacrificing deployment efficiency.

Training Large Language Models (LLMs) at ultra-low precision is critically impeded by instability rooted in the conflict between discrete quantization constraints and the intrinsic heavy-tailed spectral nature of linguistic data. By formalizing the connection between Zipfian statistics and random matrix theory, we prove that the power-law decay in the singular value spectra of embeddings is a fundamental requisite for semantic encoding. We derive theoretical bounds showing that uniform quantization introduces a noise floor that disproportionately truncates this spectral tail, which induces spectral flattening and a strictly provable increase in the stable rank of representations. Empirical validation across diverse architectures including GPT-2 and TinyLlama corroborates that this geometric degradation precipitates representational collapse. This work not only quantifies the spectral sensitivity of LLMs but also establishes spectral fidelity as a necessary condition for stable low-bit optimization.

We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving graph spectra, which are also computationally expensive due to the temporal aspect along with the graph vertex domain. We view the problem as an optimization over the Laplacian of the continuous time dynamic graph. Additionally, we propose pseudo-spectrum relaxations that decompose the transformation process, making it highly computationally efficient. The EFT method adeptly captures the evolving graph's structural and positional properties, making it effective for downstream tasks on evolving graphs. Hence, as a reference implementation, we develop a simple neural model induced with EFT for capturing evolving graph spectra. We empirically validate our theoretical findings on a number of large-scale and standard temporal graph benchmarks and demonstrate that our model achieves state-of-the-art performance.

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of modern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality reduction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

The Platonic Representation Hypothesis suggests that representations from neural networks are converging to a common statistical model of reality. We show that the existing metrics used to measure representational similarity are confounded by network scale: increasing model depth or width can systematically inflate representational similarity scores. To correct these effects, we introduce a permutation-based null-calibration framework that transforms any representational similarity metric into a calibrated score with statistical guarantees. We revisit the Platonic Representation Hypothesis with our calibration framework, which reveals a nuanced picture: the apparent convergence reported by global spectral measures largely disappears after calibration, while local neighborhood similarity, but not local distances, retains significant agreement across different modalities. Based on these findings, we propose the Aristotelian Representation Hypothesis: representations in neural networks are converging to shared local neighborhood relationships.

Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We consider the problem of learning over this Laplacian in a distributed streaming setting, where new edges of the graph are observed in real time by a network of workers. In this setting, it is hard to learn quickly or approximately while keeping a distributed representation of L. To address this challenge, we present a novel algorithm, GSQUEAK, which efficiently sparsifies the Laplacian by maintaining a small subset of effective resistances. We show that our algorithm produces sparsifiers with strong spectral approximation guarantees, all while processing edges in a single pass and in a distributed fashion.

Recent successful applications of convolutional neural networks (CNNs) to audio classification and speech recognition have motivated the search for better input representations for more efficient training. Visual displays of an audio signal, through various time-frequency representations such as spectrograms offer a rich representation of the temporal and spectral structure of the original signal. In this letter, we compare various popular signal processing methods to obtain this representation, such as short-time Fourier transform (STFT) with linear and Mel scales, constant-Q transform (CQT) and continuous Wavelet transform (CWT), and assess their impact on the classification performance of two environmental sound datasets using CNNs. This study supports the hypothesis that time-frequency representations are valuable in learning useful features for sound classification. Moreover, the actual transformation used is shown to impact the classification accuracy, with Mel-scaled STFT outperforming the other discussed methods slightly and baseline MFCC features to a large degree. Additionally, we observe that the optimal window size during transformation is dependent on the characteristics of the audio signal and architecturally, 2D convolution yielded better results in most cases compared to 1D.

Discrete speech representations have garnered recent attention for their efficacy in training transformer-based models for various speech-related tasks such as automatic speech recognition (ASR), translation, speaker verification, and joint speech-text foundational models. In this work, we present a comprehensive analysis on building ASR systems with discrete codes. We investigate different methods for codec training such as quantization schemes and time-domain vs spectral feature encodings. We further explore ASR training techniques aimed at enhancing performance, training efficiency, and noise robustness. Drawing upon our findings, we introduce a codec ASR pipeline that outperforms Encodec at similar bit-rate. Remarkably, it also surpasses the state-of-the-art results achieved by strong self-supervised models on the 143 languages ML-SUPERB benchmark despite being smaller in size and pretrained on significantly less data.

Recent studies show that self-attentions behave like low-pass filters (as opposed to convolutions) and enhancing their high-pass filtering capability improves model performance. Contrary to this idea, we investigate existing convolution-based models with spectral analysis and observe that improving the low-pass filtering in convolution operations also leads to performance improvement. To account for this observation, we hypothesize that utilizing optimal token mixers that capture balanced representations of both high- and low-frequency components can enhance the performance of models. We verify this by decomposing visual features into the frequency domain and combining them in a balanced manner. To handle this, we replace the balancing problem with a mask filtering problem in the frequency domain. Then, we introduce a novel token-mixer named SPAM and leverage it to derive a MetaFormer model termed as SPANet. Experimental results show that the proposed method provides a way to achieve this balance, and the balanced representations of both high- and low-frequency components can improve the performance of models on multiple computer vision tasks. Our code is available at https://doranlyong.github.io/projects/spanet/{https://doranlyong.github.io/projects/spanet/}.

3D Gaussian Splatting (3DGS) enables real-time, photorealistic novel view synthesis, making it a highly attractive representation for model-based video tracking. However, leveraging the differentiability of the 3DGS renderer "in the wild" remains notoriously fragile. A fundamental bottleneck lies in the compact, local support of the Gaussian primitives. Standard photometric objectives implicitly rely on spatial overlap; if severe camera misalignment places the rendered object outside the target's local footprint, gradients strictly vanish, leaving the optimizer stranded. We introduce SpectralSplats, a robust tracking framework that resolves this "vanishing gradient" problem by shifting the optimization objective from the spatial to the frequency domain. By supervising the rendered image via a set of global complex sinusoidal features (Spectral Moments), we construct a global basin of attraction, ensuring that a valid, directional gradient toward the target exists across the entire image domain, even when pixel overlap is completely nonexistent. To harness this global basin without introducing periodic local minima associated with high frequencies, we derive a principled Frequency Annealing schedule from first principles, gracefully transitioning the optimizer from global convexity to precise spatial alignment. We demonstrate that SpectralSplats acts as a seamless, drop-in replacement for spatial losses across diverse deformation parameterizations (from MLPs to sparse control points), successfully recovering complex deformations even from severely misaligned initializations where standard appearance-based tracking catastrophically fails.

The inverse problem of multilayer thin-film optical coatings design represents a complex combinatorial-continuous optimization challenge. We present PRISM (Position-encoded Regressive Inverse Spectral Model), a unified decoder-only autoregressive transformer that streamlines this process by jointly predicting discrete material selection and continuous thickness regression within a single backbone. PRISM introduces two primary architectural innovations: (1) spectrum prefix conditioning, which utilizes standard prefix tokens for in-context target injection, and (2) cumulative-depth Rotary Position Embeddings, which encode continuous thickness directly into the positional representation to preserve the physical spatial relationships of the stack. Our benchmarks demonstrate that a PRISM-13M model reduces MAE by over 50\% compared to other transformer baselines while utilizing only one-fifth of the parameters. Furthermore, a 44M-parameter variant achieves state-of-the-art performance (MAE = 0.010) on our in-distribution validation benchmark and operates significantly faster than simulated annealing, offering a highly efficient alternative to classical optimization methods.

Flow matching (FM) enables high-fidelity generation, while self-supervised learning (SSL) speech models provide hierarchical representations spanning acoustic and phonetic levels. However, existing FM-based speech enhancement (SE) methods operate primarily in the spectral domain, treating SSL features only as external conditions rather than modeling directly in the SSL latent space. To fully exploit the structural richness of SSL representations, we propose PhASE-Flow, an FM-based SE framework that operates entirely in the SSL space. It models the conditional distribution of clean acoustic representations given phonetic ones, reconstructing the waveform via a neural vocoder. Experiments show that PhASE-Flow outperforms state-of-the-art baselines in perceptual quality and intelligibility. Notably, it achieves competitive performance with only four sampling steps, enabling highly efficient inference. Audio demos are available at https://anonymous.4open.science/w/phase-flow_demo-E6E1/.

Precipitation nowcasting is critical for disaster mitigation and aviation safety. However, radar-only models frequently suffer from a lack of large-scale atmospheric context, leading to performance degradation at longer lead times. While integrating meteorological variables predicted by weather foundation models offers a potential remedy, existing architectures fail to reconcile the profound representational heterogeneities between radar imagery and meteorological data. To bridge this gap, we propose PW-FouCast, a novel frequency-domain fusion framework that leverages Pangu-Weather forecasts as spectral priors within a Fourier-based backbone. Our architecture introduces three key innovations: (i) Pangu-Weather-guided Frequency Modulation to align spectral magnitudes and phases with meteorological priors; (ii) Frequency Memory to correct phase discrepancies and preserve temporal evolution; and (iii) Inverted Frequency Attention to reconstruct high-frequency details typically lost in spectral filtering. Extensive experiments on the SEVIR and MeteoNet benchmarks demonstrate that PW-FouCast achieves state-of-the-art performance, effectively extending the reliable forecast horizon while maintaining structural fidelity. Our code is available at https://github.com/Onemissed/PW-FouCast.

Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundancy through conjugate symmetry. We introduce the Hartley Neural Operator (HNO), the exact real-valued mirror of FNO: it replaces the FFT with the purely real Discrete Hartley Transform and learns a single real multiplier per retained spectral mode, with no complex arithmetic. Because the real Hartley spectrum is not halved by conjugate symmetry, HNO retains twice as many frequency corners as FNO but one real weight where FNO carries a complex pair, so the two operators are iso-parametric at equal width and differ only in spectral basis. Our central thesis is that the best basis is a property of the operator. Self-adjoint elliptic operators (Poisson, biharmonic) have real, symmetric Green's functions that the real Hartley multiplier diagonalizes exactly, and HNO is favored there. Time-dependent operators carry phase, from oscillation in the wave equation to transport in advection, Burgers, and Navier-Stokes, which a real diagonal multiplier cannot represent, so FNO is favored there, and increasingly so with the operator's phase content, leaving the phaseless heat equation as the borderline case. Training both operators identically and benchmarking across PDE classes, initial-condition families, and boundary conditions, we find an elliptic-versus-time-dependent split that is monotone in operator phase content and matches the Green's-function theory we develop. Rather than a universal winner, our findings give a predictive rule: match the spectral basis to the symmetry of the solution operator.

Beyond cosmic noon, galaxies appear as faint whispers amid noise, yet this epoch is key to understanding massive galaxy assembly. ALMA's sensitivity to cold dust and [C II] emission allows us to probe their interstellar medium, but faint signals make robust denoising essential. We evaluate and benchmark denoising strategies including Principal Component Analysis, Independent Component Analysis, sparse unsupervised representations: iterative soft thresholding with 2D-1D wavelets, and supervised deep learning with a 3D U-Net, to identify techniques that suppress noise while preserving flux and morphology across peak SNRs of 2.5-8, applied to (i) synthetic spectral cubes of rotating toy disk galaxies, (ii) synthetic [C II] IFU cubes from FIRE simulations, and (iii) ALMA [C II] observations of CRISTAL galaxies and W2246-0526. Performance is assessed via RMSE, conservation of flux and spectra, noise reduction, and SNR improvement of the central galaxy. For synthetic cubes: PCA and ICA provide marginal improvement; IST reduces noise effectively at moderate SNRs but can suppress emission at low SNRs; and the U-Net outperforms IST, though it can produce quantifiable hallucinations at lower-SNRs. For moderate-SNR observations (ALMA-CRISTAL), U-Net and IST achieve comparable performance, conserving >91% flux and increasing SNR by >6. However, for observations with complex morphologies absent in the training set (W2246), the U-Net underperforms relative to IST, recovering ~80% flux, while IST robustly conserves flux and improves SNR by ~3, highlighting generalisation challenges and the need for physically-motivated training priors. We conclude that IST is a robust unsupervised denoiser for moderate-SNR data, and a synthetically trained U-Net generalises effectively to real data, dependent on training priors. This framework offers a pathway for transferable denoising for ALMA, VLT/MUSE, and JWST.

We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive eighth-order Dormand-Prince time integration scheme to achieve machine-precision conservation of mass and near-perfect preservation of momentum and energy for smooth solutions. The implementation accurately reproduces fundamental NLSE phenomena including soliton collisions with analytically predicted phase shifts, Akhmediev breather dynamics, and the development of modulation instability from noisy initial conditions. Four canonical test cases validate the numerical scheme: single soliton propagation, two-soliton elastic collision, breather evolution, and noise-seeded modulation instability. The solver employs a 2/3 dealiasing rule with exponential filtering to prevent aliasing errors from the cubic nonlinearity. Statistical analysis using Shannon, R\'enyi, and Tsallis entropies quantifies the spatio-temporal complexity of solutions, while phase space representations reveal the underlying coherence structure. The implementation prioritizes code transparency and educational accessibility over computational performance, providing a valuable pedagogical tool for exploring nonlinear wave dynamics. Complete source code, documentation, and example configurations are freely available, enabling reproducible computational experiments across diverse physical contexts where the NLSE governs wave evolution, including nonlinear optics, Bose-Einstein condensates, and ocean surface waves.

Recent advances in synthetic speech have made audio deepfakes increasingly realistic, posing significant security risks. Existing detection methods that rely on a single modality, either raw waveform embeddings or spectral based features, are vulnerable to non spoof disturbances and often overfit to known forgery algorithms, resulting in poor generalization to unseen attacks. To address these shortcomings, we investigate hybrid fusion frameworks that integrate self supervised learning (SSL) based representations with handcrafted spectral descriptors (MFCC , LFCC, CQCC). By aligning and combining complementary information across modalities, these fusion approaches capture subtle artifacts that single feature approaches typically overlook. We explore several fusion strategies, including simple concatenation, cross attention, mutual cross attention, and a learnable gating mechanism, to optimally blend SSL features with fine grained spectral cues. We evaluate our approach on four challenging public benchmarks and report generalization performance. All fusion variants consistently outperform an SSL only baseline, with the cross attention strategy achieving the best generalization with a 38% relative reduction in equal error rate (EER). These results confirm that joint modeling of waveform and spectral views produces robust, domain agnostic representations for audio deepfake detection.

Emotional voice conversion (EVC) involves modifying various acoustic characteristics, such as pitch and spectral envelope, to match a desired emotional state while preserving the speaker's identity. Existing EVC methods often rely on text transcriptions or time-alignment information and struggle to handle varying speech durations effectively. In this paper, we propose DurFlex-EVC, a duration-flexible EVC framework that operates without the need for text or alignment information. We introduce a unit aligner that models contextual information by aligning speech with discrete units representing content, eliminating the need for text or speech-text alignment. Additionally, we design a style autoencoder that effectively disentangles content and emotional style, allowing precise manipulation of the emotional characteristics of the speech. We further enhance emotional expressiveness through a hierarchical stylize encoder that applies the target emotional style at multiple hierarchical levels, refining the stylization process to improve the naturalness and expressiveness of the converted speech. Experimental results from subjective and objective evaluations demonstrate that our approach outperforms baseline models, effectively handling duration variability and enhancing emotional expressiveness in the converted speech.

Multi-resolution spectro-temporal features of a speech signal represent how the brain perceives sounds by tuning cortical cells to different spectral and temporal modulations. These features produce a higher dimensional representation of the speech signals. The purpose of this paper is to evaluate how well the auditory cortex representation of speech signals contribute to estimate articulatory features of those corresponding signals. Since obtaining articulatory features from acoustic features of speech signals has been a challenging topic of interest for different speech communities, we investigate the possibility of using this multi-resolution representation of speech signals as acoustic features. We used U. of Wisconsin X-ray Microbeam (XRMB) database of clean speech signals to train a feed-forward deep neural network (DNN) to estimate articulatory trajectories of six tract variables. The optimal set of multi-resolution spectro-temporal features to train the model were chosen using appropriate scale and rate vector parameters to obtain the best performing model. Experiments achieved a correlation of 0.675 with ground-truth tract variables. We compared the performance of this speech inversion system with prior experiments conducted using Mel Frequency Cepstral Coefficients (MFCCs).

Graph-structured knowledge systems -- from knowledge graphs to GraphRAG pipelines -- organize information into hierarchical communities, yet lack a principled mechanism for continuous resolution control: where do the qualitative boundaries between abstraction levels lie, and how should an agent navigate them? Current approaches rely on discrete community detection with manually tuned resolution parameters (e.g., Leiden γ), offering no continuous zoom and no formal guarantees. We introduce Semantic Level of Detail (SLoD), a framework that addresses both problems by defining a continuous zoom operator via heat kernel diffusion on a graph Laplacian whose kNN structure is induced by a Poincare-ball embedding. We prove hierarchical coherence in the tree limit (exact tree with Sarkar embedding), with bounded approximation error, and demonstrate consistent boundary-detection behaviour on noisy hierarchies; spectral gaps in the graph Laplacian then induce emergent scale boundaries -- scales where the representation undergoes qualitative transitions -- detectable without manual resolution tuning. On synthetic hierarchies (HSBM, 1024 nodes), spectral clustering at the BoundaryScan-detected scale recovers planted levels, with macro ARI saturating at 1.00 in the high-SNR regime (50-seed median) and meso ARI reaching 0.89 [0.86, 0.92] at r=200. On the full WordNet noun hierarchy (82K synsets), using 100 stratified leaf queries, detected boundaries align with true taxonomic depth (τ= 0.79), demonstrating meaningful abstraction-level discovery in real-world knowledge graphs without resolution-parameter tuning. The composite weights, MAD threshold, and kNN-parameter rule (k = max(10, min(lfloorNrfloor, 50))) use defaults that transferred unchanged between HSBM and WordNet; their behaviour on graphs with implicit or qualitatively different hierarchical structure is open.

This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory (RMT). As deep networks and large language models continue to scale, their internal behavior becomes increasingly opaque, leading to hallucinations, fragile generalization under distribution shift, and growing computational and energy demands. By analyzing the eigenvalue dynamics of hidden activations across layers and inputs, this work shows that spectral statistics provide a compact, stable, and interpretable lens on model behavior, capable of separating structured, causal representations from noise-dominated variability. Within this framework, the first contribution, EigenTrack, introduces a real-time method for detecting hallucinations and out-of-distribution behavior in large language and vision-language models. EigenTrack transforms streaming activations into spectral descriptors such as entropy, variance, and deviations from the Marchenko-Pastur baseline, and models their temporal evolution using lightweight recurrent classifiers, enabling early detection of reliability failures before they appear in model outputs while offering interpretable insight into representation dynamics. The second contribution, RMT-KD, presents a principled approach to compressing deep networks via random matrix theoretic knowledge distillation. By interpreting outlier eigenvalues in activation spectra as carriers of task-relevant information, RMT-KD progressively projects networks onto lower-dimensional subspaces through iterative self-distillation, yielding significantly more compact and energy-efficient models while preserving accuracy and dense, hardware-friendly structure.

The success of deep neural networks for pan-sharpening is commonly in a form of black box, lacking transparency and interpretability. To alleviate this issue, we propose a novel model-driven deep unfolding framework with image reasoning prior tailored for the pan-sharpening task. Different from existing unfolding solutions that deliver the proximal operator networks as the uncertain and vague priors, our framework is motivated by the content reasoning ability of masked autoencoders (MAE) with insightful designs. Specifically, the pre-trained MAE with spatial masking strategy, acting as intrinsic reasoning prior, is embedded into unfolding architecture. Meanwhile, the pre-trained MAE with spatial-spectral masking strategy is treated as the regularization term within loss function to constrain the spatial-spectral consistency. Such designs penetrate the image reasoning prior into deep unfolding networks while improving its interpretability and representation capability. The uniqueness of our framework is that the holistic learning process is explicitly integrated with the inherent physical mechanism underlying the pan-sharpening task. Extensive experiments on multiple satellite datasets demonstrate the superiority of our method over the existing state-of-the-art approaches. Code will be released at https://manman1995.github.io/.

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by millions of parameters, but valuable because it increases our ability to understand current models and create improved versions of them. In this paper we investigate the extent to which neural networks exhibit what we call convergent learning, which is when the representations learned by multiple nets converge to a set of features which are either individually similar between networks or where subsets of features span similar low-dimensional spaces. We propose a specific method of probing representations: training multiple networks and then comparing and contrasting their individual, learned representations at the level of neurons or groups of neurons. We begin research into this question using three techniques to approximately align different neural networks on a feature level: a bipartite matching approach that makes one-to-one assignments between neurons, a sparse prediction approach that finds one-to-many mappings, and a spectral clustering approach that finds many-to-many mappings. This initial investigation reveals a few previously unknown properties of neural networks, and we argue that future research into the question of convergent learning will yield many more. The insights described here include (1) that some features are learned reliably in multiple networks, yet other features are not consistently learned; (2) that units learn to span low-dimensional subspaces and, while these subspaces are common to multiple networks, the specific basis vectors learned are not; (3) that the representation codes show evidence of being a mix between a local code and slightly, but not fully, distributed codes across multiple units.

High-quality speech coding at low bitrates is crucial for bandwidth-constrained applications, yet remains challenging due to the severe loss of quality-critical information in highly compressed representations. To overcome this challenge, we propose CFMDCTCodec, a low-bitrate neural speech codec that operates entirely in the modified discrete cosine transform (MDCT) domain. CFMDCTCodec integrates a lightweight encoder-quantizer-decoder-style MDCT-spectral codec with a noise-prior-aware, conditional-flow-matching (CFM)-based MDCT-spectral enhancer. Within this framework, the codec serves as a base module that compactly discretizes the MDCT spectrum extracted from speech and produces an initial coarse reconstruction, while the enhancer further restores fine-grained spectral details. The enhancer improves the decoded MDCT spectrum by integrating a conditional MDCT velocity-field filter with an ordinary differential equation (ODE) solver, under the guidance of an MDCT-derived magnitude-adaptive noise prior, aiming to emphasize perceptually significant high-energy regions while stabilizing low-energy and silent regions. Finally, the enhanced MDCT spectrum is reconstructed into the decoded speech using the inverse MDCT. When optimizing CFMDCTCodec, we adopt a unified non-adversarial training strategy that jointly combines reconstruction, quantization and CFM objectives. Both objective and subjective evaluations show that CFMDCTCodec outperforms competitive baselines in low-bitrate regimes, e.g., 0.65 kbps, while approaching the perceptual quality of large-scale codecs with significantly fewer parameters and computations.

Feature representation in the form of spatio-spectral decomposition is one of the robust techniques adopted in automatic handwritten character recognition systems. In this regard, we propose a new image representation approach for unconstrained handwritten alphanumeric characters using sparse concept coded Tetrolets. Tetrolets, which does not use fixed dyadic square blocks for spectral decomposition like conventional wavelets, preserve the localized variations in handwritings by adopting tetrominoes those capture the shape geometry. The sparse concept coding of low entropy Tetrolet representation is found to extract the important hidden information (concept) for superior pattern discrimination. Large scale experimentation using ten databases in six different scripts (Bangla, Devanagari, Odia, English, Arabic and Telugu) has been performed. The proposed feature representation along with standard classifiers such as random forest, support vector machine (SVM), nearest neighbor and modified quadratic discriminant function (MQDF) is found to achieve state-of-the-art recognition performance in all the databases, viz. 99.40% (MNIST); 98.72% and 93.24% (IITBBS); 99.38% and 99.22% (ISI Kolkata). The proposed OCR system is shown to perform better than other sparse based techniques such as PCA, SparsePCA and SparseLDA, as well as better than existing transforms (Wavelet, Slantlet and Stockwell).

Marmoset monkeys encode vital information in their calls and serve as a surrogate model for neuro-biologists to understand the evolutionary origins of human vocal communication. Traditionally analyzed with signal processing-based features, recent approaches have utilized self-supervised models pre-trained on human speech for feature extraction, capitalizing on their ability to learn a signal's intrinsic structure independently of its acoustic domain. However, the utility of such foundation models remains unclear for marmoset call analysis in terms of multi-class classification, bandwidth, and pre-training domain. This study assesses feature representations derived from speech and general audio domains, across pre-training bandwidths of 4, 8, and 16 kHz for marmoset call-type and caller classification tasks. Results show that models with higher bandwidth improve performance, and pre-training on speech or general audio yields comparable results, improving over a spectral baseline.

This paper proposes Pix2Next, a novel image-to-image translation framework designed to address the challenge of generating high-quality Near-Infrared (NIR) images from RGB inputs. Our approach leverages a state-of-the-art Vision Foundation Model (VFM) within an encoder-decoder architecture, incorporating cross-attention mechanisms to enhance feature integration. This design captures detailed global representations and preserves essential spectral characteristics, treating RGB-to-NIR translation as more than a simple domain transfer problem. A multi-scale PatchGAN discriminator ensures realistic image generation at various detail levels, while carefully designed loss functions couple global context understanding with local feature preservation. We performed experiments on the RANUS dataset to demonstrate Pix2Next's advantages in quantitative metrics and visual quality, improving the FID score by 34.81% compared to existing methods. Furthermore, we demonstrate the practical utility of Pix2Next by showing improved performance on a downstream object detection task using generated NIR data to augment limited real NIR datasets. The proposed approach enables the scaling up of NIR datasets without additional data acquisition or annotation efforts, potentially accelerating advancements in NIR-based computer vision applications.

Neural fields have gained significant attention in the computer vision community due to their excellent performance in novel view synthesis, geometry reconstruction, and generative modeling. Some of their advantages are a sound theoretic foundation and an easy implementation in current deep learning frameworks. While neural fields have been applied to signals on manifolds, e.g., for texture reconstruction, their representation has been limited to extrinsically embedding the shape into Euclidean space. The extrinsic embedding ignores known intrinsic manifold properties and is inflexible wrt. transfer of the learned function. To overcome these limitations, this work introduces intrinsic neural fields, a novel and versatile representation for neural fields on manifolds. Intrinsic neural fields combine the advantages of neural fields with the spectral properties of the Laplace-Beltrami operator. We show theoretically that intrinsic neural fields inherit many desirable properties of the extrinsic neural field framework but exhibit additional intrinsic qualities, like isometry invariance. In experiments, we show intrinsic neural fields can reconstruct high-fidelity textures from images with state-of-the-art quality and are robust to the discretization of the underlying manifold. We demonstrate the versatility of intrinsic neural fields by tackling various applications: texture transfer between deformed shapes & different shapes, texture reconstruction from real-world images with view dependence, and discretization-agnostic learning on meshes and point clouds.

We propose BiCrossMamba-ST, a robust framework for speech deepfake detection that leverages a dual-branch spectro-temporal architecture powered by bidirectional Mamba blocks and mutual cross-attention. By processing spectral sub-bands and temporal intervals separately and then integrating their representations, BiCrossMamba-ST effectively captures the subtle cues of synthetic speech. In addition, our proposed framework leverages a convolution-based 2D attention map to focus on specific spectro-temporal regions, enabling robust deepfake detection. Operating directly on raw features, BiCrossMamba-ST achieves significant performance improvements, a 67.74% and 26.3% relative gain over state-of-the-art AASIST on ASVSpoof LA21 and ASVSpoof DF21 benchmarks, respectively, and a 6.80% improvement over RawBMamba on ASVSpoof DF21. Code and models will be made publicly available.

In this work, we study how multi-head latent attention (MLA), a popular strategy for compressing key/value memory, affects a transformer's internal capacity during pretraining. Using a lightweight suite of Marchenko-Pastur (MP) diagnostics, we analyze the spectrum of the W_{Q}W_{K}^top gram matrix throughout training, comparing three variants: the standard multi-head attention (MHA) baseline, MLA-PreRoPE with rotary applied before compression, and MLA-Decoupled, which shares a single rotary sub-vector across all heads. Our random matrix analysis reveals three key findings: i) capacity bottlenecks emerge locally: both MHA and MLA-PreRoPE exhibit sharp, early spikes in specific layers that persist and propagate, disrupting the balance between bulk and outlier directions; ii) these spikes coincide with rank collapse, concentrating the model's expressivity into narrow subspaces; iii) only the decoupled variant prevents this cascade, maintaining broad spectral support and suppressing outlier formation across layers. These results underscore that how rotary embeddings are applied is just as critical as where compression occurs. Sharing rotary components across heads mitigates spectral fragmentation and preserves representational capacity.

Adapting large-scale pre-trained generative models in a parameter-efficient manner is gaining traction. Traditional methods like low rank adaptation achieve parameter efficiency by imposing constraints but may not be optimal for tasks requiring high representation capacity. We propose a novel spectrum-aware adaptation framework for generative models. Our method adjusts both singular values and their basis vectors of pretrained weights. Using the Kronecker product and efficient Stiefel optimizers, we achieve parameter-efficient adaptation of orthogonal matrices. We introduce Spectral Orthogonal Decomposition Adaptation (SODA), which balances computational efficiency and representation capacity. Extensive evaluations on text-to-image diffusion models demonstrate SODA's effectiveness, offering a spectrum-aware alternative to existing fine-tuning methods.