Daily Papers

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaining why it improves empirical performance. Our work bridges this gap by showing momentum in Muon acts as a spectral filter. Under a structured signal-plus-perturbation gradient model, we prove that momentum suppresses perturbations while preserving the dominant signal, thereby enlarging the spectral gap between them. This enlarged gap stabilizes the singular subspaces of the matrix passed to Muon's orthogonalization step, making the resulting update more reliable. We further show that applying momentum before orthogonalization achieves provably stronger alignment with the signal component of the gradient than either reversing this order or simply removing momentum. Experiments across diverse tasks, including LLM pretraining, support our theoretical analysis. More broadly, our theory offers a starting point for understanding the benefits of momentum in other matrix-based optimizers.

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et al. (2017)). This gives rise to a novel sequence prediction architecture we call a spectral state space model. Spectral state space models have two primary advantages. First, they have provable robustness properties as their performance depends on neither the spectrum of the underlying dynamics nor the dimensionality of the problem. Second, these models are constructed with fixed convolutional filters that do not require learning while still outperforming SSMs in both theory and practice. The resulting models are evaluated on synthetic dynamical systems and long-range prediction tasks of various modalities. These evaluations support the theoretical benefits of spectral filtering for tasks requiring very long range memory.

Expanding the vocabulary of conditional text-to-speech (TTS) models typically requires extensive fine-tuning with paired audio, creating a major bottleneck for low-resource and cross-lingual adaptation. To address this, we introduce SEAM, a zero-audio initialization method that constructs embeddings for unseen tokens from known subtokens. Unlike standard pooling strategies that ignore sequential structure, SEAM applies a spectral filter to preserve temporal phonetic order and uses closed-form ridge regression to align the new embeddings with the pretrained conditioning manifold. Across three languages and two TTS architectures, SEAM approaches or matches baseline performance using up to four times less training data, reducing sample complexity by 75\% compared to random initialization and mean pooling. Our approach provides a lightweight, reproducible, and theoretically grounded solution for vocabulary expansion in low-resource speech synthesis.

Analytic Continual Learning (ACL) offers a computationally efficient alternative to gradient-based approaches. Recent ACL methods are based on Recursive Least Squares (RLS) and have achieved the state-of-the-art results compared to other alternatives. However, they falter significantly in Class-Incremental Learning scenarios characterized by Long-Tailed distributions. While the ill-conditioning of the autocorrelation (Gram) matrix is a known limitation of RLS, we demonstrate that class imbalance exacerbates this issue into a distinct spectral pathology: "tail" classes suffer from severe spectral collapse, rendering their subspaces numerically indistinguishable from noise. Standard Ridge Regression (L_2) fails to address this effectively as it applies isotropic regularization - a uniform penalty that is insufficient to stabilize the tail without over-shrinking the head. To address this, we propose Geometry-Spectral Rectification (GSR), a theoretically grounded framework that treats long-tailed learning as a spectral regularization problem. Unlike standard isotropic regularization (Ridge) which uniformly penalizes all eigenvalues, GSR acts as an anisotropic spectral filter, selectively inflating the collapsed eigenvalues of tail classes. We construct a structured, data-dependent spectral perturbation matrix Δ that selectively inflates collapsed tail eigen-directions of the Gram matrix. Theoretical analysis proves that GSR guarantees an improved stable rank for the Gram matrix, ensuring numerical stability. Extensive experiments show that GSR establishes a new state-of-the-art for analytic CIL, offering a superior trade-off between computational efficiency and robust generalization in long-tailed settings.

Doubly-stochastic matrices (DSM) are increasingly utilized in structure-preserving deep architectures -- such as Optimal Transport layers and Sinkhorn-based attention -- to enforce numerical stability and probabilistic interpretability. In this work, we identify a critical spectral degradation phenomenon inherent to these constraints, termed the Homogeneity Trap. We demonstrate that the maximum-entropy bias, typical of Sinkhorn-based projections, drives the mixing operator towards the uniform barycenter, thereby suppressing the subdominant singular value σ_2 and filtering out high-frequency feature components. We derive a spectral bound linking σ_2 to the network's effective depth, showing that high-entropy constraints restrict feature transformation to a shallow effective receptive field. Furthermore, we formally demonstrate that Layer Normalization fails to mitigate this collapse in noise-dominated regimes; specifically, when spectral filtering degrades the Signal-to-Noise Ratio (SNR) below a critical threshold, geometric structure is irreversibly lost to noise-induced orthogonal collapse. Our findings highlight a fundamental trade-off between entropic stability and spectral expressivity in DSM-constrained networks.

Model merging combines several independently fine-tuned experts into a single multi-task model without any training data, reducing the storage, serving, and decentralized-development costs of large foundation models. State-of-the-art merging methods formulate merging as a layer-wise quadratic interference minimization problem. Although this problem admits an exact closed-form pseudoinverse solution, that solution underperforms hundreds of iterations of gradient descent in practice. The iterative loop dominates the cost of the pipeline, yet its effectiveness has remained unexplained. We revisit this regime and show that the iterative solver does not primarily act as an optimizer; rather, it serves as an implicit spectral regularizer for an ill-posed normal equation, where small-eigenvalue directions of the per-layer interference operator amplify proxy noise. Building on this finding, we formalize multi-task model merging as a noisy linear inverse problem and propose a spectral filtering estimator parameterized by a per-direction filter. We instantiate this estimator with SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent, with a hard top-K truncation that suppresses noise-amplifying small-eigenvalue directions. Furthermore, we propose SWUDI-A, an adaptive variant that replaces the global rank hyperparameter with per-layer rank rules, further improving robustness across architectures. Both variants share a single symmetric eigendecomposition per linear layer and require no training data or optimizer state. Across four general benchmarks and a multimodal merging benchmark spanning VQA, Geometry, Chart, OCR, Grounding, and modality merging, our proposed spectral solvers match or outperform state-of-the-art merging methods. Crucially, they reduce wall-clock time by 28-72x and peak GPU memory by up to 50%.

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.

Previously, methods for learning marginally stable linear dynamical systems either required the transition matrix to be symmetric or incurred regret bounds that scale polynomially with the system's hidden dimension. In this work, we introduce a novel method that overcomes this trade-off, achieving dimension-free regret despite the presence of asymmetric matrices and marginal stability. Our method combines spectral filtering with linear predictors and employs Chebyshev polynomials in the complex plane to construct a novel spectral filtering basis. This construction guarantees sublinear regret in an online learning framework, without relying on any statistical or generative assumptions. Specifically, we prove that as long as the transition matrix has eigenvalues with complex component bounded by 1/poly log T, then our method achieves regret O(T^{9/10}) when compared to the best linear dynamical predictor in hindsight.

Deep neural networks are known to rely on non-robust features that align poorly with human perception. Prior work has largely framed these features as opportunistic shortcuts that help standard models on clean data. We show instead that non-robust cues can be antagonistic: they can act as Natural Jammers that actively mislead standard models on clean, unmodified images. Using disagreement between a standard model and robust models as an analysis lens, we identify a Jammed Set on which robust models outperform standard models. We provide causal evidence for Spectral-spatial Locking: jamming arises only when high-frequency components are precisely aligned with specific spatial structures. Disrupting this lock through spectral filtering or small geometric shifts can restore correct predictions. Crucially, we uncover a Substitution Paradox: while individual jammers are fragile to geometric shifts, the aggregate prevalence of jamming remains approximately stable and is redistributed rather than eliminated under such transformations. Our results reframe natural non-robustness as a failure field over the empirical model-data geometry: one that redistributes rather than disappears under small transformations.

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.

Targeted data selection has emerged as a crucial paradigm for efficient instruction tuning, aiming to identify a small yet influential subset of training examples for a specific target task. In practice, influence is often measured through the effect of an example on parameter updates. To make selection scalable, many approaches leverage optimizer statistics (e.g., Adam states) as an axis-aligned surrogate for update geometry (i.e., diagonal precondition), implicitly treating parameters as coordinate-wise independent. We show that this assumption breaks down in parameter-efficient fine-tuning (PEFT) methods such as LoRA. In this setting, the induced optimization geometry exhibits strong cross-parameter coupling with non-trivial off-diagonal interactions, while the task-relevant update directions are confined to a low-dimensional subspace. Motivated by this mismatch, we propose GIST (Gradient Isometric Subspace Transformation), a simple yet principled alternative that replaces axis-aligned scaling with robust subspace alignment. GIST recovers a task-specific subspace from validation gradients via spectral filtering (SVD), projects training gradients into this coupled subspace, and scores examples by their alignment with target directions.Extensive experiments have demonstrated that GIST matches or outperforms the state-of-the-art baseline with only 0.29% of the storage and 25% of the computational time under the same selection budget.

Conventional self-attention mechanisms incur quadratic complexity, limiting their scalability on long sequences. We introduce FFTNet, an adaptive spectral filtering framework that leverages the Fast Fourier Transform (FFT) to achieve global token mixing in O(nlog n) time. By transforming inputs into the frequency domain, FFTNet exploits the orthogonality and energy preservation guaranteed by Parseval's theorem to capture long-range dependencies efficiently. A learnable spectral filter and modReLU activation dynamically emphasize salient frequency components, providing a rigorous and adaptive alternative to traditional self-attention. Experiments on the Long Range Arena and ImageNet benchmarks validate our theoretical insights and demonstrate superior performance over fixed Fourier and standard attention models.

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

Iterative reference-conditioned image editing can introduce grid-like and granular textures, commonly described as digital ripple. We present Mi-Ripple, a diagnosis-guided restoration workflow that suppresses this digital ripple while protecting image structure. Mi-Ripple separates periodic lattice artifacts from content-entangled granular texture, then combines selective spectral notching, structure-aware smoothing, and cleaned-reference regeneration. This separation enables low-distortion filtering when artifacts are spectrally isolated and visual reconstruction when filtering would erase legitimate detail. Across fourteen notch-only executions, whole-image residual standard deviation is 0.08--0.44 in CIELAB lightness units. In a paired regeneration example, reference cleaning reduces output debris density by 45\%. Mi-Ripple links measurable artifact reduction to visibly cleaner generated images, rather than optimizing a spectral score alone.

Instruction tuning aligns large language models, including multimodal ones, with diverse user intents, but scaling to heterogeneous mixtures is hindered by gradient interference and bandwidth-heavy synchronization. We ask whether these two bottlenecks can be addressed jointly by training parts of the mixture independently and reconciling them once in parameter space. We develop a local quadratic theory inside a shared flat basin that yields three results: weight merging produces a curvature-weighted variance reduction; PCA-aligned conflict splitting maximizes this gain along high-curvature directions; and merging additionally acts as spectral filtering with implicit norm regularization. These results directly motivate MERIT, a decentralized merge-ready instruction-tuning pipeline that estimates dataset-level gradient conflicts, partitions the mixture along the top PCA conflict axes, fine-tunes each partition independently with no inter-partition communication, and merges once via token-weighted averaging. On Qwen2.5-VL-3B with 136 Vision-FLAN tasks, MERIT improves the 8-benchmark average from 54.3 (joint training) to 57.0. The same recipe scales to a 7B model on a 1.6M-example, 176-source mixture -- matching or exceeding centralized joint training with minimal cost overhead -- and transfers to text-only FLAN. Our code is available at https://github.com/naver-ai/merit.

Iterative self-training (self-distillation) repeatedly refits a model on pseudo-labels generated by its own predictions. We study this procedure in overparameterized linear regression: an initial estimator is trained on noisy labels, and each subsequent iterate is trained on fresh covariates with noiseless pseudo-labels from the previous model. In the high-dimensional regime, we derive deterministic-equivalent recursions for the prediction risk and effective noise across iterations, and prove that the empirical quantities concentrate sharply around these limits. The recursion separates two competing forces: a systematic component that grows with iteration due to progressive signal forgetting, and a stochastic component that decays due to denoising via repeated data-dependent projections. Their interaction yields a U-shaped test-risk curve and an optimal early-stopping time. In spiked covariance models, iteration further acts as an iteration-dependent spectral filter that preserves strong eigendirections while suppressing weaker ones, inducing an implicit form of soft feature selection distinct from ridge regression. Finally, we propose an iterated generalized cross-validation criterion and prove its uniform consistency for estimating the risk along the self-training trajectory, enabling fully data-driven selection of the stopping time and regularization. Experiments on synthetic covariances validate the theory and illustrate the predicted denoising-forgetting trade-off.

Graph neural networks are commonly described through family-specific equations whose notation obscures shared computations and structural differences. We introduce a common layer equation that represents covered architectures through seven components: an update domain, channel set, propagation bank, per-channel message maps, channel-fusion operator, ego/residual map, and update map. The central factorization separates where information moves, encoded by the propagation bank, from what moves, encoded by the message maps. Function-valued fillings extend the same equation across local message passing, attention, spectral filtering, global communication, relation-specific channels, higher-order domains, and geometric messages. We make this unification explicit and checkable through worked reductions of canonical layers and component assignments spanning seven nonexclusive architectural families. A fixed slot discipline assigns operations by computational role and defines the framework's coverage boundary. The decomposition also yields component-level theoretical insights: under endpoint-local messages and node-local updates, operator support bounds one-layer dependencies, and one-layer global mixing requires a full effective operator row under the stated hypotheses. The resulting framework organizes more than 200 architectures in a common design space, enables component-wise comparison and generation of structurally consistent architectures, and connects propagation choices to oversmoothing, oversquashing, heterophily, and expressivity. It further exposes the empirical inverse problem of mapping measurable graph and task properties to validated component choices.

Recently, photonic transformer accelerators (PTAs) have successfully achieved significant speedup and energy efficiency improvements over electronic accelerators for expediting Transformer inference. However, state-of-the-art rely on expensive multi-wavelength light generation and large dot-product units due to active phase-shifter components, thus making their approach inefficient and impractical. To address this, we propose MDTransformer, a novel hardware-software co-design of PTA based on mode-division optical dataflow and operations. Specifically, MDTransformer performs complex matrix operations using spatial-mode interference, that leverages the inverse-designed multi-mode couplers, crossings, and Mach-Zehnder IQ modulators into a compact mode-division photonic tensor core (MPTC), capable of executing matrix multiplications in the optical domain. Its each guided mode (i.e., TE0-TE3) acts as an independent computational lane, enabling four-fold parallelism-per-waveguide without spectral filtering or free-spectral-range limitations. Moreover, its coherent detection and IQ modulation jointly encode amplitude and phase, realizing complex-valued arithmetic for full-range operations in transformers. MDTransformer offers analog multiplication with sub-4-bit effective precision and inter-modal crosstalk below -30 dB. Its inverse-designed approach also offers scalable and full compatibility with single-laser continuous-wave operation at 1550 nm. Experimental results show that MDTransformer achieves 40.4% area reduction, 63.6% power saving, 40.6% energy saving, and comparable latency over the state-of-the-art PTA across different workloads (i.e., DeiT-Tiny/Small/Base and BERT-Base/Large). These results show that MDTransformer offers a practical solution for high-performance and energy-efficient transformer-based systems.

Real-world recommendation platforms routinely collect explicit negative feedback such as 1-star reviews, hate-button clicks, distrust between users, and very-low watch-ratio videos. Learned sign-aware recommenders exploit this signal for clear accuracy gains, but only at the cost of gradient-based training. In parallel, a line of training-free spectral collaborative filtering methods matches or beats learned graph recommenders at a fraction of the cost, yet operates on positive interactions alone. We bridge these two lines with DualSpectralCF, a training-free framework of two components that attach to any spectral backbone of the form mathbf{r}_u = F(M) r_u: a signed input signal r_u^{pm} that encodes the user's explicit dislikes, and a signed item-item operator M^{pm} that blends like-together and dislike-together similarity. The framework is backbone-agnostic and adds just two scalar hyperparameters. We instantiate DualSpectralCF on ChebyCF, GF-CF, and Turbo-CF, and evaluate on five sign-aware benchmarks: every instance matches or beats its unsigned backbone on all 5 datasets, with Recall@20 lifts up to +32.6% with backbone-specific (γ, κ) tuning and +1.9% to +16.0% for DualSpectralCF-Cheby at the fixed default (γ= -0.5, κ= 0.1), and the family runs 7.7 to 155.3times faster than SIGformer while reaching 70.7% to 90.7% of its accuracy. Sign-awareness helps most for cold-start users, with up to +29.2% Recall@20 on Epinions users with 1 to 5 training items.

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.

Fine-tuning Large Language Models with untrusted data exposes models to backdoor attacks, where poisoned samples cause targeted misbehavior. Existing sample-filtering defenses rely on clustering, which requires sufficient data and can fail at extreme poison ratios. We propose GradSentry ({Grad}ient {Sentry}), a backdoor sample filtering method based on the spectral entropy of per-sample gradients. Our key finding is that poisoned samples produce gradients with higher spectral entropy compared to clean samples. GradSentry captures output-altering backdoor signatures using per-sample gradient spectra, avoiding pairwise sample comparisons and clustering during feature construction. Importantly, our method is training-agnostic: it works for both parameter-efficient fine-tuning methods like LoRA and full-parameter tuning, as the gradient analysis operates independently of which parameters are being updated during training. GradSentry requires no clustering, operates effectively across all poison ratios (1%--90%), and introduces minimal computational overhead (20-50ms per sample for 7B model). Evaluation on four QA datasets and four attack types demonstrates the effectiveness of spectral entropy for backdoor detection. Code is available at https://github.com/dongdongzhaoUP/GradSentry.

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

Vision-Language Models (VLMs) inherit adversarial vulnerabilities of Large Language Models (LLMs), which are further exacerbated by their multimodal nature. Existing defenses, including adversarial training, input transformations, and heuristic detection, are computationally expensive, architecture-dependent, and fragile against adaptive attacks. We introduce EigenShield, an inference-time defense leveraging Random Matrix Theory to quantify adversarial disruptions in high-dimensional VLM representations. Unlike prior methods that rely on empirical heuristics, EigenShield employs the spiked covariance model to detect structured spectral deviations. Using a Robustness-based Nonconformity Score (RbNS) and quantile-based thresholding, it separates causal eigenvectors, which encode semantic information, from correlational eigenvectors that are susceptible to adversarial artifacts. By projecting embeddings onto the causal subspace, EigenShield filters adversarial noise without modifying model parameters or requiring adversarial training. This architecture-independent, attack-agnostic approach significantly reduces the attack success rate, establishing spectral analysis as a principled alternative to conventional defenses. Our results demonstrate that EigenShield consistently outperforms all existing defenses, including adversarial training, UNIGUARD, and CIDER.

Semantic segmentation of remote sensing imagery demands precise spatial boundaries and robust intra-class consistency, challenging conventional hierarchical models. To address limitations arising from spatial domain feature fusion and insufficient receptive fields, this paper introduces SAIP-Net, a novel frequency-aware segmentation framework that leverages Spectral Adaptive Information Propagation. SAIP-Net employs adaptive frequency filtering and multi-scale receptive field enhancement to effectively suppress intra-class feature inconsistencies and sharpen boundary lines. Comprehensive experiments demonstrate significant performance improvements over state-of-the-art methods, highlighting the effectiveness of spectral-adaptive strategies combined with expanded receptive fields for remote sensing image segmentation.

Neural vocoder using denoising diffusion probabilistic model (DDPM) has been improved by adaptation of the diffusion noise distribution to given acoustic features. In this study, we propose SpecGrad that adapts the diffusion noise so that its time-varying spectral envelope becomes close to the conditioning log-mel spectrogram. This adaptation by time-varying filtering improves the sound quality especially in the high-frequency bands. It is processed in the time-frequency domain to keep the computational cost almost the same as the conventional DDPM-based neural vocoders. Experimental results showed that SpecGrad generates higher-fidelity speech waveform than conventional DDPM-based neural vocoders in both analysis-synthesis and speech enhancement scenarios. Audio demos are available at wavegrad.github.io/specgrad/.

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 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/}.

Complex-valued processing has brought deep learning-based speech enhancement and signal extraction to a new level. Typically, the process is based on a time-frequency (TF) mask which is applied to a noisy spectrogram, while complex masks (CM) are usually preferred over real-valued masks due to their ability to modify the phase. Recent work proposed to use a complex filter instead of a point-wise multiplication with a mask. This allows to incorporate information from previous and future time steps exploiting local correlations within each frequency band. In this work, we propose DeepFilterNet, a two stage speech enhancement framework utilizing deep filtering. First, we enhance the spectral envelope using ERB-scaled gains modeling the human frequency perception. The second stage employs deep filtering to enhance the periodic components of speech. Additionally to taking advantage of perceptual properties of speech, we enforce network sparsity via separable convolutions and extensive grouping in linear and recurrent layers to design a low complexity architecture. We further show that our two stage deep filtering approach outperforms complex masks over a variety of frequency resolutions and latencies and demonstrate convincing performance compared to other state-of-the-art models.

We study spectral approximations of the dynamic programming semigroup for finite-horizon optimal control on a connected compact Lie group G, and of the associated first-order Hamilton-Jacobi-Bellman equation. The Bellman operator is monotone and non-expansive in the supremum norm, while the Peter-Weyl decomposition of L^{2}(G), on which every Fourier method on G rests, is orthogonal, and the mismatch is quantitative. The natural sup-norm error recursion of the Galerkin iteration is amplified at every step by the Lebesgue constant of the spectral projection, which grows logarithmically on S^{1} and polynomially on compact Lie groups of rank one, including SO(3), and in computation the iteration violates elementary bounds within a few steps. We restore the dynamic programming structure at the discrete level by replacing the orthogonal projection with spectral filters of Markov type. An auxiliary heat-kernel/vanishing-viscosity scheme yields qualitative sup-norm convergence for Lipschitz data. The main result is a Fejér-type filter on G, finite-rank, positivity preserving and non-expansive, together with a convergence theorem at the rate O(sqrtδ+ε+1/(δN^2)) for Lipschitz data, where δ is the time step, N the spectral resolution and ε the viscosity. The viscosity may be zero, and the coupling δ=N^{-1} then gives the rate N^{-1/2}. The proof interprets the filter as a small random perturbation of the controlled dynamics, requires neither a priori regularity of the value function nor a consistency argument in the viscosity sense for the filtering step, and extends to a fully discrete realization based on positive cubature, with exact Wigner transport on SO(3). Numerical experiments confirm the predicted rates and filter bias and quantify the frame dependence of two chart-based baselines.

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.

This paper presents a unified AI framework for high-accuracy audio anomaly detection by integrating advanced noise reduction, feature extraction, and machine learning modeling techniques. The approach combines spectral subtraction and adaptive filtering to enhance audio quality, followed by feature extraction using traditional methods like MFCCs and deep embeddings from pre-trained models such as OpenL3. The modeling pipeline incorporates classical models (SVM, Random Forest), deep learning architectures (CNNs), and ensemble methods to boost robustness and accuracy. Evaluated on benchmark datasets including TORGO and LibriSpeech, the proposed framework demonstrates superior performance in precision, recall, and classification of slurred vs. normal speech. This work addresses challenges in noisy environments and real-time applications and provides a scalable solution for audio-based anomaly detection.

Spectral graph neural networks (GNNs) are highly effective in modeling graph signals, with their success in recommendation often attributed to low-pass filtering. However, recent studies highlight the importance of high-frequency signals. The role of low-frequency and high-frequency graph signals in recommendation remains unclear. This paper aims to bridge this gap by investigating the influence of graph signals on recommendation performance. We theoretically prove that the effects of low-frequency and high-frequency graph signals are equivalent in recommendation tasks, as both contribute by smoothing the similarities between user-item pairs. To leverage this insight, we propose a frequency signal scaler, a plug-and-play module that adjusts the graph signal filter function to fine-tune the smoothness between user-item pairs, making it compatible with any GNN model. Additionally, we identify and prove that graph embedding-based methods cannot fully capture the characteristics of graph signals. To address this limitation, a space flip method is introduced to restore the expressive power of graph embeddings. Remarkably, we demonstrate that either low-frequency or high-frequency graph signals alone are sufficient for effective recommendations. Extensive experiments on four public datasets validate the effectiveness of our proposed methods. Code is avaliable at https://github.com/mojosey/SimGCF.

Large Audio-Language Models (LALMs) have set new benchmarks in speech processing, yet their deployment is hindered by the memory footprint of the Key-Value (KV) cache during long-context inference. While general KV cache compression techniques excel in LLMs, they often fail in the audio domain by overlooking the intrinsic temporal continuity of acoustic signals. To bridge this gap, we propose AudioKV, a novel framework that robustly prioritizes audio-critical attention heads through a hardware-friendly semantic-acoustic alignment mechanism. Specifically, we identify these modality-specialized heads by analyzing attention scores in ASR tasks and dynamically allocate KV cache budgets preferentially to them. Furthermore, we introduce Spectral Score Smoothing (SSS), an FFT-based global filtering strategy designed to suppress high-frequency noise and recover smooth global trends from importance scores, ensuring more balanced token selection with unprecedented precision. Extensive evaluations across multiple LALMs, including Qwen and Gemma series, demonstrate that AudioKV significantly outperforms baselines while enhancing computational efficiency. Notably, at a 40% compression ratio, AudioKV maintains near-full accuracy on Qwen3-Omni-30B with only a 0.45% drop, whereas traditional methods suffer from catastrophic performance degradation and repetition. Our code will be released after acceptance.

Optical resonances in nanostructures enable strong enhancement of nonlinear processes at the nanoscale, such as second-harmonic generation (SHG), with high-Q modes providing intensified light--matter interactions and sharp spectral selectivity for applications in filtering, sensing, and nonlinear spectroscopy. Thanks to the recent advances in thin-film lithium niobate (TFLN) technology, these key features can be now translated to lithium niobate for realizing novel nanoscale nonlinear optical platforms. Here, we demonstrate a large-area metasurface, realized by scalable nanoimprint lithography, comprising a slanted titanium dioxide (TiO_2) nanograting on etchless TFLN for efficient narrowband SHG. This is enabled by the optimal coupling of quasi-bound state in the continuum (q-BIC) modes with a narrowband pulsed laser pump. The demonstrated normalized SHG efficiency is 0.15%,cm^2/GW, which is among the largest reported for LN metasurfaces. The low pump peak intensity (3.64~kW/cm^2) employed, which enables SHG even by continuous-wave pumping, allows envisioning integrated and portable photonic applications. SHG wavelength tuning from 870 to 920~nm with stable output power as well as polarization control is also achieved by off-normal pump illumination. This versatile platform opens new opportunities for sensing, THz generation and detection, and ultrafast electro-optic modulation of nonlinear optical signals.

Diffusion models have been shown to implicitly generate visual content autoregressively in the frequency domain, where low-frequency components are generated earlier in the denoising process while high-frequency details emerge only in later timesteps. This structure offers a natural opportunity for efficient generation, as high-resolution computation on noise-dominated frequencies is largely redundant. We propose Spectral Progressive Diffusion, a general framework that progressively grows resolution along the denoising trajectory of pretrained diffusion models. To this end, we develop a spectral noise expansion mechanism and derive an optimal resolution schedule from the model's power spectrum. Our framework supports training-free acceleration and a novel fine-tuning recipe that further improves efficiency and quality. We demonstrate significant speedups on state-of-the-art pretrained image and video generation models while preserving visual quality.

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from complex analysis and spectral theory -- extend spectral convolutions to directed graphs. We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed theory, we conduct experiments in real world settings, showcasing that directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many datasets and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.

Hyperspectral image denoising is unique for the highly similar and correlated spectral information that should be properly considered. However, existing methods show limitations in exploring the spectral correlations across different bands and feature interactions within each band. Besides, the low- and high-level features usually exhibit different importance for different spatial-spectral regions, which is not fully explored for current algorithms as well. In this paper, we present a Mixed Attention Network (MAN) that simultaneously considers the inter- and intra-spectral correlations as well as the interactions between low- and high-level spatial-spectral meaningful features. Specifically, we introduce a multi-head recurrent spectral attention that efficiently integrates the inter-spectral features across all the spectral bands. These features are further enhanced with a progressive spectral channel attention by exploring the intra-spectral relationships. Moreover, we propose an attentive skip-connection that adaptively controls the proportion of the low- and high-level spatial-spectral features from the encoder and decoder to better enhance the aggregated features. Extensive experiments show that our MAN outperforms existing state-of-the-art methods on simulated and real noise settings while maintaining a low cost of parameters and running time.

Pixel-space diffusion models are trained on full-bandwidth noisy images, yet the useful signal available to the denoiser is strongly frequency dependent. Under rectified-flow diffusion and natural-image power-law spectra, the per-band data-to-noise contour k^{*}(t) = (1-t)^{-2/α} separates a signal-bearing low-frequency region from a noise-dominated high-frequency region at each time t. We show that this implicit coarse-to-fine structure is not merely descriptive: it induces a capacity-allocation problem. A standard pixel-space denoiser must discover the moving bandwidth boundary internally and can spend computation on frequency-time regions where the optimal prediction collapses to deterministic baselines rather than data-distribution modeling. To make this boundary explicit, we introduce Spectral Forcing, a parameter-free, time-conditional 2D-DCT low-pass operator applied to the noisy input before the patch embedder. Its cutoff expands monotonically with the diffusion time and becomes the identity at the data endpoint. Through controlled synthetic experiments, we identify the regime in which the operator is beneficial: coarse patch tokenization and data whose high-frequency content is predominantly noise rather than essential signal. On ImageNet-256 with JiT-700M/32, Spectral Forcing consistently improves both FID and Inception Score across different training epochs, demonstrating robust gains throughout training; at finer tokenization, the spectral forcing is still competitive. We further insert the unchanged operator into SenseNova-U1, a unified text-to-image model, where it improves DPG-Bench and GenEval, showing that the input-side spectral prior transfers beyond class-conditional generation. These results suggest a route to capacity-efficient pixel-space diffusion by showing the signal and hiding the noise.

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

Satellite remote sensing missions have gained popularity over the past fifteen years due to their ability to cover large swaths of land at regular intervals, making them ideal for monitoring environmental trends. The FINCH mission, a 3U+ CubeSat equipped with a hyperspectral camera, aims to monitor crop residue cover in agricultural fields. Although hyperspectral imaging captures both spectral and spatial information, it is prone to various types of noise, including random noise, stripe noise, and dead pixels. Effective denoising of these images is crucial for downstream scientific tasks. Traditional methods, including hand-crafted techniques encoding strong priors, learned 2D image denoising methods applied across different hyperspectral bands, or diffusion generative models applied independently on bands, often struggle with varying noise strengths across spectral bands, leading to significant spectral distortion. This paper presents a novel approach to hyperspectral image denoising using latent diffusion models that integrate spatial and spectral information. We particularly do so by building a 3D diffusion model and presenting a 3-stage training approach on real and synthetically crafted datasets. The proposed method preserves image structure while reducing noise. Evaluations on both popular hyperspectral denoising datasets and synthetically crafted datasets for the FINCH mission demonstrate the effectiveness of this approach.

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.

Several recent studies advocate the use of spectral discriminators, which evaluate the Fourier spectra of images for generative modeling. However, the effectiveness of the spectral discriminators is not well interpreted yet. We tackle this issue by examining the spectral discriminators in the context of perceptual image super-resolution (i.e., GAN-based SR), as SR image quality is susceptible to spectral changes. Our analyses reveal that the spectral discriminator indeed performs better than the ordinary (a.k.a. spatial) discriminator in identifying the differences in the high-frequency range; however, the spatial discriminator holds an advantage in the low-frequency range. Thus, we suggest that the spectral and spatial discriminators shall be used simultaneously. Moreover, we improve the spectral discriminators by first calculating the patch-wise Fourier spectrum and then aggregating the spectra by Transformer. We verify the effectiveness of the proposed method twofold. On the one hand, thanks to the additional spectral discriminator, our obtained SR images have their spectra better aligned to those of the real images, which leads to a better PD tradeoff. On the other hand, our ensembled discriminator predicts the perceptual quality more accurately, as evidenced in the no-reference image quality assessment task.

As with any physical instrument, hyperspectral cameras induce different kinds of noise in the acquired data. Therefore, Hyperspectral denoising is a crucial step for analyzing hyperspectral images (HSIs). Conventional computational methods rarely use GPUs to improve efficiency and are not fully open-source. Alternatively, deep learning-based methods are often open-source and use GPUs, but their training and utilization for real-world applications remain non-trivial for many researchers. Consequently, we propose HyDe: the first open-source, GPU-accelerated Python-based, hyperspectral image denoising toolbox, which aims to provide a large set of methods with an easy-to-use environment. HyDe includes a variety of methods ranging from low-rank wavelet-based methods to deep neural network (DNN) models. HyDe's interface dramatically improves the interoperability of these methods and the performance of the underlying functions. In fact, these methods maintain similar HSI denoising performance to their original implementations while consuming nearly ten times less energy. Furthermore, we present a method for training DNNs for denoising HSIs which are not spatially related to the training dataset, i.e., training on ground-level HSIs for denoising HSIs with other perspectives including airborne, drone-borne, and space-borne. To utilize the trained DNNs, we show a sliding window method to effectively denoise HSIs which would otherwise require more than 40 GB. The package can be found at: https://github.com/Helmholtz-AI-Energy/HyDe.

In this paper, we present a Hybrid Spectral Denoising Transformer (HSDT) for hyperspectral image denoising. Challenges in adapting transformer for HSI arise from the capabilities to tackle existing limitations of CNN-based methods in capturing the global and local spatial-spectral correlations while maintaining efficiency and flexibility. To address these issues, we introduce a hybrid approach that combines the advantages of both models with a Spatial-Spectral Separable Convolution (S3Conv), Guided Spectral Self-Attention (GSSA), and Self-Modulated Feed-Forward Network (SM-FFN). Our S3Conv works as a lightweight alternative to 3D convolution, which extracts more spatial-spectral correlated features while keeping the flexibility to tackle HSIs with an arbitrary number of bands. These features are then adaptively processed by GSSA which per-forms 3D self-attention across the spectral bands, guided by a set of learnable queries that encode the spectral signatures. This not only enriches our model with powerful capabilities for identifying global spectral correlations but also maintains linear complexity. Moreover, our SM-FFN proposes the self-modulation that intensifies the activations of more informative regions, which further strengthens the aggregated features. Extensive experiments are conducted on various datasets under both simulated and real-world noise, and it shows that our HSDT significantly outperforms the existing state-of-the-art methods while maintaining low computational overhead. Code is at https: //github.com/Zeqiang-Lai/HSDT.

Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising, representation learning, clustering, and latent variable modeling. In this work, we focus primarily on spectral estimators for high-dimensional factor models, where leading singular vectors of the data matrix are used to estimate latent structure and covariance parameters. In many modern applications, however, data are collected across related but heterogeneous tasks, studies, domains, or populations. Applying such estimators separately to each task can lead to unstable estimates when sample sizes are limited relative to dimension, while completely pooling the data can obscure meaningful task-specific structure. We introduce Hierarchical Spectral Shrinkage (HSS), a scalable empirical-Bayes framework for partially pooling task-specific spectral estimators. The method regularizes the leading spectral directions of each task toward a data-adaptivelylearned common basis, while allowing the amount of shrinkage to vary across tasks and spectral components. The proposed estimator arises as the posterior mean in a surrogate Bayesian regression formulation of the empirical singular vectors. For factor models, HSS yields partially pooled estimators of the group-specific loading spaces and covariance matrices and can be combined with different spectral estimators by replacing their empirical singular vectors with hierarchically regularized counterparts. More broadly, the same construction provides a mechanism for extending spectral estimators to collections of related but heterogeneous datasets. We demonstrate substantial improvements in estimation accuracy and out-of-sample performance over separate, fully pooled, and shared-subspace approaches in synthetic experiments and multi-study gene-expression data.

Spectral rendering reproduces the wavelength-dependent appearance that RGB rendering cannot: metamerism, colour shifts under spectrally rich illumination, coloured glass, metallic reflection and subsurface scattering. It requires a spectrally aware renderer, but the rendering ecosystem is predominantly RGB: game engines, cloud render farms, GPU rasterisers and most offline renderers consume RGB alone, with no access to the internal wavelength propagation that spectral rendering relies on. We introduce learned spectral codes, a compact linear representation that enables general spectral rendering through unmodified RGB pipelines. A trained encoder compresses any visible-range spectral quantity into a small latent vector; the codes are packed as RGB triplets and processed by an off-the-shelf RGB renderer. The codec preserves the arithmetic of light transport, exactly for scaling and addition and approximately for element-wise products, so two standard RGB passes suffice to produce results closely matching a full spectral rendering. The same codec handles reflectance, illumination, coloured glass, conductors, and participating media: one pipeline across material classes, with no per-material modification to the renderer. Where spectral asset data is unavailable, lightweight neural upsamplers bridge legacy RGB inputs to the latent space. Across diverse materials and illumination, the method yields substantial quality improvements on the cases where RGB rendering fails most visibly, at rendering cost comparable to efficient spectral-sampling techniques and with no changes to the renderer.

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

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.

While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on efficiently approximating the whole spectrum of the graph Laplacian constructed from the data. This is in contrast to various subsampling and quantization methods proposed in the past, which may fail in preserving the graph spectra. However, the impact of the approximation of the spectrum on the final generalization error is either unknown, or requires strong assumptions on the data. In this paper, we introduce Sparse-HFS, an efficient edge-sparsification algorithm for SSL. By constructing an edge-sparse and spectrally similar graph, we are able to leverage the approximation guarantees of spectral sparsification methods to bound the generalization error of Sparse-HFS. As a result, we obtain a theoretically-grounded approximation scheme for graph-based SSL that also empirically matches the performance of known large-scale methods.

Diffusion models typically suffer from error accumulation during iterative sampling, commonly referred to as exposure bias. We reveal systematic frequency-dependent discrepancies between training and inference, which can be interpreted as frequency-dependent SNR error. Crucially, the direction of this mismatch varies across models and timesteps, indicating that fixed correction rules do not generalize. We propose Spectral Alignment (SPA), a lightweight, guidance-based method that calibrates the power spectrum of intermediate predictions to a pre-computed prior. Our approach consists of two stages: (1) offline fitting of a parametric spectrum model from training data, and (2) inference-time guidance via efficient FFT-based gradient computation. SPA introduces minimal computational overhead (3-4\%) and is complementary to Classifier-Free Guidance (CFG). We demonstrate consistent improvements across diverse architectures, from pixel-space models (DDPM, ADM) to latent diffusion models (SD2.0, SDXL) and flow-matching models (SD3.5, FLUX). Our implementation is available at https://github.com/SonyResearch/SPA.

Adverse weather conditions such as rain, haze, and snow significantly degrade image quality, posing challenges for both human perception and physical AI. Existing restoration methods require large computational budgets, struggling to process high-resolution images and handle different degradations. In this paper, we present Frequency Reconstruction via Spectral Harmonization, a novel lightweight all-in-one restoration method that explicitly decomposes feature representations into high- and low-frequency components at each scale of a hierarchical encoder-decoder architecture. By combining spectral decomposition with spatial processing through Fourier-based skip connections, FReSH-IR captures complementary frequency information without sacrificing spatial detail. Our approach achieves similar restoration quality with 80% fewer parameters and operations than transformer-based models. Extensive experiments demonstrate that our method offers a great efficiency-performance trade-off, highlighting its practical applications in constrained-resource systems.

Recent works have established that AI models introduce spectral artifacts into generated images and propose approaches for learning to capture them using labeled data. However, the significant differences in such artifacts among different generative models hinder these approaches from generalizing to generators not seen during training. In this work, we build upon the key idea that the spectral distribution of real images constitutes both an invariant and highly discriminative pattern for AI-generated image detection. To model this under a self-supervised setup, we employ masked spectral learning using the pretext task of frequency reconstruction. Since generated images constitute out-of-distribution samples for this model, we propose spectral reconstruction similarity to capture this divergence. Moreover, we introduce spectral context attention, which enables our approach to efficiently capture subtle spectral inconsistencies in images of any resolution. Our spectral AI-generated image detection approach (SPAI) achieves a 5.5% absolute improvement in AUC over the previous state-of-the-art across 13 recent generative approaches, while exhibiting robustness against common online perturbations. Code is available on https://mever-team.github.io/spai.

While spectral-based optimizers like Muon operate directly on the spectrum of updates, standard adaptive methods such as AdamW do not account for the global spectral structure of weights and gradients, leaving them vulnerable to two empirical issues in large language model (LLM) training: (i) the optimizer updates can have large spectral norms, potentially destabilizing training and degrading generalization; (ii) stochastic gradient noise can exhibit sparse spectral spikes, with a few dominant singular values much larger than the rest. We propose SPECTRA, a general framework addressing these by (i) post-spectral clipping of updates to enforce spectral-norm constraints; (ii) optional pre-spectral clipping of gradients to suppress spectral noise spikes. We prove that post-clipping constitutes a Composite Frank-Wolfe method with spectral-norm constraints and weight regularization, recovering Frobenius and ell_{infty}-norm regularization with SGD-based and sign-based methods. We further analyze how pre-clipping mitigates sparse spectral spikes. We propose efficient soft spectral clipping via Newton-Schulz iterations, avoiding expensive SVD. Experiments on LLM pretraining show SPECTRA uniformly improves validation loss for various optimizers, including AdamW, Signum, and AdEMAMix, with the best-performing variants achieving state-of-the-art results. Models trained with SPECTRA exhibit smaller weight norms, confirming the link between spectral clipping and regularization.

Whitening loss offers a theoretical guarantee against feature collapse in self-supervised learning (SSL) with joint embedding architectures. Typically, it involves a hard whitening approach, transforming the embedding and applying loss to the whitened output. In this work, we introduce Spectral Transformation (ST), a framework to modulate the spectrum of embedding and to seek for functions beyond whitening that can avoid dimensional collapse. We show that whitening is a special instance of ST by definition, and our empirical investigations unveil other ST instances capable of preventing collapse. Additionally, we propose a novel ST instance named IterNorm with trace loss (INTL). Theoretical analysis confirms INTL's efficacy in preventing collapse and modulating the spectrum of embedding toward equal-eigenvalues during optimization. Our experiments on ImageNet classification and COCO object detection demonstrate INTL's potential in learning superior representations. The code is available at https://github.com/winci-ai/INTL.

Molecular structure elucidation from spectra is a foundational problem in chemistry, with profound implications for compound identification, synthesis, and drug development. Traditional methods rely heavily on expert interpretation and lack scalability. Pioneering machine learning methods have introduced retrieval-based strategies, but their reliance on finite libraries limits generalization to novel molecules. Generative models offer a promising alternative, yet most adopt autoregressive SMILES-based architectures that overlook 3D geometry and struggle to integrate diverse spectral modalities. In this work, we present DiffSpectra, a generative framework that directly infers both 2D and 3D molecular structures from multi-modal spectral data using diffusion models. DiffSpectra formulates structure elucidation as a conditional generation process. Its denoising network is parameterized by Diffusion Molecule Transformer, an SE(3)-equivariant architecture that integrates topological and geometric information. Conditioning is provided by SpecFormer, a transformer-based spectral encoder that captures intra- and inter-spectral dependencies from multi-modal spectra. Extensive experiments demonstrate that DiffSpectra achieves high accuracy in structure elucidation, recovering exact structures with 16.01% top-1 accuracy and 96.86% top-20 accuracy through sampling. The model benefits significantly from 3D geometric modeling, SpecFormer pre-training, and multi-modal conditioning. These results highlight the effectiveness of spectrum-conditioned diffusion modeling in addressing the challenge of molecular structure elucidation. To our knowledge, DiffSpectra is the first framework to unify multi-modal spectral reasoning and joint 2D/3D generative modeling for de novo molecular structure elucidation.

Recent developments in Parameter-Efficient Fine-Tuning (PEFT) methods for pretrained deep neural networks have captured widespread interest. In this work, we study the enhancement of current PEFT methods by incorporating the spectral information of pretrained weight matrices into the fine-tuning procedure. We investigate two spectral adaptation mechanisms, namely additive tuning and orthogonal rotation of the top singular vectors, both are done via first carrying out Singular Value Decomposition (SVD) of pretrained weights and then fine-tuning the top spectral space. We provide a theoretical analysis of spectral fine-tuning and show that our approach improves the rank capacity of low-rank adapters given a fixed trainable parameter budget. We show through extensive experiments that the proposed fine-tuning model enables better parameter efficiency and tuning performance as well as benefits multi-adapter fusion. The code will be open-sourced for reproducibility.

Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this work, we study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time: frequency-domain models (FDMs). Existing FDMs are based on complex-valued transforms i.e. Fourier Transforms (FT), and layers that perform computation on the spectrum and input data separately. This design introduces considerable computational overhead: for each layer, a forward and inverse FT. Instead, this work introduces a blueprint for frequency domain learning through a single transform: transform once (T1). To enable efficient, direct learning in the frequency domain we derive a variance-preserving weight initialization scheme and investigate methods for frequency selection in reduced-order FDMs. Our results noticeably streamline the design process of FDMs, pruning redundant transforms, and leading to speedups of 3x to 10x that increase with data resolution and model size. We perform extensive experiments on learning the solution operator of spatio-temporal dynamics, including incompressible Navier-Stokes, turbulent flows around airfoils and high-resolution video of smoke. T1 models improve on the test performance of FDMs while requiring significantly less computation (5 hours instead of 32 for our large-scale experiment), with over 20% reduction in average predictive error across tasks.

Foundation models have triggered a paradigm shift in computer vision and are increasingly being adopted in remote sensing, particularly for multispectral imagery. Yet, their potential in hyperspectral imaging (HSI) remains untapped due to the absence of comprehensive and globally representative hyperspectral datasets. To close this gap, we introduce SpectralEarth, a large-scale multi-temporal dataset designed to pretrain hyperspectral foundation models leveraging data from the Environmental Mapping and Analysis Program (EnMAP). SpectralEarth comprises 538,974 image patches covering 415,153 unique locations from more than 11,636 globally distributed EnMAP scenes spanning two years of archive. Additionally, 17.5% of these locations include multiple timestamps, enabling multi-temporal HSI analysis. Utilizing state-of-the-art self-supervised learning (SSL) algorithms, we pretrain a series of foundation models on SpectralEarth. We integrate a spectral adapter into classical vision backbones to accommodate the unique characteristics of HSI. In tandem, we construct four downstream datasets for land-cover and crop-type mapping, providing benchmarks for model evaluation. Experimental results support the versatility of our models, showcasing their generalizability across different tasks and sensors. We also highlight computational efficiency during model fine-tuning. The dataset, models, and source code will be made publicly available.

Despite the recent visually-pleasing results achieved, the massive computational cost has been a long-standing flaw for diffusion probabilistic models (DPMs), which, in turn, greatly limits their applications on resource-limited platforms. Prior methods towards efficient DPM, however, have largely focused on accelerating the testing yet overlooked their huge complexity and sizes. In this paper, we make a dedicated attempt to lighten DPM while striving to preserve its favourable performance. We start by training a small-sized latent diffusion model (LDM) from scratch, but observe a significant fidelity drop in the synthetic images. Through a thorough assessment, we find that DPM is intrinsically biased against high-frequency generation, and learns to recover different frequency components at different time-steps. These properties make compact networks unable to represent frequency dynamics with accurate high-frequency estimation. Towards this end, we introduce a customized design for slim DPM, which we term as Spectral Diffusion (SD), for light-weight image synthesis. SD incorporates wavelet gating in its architecture to enable frequency dynamic feature extraction at every reverse steps, and conducts spectrum-aware distillation to promote high-frequency recovery by inverse weighting the objective based on spectrum magni tudes. Experimental results demonstrate that, SD achieves 8-18x computational complexity reduction as compared to the latent diffusion models on a series of conditional and unconditional image generation tasks while retaining competitive image fidelity.

Diffusion models have achieved remarkable success in image synthesis, but the generated high-quality images raise concerns about potential malicious use. Existing detectors often struggle to capture discriminative clues across different models and settings, limiting their generalization to unseen diffusion models and robustness to various perturbations. To address this issue, we observe that diffusion-generated images exhibit progressively larger differences from natural real images across low- to high-frequency bands. Based on this insight, we propose a simple yet effective representation by enhancing the Frequency Forgery Clue (F^2C) across all frequency bands. Specifically, we introduce a frequency-selective function which serves as a weighted filter to the Fourier spectrum, suppressing less discriminative bands while enhancing more informative ones. This approach, grounded in a comprehensive analysis of frequency-based differences between natural real and diffusion-generated images, enables general detection of images from unseen diffusion models and provides robust resilience to various perturbations. Extensive experiments on various diffusion-generated image datasets demonstrate that our method outperforms state-of-the-art detectors with superior generalization and robustness.

Despite noise suppression being a mature area in signal processing, it remains highly dependent on fine tuning of estimator algorithms and parameters. In this paper, we demonstrate a hybrid DSP/deep learning approach to noise suppression. A deep neural network with four hidden layers is used to estimate ideal critical band gains, while a more traditional pitch filter attenuates noise between pitch harmonics. The approach achieves significantly higher quality than a traditional minimum mean squared error spectral estimator, while keeping the complexity low enough for real-time operation at 48 kHz on a low-power processor.

Teacher-Student Knowledge Transfer (KT) is ubiquitous in modern machine learning, ranging from classical model compression via Knowledge Distillation (KD) to the emergent phenomenon of Weak-to-Strong (W2S) generalization. While existing studies offer isolated insights, a unified theoretical framework explaining the efficacy of KT across these disparate regimes remains lacking. In this work, we establish a unified spectral analysis of SGD dynamics in high-dimensional linear regression, elucidating the efficiency of KT across seemingly disparate regimes. We characterize KT efficiency through two distinct mechanisms: Spectral Horizon Expansion in KD, which enables the capture of statistically inaccessible high-frequency signals, and Spectral Denoising in W2S, where the student acts as a filter for optimization noise. Our framework unifies these phenomena, revealing that the efficacy of transfer is governed by the interplay between implicit regularization and heterogeneous spectral learning speeds over the spectrum.

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.

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.

Diffusion models have become the dominant tool for high-fidelity image and video generation, yet are critically bottlenecked by their inference speed due to the numerous iterative passes of Diffusion Transformers. To reduce the exhaustive compute, recent works resort to the feature caching and reusing scheme that skips network evaluations at selected diffusion steps by using cached features in previous steps. However, their preliminary design solely relies on local approximation, causing errors to grow rapidly with large skips and leading to degraded sample quality at high speedups. In this work, we propose spectral diffusion feature forecaster (Spectrum), a training-free approach that enables global, long-range feature reuse with tightly controlled error. In particular, we view the latent features of the denoiser as functions over time and approximate them with Chebyshev polynomials. Specifically, we fit the coefficient for each basis via ridge regression, which is then leveraged to forecast features at multiple future diffusion steps. We theoretically reveal that our approach admits more favorable long-horizon behavior and yields an error bound that does not compound with the step size. Extensive experiments on various state-of-the-art image and video diffusion models consistently verify the superiority of our approach. Notably, we achieve up to 4.79times speedup on FLUX.1 and 4.67times speedup on Wan2.1-14B, while maintaining much higher sample quality compared with the baselines.

While implicit regularization facilitates benign overfitting in low-noise regimes, recent theoretical work predicts a sharp phase transition to harmful overfitting as the noise-to-signal ratio increases. We experimentally isolate the geometric mechanism of this transition: the Malignant Tail, a failure mode where networks functionally segregate signal and noise, reducing coherent semantic features into low-rank subspaces while pushing stochastic label noise into high-frequency orthogonal components, distinct from systematic or corruption-aligned noise. Through a Spectral Linear Probe of training dynamics, we demonstrate that Stochastic Gradient Descent (SGD) fails to suppress this noise, instead implicitly biasing it toward high-frequency orthogonal subspaces, effectively preserving signal-noise separability. We show that this geometric separation is distinct from simple variance reduction in untrained models. In trained networks, SGD actively segregates noise, allowing post-hoc Explicit Spectral Truncation (d << D) to surgically prune the noise-dominated subspace. This approach recovers the optimal generalization capability latent in the converged model. Unlike unstable temporal early stopping, Geometric Truncation provides a stable post-hoc intervention. Our findings suggest that under label noise, excess spectral capacity is not harmless redundancy but a latent structural liability that allows for noise memorization, necessitating explicit rank constraints to filter stochastic corruptions for robust generalization.

Modeling hyperspectral imagery (HSI) across different sensors presents a fundamental challenge due to variations in wavelength coverage, band sampling, and channel dimensionality. As a result, models trained under a fixed spectral configuration often fail to generalize to other sensors. Existing Vision Transformer (ViT) approaches either rely on implicit spectral modeling with fixed channel assumptions or adopt explicit spatial-spectral attention with prohibitive computational cost, leading to a fundamental trade-off between efficiency and expressiveness. In this work, we introduce Low-rank Efficient Spatial-Spectral ViT (LESSViT), a sensor-flexible architecture for cross-spectral generalization. LESSViT is built on LESS Attention, a structured low-rank factorization that models joint spatial-spectral interactions through separable spatial and spectral components, reducing the complexity of full spatial-spectral attention from O(N^2 C^2) to O(rNC), where N is the number of spatial tokens, C is the number of spectral channels, and r is the rank of the low-rank approximation. We further incorporate channel-agnostic patch embedding and wavelength-aware positional encoding to support flexible spectral inputs. To enable efficient and robust pretraining, we introduce a hyperspectral masked autoencoder (HyperMAE) with decoupled spatial-spectral masking and hierarchical channel sampling. We evaluate LESSViT under a cross-spectral generalization setting that simulates cross-sensor variability. Experiments on the SpectralEarth benchmark demonstrate that LESSViT improves robustness under spectral shifts while remaining competitive in-distribution, and explicit and efficient spatial-spectral modeling is essential for scalable and generalizable hyperspectral representation learning.

Harmonic retrieval techniques are the foundation of radio channel sounding, estimation and modeling. This paper introduces a Deep Learning approach for two-dimensional spectral estimation from frequency and time samples of a radio channel transfer function. Our work can estimate two-dimensional parameters from a signal containing an unknown number of paths. In contrast to existing deep learning-based methods, the signal parameters are not estimated via classification but instead in a quasi-grid-free manner. This alleviates the bias, spectral leakage, and ghost targets that grid-based approaches inherently produce. The proposed architecture also reliably estimates the number of spectral components in the measurement. Hence, the architecture jointly solves the model order selection problem and the parameter estimation task. Additionally, we propose a multi-channel windowing of the data during preprocessing, increasing the resulting estimator's robustness. We verify the performance compared to existing harmonic retrieval methods and also show how it can be integrated into an existing maximum likelihood estimator for efficient initialization of a gradient-based iteration.

Despite the proven significance of hyperspectral images (HSIs) in performing various computer vision tasks, its potential is adversely affected by the low-resolution (LR) property in the spatial domain, resulting from multiple physical factors. Inspired by recent advancements in deep generative models, we propose an HSI Super-resolution (SR) approach with Conditional Diffusion Models (HSR-Diff) that merges a high-resolution (HR) multispectral image (MSI) with the corresponding LR-HSI. HSR-Diff generates an HR-HSI via repeated refinement, in which the HR-HSI is initialized with pure Gaussian noise and iteratively refined. At each iteration, the noise is removed with a Conditional Denoising Transformer (CDF ormer) that is trained on denoising at different noise levels, conditioned on the hierarchical feature maps of HR-MSI and LR-HSI. In addition, a progressive learning strategy is employed to exploit the global information of full-resolution images. Systematic experiments have been conducted on four public datasets, demonstrating that HSR-Diff outperforms state-of-the-art methods.

Linearization of attention using various kernel approximation and kernel learning techniques has shown promise. Past methods used a subset of combinations of component functions and weight matrices within the random feature paradigm. We identify the need for a systematic comparison of different combinations of weight matrices and component functions for attention learning in Transformer. Hence, we introduce Spectraformer, a unified framework for approximating and learning the kernel function in the attention mechanism of the Transformer. Our empirical results demonstrate, for the first time, that a random feature-based approach can achieve performance comparable to top-performing sparse and low-rank methods on the challenging Long Range Arena benchmark. Thus, we establish a new state-of-the-art for random feature-based efficient Transformers. The framework also produces many variants that offer different advantages in accuracy, training time, and memory consumption. Our code is available at: https://github.com/cruiseresearchgroup/spectraformer .

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.

We introduce a new online adaptive filtering method called supervised multi-step adaptive filters (SMS-AF). Our method uses neural networks to control or optimize linear multi-delay or multi-channel frequency-domain filters and can flexibly scale-up performance at the cost of increased compute -- a property rarely addressed in the AF literature, but critical for many applications. To do so, we extend recent work with a set of improvements including feature pruning, a supervised loss, and multiple optimization steps per time-frame. These improvements work in a cohesive manner to unlock scaling. Furthermore, we show how our method relates to Kalman filtering and meta-adaptive filtering, making it seamlessly applicable to a diverse set of AF tasks. We evaluate our method on acoustic echo cancellation (AEC) and multi-channel speech enhancement tasks and compare against several baselines on standard synthetic and real-world datasets. Results show our method performance scales with inference cost and model capacity, yields multi-dB performance gains for both tasks, and is real-time capable on a single CPU core.

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.

Recently, deep neural networks such as RNN, CNN and Transformer have been applied in the task of sequential recommendation, which aims to capture the dynamic preference characteristics from logged user behavior data for accurate recommendation. However, in online platforms, logged user behavior data is inevitable to contain noise, and deep recommendation models are easy to overfit on these logged data. To tackle this problem, we borrow the idea of filtering algorithms from signal processing that attenuates the noise in the frequency domain. In our empirical experiments, we find that filtering algorithms can substantially improve representative sequential recommendation models, and integrating simple filtering algorithms (eg Band-Stop Filter) with an all-MLP architecture can even outperform competitive Transformer-based models. Motivated by it, we propose FMLP-Rec, an all-MLP model with learnable filters for sequential recommendation task. The all-MLP architecture endows our model with lower time complexity, and the learnable filters can adaptively attenuate the noise information in the frequency domain. Extensive experiments conducted on eight real-world datasets demonstrate the superiority of our proposed method over competitive RNN, CNN, GNN and Transformer-based methods. Our code and data are publicly available at the link: blue{https://github.com/RUCAIBox/FMLP-Rec}.

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.

Multi-frame algorithms for single-channel speech enhancement are able to take advantage from short-time correlations within the speech signal. Deep Filtering (DF) was proposed to directly estimate a complex filter in frequency domain to take advantage of these correlations. In this work, we present a real-time speech enhancement demo using DeepFilterNet. DeepFilterNet's efficiency is enabled by exploiting domain knowledge of speech production and psychoacoustic perception. Our model is able to match state-of-the-art speech enhancement benchmarks while achieving a real-time-factor of 0.19 on a single threaded notebook CPU. The framework as well as pretrained weights have been published under an open source license.

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogues to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting, and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.

Hyperspectral image (HSI) restoration aims at recovering clean images from degraded observations and plays a vital role in downstream tasks. Existing model-based methods have limitations in accurately modeling the complex image characteristics with handcraft priors, and deep learning-based methods suffer from poor generalization ability. To alleviate these issues, this paper proposes an unsupervised HSI restoration framework with pre-trained diffusion model (HIR-Diff), which restores the clean HSIs from the product of two low-rank components, i.e., the reduced image and the coefficient matrix. Specifically, the reduced image, which has a low spectral dimension, lies in the image field and can be inferred from our improved diffusion model where a new guidance function with total variation (TV) prior is designed to ensure that the reduced image can be well sampled. The coefficient matrix can be effectively pre-estimated based on singular value decomposition (SVD) and rank-revealing QR (RRQR) factorization. Furthermore, a novel exponential noise schedule is proposed to accelerate the restoration process (about 5times acceleration for denoising) with little performance decrease. Extensive experimental results validate the superiority of our method in both performance and speed on a variety of HSI restoration tasks, including HSI denoising, noisy HSI super-resolution, and noisy HSI inpainting. The code is available at https://github.com/LiPang/HIRDiff.

Hyperspectral unmixing is one of the crucial steps for many hyperspectral applications. The problem of hyperspectral unmixing has proven to be a difficult task in unsupervised work settings where the endmembers and abundances are both unknown. What is more, this task becomes more challenging in the case that the spectral bands are degraded with noise. This paper presents a robust model for unsupervised hyperspectral unmixing. Specifically, our model is developed with the correntropy based metric where the non-negative constraints on both endmembers and abundances are imposed to keep physical significance. In addition, a sparsity prior is explicitly formulated to constrain the distribution of the abundances of each endmember. To solve our model, a half-quadratic optimization technique is developed to convert the original complex optimization problem into an iteratively re-weighted NMF with sparsity constraints. As a result, the optimization of our model can adaptively assign small weights to noisy bands and give more emphasis on noise-free bands. In addition, with sparsity constraints, our model can naturally generate sparse abundances. Experiments on synthetic and real data demonstrate the effectiveness of our model in comparison to the related state-of-the-art unmixing models.

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.

Hyperspectral image classification remains a challenging task due to the high dimensionality of spectral data, significant inter-band redundancy, and the limited availability of annotated samples. While recent transformer-based models have improved the global modeling of spectral-spatial dependencies, their scalability and adaptability under label-scarce conditions remain limited. In this work, we propose LoLA-SpecViT(Low-rank adaptation Local Attention Spectral Vision Transformer), a lightweight spectral vision transformer that addresses these limitations through a parameter-efficient architecture tailored to the unique characteristics of hyperspectral imagery. Our model combines a 3D convolutional spectral front-end with local window-based self-attention, enhancing both spectral feature extraction and spatial consistency while reducing computational complexity. To further improve adaptability, we integrate low-rank adaptation (LoRA) into attention and projection layers, enabling fine-tuning with over 80\% fewer trainable parameters. A novel cyclical learning rate scheduler modulates LoRA adaptation strength during training, improving convergence and generalisation. Extensive experiments on three benchmark datasets WHU-Hi LongKou, WHU-Hi HongHu, and Salinas demonstrate that LoLA-SpecViT consistently outperforms state-of-the-art baselines, achieving up to 99.91\% accuracy with substantially fewer parameters and enhanced robustness under low-label regimes. The proposed framework provides a scalable and generalizable solution for real-world HSI applications in agriculture, environmental monitoring, and remote sensing analytics. Our code is available in the following https://github.com/FadiZidiDz/LoLA-SpecViT{GitHub Repository}.

This article focuses on estimating relative transfer functions (RTFs) for beamforming applications. Traditional methods often assume that spectra are uncorrelated, an assumption that is often violated in practical scenarios due to factors such as time-domain windowing or the non-stationary nature of signals, as observed in speech. To overcome these limitations, we propose an RTF estimation technique that leverages spectral and spatial correlations through subspace analysis. Additionally, we derive Cram\'er--Rao bounds (CRBs) for the RTF estimation task, providing theoretical insights into the achievable estimation accuracy. These bounds reveal that channel estimation can be performed more accurately if the noise or the target signal exhibits spectral correlations. Experiments with both real and synthetic data show that our technique outperforms the narrowband maximum-likelihood estimator, known as covariance whitening (CW), when the target exhibits spectral correlations. Although the proposed algorithm generally achieves accuracy close to the theoretical bound, there is potential for further improvement, especially in scenarios with highly spectrally correlated noise. While channel estimation has various applications, we demonstrate the method using a minimum variance distortionless (MVDR) beamformer for multichannel speech enhancement. A free Python implementation is also provided.

Hyperspectral Unmixing (HU) has received increasing attention in the past decades due to its ability of unveiling information latent in hyperspectral data. Unfortunately, most existing methods fail to take advantage of the spatial information in data. To overcome this limitation, we propose a Structured Sparse regularized Nonnegative Matrix Factorization (SS-NMF) method from the following two aspects. First, we incorporate a graph Laplacian to encode the manifold structures embedded in the hyperspectral data space. In this way, the highly similar neighboring pixels can be grouped together. Second, the lasso penalty is employed in SS-NMF for the fact that pixels in the same manifold structure are sparsely mixed by a common set of relevant bases. These two factors act as a new structured sparse constraint. With this constraint, our method can learn a compact space, where highly similar pixels are grouped to share correlated sparse representations. Experiments on real hyperspectral data sets with different noise levels demonstrate that our method outperforms the state-of-the-art methods significantly.

The quality of point clouds is often limited by noise introduced during their capture process. Consequently, a fundamental 3D vision task is the removal of noise, known as point cloud filtering or denoising. State-of-the-art learning based methods focus on training neural networks to infer filtered displacements and directly shift noisy points onto the underlying clean surfaces. In high noise conditions, they iterate the filtering process. However, this iterative filtering is only done at test time and is less effective at ensuring points converge quickly onto the clean surfaces. We propose IterativePFN (iterative point cloud filtering network), which consists of multiple IterationModules that model the true iterative filtering process internally, within a single network. We train our IterativePFN network using a novel loss function that utilizes an adaptive ground truth target at each iteration to capture the relationship between intermediate filtering results during training. This ensures that the filtered results converge faster to the clean surfaces. Our method is able to obtain better performance compared to state-of-the-art methods. The source code can be found at: https://github.com/ddsediri/IterativePFN.

Many works have been done on salient object detection using supervised or unsupervised approaches on colour images. Recently, a few studies demonstrated that efficient salient object detection can also be implemented by using spectral features in visible spectrum of hyperspectral images from natural scenes. However, these models on hyperspectral salient object detection were tested with a very few number of data selected from various online public dataset, which are not specifically created for object detection purposes. Therefore, here, we aim to contribute to the field by releasing a hyperspectral salient object detection dataset with a collection of 60 hyperspectral images with their respective ground-truth binary images and representative rendered colour images (sRGB). We took several aspects in consideration during the data collection such as variation in object size, number of objects, foreground-background contrast, object position on the image, and etc. Then, we prepared ground truth binary images for each hyperspectral data, where salient objects are labelled on the images. Finally, we did performance evaluation using Area Under Curve (AUC) metric on some existing hyperspectral saliency detection models in literature.

Diffusion models have recently received a surge of interest due to their impressive performance for image restoration, especially in terms of noise robustness. However, existing diffusion-based methods are trained on a large amount of training data and perform very well in-distribution, but can be quite susceptible to distribution shift. This is especially inappropriate for data-starved hyperspectral image (HSI) restoration. To tackle this problem, this work puts forth a self-supervised diffusion model for HSI restoration, namely Denoising Diffusion Spatio-Spectral Model (DDS2M), which works by inferring the parameters of the proposed Variational Spatio-Spectral Module (VS2M) during the reverse diffusion process, solely using the degraded HSI without any extra training data. In VS2M, a variational inference-based loss function is customized to enable the untrained spatial and spectral networks to learn the posterior distribution, which serves as the transitions of the sampling chain to help reverse the diffusion process. Benefiting from its self-supervised nature and the diffusion process, DDS2M enjoys stronger generalization ability to various HSIs compared to existing diffusion-based methods and superior robustness to noise compared to existing HSI restoration methods. Extensive experiments on HSI denoising, noisy HSI completion and super-resolution on a variety of HSIs demonstrate DDS2M's superiority over the existing task-specific state-of-the-arts.

The recent surge in contrast-based graph self-supervised learning has prominently featured an intensified exploration of spectral cues. Spectral augmentation, which involves modifying a graph's spectral properties such as eigenvalues or eigenvectors, is widely believed to enhance model performance. However, an intriguing paradox emerges, as methods grounded in seemingly conflicting assumptions regarding the spectral domain demonstrate notable enhancements in learning performance. Through extensive empirical studies, we find that simple edge perturbations - random edge dropping for node-level and random edge adding for graph-level self-supervised learning - consistently yield comparable or superior performance while being significantly more computationally efficient. This suggests that the computational overhead of sophisticated spectral augmentations may not justify their practical benefits. Our theoretical analysis of the InfoNCE loss bounds for shallow GNNs further supports this observation. The proposed insights represent a significant leap forward in the field, potentially refining the understanding and implementation of graph self-supervised learning.

We investigate data filtering for large model pretraining via new scaling studies that target the high compute, data-scarce regime. In spite of an apparently common belief that filtering data to include only high-quality information is essential, our experiments suggest that with enough compute, the best data filter is no data filter. We find that sufficiently trained large parameter models not only tolerate low-quality and distractor data, but in fact benefit from nominally ``poor'' data.

Hyperspectral image (HSI) plays a vital role in various fields such as agriculture and environmental monitoring. However, due to the expensive acquisition cost, the number of hyperspectral images is limited, degenerating the performance of downstream tasks. Although some recent studies have attempted to employ diffusion models to synthesize HSIs, they still struggle with the scarcity of HSIs, affecting the reliability and diversity of the generated images. Some studies propose to incorporate multi-modal data to enhance spatial diversity, but the spectral fidelity cannot be ensured. In addition, existing HSI synthesis models are typically uncontrollable or only support single-condition control, limiting their ability to generate accurate and reliable HSIs. To alleviate these issues, we propose HSIGene, a novel HSI generation foundation model which is based on latent diffusion and supports multi-condition control, allowing for more precise and reliable HSI generation. To enhance the spatial diversity of the training data while preserving spectral fidelity, we propose a new data augmentation method based on spatial super-resolution, in which HSIs are upscaled first, and thus abundant training patches could be obtained by cropping the high-resolution HSIs. In addition, to improve the perceptual quality of the augmented data, we introduce a novel two-stage HSI super-resolution framework, which first applies RGB bands super-resolution and then utilizes our proposed Rectangular Guided Attention Network (RGAN) for guided HSI super-resolution. Experiments demonstrate that the proposed model is capable of generating a vast quantity of realistic HSIs for downstream tasks such as denoising and super-resolution. The code and models are available at https://github.com/LiPang/HSIGene.

Effectively discerning spatial-spectral dependencies in HSI denoising is crucial, but prevailing methods using convolution or transformers still face computational efficiency limitations. Recently, the emerging Selective State Space Model(Mamba) has risen with its nearly linear computational complexity in processing natural language sequences, which inspired us to explore its potential in handling long spectral sequences. In this paper, we propose HSIDMamba(HSDM), tailored to exploit the linear complexity for effectively capturing spatial-spectral dependencies in HSI denoising. In particular, HSDM comprises multiple Hyperspectral Continuous Scan Blocks, incorporating BCSM(Bidirectional Continuous Scanning Mechanism), scale residual, and spectral attention mechanisms to enhance the capture of long-range and local spatial-spectral information. BCSM strengthens spatial-spectral interactions by linking forward and backward scans and enhancing information from eight directions through SSM, significantly enhancing the perceptual capability of HSDM and improving denoising performance more effectively. Extensive evaluations against HSI denoising benchmarks validate the superior performance of HSDM, achieving state-of-the-art results in performance and surpassing the efficiency of the latest transformer architectures by 30%.

Denoising diffusion models are widely used for high-quality image and video generation. Their performance depends on noise schedules, which define the distribution of noise levels applied during training and the sequence of noise levels traversed during sampling. Noise schedules are typically handcrafted and require manual tuning across different resolutions. In this work, we propose a principled way to design per-instance noise schedules for pixel diffusion, based on the image's spectral properties. By deriving theoretical bounds on the efficacy of minimum and maximum noise levels, we design ``tight'' noise schedules that eliminate redundant steps. During inference, we propose to conditionally sample such noise schedules. Experiments show that our noise schedules improve generative quality of single-stage pixel diffusion models, particularly in the low-step regime.

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in optimal-approximation theory, we train a network to decompose an implicit approximation operator by minimizing the reconstruction error in the learned basis over a chosen distribution of probe functions. For suitable distributions, they can be seen as an approximation of the Laplacian operator and its eigendecomposition, which are fundamental in geometry processing. Furthermore, our method recovers in a unified manner not only the spectral basis, but also the implicit metric's sampling density and the eigenvalues of the underlying operator. Notably, our unsupervised method makes no assumption on the data manifold, such as meshing or manifold dimensionality, allowing it to scale to arbitrary datasets of any dimension. On point clouds lying on surfaces in 3D and high-dimensional image manifolds, our approach yields meaningful spectral bases, that can resemble those of the Laplacian, without explicit construction of an operator. By replacing the traditional operator selection, construction, and eigendecomposition with a learning-based approach, our framework offers a principled, data-driven alternative to conventional pipelines. This opens new possibilities in geometry processing for unstructured data, particularly in high-dimensional spaces.

Polynomial filters, a kind of Graph Neural Networks, typically use a predetermined polynomial basis and learn the coefficients from the training data. It has been observed that the effectiveness of the model is highly dependent on the property of the polynomial basis. Consequently, two natural and fundamental questions arise: Can we learn a suitable polynomial basis from the training data? Can we determine the optimal polynomial basis for a given graph and node features? In this paper, we propose two spectral GNN models that provide positive answers to the questions posed above. First, inspired by Favard's Theorem, we propose the FavardGNN model, which learns a polynomial basis from the space of all possible orthonormal bases. Second, we examine the supposedly unsolvable definition of optimal polynomial basis from Wang & Zhang (2022) and propose a simple model, OptBasisGNN, which computes the optimal basis for a given graph structure and graph signal. Extensive experiments are conducted to demonstrate the effectiveness of our proposed models.

The sky is a major component of the appearance of a photograph, and its color and tone can strongly influence the mood of a picture. In nighttime photography, the sky can also suffer from noise and color artifacts. For this reason, there is a strong desire to process the sky in isolation from the rest of the scene to achieve an optimal look. In this work, we propose an automated method, which can run as a part of a camera pipeline, for creating accurate sky alpha-masks and using them to improve the appearance of the sky. Our method performs end-to-end sky optimization in less than half a second per image on a mobile device. We introduce a method for creating an accurate sky-mask dataset that is based on partially annotated images that are inpainted and refined by our modified weighted guided filter. We use this dataset to train a neural network for semantic sky segmentation. Due to the compute and power constraints of mobile devices, sky segmentation is performed at a low image resolution. Our modified weighted guided filter is used for edge-aware upsampling to resize the alpha-mask to a higher resolution. With this detailed mask we automatically apply post-processing steps to the sky in isolation, such as automatic spatially varying white-balance, brightness adjustments, contrast enhancement, and noise reduction.

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/

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.

In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.

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 a simple but effective technique to smooth out textures while preserving the prominent structures. Our method is built upon a key observation -- the coarsest level in a Gaussian pyramid often naturally eliminates textures and summarizes the main image structures. This inspires our central idea for texture filtering, which is to progressively upsample the very low-resolution coarsest Gaussian pyramid level to a full-resolution texture smoothing result with well-preserved structures, under the guidance of each fine-scale Gaussian pyramid level and its associated Laplacian pyramid level. We show that our approach is effective to separate structure from texture of different scales, local contrasts, and forms, without degrading structures or introducing visual artifacts. We also demonstrate the applicability of our method on various applications including detail enhancement, image abstraction, HDR tone mapping, inverse halftoning, and LDR image enhancement.

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.

Recent advances in Remote Sensing Foundation Models (RSFMs) have led to significant breakthroughs in the field. While many RSFMs have been pretrained with massive optical imagery, more multispectral/hyperspectral data remain lack of the corresponding foundation models. To leverage the advantages of spectral imagery in earth observation, we explore whether existing RSFMs can be effectively adapted to process diverse spectral modalities without requiring extensive spectral pretraining. In response to this challenge, we proposed SpectralX, an innovative parameter-efficient fine-tuning framework that adapt existing RSFMs as backbone while introducing a two-stage training approach to handle various spectral inputs, thereby significantly improving domain generalization performance. In the first stage, we employ a masked-reconstruction task and design a specialized Hyper Tokenizer (HyperT) to extract attribute tokens from both spatial and spectral dimensions. Simultaneously, we develop an Attribute-oriented Mixture of Adapter (AoMoA) that dynamically aggregates multi-attribute expert knowledge while performing layer-wise fine-tuning. With semantic segmentation as downstream task in the second stage, we insert an Attribute-refined Adapter (Are-adapter) into the first stage framework. By iteratively querying low-level semantic features with high-level representations, the model learns to focus on task-beneficial attributes, enabling customized adjustment of RSFMs. Following this two-phase adaptation process, SpectralX is capable of interpreting spectral imagery from new regions or seasons. The codes will be available from the website: https://github.com/YuxiangZhang-BIT.

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.

Improving the quality of hyperspectral images (HSIs), such as through super-resolution, is a crucial research area. However, generative modeling for HSIs presents several challenges. Due to their high spectral dimensionality, HSIs are too memory-intensive for direct input into conventional diffusion models. Furthermore, general generative models lack an understanding of the topological and geometric structures of ground objects in remote sensing imagery. In addition, most diffusion models optimize loss functions at the noise level, leading to a non-intuitive convergence behavior and suboptimal generation quality for complex data. To address these challenges, we propose a Geometric Enhanced Wavelet-based Diffusion Model (GEWDiff), a novel framework for reconstructing hyperspectral images at 4-times super-resolution. A wavelet-based encoder-decoder is introduced that efficiently compresses HSIs into a latent space while preserving spectral-spatial information. To avoid distortion during generation, we incorporate a geometry-enhanced diffusion process that preserves the geometric features. Furthermore, a multi-level loss function was designed to guide the diffusion process, promoting stable convergence and improved reconstruction fidelity. Our model demonstrated state-of-the-art results across multiple dimensions, including fidelity, spectral accuracy, visual realism, and clarity.

Deep learning models are intrinsically sensitive to distribution shifts in the input data. In particular, small, barely perceivable perturbations to the input data can force models to make wrong predictions with high confidence. An common defense mechanism is regularization through adversarial training which injects worst-case perturbations back into training to strengthen the decision boundaries, and to reduce overfitting. In this context, we perform an investigation of 3x3 convolution filters that form in adversarially-trained models. Filters are extracted from 71 public models of the linf-RobustBench CIFAR-10/100 and ImageNet1k leaderboard and compared to filters extracted from models built on the same architectures but trained without robust regularization. We observe that adversarially-robust models appear to form more diverse, less sparse, and more orthogonal convolution filters than their normal counterparts. The largest differences between robust and normal models are found in the deepest layers, and the very first convolution layer, which consistently and predominantly forms filters that can partially eliminate perturbations, irrespective of the architecture. Data & Project website: https://github.com/paulgavrikov/cvpr22w_RobustnessThroughTheLens

Geospatial raster data, such as that collected by satellite-based imaging systems at different times and spectral bands, hold immense potential for enabling a wide range of high-impact applications. This potential stems from the rich information that is spatially and temporally contextualized across multiple channels and sensing modalities. Recent work has adapted existing self-supervised learning approaches for such geospatial data. However, they fall short of scalable model architectures, leading to inflexibility and computational inefficiencies when faced with an increasing number of channels and modalities. To address these limitations, we introduce Low-rank Efficient Spatial-Spectral Vision Transformer with three key innovations: i) the LESS Attention Block that approximates high-dimensional spatial-spectral attention through Kronecker's product of the low-dimensional spatial and spectral attention components; ii) the Continuous Positional-Channel Embedding Layer that preserves both the continuity and physical characteristics of each spatial-spectral patch; and iii) the Perception Field Mask that exploits local spatial dependencies by constraining attention to neighboring patches. To evaluate the proposed innovations, we construct GFM-Bench, which serves as a comprehensive benchmark for such geospatial raster data. We pretrain LESS ViT using a Hyperspectral Masked Autoencoder framework with integrated positional and channel masking strategies. Experimental results demonstrate that our proposed method achieves competitive performance against state-of-the-art multi-modal geospatial foundation models while outperforming them on cross-satellite generalization tasks with higher computational efficiency. The flexibility and extensibility of our framework make it a promising direction for future geospatial data analysis tasks that involve a wide range of modalities and channels.

Spectra are a prevalent yet highly information-dense form of scientific imagery, presenting substantial challenges to multimodal large language models (MLLMs) due to their unstructured and domain-specific characteristics. Here we introduce SpecVQA, a professional scientific-image benchmark for evaluating multimodal models on scientific spectral understanding, covering 7 representative spectrum types with expert-annotated question-answer pairs. The aim comprises two aspects: spectra scientific QA evaluation and corresponding underlying task evaluation. SpecVQA contains 620 figures and 3100 QA pairs curated from peer-reviewed literature, targeting both direct information extraction and domain-specific reasoning. To effectively reduce token length while preserving essential curve characteristics, we propose a spectral data sampling and interpolation reconstruction approach. Ablation studies further confirm that the approach achieves substantial performance improvements on the proposed benchmark. We test the capability of prominent MLLMs in scientific spectral understanding on our benchmark and present a leaderboard. This work represents an essential step toward enhancing spectral understanding in multimodal large models and suggests promising directions for extending visual-language models to broader scientific research and data analysis.

Low-rank adaptation~(LoRA) has recently gained much interest in fine-tuning foundation models. It effectively reduces the number of trainable parameters by incorporating low-rank matrices A and B to represent the weight change, i.e., Delta W=BA. Despite LoRA's progress, it faces storage challenges when handling extensive customization adaptations or larger base models. In this work, we aim to further compress trainable parameters by enjoying the powerful expressiveness of the Fourier transform. Specifically, we introduce FourierFT, which treats Delta W as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. With the trained spectral coefficients, we implement the inverse discrete Fourier transform to recover Delta W. Empirically, our FourierFT method shows comparable or better performance with fewer parameters than LoRA on various tasks, including natural language understanding, natural language generation, instruction tuning, and image classification. For example, when performing instruction tuning on the LLaMA2-7B model, FourierFT surpasses LoRA with only 0.064M trainable parameters, compared to LoRA's 33.5M. Our code is released at https://github.com/Chaos96/fourierft.

Hyperspectral pansharpening has received much attention in recent years due to technological and methodological advances that open the door to new application scenarios. However, research on this topic is only now gaining momentum. The most popular methods are still borrowed from the more mature field of multispectral pansharpening and often overlook the unique challenges posed by hyperspectral data fusion, such as i) the very large number of bands, ii) the overwhelming noise in selected spectral ranges, iii) the significant spectral mismatch between panchromatic and hyperspectral components, iv) a typically high resolution ratio. Imprecise data modeling especially affects spectral fidelity. Even state-of-the-art methods perform well in certain spectral ranges and much worse in others, failing to ensure consistent quality across all bands, with the risk of generating unreliable results. Here, we propose a hyperspectral pansharpening method that explicitly addresses this problem and ensures uniform spectral quality. To this end, a single lightweight neural network is used, with weights that adapt on the fly to each band. During fine-tuning, the spatial loss is turned on and off to ensure a fast convergence of the spectral loss to the desired level, according to a hysteresis-like dynamic. Furthermore, the spatial loss itself is appropriately redefined to account for nonlinear dependencies between panchromatic and spectral bands. Overall, the proposed method is fully unsupervised, with no prior training on external data, flexible, and low-complexity. Experiments on a recently published benchmarking toolbox show that it ensures excellent sharpening quality, competitive with the state-of-the-art, consistently across all bands. The software code and the full set of results are shared online on https://github.com/giu-guarino/rho-PNN.

Pruning is a model compression method that removes redundant parameters in deep neural networks (DNNs) while maintaining accuracy. Most available filter pruning methods require complex treatments such as iterative pruning, features statistics/ranking, or additional optimization designs in the training process. In this paper, we propose a simple and effective regularization strategy from a new perspective of evolution of features, which we call feature flow regularization (FFR), for improving structured sparsity and filter pruning in DNNs. Specifically, FFR imposes controls on the gradient and curvature of feature flow along the neural network, which implicitly increases the sparsity of the parameters. The principle behind FFR is that coherent and smooth evolution of features will lead to an efficient network that avoids redundant parameters. The high structured sparsity obtained from FFR enables us to prune filters effectively. Experiments with VGGNets, ResNets on CIFAR-10/100, and Tiny ImageNet datasets demonstrate that FFR can significantly improve both unstructured and structured sparsity. Our pruning results in terms of reduction of parameters and FLOPs are comparable to or even better than those of state-of-the-art pruning methods.

General speech restoration demands techniques that can interpret complex speech structures under various distortions. While State-Space Models like SEMamba have advanced the state-of-the-art in speech denoising, they are not inherently optimized for critical speech characteristics, such as spectral periodicity or multi-resolution frequency analysis. In this work, we introduce an architecture tailored to incorporate speech-specific features as inductive biases. In particular, we propose Frequency GLP, a frequency feature extraction block that effectively and efficiently leverages the properties of frequency bins. Then, we design a multi-resolution parallel time-frequency dual-processing block to capture diverse spectral patterns, and a learnable mapping to further enhance model performance. With all our ideas combined, the proposed SEMamba++ achieves the best performance among multiple baseline models while remaining computationally efficient.

Image dehazing aims to restore image clarity and visual quality by reducing atmospheric scattering and absorption effects. While deep learning has made significant strides in this area, more and more methods are constrained by network depth. Consequently, lots of approaches have adopted parallel branching strategies. however, they often prioritize aspects such as resolution, receptive field, or frequency domain segmentation without dynamically partitioning branches based on the distribution of input features. Inspired by dynamic filtering, we propose using cascaded dynamic filters to create a multi-branch network by dynamically generating filter kernels based on feature map distribution. To better handle branch features, we propose a residual multiscale block (RMB), combining different receptive fields. Furthermore, we also introduce a dynamic convolution-based local fusion method to merge features from adjacent branches. Experiments on RESIDE, Haze4K, and O-Haze datasets validate our method's effectiveness, with our model achieving a PSNR of 43.21dB on the RESIDE-Indoor dataset. The code is available at https://github.com/dauing/CasDyF-Net.

Multi-frame algorithms for single-channel speech enhancement are able to take advantage from short-time correlations within the speech signal. Deep filtering (DF) recently demonstrated its capabilities for low-latency scenarios like hearing aids with its complex multi-frame (MF) filter. Alternatively, the complex filter can be estimated via an MF minimum variance distortionless response (MVDR), or MF Wiener filter (WF). Previous studies have shown that incorporating algorithm domain knowledge using an MVDR filter might be beneficial compared to the direct filter estimation via DF. In this work, we compare the usage of various multi-frame filters such as DF, MF-MVDR, or MF-WF for HAs. We assess different covariance estimation methods for both MF-MVDR and MF-WF and objectively demonstrate an improved performance compared to direct DF estimation, significantly outperforming related work while improving the runtime performance.

We demonstrate a compact, cost-effective snapshot spectral imaging system named Aperture Diffraction Imaging Spectrometer (ADIS), which consists only of an imaging lens with an ultra-thin orthogonal aperture mask and a mosaic filter sensor, requiring no additional physical footprint compared to common RGB cameras. Then we introduce a new optical design that each point in the object space is multiplexed to discrete encoding locations on the mosaic filter sensor by diffraction-based spatial-spectral projection engineering generated from the orthogonal mask. The orthogonal projection is uniformly accepted to obtain a weakly calibration-dependent data form to enhance modulation robustness. Meanwhile, the Cascade Shift-Shuffle Spectral Transformer (CSST) with strong perception of the diffraction degeneration is designed to solve a sparsity-constrained inverse problem, realizing the volume reconstruction from 2D measurements with Large amount of aliasing. Our system is evaluated by elaborating the imaging optical theory and reconstruction algorithm with demonstrating the experimental imaging under a single exposure. Ultimately, we achieve the sub-super-pixel spatial resolution and high spectral resolution imaging. The code will be available at: https://github.com/Krito-ex/CSST.

We analyze the stability of a class of eigensolvers that target interior eigenvalues with rational filters. We show that subspace iteration with a rational filter is robust even when an eigenvalue is near a filter's pole. These dangerous eigenvalues contribute to large round-off errors in the first iteration, but are self-correcting in later iterations. For matrices with orthogonal eigenvectors (e.g., real-symmetric or complex Hermitian), two iterations is enough to reduce round-off errors to the order of the unit-round off. In contrast, Krylov methods accelerated by rational filters with fixed poles typically fail to converge to unit round-off accuracy when an eigenvalue is close to a pole. In the context of Arnoldi with shift-and-invert enhancement, we demonstrate a simple restart strategy that recovers full precision in the target eigenpairs.

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of spectral algorithms specified by profile h(lambda), and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile h(lambda) for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

Machine unlearning (MU) aims to remove the influence of specific training data while preserving model utility. As the name suggests, MU can be viewed as the inverse of learning, using gradient-based updates to reduce the influence of a forget-set by counteracting the previously learned behavior. Recently, Muon, a gradient descent variant, has been introduced. Muon applies spectral magnitude normalization to encourage exploration of rare directions and demonstrates promising performance. Inspired by Muon, we adopt the spectral view for unlearning and propose Spectral Saliency Unlearning (SSU). SSU thresholds weak singular components and updates only those directions supported by a confident unlearning signal. We further provide theoretical justification for this thresholding approach from the perspective of the forgetting-retention trade-off. Experiments across image classifiers, diffusion models, and LLMs demonstrate SSU's effectiveness.

Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient updates through the lens of signal processing and reveal that fixed momentum coefficients inherently distort the balance between bias and variance, leading to skewed or suboptimal parameter updates. To address this, we propose SGDF (SGD with Filter), an optimizer inspired by the principles of Optimal Linear Filtering. SGDF computes an online, time-varying gain to dynamically refine gradient estimation by minimizing the mean-squared error, thereby achieving an optimal trade-off between noise suppression and signal preservation. Furthermore, our approach could extend to other optimizers, showcasing its broad applicability to optimization frameworks. Extensive experiments across diverse architectures and benchmarks demonstrate SGDF surpasses conventional momentum methods and achieves performance on par with or surpassing state-of-the-art optimizers.

This study presents a deep convolutional autoencoder network for filtering reverberation clutter from transthoracic echocardiographic (TTE) image sequences. Given the spatiotemporal nature of this type of clutter, the filtering network employs 3D convolutional layers to suppress it throughout the cardiac cycle. The design of the network incorporates two key features that contribute to the effectiveness of the filter: 1) an attention mechanism for focusing on cluttered regions and leveraging contextual information, and 2) residual learning for preserving fine image structures. To train the network, a diverse set of artifact patterns was simulated and superimposed onto ultra-realistic synthetic TTE sequences from six ultrasound vendors, generating input for the filtering network. The artifact-free sequences served as ground-truth. Performance of the filtering network was evaluated using unseen synthetic and in vivo artifactual sequences. Results from the in vivo dataset confirmed the network's strong generalization capabilities, despite being trained solely on synthetic data and simulated artifacts. The suitability of the filtered sequences for downstream processing was assessed by computing segmental strain curves. A significant reduction in the discrepancy between strain profiles computed from cluttered and clutter-free segments was observed after filtering the cluttered sequences with the proposed network. The trained network processes a TTE sequence in a fraction of a second, enabling real-time clutter filtering and potentially improving the precision of clinically relevant indices derived from TTE sequences. The source code of the proposed method and example video files of the filtering results are available at: https://github.com/MahdiTabassian/Deep-Clutter-Filtering/tree/main{https://github.com/MahdiTabassian/Deep-Clutter-Filtering/tree/main}.

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or unitarily invariant, i.e., they depend only on the eigenvalues or singular values of the matrix. This paper investigates how spectral matrix cones -- cones defined from epigraphs and perspectives of spectral or unitarily invariant functions -- can be used to enhance first-order conic solvers for semidefinite programs. Our main result shows that projecting a matrix can be reduced to projecting its eigenvalues or singular values, which we demonstrate can be done at a negligible cost compared to the eigenvalue or singular value decomposition itself. We have integrated support for spectral matrix cone projections into the Splitting Conic Solver (SCS). Numerical experiments show that SCS with this enhancement can achieve speedups of up to an order of magnitude for solving semidefinite programs arising in experimental design, robust principal component analysis, and graph partitioning.