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15 papers in the last four weeks, up 67% on the four weeks before. 0.2% of all new papers.

Jul 6Week of Sep 21

Latest papers 156

Jun 29, 2026cs.LG

I-BBS: Coordinate-Free Inference of Latent Sub-Manifolds Using Random Distance Matrix Theory

Bogomolny, Bohigas and Schmit (BBS) found that the spectrum of the pairwise distance matrix on N points sampled from a smooth d-dimensional manifold encodes a signature of the underlying geometry. We develop I-BBS (Inference-BBS), a coordinate-free method that identifies a low-dimensional latent sub-manifold embedded in a high-dimensional ambient distance matrix alone, without accessing an ambient high-dimensional vector space. It therefore applies even when that space is only partly observable or undefined. We model the ambient embedding by two classes of generative noise, model-based and model-free. The noise mixes the latent signal with off-manifold components, so the eigenvalues reorganise collectively and the latent geometry cannot be read off eigenvalue by eigenvalue. We recover it instead from two integer-stable signatures that survive the noise: the multiplicity of the top non-Perron multiplet, which fixes

d

, and a parameter-free law for how the multiplet positions shrink as the noise grows. On synthetic spheres

S^1

,

S^2

and

S^3

these integer signatures are far more stable under noise than the continuous spectral slope, and a blind test recovers both the manifold and the noise model from a single distance matrix. Applications to neural-network representations and to the dynamic training regime are developed in two companion papers.

Igor Halperin

Data Manifold Distance Spectral Theory

Jun 27, 2026cs.CV

What Color is the Sky (for a non-human) ?

The light of the daytime sky contains a mixture of many colors yet is perceived as blue by human observers. This is largely due to the particular response functions of the human cones. Under these response functions skylight and blue light are metamers: they yield the exact same excitation of the cones. In this paper we ask: is it possible to define the ``color'' of the sky for other visual systems? We present a simple computational method to determine monochromatic metamers to a given input light for arbitrary visual systems. Using published values on spectral sensitivity functions of various species, we use our method to determine the dominant wavelength of monochromatic metamers to skylight. For a wide range of species (bichromats, trichromats and tetrachormats) we find monochromatic metamers to skylight but the dominant wavelength of the metamer can vary drastically between species and be very different from the color perceived by humans.

Yair Weiss, Ofer Springer

School of Computer Science and Engineering and Edmond and Lili Safra Center for Brain Research, Hebrew Univesity of Jerusalem · School of Computer Science and Engineering, Hebrew Univesity of Jerusalem

Earth Spectral Humanoid Responses

Jun 26, 2026cs.LG

From Dataset Spectral Geometry to Network Weights: A Geometry-Aware Initialization for Sigmoidal MLPs in Image Classification

Classical universal approximation theorems (UAT) establish the expressive power of sigmoidal multilayer perceptrons, but they do not specify how the weights should be initialized. We study a supervised, data-dependent, geometry-aware initialization for one-hidden-layer sigmoidal MLPs that compiles labeled class geometry into network weights. The construction starts from the idea that sigmoid units can act as smooth half-space gates. For each class, we center the training samples at their mean, apply SVD to estimate principal directions and spectral scales, select retained directions by an energy threshold, and represent each retained direction by a pair of sigmoid slab gates. These class-specific gates are then concatenated into a shared hidden layer initialized directly from the training set. We also formulate a SVD-Mahalanobis subspace classifier as a non-neural geometric reference, which tests whether the estimated spectral class geometry is already discriminative before being embedded into the MLP. Experiments on MNIST, Fashion-MNIST, and CIFAR-10 show that the proposed initializer produces a substantially more informative zero-epoch state than a matched task-agnostic Xavier reference, while full training reaches comparable final accuracy. Frozen-hidden experiments and neutral-head ablations further show that the class-wise SVD gates remain useful fixed features, even after the initially aligned output layer is replaced by a Xavier-initialized one.

Yi-Shan Chu

Institute of Statistical Science, Academia Sinica, Taipei, Taiwan (R.O.C.)

Multilayer Perceptrons Model Weights Geometry-Aware Spectral Gating

Jun 26, 2026cs.LG

Aurora: A Leverage-Aware Spectral Optimizer

We show that for tall matrix parameters, like projection matrices in the MLP layers, the Muon update can have row norms that are arbitrarily non-uniform. This can lead to a self-reinforcing feedback loop whereby neurons receive persistently small updates and eventually do not contribute meaningfully to network outputs. This problem is effectively mitigated by an additional row normalization step, but current methods do this in a way that moves the Muon update geometry away from the polar factor of the momentum matrix, which we find is undesirable. We propose Aurora, an optimizer that enforces row-uniformity of matrix parameter updates while respecting Muon's polar factor geometry. Aurora outperforms Muon in our pre-training experiments and, when combined with existing methods, achieves state-of-the-art performance among spectral optimizers on the optimizer track of the modded-nanoGPT speedrun. Additionally, we find that Aurora's empirical gains over Muon scale with the MLP expansion factor, suggesting that Aurora may allow for effective training of very wide MLP layers.

Alec Dewulf, Dhruv Pai, Li Yang +2

Tilde Research

Muon Batch Normalization Multilayer Perceptrons Spectral Preconditioning Spectral Feedback Loop

Jun 23, 2026cs.AI

Can Aggregate Invariants Accelerate Continuous Subgraph Matching? Limits, Laws, and a Dynamic Spectral Index

Spectral filtering recently delivered substantial pruning for \emph{static} subgraph matching: Laplacian interlacing rejects candidates whose neighborhoods cannot host the query. We study whether such aggregate structural tests can accelerate \emph{continuous} subgraph matching (CSM) over dynamic graphs, and answer in three parts. First, lazily maintained spectral bounds are infeasible exactly where spectral pruning has value: we characterize the tightest safe rule over a formalized perturbation relaxation and show that even it loses essentially all pruning power within four touching updates. Second, exact maintenance is affordable when selective: pruning utility and recomputation cost are anti-correlated across vertices -- hubs provably never prune -- so recomputing small-neighborhood spectra on touch sustains exact local spectra at microseconds per update, complete by construction. Third, integrated into a decoupled CSM benchmark against an identical-minus-spectra control, the tests remove up to

51\%

of candidates or safely skip up to

47\%

of update enumerations, yet enumeration intermediates remain unchanged -- beyond the gates' skipped first-level bindings, typically zero -- across two engines, four real graphs, two stream types, and

77

solved queries; a constructed radius-stratified workload confirms the instrument detects the exception when one exists (

-99.9\%

intermediates,

748\times

faster). Aggregate tests accelerate what scales with candidate sets -- construction, list scans -- never adjacency-guided exploration. We distill an intermediate-invariance methodology for evaluating CSM filters and release a reusable dynamic local-spectra index.

Minghao Chen, Jiale Zheng

Tencent Technology Shenzhen, China · HUAWEI Noah’s Ark Lab Shenzhen, China

Subgraphs Graph Laplacians Spectral

Jun 23, 2026cs.CV

Spectral Evolution-Guided Token Pruning in Multimodal Large Language Models

Reducing visual token redundancy is critical for accelerating Multimodal Large Language Models (MLLMs) without degrading cross-modal reasoning performance. Existing token pruning methods typically rely on single-layer signals, such as attention scores or token similarities, which overlook the cross-layer transformation of visual representations and may exhibit positional bias in multimodal token sequences. To address this limitation, we propose a training-free token pruning framework based on Cross-Layer Spectral Evolution (CLSE). Instead of measuring token importance from single-layer feature magnitudes, CLSE quantifies how token representations evolve across Transformer layers in the frequency domain. This evolution reflects the transition from high-frequency structural details to low-frequency semantic abstractions. We observe that tokens with stronger spectral redistribution across layers are more likely to be semantically active and should therefore be preserved. By modeling cross-layer token dynamics, CLSE provides a stable importance criterion that mitigates positional bias. Extensive experiments on both image and video benchmarks demonstrate that CLSE achieves a superior trade-off between efficiency and accuracy under aggressive token reduction. Across multiple MLLMs, CLSE reduces FLOPs, KV cache memory, and latency while maintaining competitive or improved performance.

Bin Chen, Yuxiang Cai, Yadan Luo +3

School of Software Technology, Zhejiang University, Ningbo, China · Zhejiang Key Laboratory of Digital-Intelligence Service Technology, China · The University of Queensland, St Lucia, QLD, Australia +2

Visual Token Pruning Cross-Modal Attention Multimodal Large Language Models Spectral

Jun 23, 2026math.PR

Uniform Sampling from High-dimensional Spectral Norm Balls

Motivated by an application in machine learning optimization, this paper focuses on the challenges of sampling a matrix uniformly from the unit spectral norm ball. It is proven that all singular values of sampled matrices converge to 1 almost surely as the matrix dimensions increase. This result provides the theoretical justification for a proposed simple sampling method applicable for large dimension sizes matching matrices found in modern large language models. Experimental results demonstrate both the convergence of the singular values, as well as the exact and proposed approximate sampling methods.

Michael R. Metel

Spectral Norm Singular Value Decomposition Optimal Sample Complexity Matrix Spectral High-Dimensional

Jun 22, 2026cs.CV

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

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

Yuhan Rui, Shihan Qiao, Yibin Lou +7

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

Feature Pyramid Feature Learning High-Frequency Reconstruction Spectral Objects

Jun 22, 2026cs.LG

Differential Spectral Damping Gap Adaptive Regularization for Ill-Conditioned Kernel Methods

Kernel methods requiring matrix inversion -- particularly Least-Squares Twin Support Vector Machines (LSTSVM) -- suffer from exponential eigenvalue decay in their system matrices, producing severely ill-conditioned problems where standard Tikhonov regularization applies uniform damping regardless of eigenvector reliability. We propose Differential Spectral Damping (DSD), a regularization formula that adapts its penalty to localized eigengap structure: preserving eigenvectors with large spectral gaps (reliable per Davis-Kahan perturbation theory) while aggressively suppressing those with small gaps (directionally corrupted beyond recovery). We motivate DSD through a principled design procedure grounded in the Davis-Kahan

\sin(Θ)

theorem, systematically deriving the requirements for a reliability-aware damping function and selecting the exponential form for its smoothness, differentiability, and natural saturation properties. Through rigorous paired testing with fairly optimized baselines (including gradient-optimized Tikhonov receiving equal optimization opportunity), we demonstrate that DSD improves LSTSVM classification accuracy by +4.8 percentage points on real-world GINA (

d=970

, Cohen's

d = 4.49

,

p < 0.0001

), +10.4 percentage points at

d=200

, and +2.6 percentage points on Madelon (

d=500

) -- all using only principled spectral initialization while Tikhonov receives grid search. For pre-image reconstruction on manifold data, DSD ties Tikhonov at high perturbation noise (

p=0.99

) but slightly underperforms at lower noise levels; both reduce naive inversion error by

66\times

. We characterize the precise operating regime (

d \geq 100

, condition number

> 10^3

) and document where simpler methods suffice, providing practitioners with clear deployment guidance.

Praveg Vashishtha

Department of Computer Science and Engineering, Indian Institute of Technology Patna, India · Sopra Banking Software India

Kernel Method Singular Value Decomposition Regularization Support Vector Machines Spectral Decomposition Spectral+1

Jun 22, 2026cs.LG

The Fractal Neural Operator: Overcoming Spectral Bias in Chaotic Attractors via Prime-Harmonic Weierstrass Encodings

Deep learning models, particularly Transformers and Neural Operators, exhibit a well-documented "spectral bias," effectively acting as low-pass filters that smooth out high-frequency information. While benign in fluid dynamics, this bias is catastrophic for Chaotic Dynamical Systems, where the underlying strange attractor is characterized by fractal geometry and infinite spectral density. We introduce the Fractal Neural Operator (FNO), a novel architecture that utilizes a non-resonant prime number basis to approximate continuous dynamical systems. Unlike geometric encodings (

2^k

), which suffer from spectral gaps and resonance, our Harmonic Weierstrass Encoder injects infinite spectral resolution into the latent space. We demonstrate that FNO extends the valid prediction horizon of the Lorenz-63 system to 347 Lyapunov times, exceeding state-of-the-art Reservoir Computing baselines by a factor of 2.3x. These results suggest that "chaos" is not inherently unpredictable to neural networks, but rather requires non-differentiable, fractal embedding manifolds.

Kanishk Awadhiya

Independent Researcher

Fourier Neural Operators Chaos Reservoir Computing Spectral

Jun 19, 2026cs.CV

Few-Shot Hyperspectral Aphid Detection via FastGAN Synthetic Data Generation, Transformer-Based Classification and Explainable AI

Early detection of aphid infestation in crops is essential for preventing yield loss and reducing unnecessary pesticide use. Hyperspectral imaging combined with Spectral Information Divergence (SID) analysis offers a non-destructive approach for monitoring plant health; however, deep learning methods applied to hyperspectral data are often limited by small dataset sizes. In this study, a data-efficient generative adversarial network (FastGAN) was employed to augment a hyperspectral SID dataset of faba bean leaves containing healthy and aphid-infested samples. The trained generator produced 10,000 synthetic images preserving structural and spectral characteristics of real samples. Image quality was evaluated using Frechet Inception Distance (FID), demonstrating stable convergence and realistic reconstruction of leaf morphology and infestation patterns. The augmented dataset was used to train four classification architectures: VGG16, ResNet-50, EfficientNet, and Vision Transformer (ViT). Results showed that dataset augmentation significantly improved classification robustness, with performance progressively increasing from classical convolutional networks to transformer-based models. The ViT model achieved the highest accuracy and F1-scores, while EfficientNet provided strong balanced performance and ResNet-50 showed moderate improvements over VGG16. Confusion matrix analysis confirmed reduced false negatives and improved disease detection when using advanced architectures. The findings demonstrate that FastGAN-based augmentation effectively enhances hyperspectral plant disease classification and that transformer-based models provide the most reliable discrimination between healthy and infested leaves.

Ali Saeidan

Lancaster Medical School, Faculty of Health and Medicine, Lancaster University, Lancaster LA1 4YG, United Kingdom

Leaf Disease Classification Hyperspectral Image Generative Adversarial Network Synthetic Data Spectral Transformer Architectures+1

Jun 19, 2026cs.RO

Spectral GS-SLAM: Observability-Aware, Degeneracy-Robust Tracking for Real-Time 3D Gaussian Splatting SLAM

Recent 3DGS-SLAM systems enable real-time operation by leveraging conventional feature matching or ICP-based tracking, thereby avoiding the heavy dense photometric optimization used in earlier approaches. However, feature matching remains prone to failure in textureless environments, while ICP-based tracking struggles in structureless or geometrically degenerate scenes due to ill-conditioned optimization. To address this issue, we propose Spectral GS-SLAM, an efficient yet robust tracking framework that integrates ICP with complementary feature-based constraints. Our method mitigates numerical instability by adaptively compensating under-constrained directions in degenerate scenarios, without interfering with the shared Gaussian representation used for mapping. We further introduce a Gaussian-aware planarity weighting mechanism that exploits the intrinsic covariance structure of 3D Gaussians to characterize scene geometry and guide information fusion. Extensive evaluations on challenging TUM RGB-D sequences demonstrate that Spectral GS-SLAM achieves real-time performance (40.14 FPS) while maintaining consistent tracking in both structureless and featureless environments. The proposed method preserves trajectory integrity in degenerate scenes while maintaining competitive performance in non-adverse conditions.

Edward Beng Wai Tan, Siew-Kei Lam, Dongshuo Zhang

College of Computing and Data Science, Nanyang Technological University, Singapore.

Gaussian Splatting Simultaneous Localization And Mapping Systems Rgb-Depth Cameras Spectral

Jun 18, 2026cs.CV

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

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

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

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

Re-Identification Graph-Coherent Low-Frequency Ones Spectral

Jun 17, 2026cs.LG

Spectral Retrieval-Augmented Time-Series Forecasting

Time series forecasting leverages historical patterns to predict future values, but traditional methods face challenges when dealing with complex, non-stationary patterns that are difficult to memorize during training. Retrieval-augmented approaches have emerged as promising solutions by retrieving similar historical patterns to enhance predictions. However, existing retrieval methods suffer from two fundamental limitations: spectral blindness, which overlooks critical frequency-domain characteristics that capture underlying periodic structures, and temporal recency, which treats all historical data equally without emphasizing recent, more relevant patterns. In this paper, we propose SpecReTF, a novel retrieval method that addresses these issues by converting time series into windowed frequency representations, measuring similarity with a combined metric that captures both amplitude and phase information. To balance recency and historical context, we apply an exponential moving average weighting scheme that emphasizes recent windows. Extensive experiments on benchmark datasets demonstrate that SpecReTF outperforms time-domain retrieval methods, achieving superior forecasting accuracy across diverse, non-stationary time series.

Huu Hiep Nguyen, Minh Hoang Nguyen, Dung Nguyen +1

Applied Artificial Intelligence Initiative Deakin University Geelong, Australia

Spectral History

Jun 17, 2026cs.LG

Thermodynamic Signatures of Reasoning: Free-Energy and Spectral-Form-Factor Diagnostics for Hallucination Detection in Large Language Models

Hallucination detection in large language models (LLMs) is deployment-critical, and recent work shows that the spectrum of attention-derived graph Laplacians carries strong signal about reasoning quality. Prior spectral diagnostics, however, summarize the Laplacian spectrum by a handful of eigenvalues or hand-picked scalars, leaving most of its structure unused. We propose Free-Energy Signatures (Fes), a spectral descriptor that treats each layer's attention Laplacian as a Hamiltonian and extracts its thermodynamic potentials partition function, free energy, spectral entropy, heat capacity together with the random-matrix-theory (RMT) spectral form factor. We prove three results: (i)~Lipschitz stability of Fes under attention perturbation; (ii)~an expressiveness result showing that Fes enriches finite spectral summaries and approximates moment-derived spectral functionals under explicit regularity and grid-resolution assumptions; and (iii)~a finite-sample PAC bound on the AUROC of a training-free detector built from Fes. Empirically, across six open-weight LLMs and six benchmarks, a lightweight probe on Fes descriptors achieves the strongest aggregate AUROC among attention-spectral baselines, improving over LapEig by

+6.5

AUROC points and over GoR-4 by

+2.4

points on average, while requiring no update to the underlying LLM. In the fully unsupervised setting, an RMT-deviation score achieves mean AUROC

0.71

, providing a label-free but weaker detector. A complementary RMT analysis shows that correct generations exhibit more Wigner-Dyson like spectral statistics, whereas hallucinations exhibit more Poisson-like statistics. The anonymized code and config are provided in the supplementary material.

Salim Khazem

Talan Research & Innovation Center

Hallucination Detection Spectral Free Energy Principle Graph Laplacians Thermodynamics

Jun 17, 2026cs.CV

SpectralDiT: Timestep-Conditioned Spectral Residual Correction for Flow-Matching DiTs

We propose SpectralDiT, a lightweight modification to flow-matching Diffusion Transformers that adds timestep-conditioned spectral correction to the MLP residual branch. The module decomposes each residual update into low- and high-frequency components on the patch-token grid, then learns a zero-initialized additive gate so the model initially matches the baseline DiT. On CIFAR-10 pixel-space generation, SpectralDiT improves FID from 20.78 to 19.71 at patch size 1 and reduces the radial Fourier spectrum gap. Furthermore, we scale our method to latent diffusion on ImageNet-100. With 0.6% additional theoretical FLOPs and 1.36% additional parameters, SpectralDiT improves latent flow-matching, achieving an 8.7% relative FID reduction under classifier-free guidance (CFG 2.0). All reported results are averaged over five seeds. Ablations and gate visualizations on CIFAR-10 reveal stable block-specific spectral correction patterns.

Jiayu Tian

Peking University

Diffusion Transformers Spectral Imagenet

Jun 14, 2026stat.ML

Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Data

Conformal prediction gives prediction intervals with finite-sample coverage when the data are exchangeable. Many time-indexed datasets are not exchangeable. They have seasons, recurring regimes, changing frequencies, or other forms of structured dependence. This paper studies a simple way to use that structure. We propose spectral adaptive conformal prediction, a method that forms weighted conformal quantiles using local spectral similarity and then updates the target miscoverage level online. The spectral weights choose calibration residuals that look relevant to the current test point. The adaptive update corrects the long-run miss rate when uncertainty changes over time. We give an approximate coverage result for the fixed spectral weighted quantile and a deterministic long-run calibration result for the adaptive update. Simulations with recurring regimes and slowly changing frequencies, together with three U.S. real-data examples, show that the hybrid method can improve on fixed spectral weighting, while also showing that spectral weighting must be monitored through effective sample size diagnostics.

Jeffery Opoku, David Banahene

aUniversity of Texas Rio Grande Valley, United States · bFlorida International University, United States

Online Conformal Prediction Spectral

Jun 12, 2026cs.LG

Machine Learning for Biomedical Raman Spectroscopy: From Spectral Acquisition to Clinical Translation

Raman spectroscopy provides label-free, chemically specific characterization of biological systems and has become an important tool for cancer diagnosis, molecular subtyping, microbiological identification, and intraoperative decision support. Biomedical Raman spectra are, however, high-dimensional, noisy, and affected by fluorescence background, acquisition variability, and biological heterogeneity, making robust computational analysis essential. This review examines the role of machine learning across the biomedical Raman spectroscopy pipeline, from preprocessing and signal correction to unsupervised structure discovery, supervised diagnosis and molecular stratification, representation and transfer learning, explainability, biomarker discovery, and multimodal integration with imaging, pathology, and molecular profiling. Emphasis is placed on the use of machine learning not only for diagnostic classification, but also for biologically interpretable and clinically actionable analysis. We also discuss the main barriers to clinical translation, including limited dataset sizes, inter-instrument variability, inconsistent preprocessing, insufficient external validation, reproducibility concerns, and limited sharing of software, data, and metadata. We argue that progress will require methodological advances together with standardization, robust validation, explainability, and deployment-ready analytical frameworks. By integrating methodological, biomedical, and translational perspectives, this review outlines key directions for developing reliable and clinically deployable Raman-AI systems.

Bogdan Oancea, Ana Maria Seciu-Grama, Nicoleta Siminea +10

National Institute of Research and Development for Biological Sciences, Romania · University of Bucharest, Romania · University of Turku, Finland +1

Raman Biomarker Spectral

Jun 12, 2026cond-mat.mtrl-sci

XRDiff: Crystal Structure Prediction from Powder X-Ray Diffraction Data Using Diffusion Models

Determining the crystal structure of a material from its powder X-ray diffraction (PXRD) pattern is a central challenge in materials science. PXRD is an accessible and widely used characterization technique, yet recovering the atomic structure from diffraction data requires solving an underdetermined inverse problem due to the loss of phase information. Generative modeling can provide a prior over atomic structure and learn the mapping from PXRD patterns to crystal structures via simulated structure-spectrum pairs. We present XRDiff, a diffusion model that recovers crystal structures from PXRD given either the stoichiometry or, in a more challenging setting, the elemental constituents and total number of atoms in the unit cell. We evaluate on datasets where each stoichiometry has multiple polymorphs and all polymorphs of a given composition are held out together, ensuring that high performance reflects genuine use of the diffraction signal. XRDiff achieves strong structure recovery rates on simulated benchmarks, indicating that the model learns a spectrum-to-structure mapping precise enough to differentiate between polymorphs. To address generalization to experimental data, we compare a full-spectrum encoding against an encoding based on peak descriptors. The peak-based encoding generalizes substantially better, outperforming even a model trained on full spectra with augmentations fitted to the experimental noise distribution. These results demonstrate that representations robust to the noise and artifacts present in real-world PXRD offer a practical and scalable path toward closing the simulation-to-experiment gap, enabling zero-shot crystal structure solution from experimental PXRD with full or partial chemical composition input.

Nofit Segal, Mingda Li, Benjamin Kurt Miller +1

Department of Materials Science and Engineering, MIT, Cambridge, MA, USA. · Department of Nuclear Science and Engineering, MIT, Cambridge, MA, USA. · FAIR, Meta, San Francisco, CA, USA.

Powder X-Ray Diffraction Crystal Structure Prediction Diffusion Models Spectral

Jun 11, 2026cs.LG

Muon $^p$ : Muon with Fractional Spectral Powers

Muon is an increasingly widely used optimizer that replaces a gradient

G=USV^\top

with its polar factor

UV^\top

, thereby flattening the singular spectrum. However, full flattening discards singular-value information that may matter for adaptation. We introduce Muon

^p

, a Muon-style optimizer that instead uses fractional spectral-power updates

US^pV^\top

for rational

p\in(0,1)

, interpolating between Muon and gradient descent. To make it practical, we prove that fractional spectral powers cannot be computed by any fixed univariate polynomial iteration, and furthermore derive low-degree odd bivariate recurrences that approximate

US^pV^\top

using only matrix multiplications, preserving Muon's matrix-multiplication-only structure and compute complexity. We show that Muon

^p

maximizes the linear improvement in loss under the Schatten

q

-norm for

q=1+\frac{1}{p}

. Empirically, Muon

^p

is especially effective for finetuning: on billion-scale models, Muon

^p

improves validation perplexity and downstream task performance. We further analyze when Muon

^p

is less suitable, through the lens of spectral geometry. Our results reveal important insights on when preserving the singular spectrum can bring significant gains, and introduce a principled way to achieve them.

Yihe Dong, Will Sawin

Princeton University

Muon Spectral Gradient Descent Matrix Multiplication

Jun 11, 2026stat.ML

Recursively Trained Diffusion Models: Limiting Collapse Distribution and Spectral Characterization

Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution. Existing theoretical works bound finite-round error accumulation in the context of diffusion models, but two questions remain open:~what distribution does the recursion converge to, and how fast? We answer both, isolating a mechanism distinct from imperfect learning: even with perfect score estimation and exact sampling, the early stopping of the reverse diffusion (required for numerical stability) drives a progressive drift away from the data distribution. We prove that this recursion converges geometrically to a unique limiting distribution, which admits a closed-form characterization as an infinite mixture of increasingly Gaussian-smoothed versions of the data distribution. A Hermite spectral decomposition of this limit reveals that recursive training acts as a low-pass filter: higher-order modes, which encode fine non-Gaussian structure, are attenuated much more strongly than coarse modes. This spectral picture motivates annealed truncation schedules that progressively shrink truncation times across retraining rounds; we prove that any schedule converging to

0

asymptotically eliminates recursive compounding. Finally, we show our idealized characterization is robust: in the presence of discretization and score estimation errors, the learned distribution remains in a Wasserstein-2 ball around the ideal limit, with mode-dependent contraction rates that contract high-order errors faster than low-order ones. We validate the theory on synthetic Gaussian mixtures and CIFAR-10.

Naïl B. Khelifa, Richard E. Turner, Ramji Venkataramanan

University of Cambridge

Diffusion Models Gaussian Mixture Models Distributions Collapse Spectral

Jun 10, 2026cs.LG

A Zero-shot Generalized Graph Anomaly Detection Framework via Node Reconstruction

Cross-domain graph anomaly detection (GAD) aims to identify abnormal nodes in unseen target graphs, showing strong potential in real-world applications with heterogeneous graph data. However, existing methods often depend on dataset-specific feature semantics and structural patterns, which limits their ability to generalize across different domains. To address this challenge, we propose AlignGAD, a zero-shot generalized graph anomaly detection framework. Our framework is built upon three key components: a Global Unification Module that aligns heterogeneous node features and normalizes graph signals in the spectral domain; a Clustering Module that constructs cluster-aware graph views to capture group-level abnormal patterns; and a Node Discrepancy Scoring Module that measures reconstruction discrepancy and aggregates anomaly evidence from different graph views. Experiments on multiple real-world datasets demonstrate the effectiveness of AlignGAD under the zero-shot GAD setting.

Phan Nguyen, Dat Cao, Hien Chu +1

School of Computing, KAIST

Generalist Graph Anomaly Detection Graph Anomaly Detection Spectral

Jun 10, 2026stat.ML

Enhancing Spectral Embedding through Robust and Flexible Knowledge Transfer in Electronic Health Records

We propose a spectral-based, unsupervised representation learning framework to derive low-dimensional embeddings for clinical concepts and patients in rare disease cohorts from electronic health records, where data are high-dimensional but sample sizes are limited. To overcome this challenge, we incorporate a knowledge matrix extracted from a broader population that shares a partially overlapping subspace with the rare-disease cohort. Our method departs from existing approaches by relaxing restrictive one-to-one signal-alignment assumptions between the latent data matrix and knowledge matrix, allowing more flexible and realistic forms of structured sharing. We introduce a novel two-step spectral embedding procedure: first, we identify and remove irrelevant components from the knowledge matrix; then, we apply a projection-based method to separately recover shared and heterogeneous components. Simulations and an analysis of a real-world multiple sclerosis cohort show that the proposed method outperforms competing approaches, particularly in challenging scenarios where shared signals are weak and only partially aligned, as is common in rare-disease data.

Feiqing Huang, Zongqi Xia, Rong Ma +1

Department of Biostatistics, Harvard T.H. Chan School of Public Health · Department of Neurology, University of Pittsburgh · Department of Data Science, Dana-Farber Cancer Institute +1

Rare Disease Electronic Health Records Spectral Cross-Task Knowledge Transfer

Jun 9, 2026cs.CV

Content-Induced Spatial-Spectral Aggregation Network for Change Detection in Remote Sensing Images

The integration of spatial and spectral information is beneficial to the improvement of change detection performance. However, existing methods cannot efficiently suppress the influences of spatial and spectral differences in unchanged areas. To address these issues, in this paper we propose a content-guided spatial-spectral integration network (CSI-Net) for the fusion of global spatial details and spectral difference information. Specifically, the proposed CSI-Net is composed of a spatial reasoning (SR) module, a spectral difference (SD) module, and a content-guided integration (CGI) module. In the SR module, the spatial information is learned by cascaded graph convolution blocks for global modeling. The SD module is responsible for the extraction of spectral features, by calculating the means and variances of features to reduce the impact of spectral differences in unchanged regions. In addition, in order to integrate the spatial-spectral features efficiently, we design a CGI module to further take advantage of their complementary information. In this module, high-level content information is introduced as a guide for a proper interaction. Due to the efficient spatial-spectral fusion, the proposed CSI-Net can learn the changed features better while achieving a suppression of spectral differences. Experimental results on LEVIR-CD, WHU-CD, and CLCD datasets demonstrate that the proposed CSI-Net produces better performance compared to state-of-the-art methods, and is applicable to different scenarios

Yunlong Liu, Zekai Zhang

School of Control Science and Engineering, Shandong University, Ji’nan 250061, China

Two-Level Spatial-Frequency Fusion Strategy Remote Sensing Change Detection Spatio-Temporal Network Spectral

Jun 7, 2026cs.LG

The Spectral Dynamics and Noise Geometry of Muon

Muon replaces a matrix gradient

G=UΣV^\top

by its polar factor

UV^\top

. This keeps the singular directions selected by the gradient, but makes the update spectrum flat. We study the optimization bias created by this operation. Under explicit alignment assumptions, we prove that the polar update is the one-step entropy-maximizing choice among bounded updates that use the gradient singular directions and do not adapt to the current weight spectrum. In an underdetermined regression model, we derive exact singular-value dynamics for continuous-time Muon and identify a measurement-dependent condition under which the normalized spectrum moves toward equal nonzero singular values. This geometry also rules out a common low-rank interpretation: at fixed Frobenius norm, Muon's distinguished state has a flat spectrum, whereas nuclear-norm minimization favors spectral concentration. Controlled matrix-sensing experiments separate the effect from simple gradient rescaling, show that norm-matched gradient descent does not reproduce Muon, and recover the predicted flattening trend across broad ablations. In small NanoGPT pretraining, Muon preserves stable rank, has a broad learning-rate plateau, and improves validation loss relative to AdamW; in a matched small-ViT control, the ranking reverses. The resulting picture is regime-dependent: Muon is not universally superior, but its flat-spectrum bias can help when many spectral directions need to remain active.

Pierfrancesco Beneventano, Mahmoud Abdelmoneum, Tomaso Poggio

Massachusetts Institute of Technology

Muon Spectral Pretraining

Jun 6, 2026cs.LG

Frequency-Domain Latent Attention Gating for Cross-Domain Token Aggregation

Token aggregation is a common bottleneck in models that map token representations to sample-level predictions, yet most pooling methods operate only in the original token domain. We propose FLaG, a plug-in aggregation module that transforms token representations with the real FFT, summarizes spectral components with learnable latent queries, applies a channel-wise gate, and reconstructs enhanced time-domain tokens for final pooling. We evaluate FLaG on antimicrobial peptide (AMP) activity prediction with ESM2, image classification with ResNet18 on CIFAR-10 and CIFAR-100, and text classification with RoBERTa on IMDB and GLUE. FLaG achieves its clearest gains on the ESM2-8M antimicrobial peptide tasks and on CIFAR-100, while remaining competitive with strong text baselines on IMDB and GLUE. Then we probe its behavior on the AMP setting with band knockouts, gate summaries, residue perturbations, latent-query readouts, and structure-proxy stratification. We find that low-frequency bands contribute the most overall, and the remaining higher-band pattern is more sample-specific. The gate acts as a broadly shared spectral reweighting stage and the cross-attention patterns are sample-specific with mild query-wise differentiation, and higher-helix peptides exhibit stronger average spectral sensitivity in both bacteria. The supplementary materials, source code and data are released at https://www.healthinformaticslab.org/supp/ and https://github.com/Kewei2023/AMPCliff/tree/FLaG.

Kewei Li, Rongying Zhang, Xueli Wang +5

College of Computer Science and Technology, Jilin University, Changchun, 130012, China. · Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, 130012, China. · Institute for Quantitative and Computational Biology, University of California, Los Angeles, 90024, United States of America. +2

Gating Spectral Antimicrobial Peptide

Jun 4, 2026cs.CV

Adaptive Band Selection for Hyperspectral Classification with Spatially Disjoint Evaluation

Hyperspectral band selection methods based on differentiable selectors can be sensitive to initialization and to extracting a final discrete subset, while prescribed band counts limit flexibility. We propose SGBR-HC (Spectral-Group Band Ranking with Hard-Concrete initialization), a two-stage method that uses a supervised spectral ranking to initialize trainable sparse gates rather than treating ranking as a fixed selection rule, letting the number of selected bands be determined by training. Stage-1 scores candidate bands from training pixels by class discriminability and spectral diversity; this ranking seeds the gate logits for Stage-2, which trains the sparse gates jointly with a spatial classifier. Under spatially disjoint evaluation on Pavia University and Houston 2013, verified by retraining a fresh classifier on the selected bands, SGBR-HC achieves the highest mean overall accuracy and Cohen's kappa with approximately twenty bands. Bypassing Stage-1 degrades OA by 8.84 pp on Pavia University and 22.15 pp on Houston 2013, confirming the ranking prior's role. Random pixel splits inflate OA on Pavia University by 30.56 pp, underscoring spatial leakage as a critical evaluation confound.

Ikram El-Hajri, Ouassim Karrakchou, Alejandro Mousist

International University of Rabat, Rabat, Morocco · Thales Alenia Space, Spain

Hyperspectral Image Spectral Feature Selection Multi-Stage Training Multi-Dimensional Evaluation

Jun 4, 2026cs.CV

Jacobi-Anger Method for Deterministic Initialization in Implicit Neural Representation

Existing implicit neural representation (INR) approaches suffer from stochastic initialization that does not guarantee consistent or high-quality performance across runs, with variations reaching more than 2.5 dB (~78%) in image regression. This variation is problematic for scientific computing and simulation, where result reproducibility is crucial. To address this problem, we present Jacobi-Anger Sinusoidal Representation Network (JA-SIREN), a deterministic initialization scheme for sinusoidal networks grounded in classical spectral analysis. By computing the Discrete Sine Transform (DST) of the target signal and leveraging the Jacobi-Anger expansion, we derive closed-form weights for a two-layer sinusoidal MLP that analytically match the network's initial spectral response to the target signal, requiring no random seed or additional hyperparameter tuning. On the Kodak dataset, JA-SIREN achieves a mean PSNR of 67.18 dB, a 21.30 dB improvement over the best baseline. This is achieved with zero run-to-run variance, confirming that spectrally-informed initialization is a more effective and reproducible alternative to stochastic initialization for sinusoidal INRs.

Mohammed Alsakabi, Kejia Hu, John M. Dolan +1

Department of Electrical and Computer Engineering, College of Engineering · The Robotics Institute, School of Computer Science Carnegie Mellon University, Pittsburgh, PA, USA

Neural Representations Spectral Multilayer Perceptrons

Jun 3, 2026cs.LG

Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning

Koopman theory turns nonlinear dynamics into a linear spectral problem. In computation, however, everything depends on a hard finite-dimensional choice: the observables must be expressive, nearly invariant under the dynamics, and, ideally, compatible with composition. Deep Koopman methods learn flexible coordinates, whereas structure-preserving methods enforce operator identities on fixed dictionaries. We combine these ideas by introducing Deep Embedded Multiplicative Dynamic Mode Decomposition (DeepMDMD), a method that learns a latent space and a partition of it, while enforcing the Koopman product rule as an exact algebraic constraint. Training alternates between an exact multiplicative operator update and a differentiable latent-clustering step that promotes Koopman closure. The result is a finite transition map on learned latent cells. Its nonzero spectrum lies on the unit circle, its dictionary is shaped by the dynamics rather than by ambient geometry, and forecasts are made in latent coordinates before being decoded to physical space. Across Hamiltonian, chaotic, and fluid examples, DeepMDMD learns dictionaries that are far more compact and dynamically coherent than those produced by geometric MDMD partitions. It reduces spectral pollution, reveals richer continuous-spectrum structure, and gives stable forecasts under severe noise. In high-dimensional flows, including a 158,624-dimensional cylinder wake and a noisy

Re=20,000

lid-driven cavity, it preserves coherent structures and long-time spectral statistics where state-space MDMD fails. These results suggest a practical rule for Koopman learning: learn the coordinates, constrain the algebra.

Kelan Gray, Finlay Brown, Nicolas Boullé +1

Department of Mathematics, Imperial College London, London, SW7 2AZ, UK. · Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK.

Koopman Operator Dynamic Mode Decomposition Spectral State Space Models Dataset Distillation

Jun 3, 2026cs.CV

Beyond Symmetric Alignment: Spectral Diagnostics of Modality Imbalance in Vision-Language Models in the Medical Domain

Vision-Language Models (VLMs) struggle when applied to medical image-text data, yet the tools available to diagnose this failure remain limited. Existing representation alignment metrics are symmetric, collapsing both modalities into a single score and hiding which modality drives cross-modal degradation. We introduce the Spectral Alignment Score (SAS), an asymmetric metric that projects both modalities onto the principal eigenbasis of an anchor modality and computes eigenvalue-weighted per-eigenmode correlations, resulting in directional scores whose difference quantifies modality information imbalance. We embed SAS within a benchmarking framework evaluating 15 VLMs across natural and medical image-text datasets alongside 6 alignment metrics and bidirectional retrieval. Our experiments show that medical images retain richer structural information than their paired clinical reports, a directional asymmetry invisible to all competing metrics, and that SAS achieves the strongest zero-label correlation with retrieval performance in the medical domain, positioning it as a practical diagnostic tool for clinical deployment. Code is available at this URL: https://github.com/iamalegambetti/medical-vlms-assessment.

Alessandro Gambetti, Qiwei Han, Cláudia Soares +1

NOVA School of Science and Technology · Lisbon, Portugal · Nova School of Business and Economics +2

Medical Vision-Language Models Vision-Language Alignment Multimodal Clinical Data Medical Imaging Datasets Modalities Value Alignment+1

Jun 2, 2026cs.CV

Beyond Compression: Quantifying Spectral Accessibility in Vision Representations

Vision-language models map visual features into a shared embedding space through learned projection layers, yet it remains unclear how these transformations alter the structure of visual information. This study examines changes in representation through spatial-frequency accessibility, measured by the linear recoverability of band-limited Fourier energy from model representations. To isolate effects beyond dimensionality reduction, we introduce Residual Spectral Loss (RSL), which evaluates changes relative to a dimension-matched random projection baseline. To reduce confounding effects from optimization, the analysis uses pretrained models with all parameters frozen. The experimental results show consistent frequency-dependent changes in accessibility across CLIP and DINOv2 on ImageNet and MS-COCO datasets. Spectral accessibility follows a non-monotonic trajectory across depth, peaking at intermediate layers before decreasing toward the output representation. The final transformation differs across architectures: CLIP's learned projection is spectrally neutral, with changes explained by compression, whereas DINOv2's [CLS] pooling induces a structured loss across the spectrum. These findings identify intermediate layers and pooling mechanisms as primary drivers of spectral transformation in modern vision encoders.

Akayou A. Kitessa, Yijun Zhao

Fordham University New York City, NY

Vision Encoders Spectral Layer-Wise Projection Imagenet Data Compression Methods+1

May 31, 2026cs.LG

What Makes a Strong Model? A Unified Spectral Analysis of Knowledge Transfer over High-dimensional Linear Regression

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: \emph{Spectral Horizon Expansion} in KD, which enables the capture of statistically inaccessible high-frequency signals, and \emph{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.

Wendao Wu, Fangqing Zhang, Haihan Zhang +1

State Key Lab of General AI, School of Intelligence Science and Technology, Peking University, China · School of Mathematical Sciences, Peking University, China

Cross-Task Knowledge Transfer Knowledge Distillation Spectral Teacher

May 31, 2026cs.LG

A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent Lévy Jumps

We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent Lévy jumps, targeting a general failure mode of neural PDE methods: a learned solution can match headline scalar diagnostics while miscomputing an operator inside its training loss. The protocol pairs each neural solve with at least one from-scratch independent reference, decomposes the Hamiltonian into drift, diffusion, compensator, and nonlocal-integral components across a u-grid, and compares the value function and its low-order derivatives over a (t,x) grid before any argmax comparison. Applied to a standard CRRA-Merton-Variance-Gamma benchmark, it isolates a missing 1/2-mixture factor in the neural method's importance-proposal density that scaled the nonlocal integral by exactly half - a textbook signature of a constant proposal scale error, invisible to longer training, grid refinement, and truncation sweeps. With the bug corrected, four references - two finite-difference solvers with disjoint discretizations, the neural solver, and a semi-analytic scalar baseline obtained from CRRA homogeneity - agree on the optimal control to within ~2%. The constant-coefficient CRRA benchmark collapses by homogeneity to a scalar maximization, so the scalar baseline is the efficient method here; the contribution is the protocol, applicable in principle to non-homogeneous and higher-dimensional settings where neural HJB-PIDE solvers are genuinely needed. The episode is a concrete instance of a broader neural-PDE verification failure: pointwise agreement of a learned value or control can coexist with a systematically wrong nonlocal operator, so per-component and surface-level checks are needed before trusting the argmax policy.

R. Drissi

Neural Solvers Hamilton-Jacobi Reachability Stochastic Differential Equations Solvers Neural Network Verification Diagnosis+1

May 29, 2026cs.LG

Modeling Spectral Energy Shifts in Spatio-Temporal Graph Anomaly Detection

Graph anomaly detection methods aim to distinguish anomalous nodes. While prior methods characterize anomalies through increased variation in the spectral energy distributions, they overlook those that result in decreased variation, i.e., camouflaged anomalies that appear normal. We show that this type of anomaly persists across multiple datasets and remains undetectable by existing spectral approaches. To address this limitation, we propose a node-level spectral energy formulation that is fully compatible with message passing and enables the detection of camouflaged anomalies. Building on this formulation, we introduce an energy-aware graph learning framework that models spectral shifts through energy-driven message passing in both static and time-series graphs. Besides, our unified architecture extends to temporal settings without introducing specialized sequence modules, enabling efficient learning under long sliding windows. Extensive experiments on large-scale benchmarks demonstrate the effectiveness and scalability of our approach.

Yilin Liu, Hongchao Zhang, Taylor T. Johnson +2

College of Connected Computing, Vanderbilt University, Nashville, USA · Department of Civil and Environmental Engineering, Electrical and Computer Engineering, Vanderbilt University, Nashville, USA

Generalist Graph Anomaly Detection Spectral

May 29, 2026eess.SP

Neural Radiated-Noise Fields for Unmanned Underwater Vehicle Noise Spectrum Prediction in Three-Dimensional Scenes

Radiated noise in unmanned underwater vehicles (UUVs) is an important indicator for characterizing acoustic signatures and evaluating platform performance. To address the strong dependence of traditional physics-based modeling and numerical simulation methods on target structural information and environmental boundary conditions, and their inability to achieve continuous spatial spectrum-response modeling in three-dimensional scenes, this paper proposes a neural radiated-noise field (NRNF). An NRNF represents the UUV radiated-noise spectrum as a continuous function of the three-dimensional UUV position, the three-dimensional hydrophone position, the UUV yaw angle, and the frequency, enabling query-based prediction at arbitrary spatial locations. The proposed method employs sinusoidal encoding for position and frequency, and introduces a learnable three-dimensional scene feature grid to explicitly represent environmental structure and propagation effects. A spectrum-prediction dataset is constructed from lake trials, and the proposed model is evaluated under three settings: horizontal extrapolation, depth extrapolation, and cross-run generalization. Results show that the NRNF achieves an average prediction error of 3.5 dB in the 50 to 5000 Hz band. Horizontal extrapolation is easiest, depth extrapolation is the most challenging, and cross-run generalization is of intermediate difficulty. Further ablation results demonstrate that the scene feature grid significantly improves the prediction stability and spatial generalization of the model.

Yan Wu, Yang Yang, Jun Fan +1

Key Laboratory of Marine Intelligent Equipment and System, Ministry of Education, Shanghai Jiaotong University, Shanghai 200240, PR China

Autonomous Underwater Vehicles Radio Map Estimation Spectral

May 29, 2026cs.LG

Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail

Neural scaling laws describe predictable power-law relationships between model size, dataset size, compute, and performance. While these laws guide the development of modern foundation models, the mechanisms underpinning them remain poorly understood, in part due to the absence of scalable analysis tools. To close this gap, we introduce "spectral position": a scalable measure of which eigenvalues of the empirical neural tangent kernel (eNTK) currently drive loss reduction. Applying this measure to scaling experiments, we find that spectral position decreases throughout training: learning shifts from dominant eigenmodes into the spectral tail. Larger models reach further into the tail than smaller models, revealing a size-dependent capacity we call "spectral reach". This suggests why larger models achieve lower losses: they sustain learning on weak spectral signals inaccessible to smaller models. We further identify feature learning as a key enabler of spectral reach. It adaptively amplifies gradient magnitudes as learning advances, sustaining progress where frozen representations stall. This points to concrete interventions through architecture and optimizer design.

Konstantin Nikolaou, Jonas Scheunemann, Sven Krippendorf +2

Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany · Department of Applied Mathematics and Theoretical Physics and Department of Physics, University of Cambridge, Cambridge, UK

Scaling Laws Neural Tangent Kernel Spectral Batch Capacity

May 29, 2026cs.LG

Spectral Anatomy of Quantum Gaussian Process Kernels

Two recent results have reshaped quantum Gaussian processes (QGPs). On the one hand, \citet{lowe2025assessing} rule out the exponential speedups claimed by HHL-based QGP regression in the typical, well-conditioned regime; on the other, an independent line of work shows that highly expressive quantum kernels suffer posterior pathologies that break Bayesian optimization. We show that these seemingly unrelated phenomena are governed by the same quantity: the normalized spectral entropy

S(K)/\log n

of the kernel Gram matrix. We prove a Cauchy--Schwarz tail bound on Nyström approximation error, a finite-sample variance-contraction identity in terms of Bach's degrees of freedom

d_σ(K)

, and a characterization of the \emph{target-dependent} optimal entropy via the intrinsic dimension of the target in the kernel eigenbasis. Empirically, the diagnostic is kernel-agnostic: hardware-efficient, matchgate, IQP \emph{and} RBF/Matérn/RFF/deep-kernel families all collapse onto identical

S/\log n

curves on dequantization, ECE, and variance-contraction panels. The NLL sweet spot lives at high entropy for smooth targets and at low entropy for band-limited quantum-data targets. The diagnostic transfers from simulator to IBM Heron hardware with median absolute error

3.2\%

and mean

5.2\%

in

S/\log n

across

24

configurations at

n_q = 4

, with matchgate and IQP within

5\%

mean and a single HE configuration returning a

30\%

outlier that drops to

0.5\%

on rerun (attributed to calibration drift); the same diagnostic transfers to a second Heron backend (mean error

2.7\%

) and to a

n_q = 6

scale-up on the original backend (mean error

1.7\%

). No error mitigation is applied throughout.

Jian Xu, Chao Li, Guang Lin +4

1RIKEN iTHEMS · 2RIKEN AIP · 3South China University of Technology +1

Quantum Kernels Gaussian Process Spectral Spectral Decomposition

May 27, 2026math.OC

Implicit Regularization in Perturbed Deep Matrix Factorization: Spectral Conditions and Stability

This paper studies the stability of low-rank implicit regularization in perturbed deep matrix factorization, where the target matrix is corrupted by a noise matrix. We first derive sufficient spectral conditions under which gradient descent exhibits a low-rank phase in the noiseless setting. These conditions show how the target spectrum, initialization, and step size jointly determine the existence of a nonempty low-rank interval. We then analyze the perturbed gradient descent dynamics, proving convergence guarantees and quantifying how the perturbation affects iteration complexity and eigenvalue recovery. Finally, we show that the low-rank phase persists under perturbation, with explicit dependence on the perturbation size. Numerical experiments support the theoretical findings.

Jingzhe Wang, Hung-Hsu Chou

Department of Informatics and Networked Systems, University of Pittsburgh · Department of Mathematics, University of Pittsburgh

Low-Rank Structure Restricted Bernoulli Matrix Factorization Regularization Spectral

May 27, 2026quant-ph

Quantum principal component analysis without eigenvector recovery

Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-

k

projection. These steps can be computationally costly in high-dimensional and quantum-data settings, sensitive to small eigengaps, and unnecessary when downstream tasks only require principal-subspace scores. Such score-based objectives are important in applications such as anomaly detection, spectral-energy profiling, and other postselection tasks. To address these needs, we introduce a measurement-based soft PCA framework replacing the hard top-

k

projector with an entropy-regularized Fermi--Dirac filter. This filter is the unique optimizer of an entropy-regularized variational formulation of PCA and converges to the classical PCA projector in the zero-temperature limit. This filter has a direct interpretation as a quantum measurement, which naturally suggests a quantum approach. For centered covariance operators represented by quantum feature states, a single fixed circuit, together with threshold calibration, accesses all optimal filters for different rank budgets or retained-variance levels without rank-dependent circuit updates or eigenvector recovery. For new inputs, the same calibrated quantum circuit yields soft principal subspace scores, spectral energy profiles, and postselected filtered states. The required centering of both training and test data is performed coherently inside the quantum protocol, which is particularly important for quantum data where no classical feature vectors or centered Gram matrix are directly available. By reframing PCA as a calibrated measurement task, this framework bypasses the need for iterative eigenvector extraction and achieves a dimension-independent sample complexity

O(η^{-2})

for normalized fractional-rank or retained variance scoring at additive accuracy

η

.

Yewei Yuan, Michele Minervini, Mark M. Wilde +1

Global College, Shanghai Jiao Tong University, Shanghai 200240, China · School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14850, United States · Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China +1

Principal Component Analysis Spectral Decomposition Subspace Kullback-Leibler Regularization Spectral

May 26, 2026cs.LG

Can Entry-Wise Clipping Give Spectral Control of Stochastic Gradients?

Training instabilities such as loss spikes are frequently the result of stochastic gradient noise. Because of rare expressions in language training data, and multiple layer composition, the noise impact is heavy-tailed and survives mini-batch averaging. Existing remedies trade off structure against cost: vector-norm clipping ignores the matrix structure of weight updates, while spectral normalization (e.g., Muon (Jordan et al., 2024)) respects it at additional cost. We show that this trade-off can be balanced. Real gradient noise appears to be similar to entry-wise heavy-tailed contamination, and a first-order perturbation analysis reveals a localization property of such noise, under which a simple entry-wise method achieves spectral control. Exploiting this, we derive a tractable surrogate for the Bayes-optimal entry-wise estimator under a Gaussian signal prior. We establish

O(ε^{-4})

convergence guarantee under Cauchy-contaminated noise. Empirically, we find that smooth shrinkage improves Adam on NanoGPT pretraining, saving

{\sim}7\%

of training tokens. We further find that applying the entry-wise clipping before spectral normalization yields a

{\sim}2\%

token saving on top of Muon.

Zitao Song, Cedar Site Bai, Zhe Zhang +2

Department of Computer Science, Purdue University, West Lafayette, IN, USA. · School of Industrial Engineering, Purdue University, West Lafayette, IN, USA.

Gradient Clipping Stochastic Gradient Descent Batch Normalization Gradient Spectral Long-Tailed Distribution

May 26, 2026cs.LG

The Stability of Singular Distribution: A Spectral Perspective on the Two-Phase Dynamics of Language Model Pre-training

Large language model pre-training typically exhibits a two-phase trajectory: a fast initial loss drop followed by a prolonged slow improvement. We identify an underlying spectral phenomenon, Stability of Singular Distribution (SoSD), where the trace-normalized singular value spectrum stabilizes early, even as parameter matrices continue to evolve. We demonstrate that synchronization between SoSD and the slow-descent regime is widely observed across diverse architectures (GPT-2, LLaMA) and settings, including various schedules (Step-wise, WSD, Cosine Decay), weight decays, and optimizers (AdamW, Muon). By analyzing a simplified Transformer, we prove that growing weight norms inevitably precipitate an early SoSD threshold, after which the rate of loss decrease becomes theoretically bounded by the variation in the singular distribution. We further interpret strategies like WSD and Muon through their ability to modulate the SoSD scale, offering a spectral lens for understanding efficient pre-training dynamics.

Hongtao Zhang, Wenjie Zhou, Chenxi Jia +2

State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China +1

Large Language Model Pretraining Pretraining Singular Value Decomposition Spectral Descent Distributions

May 24, 2026cs.LG

Influence-Inspired Spectral Rotations for Extreme Low-Bit LLM Quantization

We apply the influence-adaptive Walsh geometry of a companion theory paper (arXiv:2605.01637) to extreme low-bit weight-only LLM quantization. The recipe is one math-invariant transformation: WHT-rotate each linear layer's weight matrix and rescale its columns by per-coordinate Walsh-basis activation energy before handing off to a reconstruction-error quantizer (Intel auto-round). This biases per-group integer rounding toward high-spectral-energy channels. On four pretrained decoder-only models from 135M to 1.5B parameters, BBT-spectral reduces wikitext-2 perplexity by 15-58% relative to vanilla auto-round at W2A16; we also report a TinyLlama-1.1B auxiliary data point. Three extensions transfer the recipe to families it failed on: a per-head PCA matrix-Gamma replacement of q_norm/k_norm for Qwen3 attention (PPL 136.76 -> 88.99 on Qwen3-0.6B); an SO(2) per-pair rotation that commutes with RoPE (PPL 36.93 -> 21.84 on Qwen2.5-1.5B); and an MoE-aware input-side absorption fix identified by architectural fuzzing of Laguna-style fused-expert layouts. A W2-vs-W4 ablation gives a deliberate negative control: the redistribution payoff falls within the +/-0.5 PPL noise floor at W4, consistent with the Schur-convexity intuition that the cost of unconcentrated influence vanishes as the noise budget shrinks. All quantized weights export to OpenVINO IR and run on Intel NPU + Arc dGPU + CPU with PPL invariant to device within +/-0.1. We do not claim a formal Boolean-to-real-valued transfer of the theory paper's majorization argument: the WHT activation energy used here is not the Boolean influence of the theory paper, the link is intuitive, and the contribution is engineering value rather than a transferred theorem. Head-to-head benchmarks against SpinQuant, QuaRot, QuIP-sharp, AQLM, OmniQuant, and ButterflyQuant at matched calibration are the main future-work item.

Gorgi Pavlov

Lehigh University

Large Language Model Quantization Model Weights Spectral Free-Energy Landscape Localized Lora-Moe

May 23, 2026cs.LG

A computational phase transition for learning-to-sample from Ising models

We study \emph{learning-to-sample} -- a basic algorithmic task underlying generative modeling -- for Ising models, a standard testbed for algorithmic ideas in both theoretical computer science and machine learning. Given i.i.d. samples of an unknown target distribution, the goal of learning-to-sample is to learn a computationally efficient generation procedure that produces new samples following approximately the same distribution. We construct a family of Ising models of constantly bounded-width which lie just beyond the spectral threshold

λ_{\max}(J)-λ_{\min}(J)=1

, and show that learning-to-sample for this family is computationally hard under standard cryptographic assumptions, even when the learner is given both polynomially many i.i.d. samples from the model and explicit access to its parameters. Combined with results of [AJKPV24,KLV25] showing tractability of learning-to-sample below the spectral threshold, this establishes a sharp computational phase transition at the spectral threshold. Moreover, combined with prior results on parameter learning for bounded-width Ising models [KM17,WSD19,VML20], this shows that learning-to-sample can be more difficult than parameter learning. Finally, we show that any efficient learner for these hard instances exhibits a natural memorization-hallucination dichotomy: the learner must either output configurations that, after a simple transformation, match the (transformed) training data or place substantial mass on configurations of negligible probability under the target distribution.

Andrej Risteski, Thuy-Duong Vuong

Machine Learning Department, Carnegie Mellon University. · Department of Computer Science and Engineering, UC San Diego.

Spatial Photonic Ising Machines Phase Transitions Learnability Adaptive Sampling Generative Models Spectral

May 22, 2026cs.LG

BitsMoE: Cost-Aware Bit Allocation in Spectral Space for MoE LLM Quantization

Mixture-of-Experts (MoE) large language models incur substantial memory costs due to their large expert parameter counts. Mixed-precision quantization reduces these costs by allocating different bit-widths to experts or linear blocks according to their importance. However, assigning a single precision within each expert or linear block overlooks its internal structural heterogeneity. This limitation motivates two key questions: (1) how to define a fine-grained unit for quantization within a linear transformation; and (2) how to characterize the quantization cost of each unit under actual activation patterns and different bit-widths. To address these two questions, we propose BitsMoE, a cost-aware mixed-precision quantization framework built on two complementary techniques: (1) Shared-basis Spectral Decomposition (SSD) separates expert weights into a shared basis and expert-specific spectral components, defining structural quantization units while exploiting cross-expert redundancy. (2) Factorized Quantization Cost Modeling (FQCM) estimates component-wise costs from output reconstruction loss by combining intrinsic spectral importance, activation-dependent importance, and bit-width-dependent distortion. Using these component-wise costs, we formulate bit allocation as an integer linear program (ILP) that minimizes total modeled quantization cost under a fixed memory budget. On Qwen3-30B-A3B at 2-bit, BitsMoE achieves 64.29% average accuracy over seven downstream tasks, outperforming the evaluated MoE-specific methods, including those using ILP-based bit allocation, and exceeding GEMQ by 2.80 percentage points. Under the same setting, it achieves a

16.47\times

end-to-end offline quantization speedup over GEMQ. It also achieves up to

6.46\times

the decode throughput of GPTQ.

Jiayu Zhao, Zihan Teng, Minhao Fan +4

School of Microelectronics, University of Science and Technology of China · College of Computing and Data Science, Nanyang Technological University · School of Electrical and Electronic Engineering, Nanyang Technological University

Large Language Model Quantization Localized Lora-Moe Spectral

May 22, 2026cs.LG

Spectral Probe-Circuits: A Three-Step Recipe for Identifying Attention-Head Circuits in Pretrained Transformers

We present a three-step recipe for identifying attention-head circuits in pretrained transformers. A per-head spectral signal -- the time-integrated participation ratio of each head's attention output -- ranks heads doing sustained content-dependent computation without labels or attribution gradients. A task-pattern screen filters this general indicator into a task-specific candidate circuit, and group ablation against a matched-random control completes the causal claim. We validate across an 8x parameter range (51M to 1B-active / 7B-total), two architecture families (dense, mixture-of-experts), and four pretraining pipelines. The recipe ports: a 2-6 head induction circuit is causally necessary in every model tested, with a 94-100% drop in synthetic-induction top-1 after ablation. The spectral signal is predictive without supervision: on six independent seeds of a 51M-parameter probe model, the same computation identifies the seed-specific circuit on each seed. The fraction of heads doing identifiable specialized computation is conserved at 17-19% across the Pythia family (124M to 410M), while specific induction circuits stay 3-11 heads -- sublinear in total head count. This paper is the methodology anchor of a three-paper program; companion papers extend the recipe to developmental trajectories during pretraining and to composed-task circuits where pattern selectivity decouples from task-causal structure.

Yongzhong Xu

Transformer Attention Transformer Architectures Generative Pretrained Transformers Circuits Spectral Developmental Trajectories+1

May 21, 2026cs.LG

Energy-Gated Attention: Spectral Salience as an Inductive Bias for Transformer Attention

Standard transformer attention computes pairwise similarity between queries and keys, treating all tokens as equally salient regardless of their intrinsic informational content. In turbulent fluid dynamics, coherent structures -- the energetically dominant, spatially organized patterns that persist amid background chaos -- carry a disproportionate fraction of total energy and govern all transport. We propose that tokens play an analogous role in transformer attention: informationally dense positions (morphological boundaries, syntactic heads, discourse markers) concentrate spectral energy and should attract proportionally more attention than background tokens (function words, repeated patterns, low-information filler). We propose Energy-Gated Attention (EGA): a simple modification that gates value aggregation by the spectral energy of key token embeddings, computed by a single learned linear projection that discovers the dominant spectral mode of the embedding field. On TinyShakespeare, EGA achieves +0.103 validation loss improvement with only 12,480 additional parameters (<0.26% overhead) and no measurable computational cost. The result is consistent on Penn Treebank (+0.101), demonstrating dataset independence. A systematic ablation across three wavelet families (fixed Morlet, Daubechies db2/db4, and a parametric Morlet) establishes that fixed structured bases are suboptimal -- the optimal energy direction is data-adaptive and non-sinusoidal -- while identifying learned wavelet packets as a promising open direction. The learned energy threshold converges to tau ~= 0.35 independently of initialization, corresponding to the fraction (~36%) of tokens carrying above-average spectral energy in English text, a stable linguistic property consistent with the fraction of content words in running English text.

Athanasios Zeris

Independent Researcher, Athens, Greece.

Transformer Attention Token Embeddings Spectral Inductive Bias

May 20, 2026eess.IV

HyperBench: Standardizing and Scaling Synthetic Evaluation for Hyperspectral Super-Resolution

Hyperspectral super-resolution (HSR) reconstructs a high-spatial-resolution hyperspectral image by fusing a low-resolution hyperspectral image (LR-HSI) with a high-resolution multispectral image (HR-MSI). In the absence of real-world paired data, HSR methods are evaluated almost exclusively on synthetic experiments derived from hyperspectral datasets through Wald's protocol. Despite the protocol's widespread adoption, its practical implementation varies markedly across research works, typically relying on a single (usually Gaussian) or very few point spread functions (PSFs), one or two spectral response functions (SRFs), and a couple of spatial downsampling factors. As a result, reported performance figures are difficult to compare across the literature, in addition to being often difficult to reproduce; furthermore, they may not generalize across realistic sensing conditions. We introduce HyperBench, a unified and extensible framework that standardizes synthetic experimentation for HSR. HyperBench supports diverse degradation configurations spanning ten PSFs, four SRFs derived from operational multispectral sensors, configurable spatial downsampling factors, and matched additive white Gaussian noise; its goal is to automate large-scale evaluation and structured logging. By decoupling model development from experimental design, the framework enables reproducible, apples-to-apples cross-method comparison with minimal friction. We use HyperBench to evaluate six recently proposed HSR methods across a 70-configuration sweep on four widely used hyperspectral scenes and observe that the inter-method PSNR spread widens from approximately 5 dB on the easiest PSF to over 13 dB on the hardest - a fragility that is structurally invisible to the prevailing single-configuration evaluation protocol. HyperBench code is available at https://github.com/ritikgshah/HyperBench .

Ritik Shah, Marco F. Duarte

University of Massachusetts Amherst, MA 01003

Hyperspectral Image Super-Resolution Signal Reconstruction Spectral Subsampling

May 20, 2026cs.CR

Detecting Trojaned DNNs via Spectral Regression Analysis

Modern DNNs are repeatedly fine-tuned to incorporate new data and functionality. This evolutionary workflow introduces a security risk when updated data cannot be fully trusted, as adversaries may implant Trojans during fine-tuning. We present MIST, a Trojan detection approach that analyzes how a model's internal representations change during fine-tuning. Rather than attempting to reconstruct trigger conditions, MIST characterizes benign model evolution using pre-activation spectra and flags updates whose spectral deviations are inconsistent with this reference. This framing treats Trojan detection as a regression problem over model updates. An empirical evaluation across four datasets and eight Trojan attacks shows that spectral distances reliably distinguish Trojaned updates from clean fine-tuning. MIST outperforms state-of-the-art detection accuracy after a single update, without requiring any knowledge about the poisoned data or the trigger, and remains effective under multi-step benign evolution, with graceful and bounded degradation. These results indicate that spectral evolution provides a stable and assumption-light signal for detecting malicious model updates.

Samuele Pasini, Jinhan Kim, Paolo Tonella

Università della Svizzera Italiana, Switzerland · Università della Svizzera italiana, Switzerland

Malware Unsupervised Detection Spectral Stance

May 19, 2026cs.LG

Spectral Souping: A Unified Framework for Online Preference Alignment

Reinforcement Learning from Human Feedback (RLHF) effectively aligns Large Language Models (LLMs) with aggregate human preferences but often fails to address the diverse and conflicting needs of individual users. To overcome this issue, we introduce Spectral Souping, a unified framework for efficient, online preference alignment. Our contribution is the discovery of a universal spectral representation within LLMs, which is proven to be highly amenable to model merging. This theoretical insight enables a two-phase methodology: we first learn a basis of specialized policies offline, each focused on a distinct, fine-grained preference dimension. An online adaptation algorithm then efficiently ``soups'' these policies at inference time, either by merging their outputs or parameters, enabling rapid model adaptation without the need for costly online retraining w.r.t. tailored preference rewards. Experiments on online preference alignment benchmarks demonstrate that our method achieves significant performance improvements over existing state-of-the-art approaches, presenting a scalable and computationally efficient solution for dynamically adapting LLMs to individual user preferences.

Yinlam Chow, Guy Tennenholtz, Ted Yun +4

Google DeepMind · Google Research

Preference Alignment Reinforcement Learning From Human Feedback Large Language Model Adaptation Large Language Model Personalization Spectral Unified Framework

May 19, 2026cs.LG

LionMuon: Alternating Spectral and Sign Descent for Efficient Training

In large-scale optimization, the cheapness and effectiveness of update steps are the most crucial factors for a successful optimizer. Sign-based optimizers like Lion or Signum produce cheap per-step updates, whereas Muon's spectral matrix-sign update gives a much stronger direction at a substantially higher per-step cost. In this work, we propose LionMuon, which retains the effectiveness of Muon steps while considerably cutting the averaged iteration cost, similar to sign-based methods. It alternates between Lion's and Muon's updates on a fixed period P, sharing a single dual-EMA momentum buffer between them. The optimizer state memory therefore matches Lion and is exactly half of AdamW's. A simpler single-EMA variant, SignMuon, by itself already outperforms pure Muon. At P = 2, LionMuon Pareto-dominates Muon, Lion, Signum, and AdamW on every dataset and architecture we tested at 124M model size, reaching lower validation loss at lower compute, and the same advantage persists at 355M and 720M scale. On the theory side, we prove sharp complexity bounds under heavy-tailed noise which are governed by period-averaged smoothness and noise that interpolate between Muon's and Lion's constants. These bounds predict the compute-optimal period and the conditions under which LionMuon outruns Muon and Lion. Code: https://github.com/brain-lab-research/lion-muon

Arman Bolatov, Artem Riabinin, Nikita Kornilov +4

Mohamed bin Zayed University of Artificial Intelligence (MBZUAI) · Basic Research of Artificial Intelligence Laboratory (BRAIn Lab) · Applied Artificial Intelligence Institute +1

Muon Descent Spectral

May 19, 2026cs.LG

Spectral Unforgetting: Post-Hoc Recovery of Damaged Capabilities Without Retraining

Fine-tuning a language model for a target task routinely degrades capabilities the training data never explicitly threatened. We study this phenomenon, known as catastrophic forgetting, and propose a post-hoc repair solution that uses only the pretrained checkpoint

W_{\mathrm{base}}

and its fine-tuned descendant

W_{\mathrm{ft}}

. The goal is not merely to revert the model toward the base checkpoint, but to recover capabilities damaged by fine-tuning while preserving both the target-task gains and any beneficial held-out improvements. We introduce DG-Hard, a checkpoint-only spectral repair method for the fine-tuning update

Δ= W_{\mathrm{ft}} - W_{\mathrm{base}}

. DG-Hard treats

Δ

as a low-rank task-aligned signal embedded in an IID-like noise residual that gradient descent has no incentive to remove, and applies the Donoho-Gavish hard singular-value threshold to each weight-delta matrix, keeping the structured high-energy part of the update and removing the spectral bulk. This reduces repair to a closed-form SVD filtering step requiring no data-dependent tuning. A central difficulty is evaluation: average accuracy hides per-benchmark failures, while naive recovery scores reward models that simply revert toward the base. We therefore introduce a partition-conditional metric that separately tracks healing, preservation, non-damage, and target-task retention. Across

14

(model, task) settings and nine cross-domain held-out benchmarks, DG-Hard achieves the strongest balanced repair among post-hoc baselines. DG-Hard also restores safety alignment degraded by benign fine-tuning on three independent safety axes, despite using no alignment data. These results suggest that part of fine-tuning-induced capability loss is not an unavoidable consequence of specialization, but a removable spectral residue in the weight update itself.

Aarash Abro, Muhammad Tahir

Zeta Labs · Lahore University of Management Sciences

Catastrophic Forgetting Model Fine-Tuning Retraining Post-Hoc Signal Reconstruction Spectral+1

May 18, 2026stat.ML

Geometric Dictionary Learning of Dynamical Systems with Optimal Transport

Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and long-term behavior. However, dynamical operators are typically estimated independently for each system, preventing the discovery of shared structure across related dynamics. To address this limitation, we posit that related dynamical systems lie near a low-dimensional manifold in spectral operator space. Based on this hypothesis, we introduce DOODL (Dynamical OperatOr Dictionary Learning), a framework that learns a dictionary of characteristic spectral dynamics whose combinations approximate this manifold and yield compact, interpretable embeddings of individual systems. Beyond representation learning, DOODL enables fast and interpretable operator estimation from short and partially observed trajectories by constraining the estimation to the learned operator manifold. Experiments on metastable Langevin dynamics and turbulent plasma simulations demonstrate that DOODL scales to highly complex multiscale regimes while capturing characteristic spectral structure governing the dynamics rather than merely fitting trajectories, achieving errors one to two orders of magnitude lower than independent operator estimation methods in challenging low-data regimes.

Thibaut Germain, Sami Chemlal, Rémi Flamary +2

CMAP, Ecole Polytechnique · Istituto Italiano di Tecnologia & University of Novi Sad

Dynamical Systems Learning Dynamics Spectral Representation Method Spectral Geometric Machine Learning Langevin Dynamics

May 18, 2026stat.ML

How does feature learning reshape the function space?

Feature learning is widely regarded as the key mechanism distinguishing neural networks from fixed-kernel methods, yet its impact on the induced function space remains poorly understood. In this work, we precisely characterize how the function space spanned by the features of a two-layer neural network evolves during gradient descent training. We prove that, in the high-dimensional proportional regime, after a large gradient step the post-update feature distribution is well approximated by a target-dependent spiked Gaussian covariance. This induces a data-adaptive kernel that reshapes the function space and modifies its spectral structure. Our analysis reveals that feature learning can be interpreted as a distributional transformation in either parameter space or input space, equivalently as the introduction of a target-dependent kernel. In particular, it selectively amplifies eigenvalues aligned with the target direction and mixes leading eigenfunctions, coupling the top radial mode with a target-aligned quadratic harmonic. Overall, our results provide a precise function-space perspective on early-stage feature learning: rather than just rescaling a fixed kernel, gradient descent induces a data-adaptive deformation that preferentially enhances directions aligned with the signal in the data.

João Lobo, Bruno Loureiro, Long Tran-Than +1

Department of Computer Science, University of Warwick, United Kingdom · Departement d’Informatique, École Normale Supérieure, PSL & CNRS · School of Mathematical Sciences, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University, China. Part of work was done at Department of Computer Science, and Centre for Discrete Mathematics and its Applications (DIMAP), University of Warwick, United Kingdom

Feature Learning Two-Layer Neural Networks Gradient Descent Spectral

May 17, 2026cs.LG

Olivia: Harmonizing Time Series Foundation Models with Power Spectral Density

Time series foundation models rely on large-scale pretraining over diverse datasets across domains, yet their heterogeneity in temporal patterns could hinder the effectiveness of training and learning transferable time series representations. Inspired a fundamental concept, normalized power spectral density (PSD) in signal processing, we assume harmonizing datasets via PSDs in the spectral domain could reduce mismatches and enhance pretraining. We then go beyond the direct intractable minimization optimization and innovatively reformulate it as a principled harmonization approach. Specifically, we propose Harmonizer, a module that reshapes spectral structures and implicitly harmonizing PSDs across datasets, which theoretically corresponds to a shared reparameterization of second-order temporal correlations. Our theoretical analysis further reveals token interactions with Harmonizer can be efficiently mediated by a compact set of resonators, motivating a HarmonicAttention design that performs self-attention in a low-dimensional interaction space. Then, we propose Olivia, a novel time series foundation model built upon these harmonization mechanisms. Extensive experiments on two large-scale benchmarks (TSLib and GIFT-Eval) and extra 6 datasets from GluonTS, demonstrate Olivia consistently achieves state-of-the-art performance under zero-shot, few-shot, and full-shot forecasting scenarios. Our code is available at https://github.com/TSTS13/Olivia.

Jingru Fei, Kun Yi, Alex Xing Wang +3

Beijing Institute of Technology · North China Institute of Computing Technology · State Information Center +4

Time Series Foundation Models Time Series Wireless Foundation Models Pretraining Harmonization Spectral

May 17, 2026cs.CV

SpecSem-Net: Integrating Spectral and Semantic Features for Robust AI-generated Video Detection

The remarkable visual fidelity of recent commercial video generative models, such as Sora and Veo, renders robust AI-generated video detection increasingly essential to prevent synthetic content from being indistinguishable from real videos and exploited for disinformation. However, existing detectors often fail due to an over-reliance on increasingly realistic semantic features, neglecting subtle spectral artifacts. In this paper, we propose SpecSem-Net, the first framework to introduce a semantic-guided spectral denoising mechanism specifically for high-fidelity AI-generated video detection. Specifically, we design a spectral module to extract high-frequency features via Fourier-Transform based filtering. Furthermore, to reduce misjudgments arising from spectral noise, we employ a Gated Merging Mechanism to adaptively fuse semantic context, effectively mitigating spectral noise. Additionally, to evaluate detector performance on the latest top-tier generative models, we construct a comprehensive benchmark comprising 5 SOTA commercial generators. Extensive experiments demonstrate that SpecSem-Net outperforms existing methods, achieving accuracies of 87.25% and 95.59% on our benchmark and public datasets, respectively.

Zixi Wei, Huixuaun Zhang, Xiaojun Wan

Wangxuan Institute of Computer Technology, Peking University

Ai-Generated Video Detection Generative Video Models Visual Fidelity Generative Models Spectral

May 16, 2026cs.LG

DynMuon: A Dynamic Spectral Shaping View of Muon

In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly. The essential difference, when compared to standard gradient descent methods, is to replace the usual update matrix

M=UΣV^\top

with its polar factor

UV^\top

. In this work, we consider a class of Muon-like updates, where we replace the update

M

with

UΣ^p V^\top

for some parameter

p

. We call this a "spectral-shaping" operation, and develop a theory of how to pick

p

which depends on (a) local curvature of the loss function, (b) noise stemming from stochastic gradients and label noise, and (c) training stage. Our theory and experimentation reveal a previously overlooked behavior: positive

p

helps early by emphasizing high-curvature directions and accelerating signal contraction, while mildly negative

p

helps later by reallocating update strength toward low-curvature directions that still contain useful training signals. Building on the insight, we propose DynMuon, an efficient dynamic spectral shaping method that schedules

p

from positive to mildly negative over training. Extensive experiments across model sizes, architectures, and training settings show that DynMuon consistently achieves lower validation loss than Muon, while requiring 10.6-26.5% fewer steps to reach the same target loss. Our code is available at https://github.com/fzwark/DynMuon.

Fangzhou Wu, Rikhav Shah, Sandeep Silwal +1

University of Wisconsin–Madison · MIT · Elorian AI

Muon Spectral Loss Function

May 15, 2026cs.CV

LDGuid: A Framework for Robust Change Detection via Latent Difference Guidance

Modern deep learning models for change detection (CD) often struggle to explicitly represent task-relevant semantic differences. This paper proposes the Latent Difference Guidance (LDGuid) framework that explicitly learns and injects semantic differences into CD models. LDGuid deploys adversarial autoencoding to implement a difference embedding (DE) module. The DE module is pretrained via the information bottleneck method, restricting it to learn only task-relevant differences between pre- and post-event samples. The learned latent difference is then used as an explicit guidance signal in the CD model. We validate LDGuid by integrating it into U-Net, BIT, and AERNet baselines for CD and evaluating it on LEVIR-CD, WHU-CD, SVCD, and CaBuAr datasets. Experimental results show that LDGuid enhances segmentation performance across all benchmarks, with particularly remarkable gains in challenging settings affected by spectral noise. The results further highlight the ability of LDGuid in incorporating domain knowledge, such as task-specific spectral indices. Our findings suggest that semantic difference learning can drastically enhance the robustness of CD in remote sensing.

Jiaxuan Zhao, Ali Bereyhi

University of Toronto

Change Detection Deep Learning Spectral

May 13, 2026cs.LG

Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Training

Pre-training large language models is dominated by the memory cost of storing full-rank weights, gradients, and optimizer states. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly. A central question remains open: do low-rank methods produce models that generalize comparably to full-rank training, or does the rank constraint fundamentally alter the solutions reached? Existing comparisons rely almost entirely on validation perplexity from single-seed runs, often carried forward from prior literature. Yet perplexity is a poor proxy for solution quality; two methods can match on perplexity while converging to different loss landscape regions and internal representations. We close this gap by characterizing the solutions found by five low-rank pre-training methods, GaLore and Fira (memory-efficient optimizers), CoLA and SLTrain (architecture reparameterizations), and ReLoRA (adapter-style updates with periodic resets), against full-rank training at three model scales (60M, 130M, 350M). We evaluate each along 16 metrics across four dimensions: 1-D loss landscape along random/top-K PCA directions, 1-D interpolation between checkpoints, spectral structure of the weights and learned updates, and activation similarity to full-rank training. We show that low-rank methods are not equivalent to full-rank training, nor to one another, even when validation perplexity is close. Full-rank training settles into a sharper basin than low-rank methods along random directions, while the reverse holds for the top-1 PCA direction. Each method converges to a geometrically distinct basin. Low-rank activations diverge from full-rank in later layers as training progresses, with GaLore tracking full-rank most closely. Further, validation perplexity does not translate to downstream performance at every scale. Adding geometric and spectral metrics improves the prediction.

Namrata Shivagunde, Vijeta Deshpande, Sherin Muckatira +1

University of Massachusetts Lowell

Low-Rank Structure Language Model Perplexity Anisotropic Loss Landscapes Spectral Beyond Retrieval

May 13, 2026cs.CV

Phy-CoSF: Physics-Guided Continuous Spectral Fields Reconstruction and Super-Resolution for Snapshot Compressive Imaging

Recent advances have demonstrated that coded aperture snapshot spectral imaging (CASSI) systems show great potential for capturing 3D hyperspectral images (HSIs) from a single 2D measurement. Despite the inherent spectral continuity of scenes captured by CASSI, most existing reconstruction methods are restricted to fixed, discrete spectral outputs, thereby precluding continuous spectral reconstruction or spectral super-resolution. To address this challenge, we propose Phy-CoSF, which synergizes deep unfolding networks with implicit neural representations, establishing a new paradigm for continuous spectral reconstruction and super-resolution in CASSI. Specifically, we propose a two-phase architecture that bridges discrete-wavelength training with continuous spectral rendering, enabling the synthesis of high-fidelity HSIs at arbitrary target wavelengths. At the core of our framework lies the continuous spectral fields (CoSF) module, embedded within each unfolding stage as a dynamic prior, which comprises a triple-branch cross-domain feature mixer for comprehensive spatial-frequency-channel feature fusion, alongside a spectral synthesis head that generates spectral intensities by querying continuous wavelength coordinates. Extensive experimental results demonstrate that Phy-CoSF not only achieves continuous modeling at arbitrary spectral resolutions but also outperforms many state-of-the-art methods in both reconstruction fidelity and spectral detail preservation. Our code and more results are available at: https://github.com/PaiDii/Phy-CoSF.git.

Wudi Chen, Zhiyuan Zha, Xin Yuan +6

College of Communication Engineering, Jilin University, Changchun 130012, China. · School of Engineering, Westlake University, Hangzhou, Zhejiang 310024, China. · School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore 639798. +4

Signal Reconstruction Hyperspectral Image Two-Level Spatial-Frequency Fusion Strategy Spectral

May 13, 2026cs.LG

CoRe-Gen: Robust Spectrum-to-Structure Generation under Imperfect Fingerprint Conditions

Molecular structure elucidation from tandem mass spectra (MS/MS) remains challenging, particularly for de novo generation beyond database coverage. A common approach decomposes the task into spectrum-to-fingerprint prediction followed by fingerprint-to-structure decoding, enabling the use of large-scale molecular corpora. However, at deployment, the decoder relies on predicted rather than oracle fingerprints, introducing structured errors that propagate into generation. This results in a fundamental condition mismatch, where models trained on clean inputs must operate under noisy, biased predictions, especially for long-tail substructures. We present CoRe-Gen that explicitly addresses this gap. CoRe-Gen improves the intermediate condition via synthetic-spectrum pretraining of the encoder, matches deployment-time noise through frequency-aware fingerprint corruption during decoder training, and mitigates residual errors using structure-aware autoregressive decoding with compositional SELFIES representations, auxiliary structural supervision, and lightweight chemical constraints. Experiments on standard benchmarks show that CoRe-Gen establishes a new state of the art on NPLIB1, achieving 19.54% Top-1 and 29.92% Top-10 exact-match accuracy, while remaining competitive on the more challenging MassSpecGym benchmark. Importantly, CoRe-Gen preserves the efficiency advantages of autoregressive decoding, providing a practical and scalable solution for robust spectrum-to-structure generation under realistic conditions.

Tianbo Liu, Chixiang Lu, Jing Hao +4

The University of Hong Kong · The Chinese University of Hong Kong · Zhejiang Shuren University

Tandem Mass Spectra Molecules Spectral Fingerprint Text Corpora