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

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Latest papers 156

Sep 30, 2026cs.LG

Beyond Simulation: Retain-and-Repair Neural Operators for Real-World Adaptation

Neural operators increasingly benefit from pretraining on numerical simulations, yet adapting them for real-world prediction remains challenging. We introduce the Retain-and-Repair Neural Operator (R

^2

NO), a framework for adapting simulation-pretrained operators to real-world data while retaining useful pretrained structure. The pretrained operator is first finetuned on real data and then frozen to provide a source prediction, and a shared repair module learns a sequence of refinements from the same observations. Using orthogonal Fourier projections, a spectral ensemble fits a small ridge regression within each cell of the Fourier domain and combines the refinements by weights fitted on a held-out split of the real data. The cells are defined jointly by radial ranges, angular sectors, and measured channels, allowing refinement depth to vary with frequency magnitude, with orientation, and across channels. Including the source prediction as a candidate makes retention available in every cell, and independently trained repair modules enter the same combination as additional candidates. On all RealPDEBench systems and six backbones, R

^2

NO consistently outperforms full finetuning and iterative refinement. The framework treats adaptation depth as a cell-specific choice learned from real data.

Woojin Cho, Junghwan Park

TelePIX

Neural Operators Rapid Adaptation Spectral

Sep 29, 2026cs.RO

Learning Expressive and Compositional Motion Representation via Spectral Skills

Robotic foundation models offer a promising path toward general-purpose humanoid robot control, often through hierarchical architectures. However, their effectiveness depends on the command interface between the planner and the controller, which must support accurate execution while remaining easy to predict, and ideally allow new behaviors to be composed from prior ones. In this work, we introduce spectral skills, a latent representation of this interface that meets these requirements through predictive representation learning. By design, spectral skills compactly encode short motion segments and are learned by predicting subsequent motion rather than reconstructing the encoder input. On a 29-DoF humanoid, a controller conditioned on spectral skills reduces global tracking error by 62% relative to the state of the art. The same frozen controller chains independently encoded skills without a separate transition policy. It also composes new behaviors by adding orthogonal directions to any compatible base skill, producing combinations unseen in the training data. We demonstrate tracking, chaining, and composition, as well as control through a language-conditioned planner, on Unitree G1 hardware. Project page: https://spectral-skill.github.io

Feiyang Wu, Chenxiao Gao, Chen Yang +3

Georgia Institute of Technology

Full-Body Humanoid Control Human-To-Robot Transfer Latent Motion Action-Conditioned Planning Expressivity Spectral

Sep 28, 2026cs.LG

On the spectral properties of generative denoiser Jacobians

Generative denoising models, such as diffusion and flow-matching, learn to sample from complex distributions by training a deep neural network denoiser to recover clean data from noise-corrupted samples. While such models are typically compared on the quality of their synthesized samples, these metrics provide limited insight into how the underlying denoiser, which drives generation, differs. In this work, we propose to analyze the spectrum of the denoiser Jacobian as a tool to characterize these differences. Across pre-trained denoising models, we observe that better generative performance is associated with larger Jacobian eigenvalues. Motivated by this, we introduce a regularization scheme that controls the Jacobian spectrum by training the denoiser on perturbed inputs, with perturbations suppressing or amplifying Jacobian responses. On ImageNet, we test whether directly modifying the Jacobian spectral properties leads to improved generations. Our findings suggest that denoisers benefit from both strengthening responses along data-relevant principal eigen-directions and suppressing the noisy, data-irrelevant ones. This establishes the denoiser Jacobian as a useful tool for identifying differences between generative denoising models.

Alexandros Graikos, Nebojsa Jojic, Dimitris Samaras

Stony Brook University · Microsoft Research

Denoising Diffusion Probabilistic Model Iterative Denoising Methods Jacobian Spectral Principal Component Analysis

Sep 28, 2026cs.LG

Neural networks for spectral optimization

Given a functional dependent on the spectrum of a differential operator, we address the problem of finding a domain which optimizes this functional. PDE solvers might be used to tackle this optimization. It is however computationally expensive. We propose two neural network models which learn the spectrum directly from the geometry of the domain and can be used to optimize the domain from one or more eigenvalues. We investigate two representations. The first encodes the domain through Fourier coefficients and a light MLP, which is efficient on star-shaped geometries, achieving a precision of 0.2%. Through a rescaling of the coefficients the designed models satisfy the scaling law of the eigenvalues. Additionally, averaging the outputs of the trained surrogates over rotations and reflections induces invariance for these transformations. The second is a model that takes the landscape function, the indicator function and the gradient of the landscape function. A Gram-Schmidt process produces orthogonal eigenfunctions as output of the model along with the associated eigenvalues. The landscape model reaches 1% mean relative error on the first ten eigenvalues, compared with 4% for an FNO model. Replacing the landscape by an SDF worsened both prediction and optimization errors. The trained model also generalizes from synthetic shapes to domains given as classical image dataset. The resulting surrogates of both approaches recover classical spectral optima such as the disk for the first eigenvalue or the conjectured minima of higher eigenvalues. This confirms that our models produce accurate differentiable estimates of eigenvalues, which can be used in shape optimization problems involving spectral quantities.

Alexis de Villeroché, Beniamin Bogosel, Stéphane Breuils +2

Spectral Representation Method Neural Partial Differential Equation Solvers Spectral Neural Network Optimization Neural Network Landscapes

Sep 28, 2026cs.LG

Transferable Mass Spectrum Prediction via Reference-Guided Test-time Specialization

Tandem mass spectrum prediction supports compound identification across metabolomics, natural-product discovery, and environmental analysis. However, pretrained predictors often degrade under shifts in chemical space and acquisition conditions, while retraining domain-specific models from scratch is costly. We introduce SPARC, a retrieval-guided test-time specialization framework that adapts a pretrained predictor using a spectral reference library without accessing test-query spectra. For each target query, SPARC retrieves chemically related reference spectra to recalibrate fragment intensities within the learned fragmentation space. During Transfer, SPARC combines reference-guided spectral adaptation with reliability-aware consistency, using reconstruction behavior on retrieved spectra to selectively preserve trustworthy predictions during continual specialization. Across MassSpecGym, NPLIB1 and application-specific GNPS libraries, SPARC improves spectral prediction under multiple transfer settings. These results establish retrieval-guided test-time specialization as a practical strategy for extending pretrained MS/MS predictors to specific chemical and acquisition domains, with continual test-time training providing further refinement during deployment.

Yunhua Zhong, Runting Li, Yifan Li +5

The Hong Kong University of Science and Technology (Guangzhou) · The University of Hong Kong · South China University of Technology +3

Tandem Mass Spectra Metabolic Molecular Property Prediction Spectral Test-Time Training Test Time

Sep 28, 2026cs.LG

First Learn, Then Memorize: The Spectral Bias of Diffusion Models

Diffusion models trained on a finite dataset first learn to generate novel, high-quality samples and only much later collapse onto their training set. We identify the mechanism behind this separation of timescales and the object that probes it. The training dynamics of the score function are governed---exactly, and at any width---by the Gram matrix of the Neural Tangent Kernel (NTK) evaluated on the noisy training data, so the timescales of generalization and of memorization must be encoded in its spectrum. We show that they are, and that the structure responsible has no analogue in standard kernel settings. The use of multiple noise realizations per sample (

m

noised copies at a fixed noise level) in the score-matching loss is what restructures the Gram matrix spectrum into two distinct parts. The first, of large eigenvalues, carries the global features of the target distribution and is present already for

m=1

. The second, which the repeated noising creates, consists of the smallest eigenvalues and is supported on eigenvectors aligned with the sample-specific noise directions; it sets a memorization timescale parametrically larger in the training set size

n

. We establish this picture on two fronts. Analytically, we solve the spectrum in the lazy high-dimensional limit for both linear (

n \asymp d

) and polynomial (

n \asymp d^k

) sample complexities, and prove through a bias--variance decomposition that the first bulk minimizes the approximation error while the second drives the error associated with memorization. Empirically, we show the same two-bulk structure in Convolutional NTKs on CelebA and in finite-width U-Nets trained well beyond the lazy regime, and we make the link causal: truncating the Gram matrix at rank

r

tunes the generalization--memorization transition, and an

L_2

penalty targeting the second bulk suppresses memorization in feature-learning U-Nets.

Raphaël Urfin, Tony Bonnaire, Giulio Biroli +1

Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005 Paris, France · Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405 Orsay, France · Department of Computing Sciences, Bocconi University, Milano, Italy

Neural Tangent Kernel Diffusion Models Spectral Memorization

Sep 28, 2026cs.LG

LionMuon: Alternating Spectral and Sign Descent for Efficient Training

Pretraining a language model takes enormous compute, and the right optimizer can save a good part of it. Muon's spectral step gives a stronger direction than a sign step, but it is expensive. Every step runs Newton-Schulz iterations on the full matrix and, in distributed training, an extra all-reduce. Sign steps, as in Lion and Signum, are cheap and stay local to each device. We propose LionMuon, which takes one Muon step every

P

iterations and Lion steps in between, with a single dual-EMA momentum buffer shared by both. Muon's compute and communication are paid once per

P

steps, and the optimizer state is half of AdamW's. A single-EMA variant, SignMuon, already improves on Muon. We prove complexity bounds under heavy-tailed noise in which the period sets an interpolation between Muon's and Lion's smoothness and noise constants, and which say when LionMuon is faster than both. On 124M and 355M models trained on FineWeb, LionMuon with

P=2

and

P=5

reaches a lower loss than Muon, AdamW, Lion and Signum at the same number of tokens. Under 4-GPU data-parallel training it reaches Muon's final loss with a third less wall-clock on PCIe, and it beats the communication-efficient Muon variants Dion and MuonBP on loss at no more exposed communication, while keeping the exact gradient. 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

Sep 28, 2026cs.LG

$λ$ -JEPA Spectral Anti-Collapse Regularization for Self-Supervised Learning

Joint-embedding self-supervised learning typically combines an invariance objective across augmented views with additional mechanisms to prevent representational collapse. These objectives are often applied after a projection head, while downstream tasks use the backbone representation before the projector. We find that this mismatch does not necessarily prevent dimensional collapse in the backbone, which can retain low effective rank and potentially limit downstream transfer. To address this, we introduce SACReg, a spectral anti-collapse regularizer motivated by an analysis of

λ

-balance, which captures the relative scale of weight matrices across layers. In a two-layer linear network, we show that (i)

λ

-balance prevents collapse, and (ii) our regularizer applied to the backbone induces

λ

-balance. In the nonlinear case, this regularizer leads to anti-collapse as well and, in realistic architectures on ImageNet100, it empirically increases the representations' ranks. We apply SACReg to JEPA and propose

λ

-JEPA, which improves over LeJEPA and VISReg on ImageNet-1k classification and in average linear-probe transfer performance across eight downstream image datasets. On video self-supervised learning,

λ

-JEPA improves over LeVJEPA and V-JEPA 2 on the Something-Something-v2 and Kinetics-400 benchmarks. Code is available at https://github.com/berkerdemirel/lambda-jepa.

Berker Demirel, Clémentine Dominé, Valentino Maiorca +3

Institute of Science and Technology Austria (ISTA) Am Campus 1, 3400 Klosterneuburg, Austria

Self-Supervised Learning Regularization Spectral S-Jepa Collapse Representational Collapse

Sep 28, 2026cs.LG

Harmonizing Spectral Evolution in Conditional Flow Matching for TTS

Conditional Flow Matching (CFM) models for text-to-speech (TTS) suffer from incoherent frequency evolution during inference. While similar spectral imbalances are addressed in diffusion models for other domains, those generic solutions fail to generalize to the inherently uncoordinated acoustic dynamics of CFM. We demonstrate that this issue can be effectively mitigated by introducing a novel training-free frequency-selective boosting strategy. Using the Discrete Wavelet Transform (DWT), our method dynamically modulates mel-spectrogram sub-bands during ODE integration, synchronizing spectral development by penalizing aggressive low-frequency growth and boosting lagging high-frequency details. Validated across diverse architectures (Matcha-TTS, F5-TTS, IndicF5), our approach reduces the required Number of Function Evaluations (NFE) from 32 to 26 and improves Frechet Audio Distance (FAD) by up to 61%, all without compromising mean opinion scores, speaker similarity, and speech intelligibility.

Isha Pandey, Varad Deshpande, Abhijat Bharadwaj +1

Indian Institute of Technology Bombay

Flow-Matching Text-To-Speech Speaker Similarity Spectral Features Conditional Flow Matching Acoustic Spectral+1

Sep 27, 2026cs.CV

Residual-Stream Burden Shapes Representation Learning in Diffusion Transformers

In diffusion-based generation, a neural network can be trained to predict the clean data, the noise, or the velocity from a noisy input. These prediction targets are interconvertible and describe the same generative process, yet plain Diffusion Transformers operating on large pixel patches succeed with clean prediction and fail with noise or velocity prediction. We argue that this asymmetry arises because noisy targets require the residual stream to preserve noise-dependent input variation through depth for the final readout, forcing subsequent layers to compute on noisy representations. A spectrally concentrated clean target imposes a lighter demand, leaving greater freedom to organize hidden representations for subsequent computation. We call this preservation requirement residual-stream burden and show how it shapes representation learning in Diffusion Transformers. Controlled experiments indicate that the exploitable structure is spectral concentration in patch space and that the bandwidth of the persistent residual state is a key resource for noisy prediction. We further show that this account is consistent with recent decoupled pixel-space architectures, whose diverse designs all reduce the residual-stream burden on the main pathway. To examine this understanding from a complementary direction, we expand and reorganize the residual-stream bandwidth directly, introducing Spatially Indexed Hyper-Connections (SiHC) that reach FID 1.71 on ImageNet

256^2

. Together, these results identify residual-stream burden as a mechanism through which prediction targets and architecture jointly shape representation learning in Diffusion Transformers.

Tongtong Liang, Siqi Kou, Ziqiao Xi +6

UC San Diego · Shanghai Jiao Tong University · Aether AI

Diffusion Transformers Transformer Residual Streams Residual Stream Transformer Architectures Representation Learning Spectral+1

Sep 27, 2026physics.optics

Multi-Aperture PPG with MAPIS: Spatial Optical and Temporal Coherence Fields

Conventional reflectance photoplethysmography (PPG) typically reduces tissue optical responses to one or a few detector channels. Matrix Pinhole Image Sensing (MAPIS) instead simultaneously samples multiple aperture-dependent optical signals. We analyzed 44 recordings of 30 seconds each from a single MAPIS device to characterize the spatial relationships among DC intensity, pulsatile AC, perfusion index (PI), and temporal coherence across Red and infrared channels. AC increased sublinearly with DC at both wavelengths, resulting in higher PI toward lower-DC apertures, consistent with a first-order relative path-sensitivity interpretation. A second counterintuitive spatial trend was observed in temporal coherence: lower-DC and lower-AC apertures exhibited higher autocorrelation and greater cardiac-periodic spectral concentration. IR signals also showed consistently higher temporal coherence than corresponding Red signals. These observations demonstrate that multi-aperture PPG resolves reproducible spatial relationships among optical intensity, fractional pulsatile sensitivity, and waveform coherence that are largely averaged together in conventional single-channel PPG. The present study establishes within-device relationships and motivates controlled studies of the underlying photon-path mechanisms.

Shuguang Wang, Yuanjing Wang

Remote Photoplethysmography Spatial Coherence Coherence Spectral

Sep 27, 2026cs.LG

TNF based Spectral Embedding for Effective Application of Supervised Machine Learning Techniques in Automobile Insurance Fraud Detection

Fraud detection is an important area of research in the insurance business due to its financial implications. The primary aim of a fraud detection model is to identify fraud and non-fraud cases with high accuracy along with other important metrics such as Sensitivity, Specificity, Precision, F1-score, False Positive Rate, False Discovery Rate, AUC etc. To achieve this, we need to explore a suitable classification model to identify fraud and non-fraud cases. In this work, we have used auto insurance data set and explored classification models such as Decision Tree (DT), Random Forest (RF), XGBoost, LightGBM and Gradient Boosting Machine (GBM). To overcome the problem of data imbalance, we have employed MWMOTE and TGAN techniques. We have used Topological Node Feature(TNF) based spectral embedding for low dimensional data representation along with some popular embedding methods like MDS, Isomaps and t-SNE. After studying all the 65 possible combinations of these models, we have proposed an innovative method for effective automobile insurance fraud detection. For the given dataset, our results show that using a combination of MWMOTE as a data imbalance handling technique (Phase I), TNFSE2 as data embedding (Phase II) and Random Forest as classification (Phase III) provides the best result in comparison to all other combinations. This work also highlights the efficacy of TNF based spectral embedding in automobile insurance dataset

Rohan Yashraj Gupta, Lalith Srikanth Chintalapati, Satya Sai Mudigonda +2

Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, Vidyagiri, Puttaparthi, Andhra Pradesh, India.

Fraud Detection Random Forest Insurance Semi-Supervised Learning Spectral Class Imbalance

Sep 23, 2026math.NA

Tensor Decomposition of Transformer Key-Value Caches: Spectral Structure and Format Comparison

The key-value (KV) cache of autoregressive transformers can be viewed as a fourth-order tensor spanning attention heads, tokens, features, and grouped layers. We measure the singular-value spectra of all four mode unfoldings on Mistral-7B-v0.3 and LLaMA-2-13B and compare four standard tensor decompositions: Tucker, CP, tensor train, and t-SVD, at matched storage. The spectra partition the four axes into two classes. The token and feature modes carry low-rank structure, particularly for keys. The head and layer modes are nearly full-rank and resist compression at any practical error level. Among the four decompositions, Tucker achieves the lowest reconstruction error at every compression ratio from

2\times

to

5\times

, because it can leave the full-rank modes untouched. Comparisons with two-dimensional unfolding baselines show that the preferred representation differs between keys and values: 2D methods achieve lower key error, while four-way Tucker achieves lower value error at matched storage. A mode-pinning theorem certifies the full-rank preservation from the measured spectra alone. Two further spectral properties affect the compressible modes without touching the full-rank ones: values reach a higher error floor than keys at every ratio, and post-RoPE keys lose

41\%

-

64\%

of their pre-RoPE compressibility on both models.

Rahul Krishnan, Volker Schulz

Universität Trier · Fachbereich IV, Mathematik, Universität Trier

Key-Value Cache Compression Tensor Decomposition Autoregressive Transformers Transformer Architectures Spectral Comparison

Sep 23, 2026cs.CV

Learning Spectral Allocation: A Fractional Diffusion Framework for Adaptive Volumetric Segmentation

We address adaptive computation in 3D medical image segmentation: instead of designing another backbone, we ask how much spectral mixing each network stage needs and let optimization answer. We derive FHEAT, a two-parameter operator family, from the discrete cosine transform (DCT) solution of a fractional heat equation. A fractional order alpha and a diffusion strength D govern the operator, and at D=0 it is exactly the identity. Reparametrized by the semigroup time tau = D*alpha, same-resolution instances compose exactly, so any distribution of diffusion across same-resolution stages amounts to a single Sobolev-type regularizer of learned strength. This identity limit lets the optimizer of each layer, not the designer, decide whether global mixing is needed and how sharp it should be. We instantiate FHEAT in a lightweight U-shaped architecture (Light-UNETR) paired with a Kolmogorov-Arnold mixer (KAN3D) with adaptive rational activations, yielding FHEAT-Seg. At 5% to 20% label rates on three public benchmarks, training produces gradient-driven spectral sparsification: seven of the eight stage-level operators drive D to zero, and the survivor saturates at the sharpest low-pass (alpha ~ 0.9) in the decoder layer feeding the semi-supervised attention map. The retired layers become exact identity shortcuts at inference, cutting FLOPs from 4.29G to 0.90G (a 79% drop) at 0.975M parameters. Under a standard semi-supervised protocol, FHEAT-Seg reaches Dice scores of 90.47% (left atrium), 78.79% (Pancreas-CT), and 81.90% (BraTS 2019), ahead of five semi-supervised methods and the Light-UNETR baseline. The large variant also surpasses Light-UNETR-L under full supervision (Dice 93.09%, 85.11%, and 87.19%) with 2.851M parameters and 55.75G FLOPs. These results suggest that the allocation of spectral computation is a learnable property of optimization dynamics, not a manual design commitment.

Yi-Hui Shen, Tie-Qiang Li

School of Arts and Sciences, Fujian Medical University, Fuzhou, China · School of Medical Imaging, Fujian Medical University, Fuzhou, China · Department of Medical Radiation Physics and Nuclear Medicine, Karolinska University Hospital, Stockholm, Sweden +2

3D Medical Image Segmentation U-Net Spectral Diffusion Dynamics Decoder Layers

Sep 14, 2026cs.LG

Dimension-Corrected Hitting Times for Heavy-Tailed Spectral Emergence in Neural Optimizer Dynamics

Heavy-tailed empirical spectral densities of neural-network weight matrices are widely used as diagnostics of implicit self-regularization, but the step complexity of heavy-tail emergence remains poorly understood. We formulate spectral heavy-tail formation as a right-censored hitting-time problem: a run that does not reach a heavy-tail diagnostic within the observation horizon is treated as censored rather than discarded. In controlled full-batch teacher--student dynamics, we find that the first-step spike--bulk gap alone does not explain onset time. Instead, finite-onset regression supports a dimension-corrected spectral-gap law, (\tau_{\mathrm{HT}}\approx C\Delta_1^{-\gamma}d^\rho), with (R^2=0.683), (\gamma=0.626), and (\rho=0.772) across 330 completed runs. Right-censored lognormal accelerated-failure-time models further favor the dimension-corrected model over a gap-only model, improving AIC from 706.62 to 628.70. Theoretically, we prove that exact early loss dynamics in linear networks do not determine factor spectral tails, that Adam recurrences alone do not imply spectral redistribution, and that projected singular-basis spreading implies contraction of a spectral-tail potential and hence a dimension-corrected hitting-time bound. Empirically, projected-kernel profiles support the sufficient spreading mechanism, Adam and AdamW agree under tested grids, GD and signGD do not reach onset in the same regimes, and real pretrained Qwen2.5-0.5B and Pythia-70M transformer weights show non-Gaussian spectral-tail structure relative to matched Gaussian nulls. The result is a reproducible spectral hitting-time law with rigorous conditional theory, not a claim that Adam necessarily generates heavy tails from first principles.

Zongmin Liu

Stanford University

Long-Tailed Distribution Spectral Neural Network Optimization Regularization Time-To-First-Spike

Sep 14, 2026cs.CV

Spectral Consistency-Guided Multiview Point Cloud Registration for Low-Overlap Scenes

Multiview point cloud registration is particularly challenging in low-overlap scenes, where reliable correspondences are limited and incorrect pairwise transformations can affect global pose estimation. In addition, registering all scan pairs is computationally expensive because many pairs provide weak geometric information. To address these problems, we propose GMPCR, a non-learning-based spectral consistency-guided framework for efficient and robust multiview point cloud registration. GMPCR builds a refined second-order compatibility structure from initial correspondences and uses its dominant spectral response to evaluate both correspondence reliability and scan-pair confidence. This allows unreliable correspondences to be filtered and informative scan pairs to be selected before relative transformation estimation, leading to a sparse pose graph and reduced pairwise registration cost. For each retained scan pair, maximal-clique-based hypothesis generation is used to estimate reliable relative transformations. The resulting pose graph is further refined by an adaptive history-aware synchronization scheme, in which the effect of residual history is adjusted according to changes in the global rotation residual. A recovery mechanism also allows down-weighted edges to regain confidence when their global consistency improves. Experiments on 3DMatch, 3DLoMatch, ScanNet, and ETH demonstrate the effectiveness of GMPCR. It achieves registration recalls of 97.2% and 89.6% on 3DMatch and 3DLoMatch, respectively, while maintaining competitive performance on ScanNet and ETH. The results show that GMPCR provides a favorable balance among registration accuracy, robustness to low overlap, and computational efficiency. The code is publicly available at https://github.com/swccj/gmpcr.

Tianyu Li, Yanghong Lin, Shudong Zhou +4

School of Resources and Environmental Sciences, Wuhan University, Wuhan, China · Spatial Intelligence and Urban Computing, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen, China · State Key Lab for Ecological Security of Regions and Cities, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen, China

Point Cloud Registration Category-Level Object Pose Estimation Spectral

Sep 11, 2026cs.RO

Quantifying Spectral Differences in Vehicle Kinematics Between Production Autonomous and Human-Driven Vehicles Across Driving Scenarios

Differences in vehicle kinematic characteristics between production autonomous vehicles (PAVs) and human-driven vehicles (HVs) have been limitedly investigated by empirical studies. Most recent studies rely on simulation-based models, while some further investigate low-level adaptive cruise control (ACC) systems in controlled experiments. These methods commonly adapt some time-domain metrics to characterize PAV-HV differences across limited driving conditions. However, current PAVs equipped with high-level autonomous driving systems generate driving behaviors in a black box using data-driven models. These fundamentally different mechanisms for generating behaviors may produce distinct kinematic characteristics in traffic. More importantly, these time-domain metrics cannot reflect frequency-related traffic dynamics across different driving scenarios. Thus, this study adapted a real-world PAV dataset with four PAV platforms and developed a frequency-domain framework to quantify kinematic differences between PAVs and HVs across diverse driving scenarios, including varying driving states, lighting, weather, and vehicle densities. The framework transforms kinematic signals into the frequency domain and extracts spectral features, and then compares these features between PAVs and HVs based on kernel density estimation and Wasserstein distance. The results reveal clear scenario-dependent PAV-HV spectral differences. Specifically, speed-related differences were consistently smaller during car-following than cruising, while rainy conditions consistently enlarged acceleration-related differences compared with clear conditions. These findings highlight the necessity of multi-scenario evaluations and demonstrate the value of frequency-domain analysis for characterizing PAV-HV kinematic differences under real-world conditions.

Peiyi Fang, Xiangyu Li, Yonglin Weng +1

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, 511453, China

Dynamic Driving Scenes Traffic Acceleration Spectral

Sep 11, 2026quant-ph

Learning structural balance of graphs from quantum spectral features

We develop a quantum approach to spectral feature extraction from the density of states (DOS) of a problem-dependent Hamiltonian, and apply it to machine learning on signed graphs. We propose to embed a signed graph as an Ising model instance with positive and negative interactions, and use the standardized moments of the Ising DOS as features for learning. We show that these moments count signed closed walks, are switching-invariant, and are size-free by construction. As a benchmark, we target learning the frustration index, an NP-hard measure of structural balance that can be labeled exactly at moderate size. At zero field, the models can be sampled classically, allowing the quantum extraction procedure to be certified against exact ground truth. We propose DOS-QPE, a phase estimation on a purified maximally mixed probe, which samples the spectral density with orders of magnitude fewer shots than Hadamard test-based trace sampling and feeds the resulting features directly into classically trained models. On

1.4\times10^5

labeled graphs the exact DOS determines the frustration index, and five moments recover it with a mean error of 0.4, well below one sign flip. Beyond zero field, the underlying trace-estimation problem is DQC1-complete, providing access to spectral features for which no efficient classical sampling method is known. Our work opens routes towards quantum applications in social network balance analysis, spin-glass studies, correlation clustering, and protein-interaction networks.

Stefano Scali, Oleksandr Kyriienko

Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, UK · School of Mathematical and Physical Sciences, University of Sheffield, Sheffield S10 2TN, UK

Graph Edge Sparsification Qubit Spectral Hamiltonian Balance Spectral Features+1

Sep 10, 2026cs.LG

Predicting Privacy Leakage from Weight Spectral Density

Membership inference attacks (MIAs) are widely used to audit the privacy disclosure risk of machine learning models, however current state-of-the-art attacks require training computationally expensive shadow models, making large-scale privacy evaluation impractical. In this work, we investigate whether inexpensive spectral metrics derived from the heavy-tailed self-regularisation framework can serve as proxies for MIA vulnerability. We evaluate several WeightWatcher spectral metrics on image and tabular classification tasks and compare their relationship with MIA privacy leakage against conventional measures of generalisation. Across datasets, stable rank exhibits a strong positive correlation with overall MIA success, while Log alpha-Norm shows a consistent negative correlation with MIA vulnerability at the low false-positive regime. These associations are observed to be stronger than those obtained using the generalisation gap. The results indicate that neural network spectra may contain information about privacy leakage that is not fully captured by conventional measures of overfitting, motivating spectral analysis as a promising direction for scalable privacy auditing.

Richard J. Preen, Jim Smith

Department of Computer Science and Creative Technologies University of the West of England Bristol, UK BS16 1QY

Membership Inference Attacks Privacy Spectral Regularization

Sep 8, 2026cs.CV

Temporal State Transport in Video Generation: Diagnosing and Correcting Spectral Imbalance

Reliable video generation requires more than high-quality frames to form a coherent story: a model must maintain a persistent state, transporting visual attributes such as identity, scene layout, motion, and fine details across time. Existing training-free methods mainly strengthen cross-frame attention or analyze local attention entropy, but these views do not reveal whether temporal interactions stay in a healthy transport regime. In this work, we study video generation through the perspective of Temporal State Transport. We introduce Spectral Tension, a signed diagnostic that compares local attention diffuseness with global spectral diversity, and use it to identify two opposite temporal failures: fragmented transport and over-mixing hotspots. Based on this diagnosis, we propose Spectral Transport Homeostasis, a training-free regulator that softly corrects pathological temporal states while largely preserving balanced ones. Experiments on pretrained video generation models show that the original model often occupies imbalanced temporal regimes, whereas our method selectively applies larger corrections to the worst temporal hotspots and improves temporal consistency and visual quality without finetuning. Code: https://github.com/lytang63/temporal-state-transport

Luyao Tang, Bingjun Luo, Dong Yi +5

The University of Hong Kong, Hong Kong SAR, China · Tsinghua University, Beijing, China · Harbin Engineering University, Harbin, China +2

Video Generation Spectral Class Imbalance

Sep 3, 2026cs.LG

Spectral characteristics of autoencoder parameters as a vector representation of data

This paper examines the relationship between the parameters of autoencoder models and the statistical properties of the data on which they are trained. Autoencoders are defined as models with an encoder-decoder architecture, trained to reconstruct input data through a compressed latent representation. It is proposed that the model parameters can be viewed as a dense vector representation of the corresponding sample. To test this hypothesis, a theoretical and experimental study is conducted in which a vector representation is formed based on the spectral characteristics of the autoencoder parameter matrices. Theoretical analysis shows that the singular values of the model parameter matrices are related to the eigenvalues of the covariance matrix of the training data, ensuring the transfer of information between the data space and the parameter space. Experimental results on the CIFAR-10 and FashionMNIST datasets confirm that the resulting vector representations allow for a high degree of accuracy in distinguishing between models trained on different data subsets, without resorting to complex vector generation algorithms or using the original samples. These results suggest that the parameters of trained autoencoders can be viewed as sample representations.

Maria Nikitina, Anton Bishuk, Oleg Bakhteev

Autoencoder Architectures Mnist Spectral Representation Space

Sep 1, 2026cs.CV

Benchmarking Spatial, Spectral, and Self-Supervised Cues for Face Forgery Detection under Realistic Degradation

Face forgery detectors often achieve strong results on controlled benchmarks, but their reliability under realistic image degradations remains limited. This paper presents a standardized benchmark for face forgery detection using the Multi-Dimensional Face Forgery Image (MFFI) dataset and evaluates performance on both clean and degraded test partitions. We compare six model families, including convolutional networks, transformer-based models, and a frozen self-supervised DINOv3 backbone, across spatial, spectral, and hybrid input representations. The results show that clean-set performance is not a reliable indicator of robustness under compression, resizing, and blurring. Xception with RGB obtains the best clean performance, reaching 0.884 mean ROC-AUC, but degrades substantially on the harder partition. In contrast, frozen DINOv3 achieves the strongest degraded-set result, with 0.726 mean ROC-AUC, while training only a linear classification head. The representation analysis indicates that Fourier-domain cues are most useful when combined with RGB information, whereas purely spectral inputs consistently underperform spatial representations. Qualitative attribution maps further suggest that convolutional detectors focus on localized artifacts, while DINOv3 relies on broader facial structure. These findings reinforce the need for degraded evaluation protocols and highlight self-supervised visual representations as a promising direction for robust face forgery detection. Our source code is publicly available at https://github.com/lucasdocunha/FaceForgery-Benchmark/.

Lucas Cunha, Lucas Sotomaior, Lucas Gasperin +3

Pontifical Catholic University of Paraná, Curitiba, Brazil

Face Forgery Detection Visual Degradation Dinov3 Convolutional Neural Networks Degradation Spectral

Sep 1, 2026cs.SD

MADS: A Multiview Acoustic Descriptor Set Beyond Standard Spectral Summaries

Dominant audio classification pipelines rely either on compact handcrafted summaries or on fixed time-frequency frontends such as log-mel representations prior to deep modeling. While highly successful, these representations do not explicitly expose the physical dynamics of the underlying sound-generating event. We introduce MADS (Multi-view Acoustic Descriptor Set), a compact 19-dimensional physics-informed descriptor set de- signed to capture complementary spectral, temporal, mechanical, and stochastic structure in audio signals. Rather than treating sound only as a spectral pattern, MADS encodes properties related to excitation, damping, periodicity, impulsiveness, and structural consistency within a unified multi-view representation. We evaluate MADS using standard classical machine learning models on ESC-10, ESC-50, and MSoS, and compare it against two conventional handcrafted baselines: a compact 26D MFCC- based baseline and an expanded 38D spectral-summary baseline. Across ESC-10 and ESC-50, MADS achieves the strongest peak results overall, reaching 81.00% and 52.78%, respectively, while using roughly half the dimensionality of the 38D baseline. On MSoS, MADS again delivers the strongest top-end performance, reaching 67.48%. These results establish MADS not merely as a competitive standalone descriptor set, but as the foundational descriptor layer of a broader acoustically grounded representation program for future frame-level and deep-learning-compatible audio modeling.

Utsab Ghosh, Roshni Chakraborty

ABV-Indian Institute of Information Technology and Management, Gwalior, India.

Neural Audio Music Structure Analysis Spectral

Sep 1, 2026cs.CV

Forbid Your Attention: Fooling Multimodal Large Language Models by Selectively Removing Intrinsic Focus in Spectral Domain

Multimodal large language models (MLLMs) have extended the capability of large language models (LLMs) to process more contextual multimodal information, showing remarkable progress in diverse realistic multimodal applications. Despite their strong perception and reasoning abilities, recent studies reveal that MLLMs remain highly vulnerable to adversarial inputs, especially those targeting visual components. However, existing attacks mainly focus on global perturbations, lacking an understanding of how MLLMs internally interpret visual structures. In this paper, we make the attempt to investigate the intrinsic focus of MLLMs in the frequency domain and discover that their predictions are particularly sensitive to phase information, which encodes essential structural and semantic cues. Based on this observation, we propose a novel phase-aware adversarial attack framework that explicitly restricts adversarial perturbations to structure-relevant phase regions to suppress the MLLMs' focus for effective and imperceptible attacks. To further amplify the structural influence, we also introduce an auxiliary adversarial prompt learning module to guide multimodal misalignment around phase-sensitive regions, misleading the MLLM's attention toward targeted structural patterns. Extensive experiments on multiple representative MLLM models and datasets demonstrate the superior effectiveness of our method compared to existing attacks.

Daizong Liu, Junhao Dong, Zhiyuan Ma +6

Institute for Math & AI, Wuhan University, Wuhan, 430072, China · College of Computing and Data Science, Nanyang Technological University, Singapore · School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, 430074, China +3

Multimodal Large Language Models Cross-Modal Attention Adversarial Examples Spectral

Aug 13, 2026stat.ML

Sinkhorn Linearization and the Spectral Proxy: Unifying the Statistical and Algorithmic Theory of Feature-Parameterized Inverse Optimal Transport via a Single Spectral Sandwich

We develop the statistical and algorithmic theory of inverse optimal transport (IOT) under the feature-parameterized cost C_theta(i,j) = -theta^T phi(i,j). The core technical contribution is the Sinkhorn linearization -- the implicit-function sensitivity of the entropic OT plan to the cost -- together with its spectral proxy, a formula that is spectrally exact yet geometrically transparent. The restricted Hessian on the tangent space satisfies the spectral sandwich (pi_min/epsilon) I <= H_T^{-1} <= (pi_max/epsilon) I, yielding the single core bound sigma_min >= (pi_min/(a_max epsilon)) sqrt(lambda_min(Sigma)) that drives the entire theory. On this core we establish four theorems and one observation. T1 (identifiability): theta is globally injective on the quotient of the gauge kernel, with dimension bound F <= (K-1)^2. T2 (sparsistency): the l1-penalized estimator recovers the true support under irrepresentability and score concentration, with exponential failure probability. T3 (well-posedness): the feature-moment map M(theta) = Phi^T x_theta is strongly monotone, and the inverse is Lipschitz with constant L <= epsilon ||Phi^T S_a||_op / (pi_min lambda_min(Sigma)). T4 (convergence): local strong convexity with mu >= pi_min^2 lambda_min(Sigma) / epsilon^2 guarantees monotone gradient descent convergence. O5 (misspecification): the estimator converges to the OT-model projection of the truth; the Holder continuity of the projection map is assessed numerically, yielding setting-dependent empirical exponents alpha_eff in (0,1).

Han Dong, Jiaming Li, Yongqiang Gong +2

School of Medicine, Nankai University · College of Artificial Intelligence, Nankai University

Optimal Transport Approach Proximal Operators Minimax Rate Spectral

Aug 13, 2026cs.SD

HybridSB-MoE: Dual-Domain Schrödinger Bridges with Scene-Adaptive Expert Routing for Speech Enhancement

Generative speech enhancement faces three gaps: spectral models capture harmonic structure but often disrupt phase, waveform models preserve phase but miss harmonics, and Schrödinger Bridges (SB) shorten transport from noise to clean speech but leave inference cost only loosely tied to training. We propose HybridSB-MoE, a dual-domain framework that fills these gaps through three contributions unified by a single asymmetric design principle. (i) Asymmetric uncertainty fusion: The spectral path captures epistemic uncertainty via expert disagreement, while the waveform bridge models aleatoric variance through stochastic dynamics. We fuse them asymmetrically, allowing the mixing weight to adapt to distinct error regimes rather than average predictions. (ii) Heterogeneous MoE with top-k=2 routing across five distinct architectural archetypes, where architectural diversity makes the epistemic signal indicate which inductive bias fails rather than small perturbations among similar experts. (iii) Discretization bound (Theorem 1): path-consistency and trajectory regularizers together bound the K-step bridge sampling error in 2-Wasserstein distance at rate K-alpha, making small-K inference an objective-level guarantee rather than an empirical claim. On VoiceBank+DEMAND, HybridSB-MoE outperforms diffusion- and SB-based baselines at their step budgets while remaining competitive with consistency-distilled few-step methods.

Zhengyi Lu, Aswini Sivakumar, Jie Hu +1

Department of Computer Science and Engineering, Oakland University, Rochester, MI 48309

Speech Enhancement Schrödinger Bridges Speech Synthesis Localized Lora-Moe Waveforms Spectral+1

Aug 11, 2026cs.LG

$β$ -VAEs as Effective Theories: Tolerance-Dependent Dimension

In a

β

-VAE, increasing the regularization strength acts as a spectral cutoff by collapsing low-utility latent coordinates. In the linear Gaussian VAE, the collapse order matches the ranking of reconstruction utilities exactly, because both are set by the PCA spectrum. We ask which parts of this picture survive in fully connected nonlinear VAEs trained on WorldClim. We find that nonlinear interactions shift and broaden collapse onsets, so thresholds no longer coincide exactly with utilities. However, the common ordering is preserved over the resolved ranks, so the spectral cutoff still acts as a utility cutoff and the effective-description logic carries through. The resulting effective-dimension curves reveal a head--tail tradeoff: increasing depth concentrates utility into the first few coordinates but worsens tail fidelity.

Johannes Hirn

Image Processing Laboratory (IPL), Universitat de València, Paterna, València 46980, Spain

Representation Collapse Nonlinearity Conditional Variational Autoencoder Latent Variable Regularization Spectral

Aug 5, 2026cs.CV

When does training on downscaled images yield the same gradients?

Diffusion transformers deliver strong image generation, but their training cost grows superlinearly with resolution. Recent work justifies training or sampling at reduced resolution on a spectral premise: at high noise, a downscaled latent preserves almost the full surviving signal. Whether a downscaled step also preserves the native training gradient signal, however, has remained unresolved. We reduce how that signal changes under downscaling to two terms: a noise-dependent term governed by the downscale ratio, which decays at high noise as the spectral premise predicts, and a σ-independent floor governed by the target grid's absolute token count, carried by the compute graph itself and removed by no noise level. The measured (route, σ) map corroborates the account and uncovers structure the spectral picture cannot express: on the 1024->768 route, a window (0.65 < σ< 0.95), predicted by no spectral criterion at any tolerance, where the downscaled gradient stays within a small margin of the native one. Training LoRA adapters with downscaled steps restricted to the routes and noise windows the map validates reduces training time by 14.6% at a fixed step budget while remaining near-native in weight space. Code is available at https://github.com/sorryhyun/anima_lora.

Seunghyun Ji

Independent researcher

Diffusion Transformers Gradient Dynamical Downscaling Low-Rank Adaptation Adapters Spectral

Aug 4, 2026cs.LG

Joint Affine Spectral Shaping: Coupling Weight and Bias Updates Beyond Weight-Only Muon

Matrix spectral optimizers reshape weight-update spectra but usually delegate vector-valued biases to a separate optimizer. We study whether this separation is neutral. We formulate each affine layer as a joint momentum matrix

A=[M_W,αm_b]

and apply a capped regularized-inverse spectral map to the complete matrix, producing both the weight and physical bias updates. A strict five-seed ablation on a four-layer BERT-mini trained from scratch on IMDb compares exact-SVD Muon, weight-only inverse shaping, affine-probe inverse shaping, and the proposed joint regularized inverse (JRI). Weight-only inverse shaping raises validation-loss-selected test accuracy from

84.903\pm0.242\%

to

85.562\pm0.308\%

and lowers selected test loss from

0.3479

to

0.3345

. Allowing bias to alter the joint SVD while retaining an independent Adam bias update does not improve over weight-only inverse shaping. Using the transformed bias jointly raises selected test accuracy to

85.738\pm0.180\%

and lowers test loss to

0.3291

, with all five seeds improving relative to the probe baseline. During the peak-performance window, JRI preserves the eligible weight-update norm while reducing the bias-update norm from

0.02095

to

0.00301

, lowers boundary-function share from

86.58\%

to

78.97\%

, and changes the cosine between weight-induced boundary motion and explicit bias from

+0.030

to

-0.137

. An independent 22-seed replication yields

85.743\pm0.203\%

selected test accuracy. These results identify joint affine spectral allocation as a small but consistent extension to weight-only spectral optimization.

Gongyue Zhang, Honghai Liu

State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Shenzhen, Shenzhen, 518055, China.

Affine Muon Spectral Regularization Adam

Aug 3, 2026cs.LG

RamanPFN: learning from Raman spectral structure with a tabular foundation model

Raman spectroscopy enables label-free molecular characterization across materials science, analytical chemistry, biomedicine, and industrial process monitoring. However, machine learning for high-dimensional spectroscopy remains constrained by limited labelled data and a mismatch between the physical organization of spectra and feature-agnostic models. Channel coverage alone does not ensure that related bands share a common inference context. Here we present RamanPFN, a general-purpose spectral foundation framework that enables unified in-context inference through physics-guided spectral learning. It captures full-spectrum compositional covariation via Global Compositional Unmixing (GCU), which decomposes distributed, multi-band mixture signatures into shared non-negative latent bases. Simultaneously, it resolves local vibrational structure through Local Vibrational Subspace Encoding (LVSE), which preserves fine-grained peak morphology, intensity fluctuations, and peak shifts within contiguous spectral neighborhoods. Extensive evaluation across 74 diverse public Raman datasets covered 129 regression targets and was further extended to 21 classification tasks. RamanPFN achieved state-of-the-art performance across all reported aggregate metrics against 28 independently reproduced methods spanning chemometrics, spectral neural networks, deep tabular learners and tabular foundation models. RamanPFN establishes a physics-guided paradigm for scientific spectroscopy, enabling data-efficient predictive learning across diverse chemical systems.

Xingyu Pan, Huan Wang, Jinjia Guo +3

Beihang University · Cleer Science

Raman Spectral Label-Free Subspace

Aug 3, 2026cs.CV

HAFI-VLM: A Frequency Perspective for Diagnosing and Enhancing Visual Perception in Vision-Language Models

Vision-language models (VLMs) remain unreliable when predictions require fine-grained visual evidence. We identify a previously overlooked cause: spectral response rigidity. Despite substantial frequency variation across images and tasks, pretrained vision encoders exhibit persistent, encoder-specific layerwise spectral profiles that change only marginally under downstream fine-tuning. Since pretrained vision encoders only receive images, they cannot adapt spectral extraction to the evidence required by the current query. We therefore propose HAFI-VLM, which introduces a task-conditioned frequency pathway while preserving the pretrained semantic representation. Hierarchical Adaptive Frequency Injection (HAFI) retrieves complementary low-, mid-, and high-frequency evidence at multiple encoder depths using text-modulated, spatially aligned cross-attention. A Visual Enrichment Layer Adapter further recalibrates shallow LLM attention to effectively utilize the enriched visual tokens. Experiments on LLaVA-1.5 and Qwen2.5-VL demonstrate consistent improvements in general VQA, text-rich understanding, and hallucination robustness, outperforming representation-level enhancement methods and most resolution- or cropping-based approaches without additional high-resolution encoding. Mechanistic analyses show that HAFI restores task-dependent spectral allocation while retaining semantic attention, establishing frequency enrichment as a distinct and effective route for improving VLM perception.

Jin Cui, Chuanchang Su, Jiayi Lu +3

1State Key Laboratory of Human-Machine Hybrid Augmented Intelligence, and Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University · School of Computer Science and Technology, Xi’an Jiaotong University · School of Software Engineering, Xi’an Jiaotong University

Ava-Vlm Vision Encoders Visual Perception Frequency Spectral Perspective

Aug 3, 2026cs.LG

Understanding and Correcting Low-Frequency Bias in EEG Foundation Model

Increasing EEG pretraining data scale or model capacity does not consistently improve downstream performance. We identify a persistent low-frequency bias in representations learned by diverse EEG foundation models, which remains across dataset scales, model capacities, and pretraining objectives. Our analysis links this bias to the interaction between EEG's

1/f^α

-like spectral structure and neural networks' tendency to preferentially learn low-frequency components. In masked autoencoders, the

\ell_2

reconstruction objective further amplifies this imbalance: under comparable relative reconstruction errors, high-power low-frequency components contribute disproportionately to the loss. To address this issue, we introduce FAME, a frequency-balanced masked autoencoding framework that reconstructs time--frequency activity in predefined EEG bands from masked EEG inputs. FAME independently standardizes the reconstruction targets within each band and assigns equal weight to all band-specific losses, thereby balancing supervision across the EEG spectrum. Evaluated on 41 downstream tasks in OmniEEG-Bench, FAME learns more spectrally balanced representations and achieves state-of-the-art performance on 24 of them. These results underscore the importance of balanced spectral supervision for learning transferable EEG representations.

Junjie Yu, Zihan Deng, Jianyu Zhang +8

Department of Biomedical Engineering, Southern University of Science and Technology, Shenzhen, China · Omni-Intelligence, Shenzhen, China · College of Design and Engineering, National University of Singapore, Singapore +4

Electroencephalography Foundation Models Electroencephalography Graph-Coherent Low-Frequency Ones 3D Masked Autoencoders Auditory Attention Electrocardiogram Foundation Models+1

Aug 3, 2026stat.ME

Statistical comparisons of time-series feature sets on classification tasks

In recent years, numerous open-source software libraries have been developed for computing sets of features from univariate time series. The type and number of features vary across these feature sets, which have been constructed with varying disciplinary perspectives on quantifying structure in time-series data. To date, the relative strengths and weaknesses of these feature sets on time-series classification problems remains largely unexplored. Here we aimed to understand the relative performance of six open-source feature sets and three baseline feature sets (based on distributional and/or basic spectral structure) across 124 univariate time-series classification problems using a normalization-based approach to problem-level benchmarking that better indexes the relative strengths and weaknesses of different algorithms compared to prior rank-based approaches. Despite their dramatic differences in size, composition, and computation time, we found that feature sets performed relatively similarly overall (85.3% of pairwise comparisons resulted in ties), with the largest feature set, tsfresh, exhibiting the strongest overall performance (29.03% wins across all pairwise comparisons against other feature sets). We also highlighted specific problems on which the specific composition of a given feature set gave it a substantial performance advantage or disadvantage, and problems where simple baselines comprised of Fourier coefficients and quantiles were sufficient to achieve strong performance. Our results demonstrate the need to consider problem-level performance when benchmarking time-series feature sets, and highlight the importance of feature make-up in driving relative classification performance.

Trent Henderson, Ben D. Fulcher

Dynamics and Neural Systems Lab, The University of Sydney, Camperdown, 2006, NSW, Australia.

Time-Series Classification Time Series Feature Selection Spectral

Aug 1, 2026cs.SD

AnyBand: Unified Multi-Bandwidth Speech Extension via Frequency-Aware In-Context Spectral Infilling

Bandwidth extension (BWE) aims to recover missing high-frequency content from band-limited speech. Existing methods often formulate BWE as a fixed or predefined bandwidth conversion problem, potentially requiring cutoff-specific models or retraining when the input bandwidth changes. This assumption limits their applicability to practical scenarios where speech may arrive with diverse cutoff frequencies. We propose AnyBand, a unified BWE framework that recasts bandwidth extension as in-context spectral infilling. Motivated by prompt-based zero-shot speech generation, AnyBand conditions high-frequency generation on the observed low-frequency spectrum, using the available band as a frequency-domain prompt that conveys content, speaker, prosodic, and spectral-envelope cues. This formulation enables a single model to perform cutoff-conditioned generation over a continuous range of input bandwidths. AnyBand is trained with missing-band conditional flow matching and an Easy-to-Balanced cutoff curriculum over continuously sampled cutoff frequencies. To better exploit the spectral prompt, we introduce a frequency-aware Diffusion Transformer that models cross-frequency interactions and long-range temporal dependencies, followed by a physically motivated multi-view adversarial refinement stage to enhance spectral realism, envelope coherence, and harmonic consistency. Experiments on multiple datasets and bandwidth settings show that AnyBand consistently improves spectral reconstruction over existing baselines while achieving competitive perceptual quality across both standard and irregular input cutoffs. Audio samples are available.

Junchuan Zhao, Minh Duc Vu, Bowen Zhang +1

School of Computing, National University of Singapore · Department of Statistics & Data Science, National University of Singapore · College of Computing and Data Science, Nanyang Technological University

Speech Enhancement Bandwidth Extension Modern Generative Audio Models Frequency-Aware Regularization Flow-Matching Text-To-Speech Spectral+1

Jul 31, 2026cs.CV

LegoQ: Density-Matrix Representation Learning with Spectral-Spatial State Transitions for Hyperspectral Classification

Hyperspectral image classification is complicated by mixed pixels, spectral ambiguity, class imbalance, and limited annotations. Most current classifiers encode a pixel or patch as a deterministic vector and apply a linear or multilayer softmax head. Although effective for discrimination, this representation does not directly expose how mixed or uncertain a sample is. This paper presents \method, a classical density-matrix representation learning framework for hyperspectral images. The spectral bands are divided into groups and each group is mapped to a positive semi-definite, Hermitian, trace-normalized matrix state. A composable stack of spectral, spatial, and inter-group transitions then updates the states while repeatedly projecting them back to the valid state set. Instead of flattening the final features, \method\ aggregates the group states and compares them with learnable class-prototype density matrices through Uhlmann fidelity. The normalized eigenspectrum, von Neumann entropy, purity, and prototype fidelity provide sample-level diagnostics that are unavailable from a conventional vector head. On Indian Pines, ten runs yield an overall accuracy of

96.20\pm0.70\%

, an average accuracy of

95.57\pm1.29\%

, and a kappa coefficient of

95.66\pm0.80\%

. On WHU-Hi-LongKou, the best of ten runs reaches

97.52\%

overall accuracy. Classification maps and feature projections show that the transition stack produces compact and better separated class structures. The results support constrained matrix-state learning as a practical alternative to vector-only hyperspectral classification without requiring quantum hardware.

Weijia Cao, Xiaofei Yang, Fu Wang +2

Hyperspectral Image Image Classification Spectral Representation Learning

Jul 30, 2026cs.AI

Dynamic Spectral Filtering for Temporal Graph Learning: Learning Evolving Propagation Operators

Temporal graph learning is commonly organized around the evolution of node states or the encoding of interaction histories. We study an underexplored, operator-centric question: should the graph propagation mechanism itself evolve over time? We introduce Dynamic Spectral Filtering (DSF), which represents propagation at snapshot t by a Chebyshev polynomial filter with vector-valued, time-dependent coefficients. DSF explicitly treats these compact multi-order coefficients as recurrent temporal states. A recurrent branch proposes updates, while multiplicative global and order-specific gates regulate their magnitude. The temporal state is independent of the number of nodes. On MOOC, Wikipedia, and Reddit temporal link-prediction benchmarks, converged DSF runs attain AP scores of 0.7851, 0.9088, and 0.9860, respectively, with 93K to 133K trainable parameters, 68 to 182 MB peak GPU memory, and 1.6 to 2.1 seconds of training per epoch. Against the closely related DEFT baseline, DSF is better on MOOC, within 0.001 AP on Reddit, and modestly lower on Wikipedia, while using 8.3 to 8.6 times fewer parameters, 25 to 33 times less GPU memory, and 5 to 19 times less time per epoch. Relative to all measured alternatives, it uses 3.3 to 38.6 times less GPU memory. These results support direct spectral-response evolution as a useful temporal inductive bias when computational efficiency is a first-class requirement.

Yan Kong

Nanjing University of Information Science and Technology, China

Temporal Graph Neural Networks Spectral Filtering Temporal Dynamics Zero-Shot Link Prediction Spectral Propagation+1

Jul 30, 2026cs.AI

SpecCal: Ambiguity-Aware Candidate Calibration for Infrared Spectrum-Based Molecular Structure Reconstruction

Inferring molecular structures from infrared (IR) spectra is a fundamental yet challenging problem. A key difficulty is that an IR spectrum provides limited structural information: different molecules may share similar functional groups and local vibrational patterns, leading to highly similar spectral responses. Thus, even when an observed spectrum has a unique underlying structure, reconstructing it from the spectrum remains ambiguous. Existing IR-to-molecule models usually generate a ranked set of candidate molecules, but this set is largely determined by the model's learned generation preference and may not fully capture the structures that best satisfy the observed spectral constraints. To address this limitation, we propose SpecCal, a training-free candidate calibration framework for IR-to-molecule prediction. SpecCal operates on the candidate outputs of existing base models and improves the prediction set by re-ranking current candidates while introducing additional structurally plausible alternatives guided by spectral consistency. The framework is plug-and-play and model-agnostic, requiring no parameter updates for integration with diverse base models. Experiments on multiple benchmarks show that SpecCal consistently improves top-k reconstruction at both SMILES and scaffold levels across different base models. Further analyses demonstrate that calibrating candidate sets under spectral ambiguity provides a practical way to improve molecular reconstruction from IR spectra. The code is available at: https://anonymous.4open.science/r/SpecCal-B18A.

Yixuan Chen, Bo Liu, Yusen Tan +3

College of Computer Science and Technology, Jilin University · School of Mathematics, Jilin University · Information Hub, HKUST(GZ) +3

Molecules Moleculenet Infrared Spectral Candidate

Jul 29, 2026cs.CV

FreqForcing: Autoregressive Long Video Generation via Spectral Self-Anchoring

Autoregressive video diffusion models enable real-time streaming video generation. However, errors introduced during self-rollout accumulate over long horizons, manifesting as color drift, motion stagnation, and eventual visual collapse. In this paper, we characterize this phenomenon from a frequency-domain perspective: error accumulation appears as a pronounced energy drift in the low-frequency bands. We further investigate the effectiveness of attention sink in the frequency domain, and find that it improves the video quality by alleviating the spectral energy drift to some extent, but cannot fully resolve it. Motivated by the above analysis, we propose FreqForcing, a training-free framework that addresses error accumulation in long-video generation via Spectral Self-Anchoring (SSA). The proposed SSA leverages the low-frequency components of anchor attention to maintain long-horizon visual stability, while preserving dynamic motion through the high-frequency components of local attention. Our FreqForcing extends Self-Forcing pretrained on 5s clips to two-minute generation, achieving 24x extrapolation. Extensive experiments show that FreqForcing outperforms existing training-free methods quantitatively and qualitatively while remaining competitive with representative training-based approaches.

Jiatong Li, Leo Liang, Linghe Kong +1

Shanghai Jiao Tong University · Tencent HY Team

Autoregressive Video Diffusion Models Autoregressive Video Generation Long Video Generation Video Generation Spectral

Jul 28, 2026cs.LG

Sharpness-Aware Minimization and Muon: Robustness under the Spectral Norm

Sharpness-Aware Minimization (SAM) aims to improve generalization by encouraging insensitivity to small, worst-case parameter perturbations. However, the notion of a "small" perturbation is inherently geometry-dependent: while existing SAM variants have explored a wide range of choices, a clear perspective on which geometries are most effective in practice remains elusive. Recent work on matrix-aware optimization, particularly the Muon optimizer, suggests that respecting the matrix structure of hidden-layer weights can lead to strong empirical performance. Motivated by this, we study matrix-aware geometry in both stages of SAM: we introduce a layerwise spectral inner perturbation for matrix-valued hidden-layer parameters and combine it with either AdamW/SGDW or Muon in the outer update. Across ImageNet-1K experiments on ViT-Small/16 and ResNet-50, we find that the combination of a spectral inner step with a Muon outer step performs consistently strongly, achieving the best validation accuracy on both models among the evaluated methods.

Wenzhi Zhong, Edward Milsom, Michael Murray

Department of Mathematical Sciences University of Bath · Department of Computer Science University of Bath

Sharpness-Aware Minimization Regularization Muon Spectral Norm Spectral

Jul 26, 2026cs.LG

The Intruder Threshold: A Spectral Law for LoRA Fine-Tuning

LoRA fine-tuning can create intruder dimensions: new leading singular vectors of the updated weight matrix

W+BA

that are nearly orthogonal to all pretrained singular vectors and that drive catastrophic forgetting. Since their discovery, no theory has predicted, layer by layer on measured spectra, when they appear. We derive a per-layer critical update strength

s^\ast=\barθ/(γσ_1(BA))

, computed from the measured spectrum of

W

alone through the rectangular spiked-deformation transform, together with an exact secular-equation characterization of the updated spectrum, with no fitted parameters. In a pre-specified study spanning four dense Transformer families, a state-space model, a mixture-of-experts model, and an encoder-decoder (18 adapters, 9{,}840 layer scans), the law localizes the empirical threshold within a factor of two on

82\%

of layers, separates intruder-bearing from intruder-free layers at deployment with a mean AUC of

0.89

, holds unchanged on six third-party adapters, and predicts where WikiText-2 perplexity begins to degrade; a combination of the two pre-specified edge evaluations reaches

98\%

and is confirmed out-of-bag on the external adapters (

0.997

). Full fine-tuning disperses its update far below the threshold of every layer, which resolves the asymmetry between LoRA and full fine-tuning. Norm-matched interventions confirm that threshold-crossing layers, rather than update magnitude, carry the forgetting, and a spike-budget rule derived from the thresholds, requiring one SVD and no validation sweeps, reduces forgetting by

62\%

on the most fragile model at no task cost.

Peng Xie

Technical University of Munich, Campus Heilbronn

Model Fine-Tuning Layer-Wise Catastrophic Forgetting Spectral Intrusion Detection

Jul 24, 2026cs.CV

Hybrid Semantic and Spectral Ensemble for Robust Synthetic Image Source Attribution

The rapid advancement of text-to-image (T2I) models has necessitated robust Synthetic Image Source Attribution (SIA) methodologies. A critical challenge in SIA is the distribution shift between pristine training images and real-world deployed images, which undergo unknown post-processing operations such as JPEG compression and blurring. In this work, proposed for the DLMMDD Challenge at ICANN 2026, we introduce a dual-branch ensemble framework fusing Semantic Deep Learning with Mathematical Forensic Feature Extraction. The semantic branch employs EfficientNet-B0 regularized with Exponential Moving Averaging (EMA) and Label Smoothing. The forensic branch extracts 126 mathematical features -- including SVD spectral profiles and Local Binary Patterns -- from high-pass noise residuals, compressed via Truncated SVD and classified with XGBoost. Evaluated on a dataset of 10 generators where 55% of the test set is degraded, our approach achieves a private leaderboard accuracy of 95.60%. Furthermore, the entire pipeline is highly computationally efficient, requiring no GPU acceleration and executing end-to-end on a standard CPU in under 6.5 hours, highlighting the practicality and scalability of mathematical forensics for real-world deployment.

Md. Ajwad Hossain

Chittagong University of Engineering and Technology Chittagong, Bangladesh

Synthetic Image Detection Deep Semantic Representations Ensemble Spectral Singular Value Decomposition

Jul 23, 2026cs.MA

Spectral Dynamics of Semantic Drift in Clinical Multi-Agent Language Model Networks

The integration of iterative LLMs within multi-agent diagnostic frameworks requires a rigorous quantitative reevaluation of underlying communication topologies. Frequently used architectural paradigms depend on scale-free or small-world networks, assuming optimal communication efficiency. Our study mathematically dismantles that assumption for semantic data. By mapping multi-agent communication uncertainty trajectories onto a 768-dimensional Bio_ClinicalBERT embedding space via an analytical isotropic variance proxy using Barab'asi--Albert (BA) and Watts--Strogatz (WS) networks, we prove that structural bottlenecks compromise diagnostic safety. Our phase transition matrices illustrate that localized dense cliques confine hallucinated data, preventing global consensus and forcing the system toward a permanent entropy saturation threshold of

H_{\infty} \approx 5.947

. As a result, we measure a severe terminal cosine similarity degradation of 53.29%, completely overwriting the original ground-truth. Moreover, the terminal semantic drift reveals a catastrophic variance amplification of 51.81% (

ρ= 1.5181

) in highly clustered architectures, proving total system unpredictability when compared to Erdős--R'enyi configurations (

ρ= 1.0766

). Instead of reducing errors, hub-centric systems autonomously compound localized hallucinations. By introducing dynamic spectral monitoring operating at an

\mathcal{O}(N^3)

time complexity and imposing a strict lower bound on algebraic connectivity (

λ_{2_{min}}

) via the continuous eigen-decomposition of the graph Laplacian, we present a mathematically rigorous technique to ensure global state diffusion. Securing the reliability of autonomous medical diagnostics necessitates treating topological stability as a non-negotiable quantitative imperative.

Amritesh Banerjee

University of Massachusetts Amherst, USA

Multi-Agent Large Language Model Systems Diagnosis Network Science Clinical Spectral

Jul 22, 2026cs.LG

Detecting Neural Network Failures through Spectral Analysis of Internal Activations

Neural network misclassifications exhibit characteristic spectral instability in internal activations that is invisible at the output layer. This phenomenon is identified and formalized as Spectral Drift -- the frequency-domain distance between consecutive layer activations -- with empirical validation showing that failures exhibit significantly higher drift than correct predictions (1.9% increase, p<0.001). This spectral signature emerges during internal processing but becomes masked in final outputs, explaining why confidence-based detection methods struggle. This work introduces Self-Detecting Neural Networks (SDNN), a framework that monitors spectral dynamics across network depth using Short-Time Fourier Transform, wavelet decomposition, and statistical moments to capture multi-scale spectral features. A lightweight detector network (5% parameter overhead) learns to identify failure-indicative patterns via curriculum learning on progressively challenging distributions: natural misclassifications, distribution shifts, and adversarial perturbations. Experiments on CIFAR-10 demonstrate that SDNN achieves 79.0 +/- 25.3% AUROC across three seeds, substantially outperforming confidence-based baselines including MaxSoftmax (50.5%) and Energy Score (52.9%) by approximately 25-30 percentage points. Ablation studies reveal that wavelet decomposition and statistical features make consistent contributions, while STFT's role remains unclear. This work establishes spectral analysis of internal activations as a promising direction for neural network reliability, revealing diagnostic information inaccessible to output-based approaches.

Arunan J

Independent Researcher

Spectral Model Activations

Jul 22, 2026cs.LG

An Isotropy-Preserving Spectral Cap for Muon: Theory and Three Case Studies

Muon and related matrix-sign optimizers are increasingly used to pre-train large language models, but their effect on the internal geometry of individual weight matrices is not well understood. This preliminary report proposes a unified framework built on a single idealizing assumption -- exact scale invariance of the loss under weight rescaling, which holds approximately in normalization-heavy networks. Under this assumption, plain SGD carries a built-in 1/||W|| brake on its update size, whereas Muon's matrix-sign step removes that brake, so both the Frobenius and spectral norms drift outward faster (t^{1/2} versus t^{1/4}). We further observe that the spectral-norm perturbation has a non-negative second-order term. This implies that a lightweight "spectral cap" -- which projects out only the first-order growth of the single top singular direction from each update -- can control the output covariance W K_X W^T without freezing training: the weight keeps learning through non-top directions, top-direction rotation, and top switching. We relate this cap to the min-entropy (H-infinity) of the singular-value spectrum. We then study three systems trained with Muon: a nanoGPT feed-forward projection, a 64-expert mixture-of-experts router, and the query/key projections of a bf16 FlashAttention block. In each case the cap increases isotropy and, at the margins -- a router collapsing to a single expert, and the near-divergence of one attention head -- prevents a concrete failure, while leaving validation loss essentially unchanged. We emphasize that the scale-invariance assumption is strong and that these small-scale results are preliminary; comments are welcome.

Jiachun Li

Muon Spectral Stochastic Gradient Descent Theory

Jul 21, 2026cs.LG

ISO: An RLVR-Native Optimization Stack

Reinforcement learning with verifiable rewards (RLVR) is rapidly advancing the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood. Building on our prior analysis (Zhu et al., 2025), we study this missing layer through the singular structure of model weights and identify spectral inheritance: RLVR can reuse the base model's weight spectra while acquiring new behavior through changes in the associated input and output singular frames. We operationalize spectral inheritance as Isospectral Optimization (ISO), an RLVR-native, fixed-spectrum optimization framework with complementary offline and online instantiations. Offline, ISO-Merger combines the frame changes of shared-base specialists into a single fixed-spectrum model, requiring no post-merge data, rollouts, gradient updates, or on-policy distillation (OPD). It recovers complementary specialist capabilities and achieves the strongest aggregate performance among the compared data-free merging methods. Online, ISO-Optimizer applies a chosen base optimizer, including AdamW and Muon, to the frame variables while keeping the base spectra fixed. Across reasoning and coding tasks ranging from 1.5B to 8B parameters, ISO-Optimizer improves accuracy in the reported runs and reaches matched scores with substantially fewer training steps. On Qwen3-8B-Base, AdamW reaches an aggregate accuracy of 0.495 after 270 training steps. ISO-AdamW reaches the same accuracy after only 100 training steps and improves further to 0.509 after 210 training steps. Together, ISO offers a concrete answer to RLVR's missing optimization layer: rather than inheriting pre-training optimization wholesale, design post-training around the structure of reward-driven adaptation: inherit the spectrum, optimize the frames.

Hanqing Zhu, Wenyan Cong, Zhizhou Sha +8

The University of Texas at Austin · UIUC · Emory University +3

Reinforcement Learning With Verifiable Reward Verifiable Rewards Spectral

Jul 20, 2026cs.SD

Dense-Sparse Dynamic Time Warping for Customizing Piano Concerto Accompaniments

In this study, we explore how pianists can customize Music Minus One (MMO) concerto accompaniments to match their playing style. Bypassing the need for a symbolic score, often not available digitally, we use three types of audio data: solo piano recordings, MMO orchestra-only recordings, and mixed recordings of both piano and orchestra (e.g., from YouTube). The mixed recording serves as an intermediary reference to align the solo and orchestra parts, with only the orchestral part being adjusted through time-scale modification to synchronize with the user's playing. The main challenge with estimating these alignments is the spectral mismatch between recordings containing different musical parts. Motivated by this application scenario, we introduce Dense-Sparse DTW, a variant of Dynamic Time Warping (DTW) that is designed to improve robustness of alignments to spectral mismatch by focusing on aligning a selected subset of audio frames containing prominent timing cues. We collect and annotate data from four piano concerto movements and establish a framework for generating and evaluating customized accompaniment recordings. On this benchmark, we show that Dense-Sparse DTW has better or comparable performance than more complex approaches based on source separation and spectral subtraction techniques.

TJ Tsai, Kavi Dey, Yigitcan Ozer +1

Harvey Mudd College · Claremont, CA USA · International Audio Laboratories +1

Accompaniment Instrument Speech-To-Text Alignment Spectral Scores

Jul 18, 2026math.ST

De-floored Principal Component Regression: When Rank Selection Alone Is Insufficient for Prediction

Principal component regression (PCR) regularizes high-dimensional prediction by choosing a spectral cutoff, but rank selection cannot correct systematic inflation of the retained empirical eigenvalues. We study clean Gaussian random designs in which the aggregate covariance tail creates a nearly scalar sample-space floor comparable to the predictive head scale. De-floored principal component regression (dPCR) retains the cutoff and subtracts an estimated floor from the retained denominators. We prove an ordinary-PCR prediction-risk lower bound uniform over all ranks and a high-probability dPCR upper bound. When the floor is sharp and inexpensive to remove in population prediction risk, the conditional risk of dPCR is asymptotically negligible relative to that of the best ordinary PCR rank. An exact risk decomposition explains the separation: denominator inflation is governed by first spectral mass, whereas the clean prediction cost of correction is governed by squared spectral mass. A same-sample trimmed-mean floor estimate attains the oracle dPCR upper-bound rate at a prespecified rank, and the separation persists under approximate predictive alignment when the tail prediction-energy fraction vanishes. Separate pointwise fixed-aspect formulas show that the risk-optimal positive scalar correction improves rank-

1

PCR, whereas mean-floor subtraction is generally not optimal for a broad Marchenko--Pastur bulk.

Peng Zhao

Department of Applied Economics and Statistics, University of Delaware

Principal Component Analysis Kernel Ridge Regression Spectral

Jul 16, 2026cs.CV

DAPGNet: Dynamic Adaptive Physics-Guided Graph Diffusion Network for Hyperspectral Image Classification

Hyperspectral image (HSI) classification requires reliable pixel-relation modeling under spectral variability, mixed pixels, and heterogeneous boundaries. Existing graph-based HSI classifiers usually construct graph topology from spatial proximity, superpixel connectivity, or learned feature affinity. However, the spectral physical prior carried by contiguous bands has limited influence on topology estimation and message propagation. This paper presents DAPGNet, a dynamic adaptive physics-guided graph diffusion network that injects a structure-constrained physical prior into relation-level graph learning. DAPGNet first encodes contiguous spectral responses into node-wise multiscale physical-prior representations. A two-stage graph constructor then combines spectral-spatial affinity, physical-prior consistency, and spatial distance to form a physical-prior-aware sparse topology. During graph diffusion, learned edge weights are transformed into additive attention biases, while a physical gate performs node-wise and feature-wise interpolation between graph-aggregated features and projected physical-prior features. Cross-scale fusion integrates node states from different diffusion depths, and the network is optimized with main classification, auxiliary supervision, and second-order spectral smoothness regularization. Experiments on Indian Pines, WHU-Hi-LongKou, Houston2013, and Houston2018 show that DAPGNet achieves the best OA, AA, and Kappa among representative CNN-, Transformer-, Mamba-, and graph-based baselines. It improves AA over the strongest competing method by 3.64 to 7.31 percentage points across the four datasets. Ablation and sensitivity analyses further support the complementary effects of physical-prior extraction, prior-aware topology construction, physics-gated propagation, and spectral smoothness regularization.

Pengkun Wang, Weijia Cao, Ning Wang +1

National Engineering Laboratory for Satellite Remote Sensing Applications, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China · Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China · Guangzhou University, Guangzhou 510006, China

Hyperspectral Image Image Classification Multi-Scale Convolution Spectral Prior Knowledge Integration

Jul 15, 2026stat.ML

Spectral Concentration and Recovery in Sparse High-Dimensional Random Geometric Graphs

We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold. The latent vectors are sampled either uniformly from the sphere or from a standard Gaussian distribution. Although every edge appears with probability

p

, the edges are dependent through their shared latent vectors. For the spherical model, at the connectivity scale

np=Ω(\log n)

, we prove

\|A-\mathbb E A\|=O\left(\sqrt{np\log n}+npτ\right)

, with high probability, where

τ

is the cap threshold. This sharpens the spectral norm bound of Liu, Mohanty, Schramm, and Yang (2023) under weaker assumptions. An analogous result holds for the Gaussian model after removing the fluctuations of the vector norms, yielding improved global synchronization guarantees for the homogeneous Kuramoto model. We then recover the latent geometry from the leading eigenspace. When

np\gg\log n

, both the latent vector and relative Gram matrix errors vanish provided

d\ll np\log(1/p)/\log n

. The required lower dimension is only

d\gg\log(1/p)

for the spherical model and

d\gg\log^2(1/p)\log n

for the Gaussian model, improving the recovery guarantees of Li and Schramm (2023). Finally, we prove the first exact recovery result for the Gaussian mixture block model of Li and Schramm (2023). At the optimal connectivity scale

np=Ω(\log n)

, a polynomial-time semidefinite program exactly recovers all labels in a moderate-separation regime, whereas larger separation makes exact recovery impossible because isolated vertices appear with high probability. Our proofs combine orthogonal polynomial expansions, decoupling, and matrix concentration, avoiding the trace-moment arguments used in previous work.

Manuel Fernandez, Yizhe Zhu

Department of Mathematics, University of Southern California

Inhomogeneous Random Graphs Discriminative Congruence Transform Gaussian Mixture Models Spectral Norm Spectral Sphere

Jul 15, 2026cs.LG

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth

We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization. We reinterpret skip connections and normalization, long understood as controlling magnitude, as mechanisms for preserving gradient rank across depth, since the very matrix multiplications and nonlinear activations that make the network expressive also reduce the rank. We show that skip connections trade off rank collapse against ensemble-like behavior, controlled by the relative scales of the branch and the skip: skip connections route the gradient around the residual branch, where rank is lost, rather than along the long gradient paths that encourage the layers to compose. The placement of the normalization layer controls this same tradeoff by setting the branch-to-skip ratio across depth, unifying much of the normalization placement and depth scaling literature, in particular why rank collapses for Post-Norm but plateaus for Pre-Norm. Other aspects of the architecture, like the two-matrix structure that expands and contracts the width, use additional parameters to preserve the representation or branch Jacobian rank. The second matrix decorrelates a coherent mean spike that would grow across blocks with a single matrix and uncentered activation, preventing the residual representation from collapsing. The width expansion between the two matrices keeps the branch Jacobian full rank: applying the rank-reducing activation in this expanded space leaves enough directions to span the original, at a width that follows a Marchenko--Pastur law. The initialization rank of the input--output Jacobian predicts which networks train on CIFAR-10. Taken together, we recast architecture design for deep networks as navigating an intrinsic tradeoff among rank collapse, ensemble-like behavior, and parameter count.

Katie Everett

MIT CSAIL

Deep Network Low-Rank Structure Transformer Architectures Jacobian Ranking Spectral

Jul 14, 2026cs.LG

The Geometry of Memorization: Finite-Time Spectral Sensitivity as a Diagnostic for Flow Matching Models

Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields. While theoretical targets favor straight trajectories, empirical networks develop complex path deformations. This paper presents the Finite-Time Spectral Sensitivity (FTSS) g(t), a gradient-free, forward-pass metric that exposes flow geometry by tracking the root-mean-square singular value of the state-transition matrix. Serving as a continuous proxy for stable rank, g(t) reveals a distinct geometric pathology under data scarcity: while generalizing models maintain stable effective dimensions, overfitting causes a spectral collapse. We leverage this structural phenomenon to develop an internal geometric audit based on g(t). Our framework detects generative memorization using purely internal trajectory dynamics, removing the need for external membership queries or baseline data comparison.

Shuchan Wang

Memorization Spectral Generative Models Forward Propagation Diagnosis

Jul 12, 2026cs.LG

The Spectral Structure of Latent Treatment Effects

Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.

Hamza Virk, Bijan Mazaheri, Yihren Wu

1Dartmouth College · 2Broad Institute of MIT and Harvard · 3Hofstra University

Heterogeneous Treatment Effects Latent Confounders Causal Inferences Spectral Latent Variable Subspace

Jul 9, 2026cs.LG

Spectral Origins of the Self-Correction Blind Spot in Autoregressive Generation

Large autoregressive language models exhibit a self-correction blind spot: they reliably fix identical errors when attributed to an external source yet fail to fix the same errors in their own outputs. Prior work has documented this phenomenon empirically, through controlled error injection, error-depth decompositions, RL-based verifier-corrector training, and intrinsic self-verification, but offers no formal model of why generating a token suppresses the ability to detect its error, no quantitative activation condition for correction markers, and no convergence guarantee for reinforcement-learning-based self-correction. We close these gaps with SPARC, a spectral-algebraic theory of self-correction in autoregressive generation. We define the error-propagation operator as the product of per-step attention Jacobians on the residual stream and prove that the blind spot arises if and only if the spectral radius of this operator is at least one. We derive a sharp activation threshold, given as a function of the spectral radius, that a correction marker must exceed, recovering the 89.3% blind-spot reduction observed with a simple ``Wait'' marker. We further prove that RL-based verifier-corrector training converges at a rate proportional to the squared coupling strength over the square root of the number of samples if and only if the verifier-corrector coupling matrix has spectral norm below one, and that this criterion is invariant across residual-stream autoregressive modalities, unifying text LLMs and autoregressive image and video generation. Experiments across four backbones and a visual autoregressive probe validate every theorem, with spectral predictions matching measured blind-spot rates within 3.2% RMSE.

Ingrid Petrova, Luan Vejsiu

European University of Tirana

Iterative Self-Correction Autoregressive Generation Autoregressive Language Models Blind Spots Visual Autoregressive Models Spectral+2

Jul 9, 2026cs.LG

Spectral Analysis of Dueling Q-Learning

Q-learning is a fundamental algorithm in reinforcement learning (RL) for solving discounted Markov decision processes (MDPs) when the transition kernel is unknown. The deep Q-network (DQN) extends Q-learning by using a deep neural network for Q-function approximation, which makes Q-learning applicable to more practical high-dimensional problems. Dueling Q-learning decomposes the Q-function into a value function and an advantage function and learns the two components jointly, which can improve learning efficiency. However, the theoretical understanding of dueling Q-learning is still limited. Recent work has initiated an analysis of tabular dueling Q-learning, but existing guarantees focus on a regularized formulation and leave the pure tabular update less completely understood. This paper strengthens that line of analysis by adding a direct interpretation of the centered tabular decomposition and by establishing convergence guarantees for the unregularized, unprojected constant step-size recursion. In particular, we derive an exact switching linear system representation for deterministic dueling Q-learning and a finite-time error bound in expectation for the sampled stochastic version. The analysis clarifies how the value and advantage updates act as different gains on the action-common (value function) and action-differential (advantage function) components of the Q-function.

Donghwan Lee

Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST) Daejeon 34141, South Korea

Q-Learning Deep Q-Networks Spectral

Jul 7, 2026cs.LG

Graph Convolutional Attention: A Spectral Perspective on Graph Denoising and Diffusion

Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs. However, our principled understanding of attention-based graph denoising remains limited, making it unclear whether standard attention is the right mechanism for this task. Here we show that, under a denoising objective, linear attention is suboptimal and can only learn an average spectral denoising filter over the training distribution. This creates a fundamental limitation as graphs often vary spectrally across the distribution. To overcome this limitation, we introduce Spectral Attention, which directly utilizes the input graph spectrum and provably outperforms linear attention by a margin governed by the spectral diversity of the distribution. We then derive Graph Convolutional Attention (GCA), a practical and permutation-equivariant realization of this idea that implements spectral denoising through graph-filtered queries and keys. For stochastic block models, GCA provably matches the idealized Spectral Attention mechanism. We further show that the softmax operation, that follows the attention, provides additional denoising by approximately projecting noisy eigenvectors onto the clean eigenspace. Empirically, replacing linear attention with GCA consistently improves graph denoising and diffusion on synthetic and real datasets, with gains strongly correlated with spectral diversity. In DiGress, GCA matches standard graph-transformer performance without computing expensive structural features, and when combined with the recently proposed PEARL positional encodings, avoids explicit eigendecomposition computations resulting in faster inference without degrading quality. The code can be found here: github.com/shervinkhalafi/graph_conv_att

Shervin Khalafi, Igor Krawczuk, Sergio Rozada +3

University of Pennsylvania · King Juan Carlos University · Stanford University

Interleaved Graph Attention Iterative Denoising Methods Convolutional Block Attention Module Spectral Transformer Architectures

Jul 7, 2026cs.LG

Fingerprint, Not Blueprint: How Positional Schemes Set the Default Spectral Algebra of Attention

The pre-softmax score of an attention head is a bilinear form

score(i,j) = x_i^T M x_j

in a learned operator

M = W_q^T W_k

. Because M is generally non-symmetric, hence non-normal, it has a complex eigenspectrum and non-orthogonal eigenvectors, the regime where non-Hermitian and random-matrix tools apply. We ask what this spectrum encodes, at three levels for previous-token and induction circuits. Statically, across seven pretrained models spanning three positional schemes, the strongest previous-token heads are spectrally rotational under RoPE and non-rotational, or content-like, where position enters outside QK (learned-absolute and ALiBi); the model-level separation is perfect at every top-k examined (exact permutation

p=0.029

), and zeroing the per-frequency RoPE phase

Im(M_t)

eliminates induction on a pre-identified previous-token head in all three RoPE models. Dynamically, over public Pythia checkpoints every head originates at the random-matrix (Ginibre) null; the rotational signature emerges with the behavior, not before it, and the population-median suppression that yields the final profile follows circuit formation, so the profile is a consolidated fingerprint, not a precursor. Causally, and at toy scale, no spectral channel is necessary: constrained two-layer training reroutes around every ban with capability intact, albeit at a significant formation delay (four pre-registered contrasts,

q_BH <= 0.016

). The cost structure exposes each scheme's default: imposing symmetry slows learned-absolute models by a factor of 2.9, whereas a RoPE head with a fully symmetric static M still routes directionally via the phase channel, impossible under absolute positions. Within the settings examined, the positional scheme sets the default spectral algebra of an attention head's solution: a fingerprint sculpted after function, not a hard constraint upon it.

Li Hengyu

Institute for Solid State Physics, The University of Tokyo

Multi-Head Attention Spectral Spectral Decomposition Fingerprint Circuits

Jul 6, 2026cs.MM

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

Generalizing sleep staging models to unseen datasets is challenging, and typical domain generalization (DG) methods often rely on multiple source domains or domain labels that are rarely available in practice. We tackle the stricter and more practical setting of single-source domain generalization: training on a single labeled source dataset, without domain labels or access to target data. We present SleepBand, a physiology-guided framework that embeds oscillatory priors via a learnable Morlet filter bank and a structured integration-and-recalibration pipeline. This anchors representations to domain-invariant sleep rhythms (e.g., slow waves, spindles), reducing reliance on dataset-specific artefacts. On five public datasets, SleepBand achieves state-of-the-art SDG performance and remains competitive under leave-one-domain-out (multi-source) DG. Analyses show that the learned filters align with canonical neurophysiology and that robustness stems from focusing on narrowband, physiologically meaningful cues. Our results suggest that principled, physiology-aware inductive biases are a promising path for robust single-domain sleep staging. Code is available at https://github.com/lzcn/sleep-band

Zhi Lu, Yang Hu, Yan Chen

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

Sleep Multimodal Domain Generalization Physiological Data Small-Sample Electroencephalogram Datasets Spectral Physics-Guided Machine Learning

Jul 2, 2026cs.CV

Learning Spectral and Polarimetric Clues for One-to-Multimodal Novel View Synthesis

Neural rendering techniques allow for accurate reconstruction of the geometry and color appearance of 3D scenes. Some methods have extended their use to additional imaging modalities, such as multispectral, infrared, or polarimetric data. However, all of these approaches require expensive sensors and calibrated setups to capture new multimodal frames for each new scene. We propose Spectral and Polarimetric Implicit Learned Representation (SPoILeR), a novel method to obtain multi-view consistent renderings of unconventional modalities for scenes where either only RGB frames or very few of the additional modalities are available. Thanks to a multimodal pre-training phase, the model learns the mutual correlation between different modalities. This step allows predicting accurate renderings of unconventional modalities during a fine-tuning phase supervised only by RGB images. Experimental results show that the approach can accurately render infrared, polarimetric, and multispectral frames for scenes where no input sample captured by these types of sensors is provided.

Federico Lincetto, Gianluca Agresti, Mattia Rossi +2

MEDIA Lab, University of Padova, Padova, Italy · Sony EUISPC, Sony Semiconductor Solutions Europe, Stuttgart, Germany

Neural Rendering Multimodal Pretraining Novel View Synthesis Hyperspectral Image Spectral

Jul 2, 2026cs.LG

Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model

We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix. By affine invariance, the model is written as q

\sim

N(0, I), p

\sim

N(

Δ

, I), with linear features, where

Δ

is a mean vector. The variational estimator is the empirical Kullback-Leibler (KL) log-normalized fit with a squared L2-penalty on its nonconstant coefficient, and the spectral estimator recently introduced in [1] replaces a single variational problem by a continuum of ridge-regularized least-squares problems. We derive high-dimensional deterministic asymptotic equivalents when the numbers of observations and dimension tend to infinity with fixed ratios. The regularized variational limit is characterized by a scalar entropy minimization problem derived from the convex-Gaussian-min-max theorem (CGMT), while the regularized spectral limit follows from deterministic equivalents for resolvents of weighted sums of two independent Gaussian sample covariance matrices. We use these formulas to compare population risks, with experiments focused on fixed-signal aspect-ratio sweeps and optimized regularization. Our conclusion is that with many observations, under the criteria and asymptotic regimes analyzed here, the well-specified variational estimator has the smaller risk, while with fewer observations, the spectral estimator is favored because its covariance-based construction has lower variance. We also study how a nuclear penalty can be used and partially analyzed to perform feature learning.

Francis Bach

SIERRA · Inria - Ecole Normale Sup´erieure PSL Research University

Density Ratio Estimation Covariance Spectral

Jul 2, 2026cs.LG

Geometric Signatures of Reasoning: A Spectral Perspective on Task Hardness

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to solve complex problems by generating intermediate reasoning steps. While much attention has been paid to the length and content of these reasoning chains, far less is known about their internal geometry. We study the \emph{geometry} of CoT trajectories in the hidden state space of transformer models, formalizing each reasoning chain as a discrete curve in

\mathbb{R}^d

and characterizing it through spectral, positional, and kinematic geometric functionals. We introduce the effective dimension

d_ρ

as a measure of trajectory complexity and show theoretically that trajectories with flatter eigenvalue spectra correspond to harder tasks, as they explore more of the hidden dimensions. Lastly, we explore how kinematic features of the trajectory, mean position, positional dispersion, initial and current hidden states, mean velocity, mean speed, and speed dispersion, can be used to predict solution correctness before generation is complete, and may inform future early-stopping strategies. Experimentally, on mathematical reasoning problems from the MATH500 dataset,

d_ρ

achieves

0.93

AUC in distinguishing easy from hard problems, while kinematic features potentially can predict correctness from only the first

20\%

of generated tokens. These correctness signatures transfer across questions of varying difficulty, establishing that the shape of a model's internal reasoning trajectory is a principled window into both task hardness and solution quality.

Aria Masoomi, Mahsa Bazzaz, Adel Javanmard +1

1Northeastern University · University of Southern California · 3Google Research

Chain-of-Thought Reasoning Hard Spectral Trajectory Generation