Spectral Methods

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Spectral methods study problems by expressing data or operators in terms of eigenvalues, eigenvectors, or frequency modes. Classical approaches include Fourier and graph-Laplacian transforms, PCA and low-rank approximation, kernel methods, and polynomial filters; they are used for tasks such as clustering networks, estimating dimensions, and solving or learning partial differential equations. Newer work also uses spectral structure to design neural operators and optimizers, diagnose model behavior, and speed up large matrix computations. A central challenge is balancing efficient, robust approximations with the assumptions and information lost when choosing a fixed basis, truncating modes, or relying on noisy spectra.

Latest papers

238 papers21 papers in the last four weeks, down 30% on the four weeks before. 0.1% of all new papers.

TimeMM: Time-as-Operator Spectral Filtering for Dynamic Multimodal Recommendation
Apr 29, 2026Wei Yang, Rui Zhong, Zihan Lin +4Dynamic Graph Learning Recommender Systems
Xiaohongshu Inc. · Beijing, China
Sparse Graph Learning from Sparse Data via Fiedler Number Maximization
Apr 28, 2026Bahar Oveisgharan, Gene Cheung, Andrew EckfordGraph Structure Learning Spectral Methods
York University, Canada
Diffusion-Guided Feature Selection via Nishimori Temperature: Noise-Based Spectral Embedding
Apr 27, 2026Vasiliy S. Usatyuk, Denis A. Sapozhnikov, Sergey I. EgorovFeature Selection Dimensionality Reduction
R&D Department T8 LLC Moscow, Russia · Department of Computer Science South-West State University Kursk, Russia
Learning Curves and Benign Overfitting of Spectral Algorithms in Large Dimensions
Apr 25, 2026Weihao Lu, Qian Lin, Yingcun Xia +1Kernel Ridge Regression Benign Overfitting
Department of Statistics and Data Science, National University of Singapore. · Department of Statistics and Data Science, Tsinghua University.
A Brain-Inspired Deep Separation Network for Single Channel Raman Spectra Unmixing
Apr 24, 2026Gaoruishu Long, Jinchao Liu, Bo Liu +2Raman Spectroscopy Spectral Methods
College of Artificial Intelligence, Nankai University, Tianjin, China · Guangdong Laboratory of Chemistry and Fine Chemical Industry, Guangdong, China · Smekal Tech (Shantou) Ltd. +1
Spectral Embeddings Leak Graph Topology: Theory, Benchmark, and Adaptive Reconstruction
Apr 22, 2026Thinh Nguyen-Cong, Truong-Son Hy, Thang N. DinhGraph Reconstruction Spectral Methods
Department of Computer Science Virginia Commonwealth University Richmond, VA, USA · Department of Computer Science The University of Alabama at Birmingham Birmingham, AL, USA
Improved large-scale graph learning through ridge spectral sparsification
Apr 22, 2026Daniele Calandriello, Ioannis Koutis, Alessandro Lazaric +1Graph Sparsification Spectral Methods
SequeL team, INRIA Lille - Nord Europe, France · LCSL, IIT, Italy · New Jersey Institute of Technology, USA +1
Analysis of Nystrom method with sequential ridge leverage scores
Apr 22, 2026Daniele Calandriello, Alessandro Lazaric, Michal ValkoKernel Ridge Regression Kernel Regression
SequeL team INRIA Lille - Nord Europe
Achieving the Kesten-Stigum bound in the non-uniform hypergraph stochastic block model
Apr 21, 2026Manuel Fernandez, Ludovic Stephan, Yizhe ZhuSpectral Clustering Stochastic Block Model
Department of Mathematics, University of Southern California · Univ Rennes, Ensai, CNRS, CREST-UMR 9194, F-35000 Rennes, France
Predicting LLM Compression Degradation from Spectral Statistics
Apr 20, 2026Mingxue XuLLM Compression Low-Rank Matrix Decomposition
Department of Electrical and Electronic Engineering, Imperial College London, London, United Kingdom
Spectral Forensics of Diffusion Attention Graphs for Copy-Move Forgery Detection
Apr 19, 2026H. M. Shadman Tabib, Tasriad Ahmed Tias, Nafis TahmidImage Forgery Detection Digital Image Forensics
Department of Computer Science and Engineering Bangladesh University of Engineering and Technology (BUET) Dhaka, Bangladesh
Spectral Analysis of Fake News Propagation
Apr 18, 2026Weibin Cai, Reza ZafaraniSocial Media Analysis Fake News Detection
Data Lab, Department of EECS, Syracuse University, New York, USA.
Convergence theory for Hermite approximations under adaptive coordinate transformations
Apr 18, 2026Yahya SalehSpectral Methods
Spectral Kernel Dynamics for Planetary Surface Graphs: Distinction Dynamics and Topological Conservation
Apr 17, 2026Jnaneshwar DasDynamical Systems Spectral Methods
School of Earth and Space Exploration, Arizona State University
Spectral Thompson sampling
Apr 15, 2026Tomas Kocak, Michal Valko, Remi Munos +1Thompson Sampling Graph Bandits
SequeL team, INRIA Lille - Nord Europe, France · SequeL team, INRIA Lille, France · Microsoft Research NE, USA +1
STS-Mixer: Spatio-Temporal-Spectral Mixer for 4D Point Cloud Video Understanding
Apr 13, 2026Wenhao Li, Xueying Jiang, Gongjie Zhang +3Point Cloud Learning 4D Scene Understanding
Nanyang Technological University · Alibaba Group · Zhejiang University of Technology +1
Spectral Kernel Dynamics via Maximum Caliber: Fixed Points, Geodesics, and Phase Transitions
Apr 10, 2026Jnaneshwar DasKernel Methods Spectral Methods
School of Earth and Space Exploration, Arizona State University
The Lifecycle of the Spectral Edge: From Gradient Learning to Weight-Decay Compression
Apr 8, 2026Yongzhong XuNeural Network Training Dynamics Grokking
Subspace Control: Turning Constrained Model Steering into Controllable Spectral Optimization
Apr 5, 2026Yancheng Huang, Changsheng Wang, Chongyu Fan +7Spectral Optimization Spectral Methods
OPTML, Michigan State University · MIT-IBM Watson AI Lab, IBM Research · University of Minnesota +2
Spectral Path Regression: Directional Chebyshev Harmonics for Interpretable Tabular Learning
Apr 5, 2026Milo CoombsTabular Regression Spectral Methods
Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem
Apr 4, 2026Mitchell A. ThorntonCovariance Estimation Spectral Methods
Richardson, TX 75080 USA
Algebraic Diversity: Group-Theoretic Spectral Estimation from Single Observations
Apr 4, 2026Mitchell A. ThorntonSpectral Methods
Richardson, TX 75080 USA
The Spectral Lifecycle of Transformer Training: Transient Compression Waves, Persistent Spectral Gradients, and the Q/K--V Asymmetry
Apr 3, 2026Yi LiuTransformer Training Dynamics Transformer
A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction
Apr 2, 2026Zeyang Huang, Angelos Chatzimparmpas, Thomas Höllt +1Dimensionality Reduction Spectral Methods
Linköping University, Sweden · Utrecht University, The Netherlands · University of Bergen, Norway +1
Generalization Bounds for Spectral GNNs via Fourier Domain Analysis
Apr 1, 2026Vahan A. Martirosyan, Daniele Malitesta, Hugues Talbot +2Generalization Bounds Neural Network Generalization
Université Paris-Saclay, CentraleSupélec, Inria, France · LTCI, Télécom Paris, Institut Polytechnique de Paris, France
Foundations of Polar Linear Algebra
Mar 30, 2026Giovanni GuastiOperator Learning Spectral Methods
NeiGAD: Augmenting Graph Anomaly Detection via Spectral Neighbor Information
Mar 30, 2026Qing Qing, Huafei Huang, Mingliang Hou +2Graph-Based Anomaly Detection Anomaly Detection
College of Computer Science and Technology, Jilin University, Changchun 130012, China · School of Computer Science and Information Technology, Adelaide University, SA 5095, Australia · Guangdong Institute of Smart Education, Jinan University, Guangzhou 510632, China +1
Spectral Signatures of Data Quality: Eigenvalue Tail Index as a Diagnostic for Label Noise in Neural Networks
Mar 29, 2026Matthew LoftusSpectral Methods Noisy-Label Learning
Independent researcher
Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory
Mar 27, 2026Juno Kim, Eshaan Nichani, Denny Wu +2Spectral Optimization Neural Network Optimization
UC Berkeley · Princeton University · New York University +1
Spectral methods: crucial for machine learning, natural for quantum computers?
Mar 25, 2026Vasilis Belis, Joseph Bowles, Rishabh Gupta +2Quantum Machine Learning Spectral Methods
Xanadu Quantum Technologies Inc., Toronto, Ontario, M5G 2C8, Canada

Apr 29, 2026J/K move · Enter open · S save

TimeMM: Time-as-Operator Spectral Filtering for Dynamic Multimodal Recommendation

Wei Yang, Rui Zhong, Zihan Lin, Xiaodan Wang+3

Xiaohongshu Inc. · Beijing, China

Dynamic Graph Learning Recommender Systems Multimodal Recommendation Spectral Methods Multimodal Fusion

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Multimodal recommendation improves user modeling by integrating collaborative signals with heterogeneous item content. In real applications, user interests evolve over time and exhibit nonstationary dynamics, where different preference factors change at different rates. This challenge is amplified in multimodal settings because visual and textual cues can dominate decisions under different temporal regimes. Despite strong progress, most multimodal recommenders still rely on static interaction graphs or coarse temporal heuristics, which limits their ability to model continuous preference evolution with fine-grained temporal adaptation. To address these limitations, we propose TimeMM, a time-conditioned spectral filtering framework for dynamic multimodal recommendation. TimeMM instantiates Time-as-Operator by mapping interaction recency to a family of parametric temporal kernels that reweight edges on the user--item graph, producing component-specific representations without explicit eigendecomposition. To capture non-stationary interests, we introduce Adaptive Spectral Filtering that mixes the operator bank according to temporal context, yielding prediction-specific effective spectral responses. To account for modality-specific temporal sensitivity, we further propose Spectral-Aware Modality Routing that calibrates visual and textual contributions conditioned on the same temporal context. Finally, a ranking-space Spectral Diversity Regularization encourages complementary expert behaviors and prevents filter-bank collapse. Extensive experiments on real-world benchmarks demonstrate that TimeMM consistently outperforms state-of-the-art multimodal recommenders while maintaining linear-time scalability.