Spectral Methods

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17 papers in the last four weeks, up 42% on the four weeks before. 0.2% of all new papers.

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From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning
Aug 7, 2026Zhentao Tan, Ruijie Quan, Yi YangPDE Surrogate Modeling PDE Operator Learning
Collaborative Innovation Center of Artificial Intelligence (CCAI), Zhejiang University, China
Explicit and Stable Pseudospectral Time-Domain Method for the Föppl-von Kármán Equations
Aug 6, 2026Victor Zheleznov, Stefan BilbaoPDE Solving Structural Mechanics
Acoustics and Audio Group, University of Edinburgh, Edinburgh, UK · STMS (UMR9912), IRCAM, CNRS, Sorbonne Universit´e, Paris, France
Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Models
Aug 5, 2026Liane Galanti, Devan Shah, Shlomo Fortgang +1Dynamical Systems Nonlinear System Identification
Princeton University
Physics-Based Molecular Fingerprints from Spectral Graph Theory Provide Efficient Geometry-Aware Measures of Chemical Similarity
Aug 5, 2026Jacob W. Toney, Ayleen Y. Farnood, Samir Darouich +13D Representation Learning Spectral Methods
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Center for Computational Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Institute for Theoretical Chemistry, University of Stuttgart, 70569 Stuttgart, Germany +2
Tight Worst-Case Bounds for the Smallest Eigenvalue of ReLU NTK Gram Matrices
Aug 4, 2026Zhao SongReLU Neural Networks Spectral Methods
Joint Affine Spectral Shaping: Coupling Weight and Bias Updates Beyond Weight-Only Muon
Aug 4, 2026Gongyue Zhang, Honghai LiuNeural Network Optimization Muon Optimizer
State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Shenzhen, Shenzhen, 518055, China.
RamanPFN: learning from Raman spectral structure with a tabular foundation model
Aug 3, 2026Xingyu Pan, Huan Wang, Jinjia Guo +3Tabular Foundation Models Representation Learning
Beihang University · Cleer Science
Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling
Aug 2, 2026Gabriele D'Acunto, Leonardo Di Nino, Paolo Di Lorenzo +1Graph Signal Processing Sheaf Theory
Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, 00184 Rome, Italy · National Inter-University Consortium for Telecommunications (CNIT), Parma, Italy
Rethinking Total Absorption Gamma Spectroscopy Deconvolution: Supervised Machine Learning vs Response-Matrix Methods
Jul 30, 2026J. Balibrea-Correa, E. N{á}cher, C. Fonseca-Vargas +1Spectral Methods Inverse Problems
Instituto de Física Corpuscular, CSIC - Universidad de Valencia, Spain, 46980, Valencia, Spain
Dynamic Spectral Filtering for Temporal Graph Learning: Learning Evolving Propagation Operators
Jul 30, 2026Yan KongTemporal GNNs Temporal Link Prediction
Nanjing University of Information Science and Technology, China
Breaking the Periodicity Assumption: Robust Tensorial Multi-View Clustering via Graph-Spectral Low-Rank Learning
Jul 28, 2026Jintian Ji, Xingsu Li, Songhe FengRepresentation Learning Multi-View Learning
Computer Science and Engineering The Hong Kong University of Science and Technology Hong Kong, China · School of Computer and Information Technology Beijing Jiaotong University, Beijing, China
Spectral Truncation in Synthetic Control
Jul 27, 2026Mojtaba EslamiSpectral Regularization Causal Effect Estimation
University of Calgary
Perturbative-NeuSA: A Structured Spectral Framework for Time-Dependent PDEs
Jul 27, 2026Xianli Zhu, Jia YinNeural Surrogate Modeling Neural PDE Solvers
School of Mathematical Sciences, Fudan University Shanghai, China
Quantum Spectral Model: Data Reuploading with Input-Conditioned Frequency Support
Jul 24, 2026Peiyong Wang, Udaya Parampalli, Casey R. MyersQuantum Machine Learning Spectral Methods
CSIRO Technology · Research Way, Clayton VIC 3168, Australia · School of Computing and Information Systems +6
Spectral Dynamics of Semantic Drift in Clinical Multi-Agent Language Model Networks
Jul 23, 2026Amritesh BanerjeeLanguage Modeling Spectral Methods
University of Massachusetts Amherst, USA
Filter Learning for Subgraphs: Algebras and Performance Risk Bounds
Jul 23, 2026Purui Zhang, Feng Ji, Yanan Zhao +2Graph Signal Processing Spectral Methods
Regularized Optimization on Grassmann Manifold: Theory, Algorithm and Applications
Jul 23, 2026Zhuan Liang, Zheng ZhaiSpectral Regularization Riemannian Optimization
Department of Statistics, Faculty of Arts and Sciences at Beijing Normal University, Zhuhai
Spectral Concentration and Recovery in Sparse High-Dimensional Random Geometric Graphs
Jul 15, 2026Manuel Fernandez, Yizhe ZhuGraph Clustering Spectral Methods
Department of Mathematics, University of Southern California
Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs
Jul 15, 2026Tianchi Yu, Ivan OseledetsPDE Solving Physics-Informed ML
1AXXX · 2Applied AI Institute · 3INM
The Spectral Structure of Latent Treatment Effects
Jul 12, 2026Hamza Virk, Bijan Mazaheri, Yihren WuCausal Effect Estimation Latent Variable Models
1Dartmouth College · 2Broad Institute of MIT and Harvard · 3Hofstra University
Complexity-Guided Component-wise Initialization for Language Model Pretraining
Jul 10, 2026Konstantin Garbers, Nicholas OhLanguage Model Pretraining Neural Network Initialization
Peking University Beijing, China
Group Invariant Spectral Embedding
Jul 9, 2026Yeari Vigder, Paulina Hoyos, David Thong +3Manifold Learning Dimensionality Reduction
Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv, Israel · Department of Mathematics, University of Texas at Austin, Austin, TX, USA · Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
Eigenbasis-Independent Learnable Spectral Positional Encodings for Directed Graphs via Hermitian Block Krylov Subspaces
Jul 8, 2026Jiaqing Xie, Yuxin WangPositional Encoding Spectral Methods
Fudan University
Quantum Spectral Anomaly Detection
Jul 6, 2026Yewei Yuan, Michele Minervini, Mark M. Wilde +1Spectral Methods Anomaly Detection
Global College, Shanghai Jiao Tong University, Shanghai 200240, China · School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14850, United States · Shanghai Jiao Tong University, Shanghai 200240, China +1
PIEFS: Physics-Informed Eigenfunction Features with Learnable Scaling
Jul 4, 2026Varvara Nazarenko, Timur Lidzhiev, Alexander TarakanovSpectral Regularization Representation Learning
Faculty of Computer Science, HSE University, Moscow, Russia · AI VK, Moscow, Russia
Spectral Signatures of Large Language Models
Jul 3, 2026Zhuoying Zhang, Ishan V. Prasad, Yuanzhe Hu +4LLM Evaluation Language Model Fingerprinting
Dartmouth College Hanover, NH, USA · University of California, Berkeley Berkeley, CA, USA · Lawrence Berkeley National Laboratory Berkeley, CA, USA
Complexity of Normalized Persistence Problems for Topological Data Analysis and Local Hamiltonians
Jul 3, 2026Dominic Lowe, M. S. Kim, Roberto Bondesan +1Spectral Methods Persistent Homology
Blackett Laboratory, Imperial College London, SW7 2AZ, United Kingdom · Department of Computing, Imperial College London, SW7 2AZ, United Kingdom · Yukawa Institute for Theoretical Physics & The Hakubi Center, Kyoto University, Japan
Recovering Candidate Circadian Regulators of Arrhythmic Pituitary Hormone Genes Using Reliability-Weighted Magnetic Laplacian with rwMagLap
Jul 3, 2026Shabnam Sodagari, Nick JaspersonGraph Signal Processing Graph-Based Retrieval
Repair the Amplifier, Not the Symptom: Stable World-Model Correction for Agent Rollouts
Jul 2, 2026Xinyuan Song, Zekun CaiSpectral Methods Long-Horizon LLM Agents
Emory University, Atlanta, GA, USA · The University of Tokyo, Tokyo, Japan · LocationMind, Tokyo, Japan
Characterizing Optimizer-Dependent Training Dynamics Through Hessian Eigenvector Displacement and Localization
Jun 29, 2026Marcelina Marjankowska, Valerio Modugno, Paolo BaruccaSpectral Methods Adaptive Gradient Methods
Financial Computing and Analytics Group, University College London · Robot Perception and Learning Lab, University College London

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From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning

Zhentao Tan, Ruijie Quan, Yi Yang

Collaborative Innovation Center of Artificial Intelligence (CCAI), Zhejiang University, China

PDE Surrogate Modeling PDE Operator Learning Spectral Methods Neural Operators

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Neural operators have become a central tool for solving partial differential equations (PDEs), with spectral operators offering efficient global mixing across spatial locations. However, many PDEs contain physics-sensitive local structures that are critical to the underlying physical behavior. For example, in Darcy flow, local material interfaces are often reflected by sharp changes in the permeability field and can strongly influence the solution. Existing spectral operators primarily adapt modal mixing based on center-point representations, making them insufficiently responsive to such localized structural variations. We propose the Edge-Conditioned Spectral Operator (ESO), a novel spectral operator framework that modulates global spectral mixing using local edge-wise variations. By incorporating the Pairwise-Variation Modal Mixer (PVMM) to inject local edge information into spectral mode selection, ESO preserves the global approximation capability of spectral neural operators while enabling the learned kernel to adapt to physics-sensitive local structures. Furthermore, we introduce a task-adaptive Physics-Aware Reweighting (PAR) that emphasizes physically important regions, identified by taskspecific physical quantities. Across nine PDE benchmarks, ESO consistently achieves state-of-the-art performance. Visual and region-wise analyses further demonstrate that ESO reduces solution errors near coefficient jumps, high-gradient flow structures, and other physically sensitive regions. The code is available at https://github.com/Tanpig-X/ESO.

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