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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Pseudospectral Bounds for Transient Amplification in Coupled Gradient Descent
Jun 1, 2026Ahanaf Hasan AriqStochastic Approximation Two-Timescale Stochastic Approximation
Ideal School and College
Localizing broadband noise sources using the Loève spectrum and a 2.5D approach
Jun 1, 2026Christian H. Kasess, Wolfgang Kreuzer, Holger WaubkeDirection-of-Arrival Estimation Spectral Methods
Acoustics Research Institute, Austrian Academy of Sciences, Dominikanerbastei 16, Vienna, A-1010, Austria
Easy, robust approximate message passing for planted spike models
May 30, 2026Misha Ivkov, Tselil SchrammRandom Matrix Theory Principal Component Analysis
*Stanford University. · †Stanford University.
Data-Driven Spectral Prediction for Accelerating Large-Scale Electronic Structure Calculations
May 29, 2026Abhiram Badrinarayanan, Davor Davidovic, Edoardo Di Napoli +4Quantum Chemistry Scientific ML
Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany · CEA / IRIG / MEM / L_Sim, France
Modeling Spectral Energy Shifts in Spatio-Temporal Graph Anomaly Detection
May 29, 2026Yilin Liu, Hongchao Zhang, Taylor T. Johnson +2Spectral Methods Spatiotemporal GNNs
College of Connected Computing, Vanderbilt University, Nashville, USA · Department of Civil and Environmental Engineering, Electrical and Computer Engineering, Vanderbilt University, Nashville, USA
Spectral Anatomy of Quantum Gaussian Process Kernels
May 29, 2026Jian Xu, Chao Li, Guang Lin +4Quantum Machine Learning Gaussian Processes
1RIKEN iTHEMS · 2RIKEN AIP · 3South China University of Technology +1
Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling
May 26, 2026Pengzhen Chen, Yanwei Liu, Xiaoyan Gu +3Robust Watermarking Spherical Harmonics
Institute of Information Engineering, Chinese Academy of Sciences · School of Cyber Security, University of Chinese Academy of Sciences · State Key Laboratory of Cyberspace Security Defense +2
MuCon: Clipped Muon Updates for LLM Training
May 26, 2026Albert YiMuon Optimizer Spectral Methods
Mean-Shift PCA by Knockoff Mean
May 25, 2026Mengda Li, Zeng Li, Jianfeng YaoDistribution Shift Robustness Principal Component Analysis
School of Data Science, The Chinese University of Hong Kong, Shenzhen, China · Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, China
Learning Laplacian Eigenspace with Mass-Aware Neural Operators on Point Clouds
May 23, 2026Zherui Yang, Tao Du, Ligang LiuPoint Cloud Learning Geometric Representation Learning
University of Science and Technology of China, China · Tsinghua University, China · Shanghai Qi Zhi Institute, China +1
Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries
May 22, 2026Dongmin Lee, Anuran Makur, Japneet SinghLearning to Rank Pairwise Ranking
Department of Computer Science Purdue University West Lafayette, IN, USA · Department of Computer Science Elmore Family School of Electrical and Computer Engineering Purdue University West Lafayette, IN, USA
The ASE-LSE Disagreement Landscape: An End-to-End Characterisation of Extremes and Structural Drivers
May 21, 2026Minh Triet Pham, Ian GallagherGraph Embedding Spectral Methods
School of Mathematics and Statistics The University of Melbourne, Australia
Spectral Unforgetting: Post-Hoc Recovery of Damaged Capabilities Without Retraining
May 19, 2026Aarash Abro, Muhammad TahirLLM Fine-Tuning Spectral Methods
Zeta Labs · Lahore University of Management Sciences
Neural Acceleration for Graph Partitioning
May 18, 2026Joshua Dennis Booth, Vishvam PatelGraph Clustering Spectral Methods
Department of Computer Science University of Alabama in Huntsville Huntsville AL, USA
A Practical Noise2Noise Denoising Pipeline for High-Throughput Raman Spectroscopy
May 18, 2026David Martin-Calle, Cesar Alvarez Llamas, Vincent Motto- Ros +3Denoising Autoencoders Convolutional Autoencoder
ILM,UCBL,CNRS · Universit´e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France · ILM,UCBL,CNRS,IUF +1
Prism: Structural Symmetry Scanning via Duality-Constrained Laplacian Projection
May 18, 2026Jiatong XieGraph Clustering Spectral Methods
Independent researcher.
Self-Distillation is Optimal Among Spectral Shrinkage Estimators in Spiked Covariance Models
May 18, 2026Radu Lecoiu, Debarghya Mukherjee, Pragya SurSelf-Distillation Spectral Methods
Department of Statistics, Harvard University · Department of Mathematics & Statistics, Boston University
CHASM: Cross-frequency Harmonized Axis-Separable Mixing for Spectral Token Operators
May 14, 2026Pengcheng Fang, Hongli Chen, Yuxia Chen +3Frequency-Domain Feature Learning Accelerated MRI Reconstruction
University of Southampton · University of Queensland · 3Chengdu University of Technology +1
Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model
May 14, 2026Arie Wortsman-Zurich, Hugo Tabanelli, Yatin Dandi +2Hierarchical Representation Learning Scaling Laws
Département d’Informatique, Ecole Normale Supérieure, PSL & CNRS · Information Learning and Physics Laboratory, École Polytechnique Fédérale de Lausanne (EPFL) · Statistical Physics of Computation Laboratory, École Polytechnique Fédérale de Lausanne (EPFL)
Dynamics of the Transformer Residual Stream: Coupling Spectral Geometry to Network Topology
May 14, 2026Jesseba Fernando, Grigori GuitchountsDynamical Systems Transformer
Network Science Institute, Northeastern University · Flagship Pioneering
Reframing preprocessing selection as model-internal calibration in near-infrared spectroscopy: A large-scale benchmark of operator-adaptive PLS and Ridge models
May 13, 2026Gregory Beurier, Robin Reiter, Camille Noûs +2Linear Regression Spectral Methods
CIRAD, UMR AGAP Institut, Montpellier, France · UMR AGAP Institut, Univ Montpellier, CIRAD, INRAE, Institut Agro, Montpellier, France · CIRAD, UMR AGAP Institut, F-34398 Montpellier, France +1
Spectral Flattening Is All Muon Needs: How Orthogonalization Controls Learning Rate and Convergence
May 13, 2026Tien-Phat Nguyen, Truong Nguyen, Minh-Phuc Truong +3Momentum Methods Gradient Descent
Hanoi University of Science and Technology Hanoi, Vietnam · Indiana University 107 S. Indiana Ave, Bloomington, IN 47405, USA · Monash University Clayton, VIC 3800, Australia
Modeling Heterophily in Multiplex Graphs: An Adaptive Approach for Node Classification
May 12, 2026Kamel Abdous, Nairouz Mrabah, Mohamed BouguessaGraph Representation Learning Spectral Methods
Department of Computer Science, University of Quebec at Montreal, Montreal, QC, Canada
Minimax Rates and Spectral Distillation for Tree Ensembles
May 12, 2026Binh Duc Vu, David S. WatsonModel Compression Gradient-Boosted Decision Trees
King’s College London
Bin Latent Transformer (BiLT): A shift-invariant autoencoder for calibration-free spectral unmixing of turbid media
May 12, 2026Martin HohmannAutoencoders Transformer Attention
Institute of Photonic Technologies (LPT), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Konrad-Zuse-Straße 3/5, 91052 Erlangen, Germany
A Spectral Framework for Closed-Form Relative Density Estimation
May 11, 2026Francis BachDensity Ratio Estimation Spectral Methods
SIERRA · Inria - Ecole Normale Supérieure · PSL Research University
Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs
May 11, 2026Xuxiang Zhao, Angelica I. Aviles-RiveroFourier Neural Operator Representation Learning
Qiuzhen College, Tsinghua University · YMSC, Tsinghua University
Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators
May 11, 2026Xiaoxiao Lu, Ye Yuan, Jiahao ShiLatent Dynamics Modeling PDE Surrogate Modeling
School of AIA, Huazhong University of Science and Technology
Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation
May 10, 2026Shabarish Chenakkod, Michał DerezińskiLow-Rank Matrix Decomposition Randomized Sketching
University of Michigan, Ann Arbor, MI 48105.
Bridging Spectral Operator Learning and U-Net Hierarchies: SpectraNet for Stable Autoregressive PDE Surrogates
May 9, 2026Enrique Hernández Noguera, Md Meftahul Ferdaus, Elias Ioup +2U-Net PDE Surrogate Modeling
University of New Orleans, New Orleans, LA, USA · Naval Research Laboratory, Stennis Space Center, MS, USA

Jun 1, 2026, cs.LGJ/K move · Enter open · S save

Pseudospectral Bounds for Transient Amplification in Coupled Gradient Descent

Ahanaf Hasan Ariq

Ideal School and College

Stochastic Approximation Two-Timescale Stochastic Approximation Spectral Methods Gradient Descent Dynamics

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Coupled gradient descent - where the update of one parameter depends on another - arises naturally in bilevel optimization, two-time-scale stochastic approximation, and generative adversarial networks. When the coupled Jacobian is block-triangular, asymptotic stability is determined by the spectral radii of the diagonal blocks, yet transient amplification before convergence can be arbitrarily large due to non-normality. We develop a sharp pseudospectral theory for block-triangular Jacobians J = [[A, 0], [C, D]], proving Kreiss-constant bounds of the form K(J) <= 2/(1-γ) + ||C||/(4(1-γ)) when ρ(A), ρ(D) <= γ< 1 and A, D are symmetric, and establishing matching minimax lower bounds. We characterize the critical coupling threshold for spectral instability and extend the theory to nearly self-referential systems via a Neumann-series perturbation framework. As a consequence, we obtain a finite-horizon O(K(J)^2 log(1/δ)) iteration complexity bound. Framed as scaling laws for stochastic two-time-scale optimization, our results expose a non-asymptotic, instance-dependent regime of high-dimensional learning dynamics that is invisible to spectral-radius analysis. Experiments on linear-quadratic problems, IQC-based comparisons, and neural-network training confirm the theory.

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Latest papers 169