Kernel Methods

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Kernel methods represent data through similarity functions, allowing linear algorithms in feature spaces to model nonlinear patterns without explicitly constructing those spaces. Common approaches include support vector machines and kernel ridge regression for prediction, Gaussian processes for uncertainty, and kernel mean embeddings and maximum mean discrepancy for comparing distributions and testing dependence. Researchers also use kernels to learn dynamical systems and operators, and scale computations with random features, Nyström approximations, and structured kernels. A central tension is balancing expressive, well-chosen kernels and reliable guarantees against the computation and sensitivity to kernel or bandwidth selection that can limit practical use.

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234 papers40 papers in the last four weeks, up 111% on the four weeks before. 0.2% of all new papers.

Lipschitz bounds for integral kernels
Apr 3, 2026Justin Reverdi, Sixin Zhang, Fabrice Gamboa +1Kernel Methods
IRIT, IMT, LIEBHERR Aerospace, Toulouse, France · Univ Toulouse, Toulouse INP, CNRS, IRIT, Toulouse, France · IMT, Toulouse, France
A Novel Theoretical Analysis for Clustering Heteroscedastic Gaussian Data without Knowledge of the Number of Clusters
Apr 2, 2026Dominique Pastor, Elsa Dupraz, Ismail Hbilou +1Clustering Unsupervised Clustering
Lab-STICC, IMT Atlantique, 29238 Brest, France · OPTI’SEA 23 rue du Bourgneuf 29300 Quimperlé, France
Breaking Data Symmetry is Needed For Generalization in Feature Learning Kernels
Mar 31, 2026Marcel Tomàs Bernal, Neil Rohit Mallinar, Mikhail BelkinSymmetry Breaking Kernel Methods
CFIS UPC · UC San Diego
KMM-CP: Practical Conformal Prediction under Covariate Shift via Selective Kernel Mean Matching
Mar 27, 2026Siddhartha Laghuvarapu, Rohan Deb, Jimeng SunWeighted Conformal Prediction Covariate Shift
Siebel School of Computing and Data Science, University of Illinois Urbana-Champaign, IL, USA.
Subspace Kernel Learning on Tensor Sequences
Mar 20, 2026Lei Wang, Xi Ding, Yongsheng Gao +1Nyström Method Kernel Methods
Griffith University · Data61 CSIRO · University of New South Wales
From ex(p) to poly: Gaussian Splatting with Polynomial Kernels
Mar 19, 2026Joerg H. Mueller, Martin Winter, Markus Steinberger3D Gaussian Splatting 3DGS Acceleration
Huawei Technologies, Switzerland · Huawei Technologies, Austria · Graz University of Technology, Austria
Variational Kernel Design for Internal Noise: Gaussian Chaos Noise, Representation Compatibility, and Reliable Deep Learning
Mar 18, 2026Ziran LiuKernel Methods Model Calibration
Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS), Shanghai 200433, China · Research Institute of Intelligent Complex Systems, Fudan University, Shanghai 200433, China
Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty
Mar 18, 2026Hengrui Luo, Xiaoye S. Li, Yang Liu +3Gaussian Process Regression Uncertainty Quantification
Department of Statistics Rice University, Houston, TX 77005 · Lawrence Berkeley National Laboratory, Berkeley, CA 94709
Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual function
Mar 17, 2026Amon Lahr, Anna Scampicchio, Johannes Köhler +1Kernel Methods Gaussian Process Regression
Institute for Dynamical Systems and Control, ETH Zurich, Zurich, Switzerland
Kriging via variably scaled kernels
Mar 16, 2026Gianluca Audone, Francesco Marchetti, Emma Perracchione +1Gaussian Processes Gaussian Process Regression
Faculty of Engineering and Physical Sciences, University of Southampton, United Kindom · Dipartimento di Matematica “Tullio Levi-Civita”, Universit`a di Padova, Italy · Dipartimento di Scienze Matematiche Giuseppe Luigi Lagrange, Politecnico di Torino, Italy +1
A Fractional Fox H-Function Kernel for Support Vector Machines: Robust Classification via Weighted Transmutation Operators
Mar 13, 2026Gustavo DorregoRobust Classification Kernel Methods
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Corrientes, Argentina.
Bases of Steerable Kernels for Equivariant CNNs: From 2D Rotations to the Lorentz Group
Mar 12, 2026Alan GarbarzEquivariant Neural Networks Kernel Methods
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de F´ısica. Ciudad Universitaria, pabell´on 1, 1428, Buenos Aires, Argentina. · CONICET - Universidad de Buenos Aires, Instituto de F´ısica de Buenos Aires (IFIBA). Ciudad Universitaria, pabell´on 1, 1428, Buenos Aires, Argentina.
ReHARK: Refined Hybrid Adaptive RBF Kernels for Robust One-Shot Vision-Language Adaptation
Mar 12, 2026Md Jahidul IslamVLM Adaptation Test-Time Adaptation of VLMs
Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
Margin in Abstract Spaces
Mar 7, 2026Yair Ashlagi, Roi Livni, Shay Moran +1Kernel Methods Statistical Learning Theory
School of Electrical and Computer Engineering, Tel Aviv University. · Departments of Mathematics, Computer Science, and Data and Decision Sciences, Technion, and Google Research. · Departments of Mathematics, Technion.
Tiny, Hardware-Independent, Compression-based Classification
Mar 6, 2026Charles Meyers, Aaron MacSween, Erik Elmroth +1Kernel Methods Data-Efficient Learning
Institute for Experiential AI, Northeastern University, Boston, United States · Department of Computer Science, Umeå University, Umeå, Sweden
CRESTomics: Analyzing Carotid Plaques in the CREST-2 Trial with a New Additive Classification Model
Mar 4, 2026Pranav Kulkarni, Brajesh K. Lal, Georges Jreij +11Medical Image Classification Explainable Medical Image Analysis
University of Maryland Institute for Health Computing · University of Maryland, College Park · University of Maryland School of Medicine +3
Beyond Cross-Validation: Adaptive Parameter Selection for Kernel-Based Gradient Descents
Mar 3, 2026Xiaotong Liu, Yunwen Lei, Xiangyu Chang +1Kernel Methods Hyperparameter Optimization
Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi’an Jiaotong University, Xi’an, China · Department of Mathematics, The University of Hong Kong, Hongkong, China
Random Features for Operator-Valued Kernels: Bridging Kernel Methods and Neural Operators
Mar 1, 2026Mike Nguyen, Nicole MückeRandom Feature Methods Kernel Methods
Technical University of Braunschweig
Regular Fourier Features for Nonstationary Gaussian Processes
Feb 26, 2026Arsalan Jawaid, Abdullah Karatas, Jörg SeewigFourier Feature Embeddings Gaussian Processes
Institute of Measurement and Sensor Technology, University of Kaiserslautern-Landau, Kaiserslautern, Germany · Independent Researcher, Mannheim, Germany
Kernel Integrated $R^2$ : A Measure of Dependence
Feb 26, 2026Pouya Roudaki, Shakeel Gavioli-Akilagun, Florian Kalinke +2Kernel Methods
Department of Statistics, London School of Economics, London, UK · Department of Decision Analytics and Operations, City University of Hong Kong, Hong Kong, China · Chair of Information Systems, Karlsruhe Institute of Technology, Karlsruhe, Germany
An automatic counting algorithm for the quantification and uncertainty analysis of the number of microglial cells trainable in small and heterogeneous datasets
Feb 26, 2026L. Martino, M. M. Garcia, P. S. Paradas +1Microscopy Image Analysis Uncertainty Quantification
Universit´a degli studi di Catania, Catania, Italy. · Area of Pharmacology, Nutrition and Bromatology, Dep. of Basic Health Sciences, Faculty of Health Sciences, Universidad Rey Juan Carlos (URJC), Unidad Asociada de I+D+i al Instituto de Quimica Medica (IQM), CSIC-URJC. · Universidad Carlos III de Madrid, Madrid, Spain.
Generative Modeling via Kernelized Stochastic Interpolants
Feb 23, 2026Florentin Coeurdoux, Etienne Lempereur, Nathanaël Cuvelle-Magar +2Stochastic Differential Equations Stochastic Interpolants
Capital Fund Management, Paris, France · Département d’informatique, ENS, Université PSL, Paris, France · Collège de France, Paris, France +2
No More DeLuLu: Physics-Inspired Kernel Networks for Geometrically-Grounded Neural Computation
Feb 22, 2026Taha BouhsineKernel Methods Reproducing Kernel Hilbert Spaces
Azetta AI.
Tighter Regret Lower Bound for Gaussian Process Bandits with Squared Exponential Kernel in Hypersphere
Feb 20, 2026Shogo IwazakiGaussian Process Bandits Minimax Regret
LY Corporation, Tokyo, Japan
Random Wavelet Features for Graph Kernel Machines
Feb 17, 2026Valentin de Bassompierre, Jean-Charles Delvenne, Laurent JacquesGraph Representation Learning Graph Embedding
INMA/ICTEAM, UCLouvain, Belgium
Sparse Attention as Compact Kernel Regression
Jan 30, 2026Saul Santos, Nuno Gonçalves, Daniel C. McNamee +2Transformer Attention Sparse Attention
Instituto Superior Técnico & Instituto de Telecomunicações, Universidade de Lisboa, Portugal · Carnegie Mellon University, Pittsburgh, USA · Champalimaud Research, Lisbon, Portugal +1
Mechanistic Evidence for Spectral Structures in Prior-Data Fitted Networks
Jan 29, 2026Kaustubh Sharma, Srijan Tiwari, Ojasva Nema +1Prior-Data Fitted Networks Neural Network Interpretability
Indian Institute of Technology Roorkee, India
Finite-Sample Unbiased Variance of MMD under Unbalanced Sampling: Exact Estimation and Quasi-Linear Computation
Jan 20, 2026Shijie Zhong, Yikun Yang, Da Gong +1Maximum Mean Discrepancy Kernel Methods
School of Power and Energy, Northwestern Polytechnical University, 1 Dongxiang Road, Xi’an, 710129, Shanxi, China. · Advanced Power Research Institute, Northwestern Polytechnical University, 619 Jicui Road, Chengdu, 610299, Sichuan, China. · Taihang Laboratory, Chengdu, 610200, Sichuan, China. +1
Minimum distance classification for nonlinear dynamical systems
Jan 7, 2026Dominique MartinezDynamical Systems Time Series Classification
Aix-Marseille University, CNRS, ISM, 13009 Marseille, France
Computationally efficient goodness-of-fit tests through kernelized Stein discrepancy
Dec 23, 2025Zhihan Huang, Ziang NiuKernel Methods Statistical Hypothesis Testing
Department of Statistics and Data Science University of Pennsylvania

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Lipschitz bounds for integral kernels

Justin Reverdi, Sixin Zhang, Fabrice Gamboa, Serge Gratton

IRIT, IMT, LIEBHERR Aerospace, Toulouse, France · Univ Toulouse, Toulouse INP, CNRS, IRIT, Toulouse, France · IMT, Toulouse, France

Kernel Methods

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Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite their importance, explicit characterizations of the Lipschitz constant of kernel feature maps are available only in a limited number of cases. In this paper, we study the Lipschitz regularity of feature maps associated with integral kernels under differentiability assumptions. We first provide sufficient conditions ensuring Lipschitz continuity and derive explicit formulas for the corresponding Lipschitz constants. We then identify a condition under which the feature map fails to be Lipschitz continuous and apply these results to several important classes of kernels. For infinite width two-layer neural network with isotropic Gaussian weight distributions, we show that the Lipschitz constant of the associated kernel can be expressed as the supremum of a two-dimensional integral, leading to an explicit characterization for the Gaussian kernel and the ReLU random neural network kernel. We also study continuous and shift-invariant kernels such as Gaussian, Laplace, and Matérn kernels, which admit an interpretation as neural network with cosine activation function. In this setting, we prove that the feature map is Lipschitz continuous if and only if the weight distribution has a finite second-order moment, and we then derive its Lipschitz constant. Finally, we raise an open question concerning the asymptotic behavior of the convergence of the Lipschitz constant in finite width neural networks. Numerical experiments are provided to support this behavior.