Basis Functions

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2 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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RBF-GNN: Rational Basis Functions for Pseudo-Coordinate based Graph Convolutions
Sep 29, 2026Paweł Batorski, Abtin Pourhadi, Paul SwobodaBasis Functions Graph Neural Networks
Heinrich Heine University Düsseldorf
On Basis Function Selection for Sparse Gaussian Process Regression
Sep 22, 2026Marnix Van Soom, Ivan De BoiGaussian Process Basis Functions
AI Lab Vrije Universiteit Brussel · InViLab University of Antwerp
RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis
Sep 1, 2026Amirhosein AzarpourKolmogorov-Arnold Networks Basis Functions
Department of Computer Science Shahid Beheshti University Tehran, Iran
Hierarchical rank-evolving representation for physics-informed neural networks
Aug 10, 2026Ruoyang Su, Xi-Le Zhao, Kun Li +1Parametric Physics-Informed Neural Network Basis Functions
University of Electronic Science and Technology of China, No.2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu, 611731, Sichuan, P.R.China · Southwestern University of Finance and Economics, 555, Liutai Avenue, Wenjiang District, Chengdu, 611130, Sichuan, P.R.China
Fast Trainable Multilinear Bases for Image Compression
Jul 26, 2026Shiwen An, Zhongyi Ni, Huanhai Zhou +1Learned Image Compression Basis Functions
Department of Information and Communication Engineering, Institute of Science Tokyo, Yokohama 226-8501, Japan · Center for Advanced Intelligence Project (AIP), RIKEN, Tokyo 103-0027, Japan · Thrust of Advanced Materials, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong 511453, China
Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems
Jul 14, 2026Marc Haltmayer, Jaemin Seo, Yuseung Lee +3Surrogate Models Basis Functions
Department of Artificial Intelligence, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul, 06974, Republic of Korea · Computational Science and Engineering Team, Samsung Electronics, 41 Samsung-ro, Giheung-gu, Yongin-si, 17113, Republic of Korea
Non-negative Matrix Factorisation with Topological Regularisation
Jun 16, 2026Matias de Jong van Lier, Shizuo Kaji, Keunsu KimNonnegative Matrix Factorization Basis Functions
Recursive Inc. · Tokyo, 150-0002, Japan · Graduate School of Science +5
Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs
May 29, 2026Qihong Yang, Qiaolin HeNeural Partial Differential Equation Solvers Partial Differential Equations
School of Mathematics, Sichuan University, city=Chengdu, postcode=610065, country=China
A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations
May 28, 2026Qihong Yang, Yangtao Deng, Qiaolin He +1Neural Partial Differential Equation Solvers Partial Differential Equations
School of Mathematics, Sichuan University, Chengdu, 610065, China
Learning Orthonormal Bases for Function Spaces
May 19, 2026Hamidreza Kamkari, Mohammad Sina Nabizadeh, Justin SolomonBasis Functions Orthogonality
MIT CSAIL Cambridge, MA
Graph Neural Networks for Community Detection in Graph Signal Analysis
May 19, 2026Roberto Cavoretto, Alessandra De Rossi, Enrico MontiniCommunity Detection Graph Neural Networks
Department of Mathematics “Giuseppe Peano”, University of Torino, via Carlo Alberto 10, 10123 Torino, Italy
Time-Varying Deep State Space Models for Sequences with Switching Dynamics
May 14, 2026Sanja Karilanova, Subhrakanti Dey, Ayça ÖzçelikkaleTime-Varying Systems State Space Models
Department of Electrical Engineering, Uppsala University, Sweden
MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functions
May 12, 2026Zichuan YangNeural Partial Differential Equation Solvers Partial Differential Equations
School of Mathematical Sciences Tongji University Shanghai, P.R. China
Discovery of Nonlinear Dynamics with Automated Basis Function Generation
May 10, 2026Mohammad Amin Basiri, Charles NicholsonSymbolic Regression System Identification
Data Science and Analytics Institute, University of Oklahoma, Norman, OK, USA · School of Industrial and Systems Engineering, University of Oklahoma, Norman, OK, USA
Smoothing Out the Edges: Continuous-Time Estimation with Gaussian Process Motion Priors on Factor Graphs
May 9, 2026Connor Holmes, Sven Lilge, Zi Cong Guo +2Factor Graphs State Estimation
University of Toronto · Georgia Institute of Technology
Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning
May 7, 2026Masahiro KatoCovariate Balancing Bias-Variance Decomposition
Data Analytics Department, Mizuho-DL Financial Technology, Co., Ltd.
Time-varying Interaction Graph ODE for Dynamic Graph Representation Learning
Apr 27, 2026Xiaoyi Wang, Zhiqiang Wang, Jianqing Liang +4Temporal Graph Neural Networks Graph Representation Learning
Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi 030006, China. · Department of System Engineering and Engineering Management, City University of Hong Kong, Kowloon 999077, Hong Kong, China. · Key Laboratory of Complex Systems and Data Science of Ministry of Education, Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China.
Partition-of-Unity Gaussian Kolmogorov-Arnold Networks
Apr 26, 2026Amir NoorizadeganKolmogorov-Arnold Networks Basis Functions
Department of Mathematics, Hong Kong Baptist University, Hong Kong SAR, China
Scale-Parameter Selection in Gaussian Kolmogorov-Arnold Networks
Apr 23, 2026Amir Noorizadegan, Sifan WangKolmogorov-Arnold Networks Basis Functions
Department of Mathematics, Hong Kong Baptist University, Hong Kong SAR, China · Institution for Foundations of Data Science, Yale University, New Haven, CT 06520, USA
Data-Driven Variational Basis Learning Beyond Neural Networks: A Non-Neural Framework for Adaptive Basis Discovery
Apr 17, 2026Andrew KirulutaBasis Functions Unsupervised Dictionary Learning
UC Berkeley, CA
Lag Operator SSMs: A Geometric Framework for Structured State Space Modeling
Dec 22, 2025Sutashu Tomonaga, Kenji Doya, Noboru MurataState Space Models State Space
Okinawa Institute of Science and Technology · Waseda University
Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential
Feb 26, 2025Shijun Zhang, Hongkai Zhao, Yimin Zhong +1Two-Layer Neural Networks Neural Network
Department of Applied Mathematics Hong Kong Polytechnic University · Department of Mathematics Duke University · Department of Mathematics and Statistics Auburn University +1

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RBF-GNN: Rational Basis Functions for Pseudo-Coordinate based Graph Convolutions

Paweł Batorski, Abtin Pourhadi, Paul Swoboda

Heinrich Heine University Düsseldorf

Basis Functions Graph Neural Networks Gnn-Based Detectors Keypoint Detection Inductive Bias

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We propose RBF-GNN, a new pseudo-coordinate based graph neural network architecture that takes into account Euclidean, spherical or angular coordinates and uses them to induce a powerful spatial inductive bias. Similar in architecture to SplineCNN, we improve upon the latter by replacing the less efficient sparse-activation based B-splines whose number grows exponentially with dimension by rational Padé basis functions. For effective training we propose a spline-subspace initialization and a variance-preserving weight rescaling. Experimentally, we evaluate on a number of popular neural network architectures that use SplineCNNs. We replace only the SplineCNNs with RBF-GNN. We achieve improved results, including on semantic keypoint matching, shape matching, event based camera computer vision tasks. Code is available at https://github.com/pawelswoboda/RationalBasisCNN.

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