Deep neural networks typically treat nonlinearities as fixed primitives (e.g., ReLU), limiting both interpretability and the granularity of control over the induced function class. While recent additive models (like KANs) attempt to address this using splines, they often suffer from computational inefficiency and boundary instability. We propose the Rational-ANOVA Network (RAN), a foundational architecture grounded in functional ANOVA decomposition and Padé-style rational approximation. RAN models f(x) as a composition of main effects and sparse pairwise interactions, where each component is parameterized by a stable, learnable rational unit. Crucially, we enforce a strictly positive denominator, which avoids poles and numerical instability while capturing sharp transitions and near-singular behaviors more efficiently than polynomial bases. This ANOVA structure provides an explicit low-order interaction bias for data efficiency and interpretability, while the rational parameterization significantly improves extrapolation. Across controlled function benchmarks and vision classification tasks (e.g., CIFAR-10) under matched parameter and compute budgets, RAN matches or surpasses parameter-matched MLPs and learnable-activation baselines, with better stability and throughput. Code is available at https://github.com/jushengzhang/Rational-ANOVA-Networks.git.
Tensor Product Neural Networks for Functional ANOVA Model
Department of Statistics, Seoul National University, Seoul, Republic of Korea（统计系，首尔国立大学）；Department of Applied Mathematics, University of Twente, Enschede, Netherlands（应用数学系，埃因霍温理工大学）；Samsung Electronics Co., Ltd, Republic of Korea（三星电子有限公司）
Rational Neural Networks have Expressivity Advantages
Center for Applied Mathematics, Cornell University, United States（应用数学中心，康奈尔大学，美国）；Department of Mathematics, Cornell University, United States（数学系，康奈尔大学，美国）
Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons
Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学机械化重点实验室）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（北京雁栖湖应用数学研究院）；Yau Mathematical Sciences Center and Department of Mathematics, Tsinghua University（清华大学丘成桐数学科学中心与数学系）
Discovering hidden partial differential equations (PDEs) and operators from data is an important topic at the frontier between machine learning and numerical analysis . This doctoral thesis introduces theoretical results and deep learning algorithms to learn Green's functions associated with linear partial differential equations and rigorously justify PDE learning techniques. A theoretically rigorous algorithm is derived to obtain a learning rate, which characterizes the amount of training data needed to approximately learn Green's functions associated with elliptic PDEs. The construction conn…
Bounded Rational Decision-Making in Feedforward Neural Networks
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Max Planck Institute for Biological Cybernetics（马克斯·普朗克生物控制论研究所）；Graduate Training Center of Neuroscience（神经科学研究生培训中心）
$\mathcal{C}^1$-approximation with rational functions and rational neural networks
IDea_Lab - The Interdisciplinary Digital Lab at the University of Graz（interdisciplinary digital lab at the university of graz）；NAWI Graz；BioTechMed Graz
Human-like Category Learning by Injecting Ecological Priors from Large Language Models into Neural Networks
Max Planck Institute for Biological Cybernetics（马克斯·普朗克生物控制论研究所）；Helmholtz Computational Health Center（亥姆霍兹计算健康中心）；Institute for Human-Centered AI（以人为本人工智能研究所）
CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters
Technische Universität Berlin（柏林工业大学）；Universitá della Svizzera italiana（瑞士意大利语区大学）；Nanyang Technological University（南洋理工大学）；Imperial College London（帝国理工学院）；Intel Perceptual Computing（英特尔感知计算部门）
ERGNN: Spectral Graph Neural Network With Explicitly-Optimized Rational Graph Filters
Dept. of Machine Learning（机器学习系）；MBZUAI（穆罕默德·本·拉希德人工智能技术研究所）；Institute of Automation（自动化研究所）；Chinese Academy of Sciences（中国科学院）；Sun Yat-sen University（中山大学）
Adaptive Rational Activations to Boost Deep Reinforcement Learning
TU Darmstadt（达姆施塔特工业大学）；German Center for Artificial Intelligence（德国人工智能研究中心）；Hessian Center for Artifical Intelligence（黑森人工智能中心）；Centre for Cognitive Science（认知科学中心）
Classification and detection of multiple UAVs using rational Gaussian wavelet neural networks
Department of Numerical Analysis（数值分析系）；Eötvös Loránd University（欧多维奇·劳尔大学）；System and Control Laboratory（系统与控制实验室）；HUN-REN Institute for Computer Science and Control（HUN-REN计算机科学与控制研究所）；UniDistanceSuisse；Siemens Mobility Kft.（西门子移动有限公司）；HUN-REN Centre for Energy Research（HUN-REN能源研究中心）
Fractional Laplace Neural Operators: Exact Architectures, an Expressivity Frontier at Criticality, and Certified Stability for Memory-Driven Network Dynamics
