Neural Network Approximation Theory

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15 papers in the last four weeks, up 15% on the four weeks before. 0.1% of all new papers.

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Learning Latent Graph Geometry via Fixed-Point Schrödinger-Type Activation: A Theoretical Study
Jul 27, 2025Dmitry Pasechnyuk-Vilensky, Martin TakáčGraph Structure Learning Graph Neural Networks
MBZUAI, UAE
Understanding Two-Layer Neural Networks with Smooth Activation Functions
Jul 11, 2025Changcun HuangNeural Network Activation Functions Neural Network Approximation Theory
Shuitu Institute of Applied Mathematics, Chongqing 400700, P.R.C
Discretization-independent operator learning for partial differential equations
Jul 9, 2025Jacob Hauck, Yanzhi ZhangPDE Operator Learning Neural Network Approximation Theory
Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409
Uniform Approximation of Functions with Asymmetric Growth and Decay by Deep Weighted Polynomials
Jun 26, 2025Kingsley Yeon, Steven B. DamelinNeural Network Approximation Theory
Department of Statistics and CCAM, University of Chicago, Chicago, 60637, IL, USA · Department of Mathematics, ZBMATH-OPEN, Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen, 76344, Germany
Causal pieces: analysing and improving spiking neural networks piece by piece
Apr 18, 2025Dominik Dold, Philipp Christian PetersenNeural Network Initialization Spiking Neural Networks
New universal operator approximation theorem for encoder-decoder architectures
Mar 31, 2025Janek Gödeke, Pascal FernselNeural Network Approximation Theory Deep Operator Networks
Center for Industrial Mathematics University of Bremen
Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon
Mar 3, 2025Hao YuDouble Descent Neural Network Generalization
Department of Automation, Tsinghua University, Beijing, 100086, China
Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential
Feb 26, 2025Shijun Zhang, Hongkai Zhao, Yimin Zhong +1Fourier Feature Embeddings Neural Network Optimization
Department of Applied Mathematics Hong Kong Polytechnic University · Department of Mathematics Duke University · Department of Mathematics and Statistics Auburn University +1
Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEs
Oct 18, 2024Takashi Furuya, Anastasis KratsiosStochastic Differential Equations PDE Solving
Doshisha University, Japan · Department of Mathematics McMaster University and Vector Institute, Canada
Statistical Properties of Deep Neural Networks with Dependent Data
Oct 14, 2024Chad BrownNonparametric Regression Neural Network Approximation Theory
Department of Economics, University of Colorado Boulder, 80309, USA.
Deep Network Approximation: Beyond ReLU to Diverse Activation Functions
Jul 13, 2023Shijun Zhang, Jianfeng Lu, Hongkai ZhaoReLU Neural Networks Neural Network Activation Functions
Department of Mathematics Duke University
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations
Dec 15, 2021Carlo Marcati, Christoph SchwabPDE Solving PDE Operator Learning
Seminar for Applied Mathematics, ETH Zurich, Switzerland
Autonomous-Flow-Based Generation
Date pendingHossein Rouhvarzi, Anastasis KratsiosUniversal Approximation Continuous Normalizing Flows
McMaster University and the Vector Institute Department of Mathematics 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada

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Learning Latent Graph Geometry via Fixed-Point Schrödinger-Type Activation: A Theoretical Study

Dmitry Pasechnyuk-Vilensky, Martin Takáč

MBZUAI, UAE

Graph Structure Learning Graph Neural Networks Graph Representation Learning Sheaf Neural Networks Neural Network Approximation Theory

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We study neural architectures in which each hidden layer is defined by the stationary state of a dissipative Schrödinger-type dynamics on a learned latent graph. On stable branches, the local stationary problem defines a differentiable implicit graph layer. To learn the graph itself, we optimize over the stratified moduli space of weighted graphs and equip each stratum with a non-degenerate Kähler-Hessian metric that keeps natural-gradient descent and face crossing well posed. We then show that a multilayer stationary network is equivalent to an exact global stationary problem on a supra-graph, and that it admits a penalized global relaxation whose stationary states converge to the exact one as the penalty parameter tends to infinity. Reverse-mode differentiation is recovered as the adjoint of the exact global system, and the penalized adjoint converges to it in the same limit. Finally, under finite-dimensional strong-monotonicity and admissible-lift assumptions, the corresponding represented hypothesis classes coincide among resolvent feed-forward networks, graph-stationary networks, supra-graph stationary systems, and sheaf-based architectures with unitary connection. The resulting structural identifications yield complexity bounds controlled by sparse graph or supra-graph geometry rather than dense ambient connectivity.

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