arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.
arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.
arXiv:2606. 08727v1 Announce Type: cross Abstract: Many classically studied function classes are known to be approximated optimally by superpositional methods, i.
arXiv:2607. 05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks.
arXiv:2505. 18113v2 Announce Type: replace Abstract: Training quantized neural networks requires addressing the non-differentiable and discrete nature of the underlying optimization problem.
arXiv:2607. 01266v1 Announce Type: cross Abstract: We study binary classification problems whose decision sets are given by definable sets in o-minimal expansions of the real field.
arXiv:2607. 10589v1 Announce Type: cross Abstract: In contrast to most studies on neural network approximation theory that characterize results through a single parameter, such as the total number of network parameters, \cite{shen2020deep} pioneered the characterization of approximation rates as a joint function of the width parameter $N$ and the depth parameter $L$, thereby granting greater architectural flexibility.
arXiv:2606. 29043v1 Announce Type: new Abstract: Sharpness and complexity are two central factors in the generalization analysis of deep neural networks.
arXiv:2510. 10101v4 Announce Type: replace Abstract: Understanding the interplay between generalization, expressivity, and the geometry of the input space is a central challenge in graph learning.
arXiv:2407. 00809v4 Announce Type: replace Abstract: This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from functions to functions).
arXiv:2607. 05735v1 Announce Type: cross Abstract: Infinite-width limits are a standard way to reason about neural networks, but it is not automatic that the limiting learner has the same complexity-theoretic inductive bias as large finite networks.
arXiv:2510. 02779v4 Announce Type: replace Abstract: Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks.
In this work, we investigate the fixed-architecture neural network approximation with explicit parameter bounds and elementary activations. While prior work demonstrated super-expressive approximation using fixed-size networks, they lack quantitative and non-asymptotic characterizations of parameter magnitude with respect to the approximation error.