arXiv:2506. 21306v2 Announce Type: replace-cross Abstract: Functions that grow without bound on one side of the real line and decay to zero on the other cannot be approximated uniformly by ordinary polynomials on unbounded domains.
arXiv:2606. 17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube.
arXiv:2609.25874v1 Announce Type: new Abstract: Deep neural networks approximate functions by composing affine maps with nonlinear activations, but how composition itself creates approximation power...
arXiv:2606. 20325v1 Announce Type: new Abstract: Classical approximation theorems ask for a new neural network whenever the target accuracy is improved.
arXiv:2606. 01764v1 Announce Type: cross Abstract: We revisit the convergence guarantees of the Extragradient (EG) method for unconstrained biaffine min-max optimization.
Consistent submodular maximization studies the tradeoff between solution quality and stability when elements arrive over time. For a monotone submodular objective, which models diminishing returns, an...
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:2410. 14788v4 Announce Type: replace-cross Abstract: Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery.
arXiv:2607. 21094v1 Announce Type: new Abstract: We study feature-level and node-level explanations for graph neural networks (GNNs) through the lens of Aumann-Shapley attribution.
arXiv:2501. 18530v3 Announce Type: replace-cross Abstract: We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional.
The paper introduces SW-KAN, a Kolmogorov‑Arnold Network that replaces traditional B‑spline activations with Stieltjes‑Wigert q‑orthogonal polynomials defined on the semi‑infinite domain (0, ∞). It addresses the domain mismatch between unbounded inputs and bounded polynomial bases by applying a smooth exponential‑of‑tanh mapping, and uses a numerically stable three‑term recurrence to evaluate polynomial expansions efficiently. Experiments on image classification and continuous function approximation show that SW‑KAN achieves better accuracy‑efficiency trade‑offs than existing polynomial KANs, especially in resource‑constrained scenarios with limited data or feature dimensionality.
arXiv:2610. 00545v1 Announce Type: new Abstract: We study adversarial online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed sets.
arXiv:2604. 07328v3 Announce Type: replace Abstract: How does the choice of training data influence an AI model?