arXiv Artificial Intelligence

Universal Approximation of Nonlinear Operators and Their Derivatives

9 days ago 02.09.2026 07:00 👁 3 views
Universal Approximation of Nonlinear Operators and Their Derivatives

Quick summary

arXiv:2605.15285v3 Announce Type: replace-cross Abstract: Establishing Universal Approximation Theorems (UATs) for nonlinear operators and their derivatives is a foundational open problem in Operator Learning (OL) and raises delicate questions in Nonlinear Functional Analysis. We prove the first UATs for $k$-times differentiable nonlinear operators and their derivatives via OL architectures, uniformly on compact sets and in weighted Bastiani--Sobolev spaces for general finite input measures. In full Banach-space generality, these are the first complete generalizations of the corresponding infl

Key takeaways

  • arXiv:2605.15285v3 Announce Type: replace-cross Abstract: Establishing Universal Approximation Theorems (UATs) for nonlinear operators and their derivatives is a foundational open problem in Operator Learning (OL) and raises delicate questions in Nonlinear Functional Analysis.
  • We prove the first UATs for $k$-times differentiable nonlinear operators and their derivatives via OL architectures, uniformly on compact sets and in weighted Bastiani--Sobolev spaces for general finite input measures.
  • In full Banach-space generality, these are the first complete generalizations of the corresponding infl

Why it matters

“Universal Approximation of Nonlinear Operators and Their Derivatives” illustrates how changes in the AI ecosystem can affect products, workflows and user expectations together. Its lasting significance depends on measurable adoption, cost and safety outcomes.

Kaynak sitede devamını oku: arXiv Artificial Intelligence ↗