Abstract:This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and neural network approximations. Next, it illustrates fundamental performance limits in terms of sample size by adopting a minimax perspective and considering various notions of regularity beyond holomorphy. The paper ends with a discussion on the interplay between these two perspectives and related open questions.
From: Nicholas H. Nelsen [view email]
[v1]
Sat, 28 Feb 2026 21:36:40 UTC (39 KB)
[v2]
Fri, 3 Jul 2026 01:12:54 UTC (42 KB)
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