This paper provides a survey of recent advancements in operator learning theory, focusing on convergence rates and statistical limits. It examines error bounds for empirical risk minimization, particularly concerning holomorphic operators and neural network approximations. The survey also explores fundamental performance limitations based on sample size from a minimax perspective, considering various regularity notions beyond holomorphy. Finally, it discusses the relationship between these viewpoints and identifies related open questions in the field. AI
IMPACT Provides theoretical grounding for understanding the performance and limitations of neural network approximations in operator learning.
RANK_REASON The item is a survey paper published on arXiv detailing theoretical advancements in a specific area of mathematics and machine learning. [lever_c_demoted from research: ic=1 ai=1.0]
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