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By tightly characterizing the sample complexity, this work confirms the intrinsic difficulty of learning Lipschitz operators, regardless of the data or learning technique.
A key question in operator learning is how to design surrogate operators with provable approximation guarantees in reasonable computational time. Whereas smooth operators can be approximated efficiently, i.e., with at least algebraic convergence in the amount of training data, learning finitely regular operators is kno...
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