AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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This work identifies classes of holomorphic functions and operators for which the OOD generalization error converges at algebraic rates even in the presence of large distribution shifts, leading to what is termed a `blessing of high dimensionality'.
Out-of-distribution (OOD) generalization is a central challenge in scientific machine learning. We study regression problems in which the test distribution differs from the training distribution and ask: under what assumptions on the target function or operator is stable extrapolation possible, and how far beyond the t...
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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