Into the danger zone: stable extrapolation in high-dimensional function and operator learning
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 training domain can one extrapolate? Existing theory controls the test error through additive penalties measuring the discrepancy between the training and test distributions. Such guarantees show robustness to small distribution shifts, but can be very pessimistic in comparison to OOD performance observed empirically. We identify classes of holomorphic functions and operators...
| Authors | Ben Adcock, Simone Brugiapaglia, Xuemeng Wang |
|---|---|
| Primary category | math.NA |
| Published | 29 September 2026 |
| Last updated at source | 3 October 2026 |
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