arXiv Machine Learning
Into the danger zone: stable extrapolation in high-dimensional function and operator learning
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Related stories
arXiv Machine Learning
Sep 22
Predicting Out-of-Distribution Generalization of Neural Operators via Observable Spectral Error Decomposition
arXiv:2609. 23529v1 Announce Type: new Abstract: Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to deployment.
arXiv AI
Jun 4
Does Order Matter : Connecting The Law of Robustness to Robust Generalization
arXiv:2602. 20971v3 Announce Type: replace-cross Abstract: Bubeck and Selke (2021) propose the connection between the Law of Robustness and robust generalization error as an open problem.
arXiv Machine Learning
Jul 7
A short tour of operator learning theory: Convergence rates, statistical limits, and open questions
arXiv:2603. 00819v2 Announce Type: replace-cross Abstract: This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory.
arXiv Statistics ML
Sep 10
A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning
arXiv:2109.02355v2 Announce Type: replace Abstract: The last decade of progress in machine learning (ML), especially the deep learning era, has raised a number of scientific questions that challenge...
arXiv Machine Learning
Sep 7
The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures
The paper investigates how many linear samples are needed to learn Lipschitz operators under Gaussian measures. It establishes both lower and upper bounds on the Hermite polynomial approximation error and shows that the minimal worst‑case error cannot converge algebraically with the number of samples. However, if the covariance operator of the Gaussian measure decays rapidly, convergence rates arbitrarily close to any algebraic rate can be achieved.
arXiv Machine Learning
Sep 17
Reliable learning in challenging environments
The paper addresses the challenge of creating machine learning learners that can guarantee provably correct predictions in difficult test-time scenarios, such as adversarial attacks and natural distribution shifts. It introduces a reliable learner with optimal theoretical guarantees for these settings and discusses practical implementations. The authors demonstrate strong performance on examples like linear separators under log-concave distributions and smooth boundary classifiers under smooth probability distributions.