arXiv:2503. 18219v2 Announce Type: replace Abstract: This work studies the sampling complexity of learning with ReLU neural networks and neural operators.
By Philipp Grohs, Samuel Lanthaler, Margaret Trautner
arXiv:2402.04691v5 Announce Type: replace-cross
Abstract: This study investigates the use of stochastic gradient descent (SGD) to learn operators between general Hilbert spaces. We study weak and str...
By Lei Shi, Jia-Qi Yang
arXiv:2609.36709v1 Announce Type: cross
Abstract: Out-of-distribution (OOD) generalization is a central challenge in scientific machine learning. We study regression problems in which the test distri...
By Ben Adcock, Simone Brugiapaglia, Xuemeng Wang
arXiv:2504.18184v5 Announce Type: replace
Abstract: We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert sp...
By Jia-Qi Yang, Lei Shi
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.
By Ben Adcock, Michael Griebel, Gregor Maier
arXiv:2609.39512v1 Announce Type: new
Abstract: The small-sample learning problem remains a fundamental challenge in machine learning because limited training data lead to unstable model estimation a...
By Hong Zheng