arXiv:2502. 11665v3 Announce Type: replace-cross Abstract: The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space.
arXiv:2601. 19791v4 Announce Type: replace Abstract: We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting.
arXiv:2607. 00257v1 Announce Type: new Abstract: Accurate prediction of complex dynamical systems from noisy measurements remains a significant challenge in scientific computing.
arXiv:2506. 13139v3 Announce Type: replace-cross Abstract: Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down.
arXiv:2609.38842v1 Announce Type: cross Abstract: Learn-then-differentiate (LTD) estimates gradients by fitting a model to simulation outputs and differentiating it. We develop a unified framework ex...
arXiv:2608. 11831v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning.
arXiv:2606. 06772v1 Announce Type: cross Abstract: Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory.
The paper introduces a compositional variant of kernel ridge regression where the predictor reweights input coordinates, framing the approach as a variational problem to study feature learning in compositional architectures. It demonstrates that both global minimizers and stationary points can discard Gaussian noise variables while retaining relevant ones, and shows that α1-type kernels (e.g., Laplace) recover features contributing to nonlinear effects at stationary points, whereas Gaussian kernels recover only linear ones.
arXiv:2602. 02431v2 Announce Type: replace-cross Abstract: It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning.
arXiv:2508. 08517v2 Announce Type: replace-cross Abstract: Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire.
arXiv:2406. 04425v2 Announce Type: replace Abstract: A fundamental problem in machine learning is understanding the effect of early stopping on the parameters obtained and the generalization capabilities of the model.
arXiv:2609.38011v1 Announce Type: new Abstract: Modern machine learning systems are trained on mixtures of data from different domains, and choosing the right mixture can substantially improve downst...