arXiv:2510.02532v2 Announce Type: replace-cross
Abstract: Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensio...
By Shuo Huang, Hippolyte Labarri\`ere, Ernesto De Vito, Tomaso Poggio, Lorenzo Rosasco
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.
By Feng Ruan, Keli Liu, Michael Jordan
arXiv:2606. 08799v1 Announce Type: cross Abstract: We study the generalization of ridge-regularized nonlinear least-squares models via on-average algorithmic stability, deriving error bounds for local minimizers in terms of a data-dependent effective dimension that reflects the geometry of the gradient model at the trained parameters, through the empirical Jacobian Gram matrix and a residual--curvature term.
By Ayub Kharel, Ilja Kuzborski, Patrick Rebeschini, Yasin Abbasi-Yadkori
The paper investigates diffusion models trained in a lazy high‑dimensional regime, extending benign overfitting theory to generative settings. By analyzing denoising score matching in a vector‑valued RKHS with an inner‑product kernel, the authors derive exact risk trajectories under gradient flow when the number of samples scales proportionally with dimensionality. These trajectories reveal three distinct phases—spectral generalization, noise‑dominated interpolation, and empirical Bayes memorization—whose interplay shapes the distribution of generated samples.
By Hugo Latourelle-Vigeant, Sinho Chewi, Aram-Alexandre Pooladian, John Sous, Theodor Misiakiewicz
arXiv:2501. 10870v2 Announce Type: replace-cross Abstract: The principal objective of this work is twofold within nonparametric regression settings: (1) to establish the minimax optimal convergence rates for fixed-bandwidth Gaussian kernel spectral algorithms when the true regression function resides in a Sobolev space, and (2) to apply Gaussian spectral algorithms for achieving robust and adaptive transfer learning under concept shift.
By Haotian Lin, Matthew Reimherr
arXiv:2608. 11831v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning.
By Adrien Weihs, Chunyang Liao, Jingmin Sun, Hayden Schaeffer