arXiv:2605.15240v2 Announce Type: replace-cross Abstract: This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalizatio...
arXiv:2604. 00316v2 Announce Type: replace-cross Abstract: Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that.
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.
arXiv:2609.34474v2 Announce Type: replace Abstract: We introduce a deep kernel hedging framework that combines the flexibility of deep learning with the structural inductive bias of kernel methods. T...
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...
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:2608. 28564v1 Announce Type: cross Abstract: We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels.
arXiv:2303. 08777v3 Announce Type: replace-cross Abstract: Cross-validation is one of the most widely used tools for risk estimation and model selection in statistics and machine learning, yet its theoretical properties when embedded in a learning procedure remain insufficiently understood.
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
The paper introduces SCORE, a scalable framework that learns an expressive covariance approximation for high‑dimensional Gaussian targets by combining scoring rule training with spectral‑space modeling. It decomposes the learning task into marginal distribution estimation and structured correlation matrix learning, achieving dense dependencies with linear storage and ≠(d log d) computational cost. The method employs a closed‑form Gaussian kernel score that remains valid for degenerate covariances, provides bounded gradients, and is invariant under unitary transforms, with theoretical guarantees on marginal recovery and correlation projection, and demonstrates improved performance on time‑series forecasting, monocular depth estimation, and spatial weather prediction.
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: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.