arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.
By Raziyeh Takbiri
The paper presents a near-complete, nonasymptotic generalization theory for multilayer neural networks using path regularization, applicable to broad Lipschitz loss functions without requiring bounded loss or extreme network hyperparameters. It provides an explicit upper bound that addresses approximation rates in generalized Barron spaces and demonstrates the double descent phenomenon for ReLU networks. The authors claim near-minimax optimality for regression problems and plan to establish matching lower bounds in future work.
By Hao Yu
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.
By Abhishake Rastogi, Tatiana A. Bubba, Tapio Helin, Luca Ratti
arXiv:2601. 18115v2 Announce Type: replace Abstract: We study the problem of learning a single neuron under standard squared loss in the presence of arbitrary label noise and group-level distributional shifts, for a broad family of covariate distributions.
By Guyang Cao, Shuyao Li, Sushrut Karmalkar, Jelena Diakonikolas
arXiv:2606. 01527v2 Announce Type: replace Abstract: Machine unlearning is motivated by legal and user-facing requirements to remove the influence of individuals' data from trained models, such as the right to be forgotten.
By Matthew Regehr, Gautam Kamath, Andrew Lowy
The paper presents high‑probability generalization guarantees for Randomized Block Coordinate Descent (RBCD) when applied to nonconvex learning problems. It derives bounds on the gradients of both empirical and population risks under standard smoothness assumptions, and shows how polynomially decaying step sizes and early stopping can achieve optimal convergence rates for population gradients. In settings where the objective is gradient‑dominated, the authors provide functional suboptimality bounds that approach optimistic rates seen in convex or low‑noise scenarios, and they also establish dimension‑independent bounds for loss functions with a particular structure, extending applicability to high‑dimensional problems.
By Ruixi Hu, Liang Wu
arXiv:2610.35428v1 Announce Type: new
Abstract: Structured sparse learning is a leading paradigm for high-dimensional data modeling, as it enables rigorous integration of domain-validated structural...
By Wanling Xie, Hu Yang
arXiv:2201. 01973v3 Announce Type: replace-cross Abstract: The problem of linear predictions has been extensively studied for the past century under pretty generalized frameworks.
By Saptarshi Chakraborty, Debolina Paul, Swagatam Das
arXiv:2606. 01527v1 Announce Type: new Abstract: Machine unlearning is motivated by legal and user-facing requirements to remove the influence of individuals' data from trained models, such as the right to be forgotten.
By Matthew Regehr, Gautam Kamath, Andrew Lowy
Structured sparse learning is a leading paradigm for high-dimensional data modeling, as it enables rigorous integration of domain-validated structural priors into the learning process. Among these pri...
arXiv:2605. 02141v2 Announce Type: replace-cross Abstract: Kullback-Leibler (KL) regularization is widely used in offline decision-making and offers several benefits, motivating recent work on the sample complexity of offline learning with respect to KL-regularized performance metrics.
By Kaixuan Ji, Qiwei Di, Heyang Zhao, Qingyue Zhao, Quanquan Gu
The paper investigates the computational and statistical challenges of the calibration distance, a key metric for measuring miscalibration in probabilistic predictors. It presents an efficient algorithm for exact computation when the distribution has a uniform marginal and noiseless labels, and shows that the problem becomes NP‑hard if either assumption is dropped. The authors also provide a polynomial‑time approximation scheme for the general case and establish tight sample complexity bounds for estimating the calibration distance from data.
By Mingda Qiao