The paper investigates restricted eigenvalue (RE) bounds for norm‑regularized estimators under heavy‑tailed designs. It shows that the previously conjectured sample‑size law based on Gaussian width fails for heavy‑tailed measurements, due to a phenomenon called simultaneous threshold occupancy. The authors provide explicit counterexamples, derive worst‑case sample‑complexity bounds, and compare the behavior of heavy‑tailed versus Gaussian designs on constant‑width polyhedral descent cones.
By Shi Fu, Huibo Xu, Qixin Zhang, Dacheng Tao
arXiv:2609. 25710v1 Announce Type: cross Abstract: The statistical accuracy of neural networks depends on both their approximation power and the complexity of the class fitted from data.
By Baicheng Li, Zuowei Shen, Haizhao Yang, Shijun Zhang
arXiv:2610.01459v1 Announce Type: cross
Abstract: We study logistic regression on linearly separable data under gradient descent with a large constant stepsize $\eta$. Such dynamics may exhibit a cha...
By Haodong Wen, Kaiyue Wen, Jiaye Teng
arXiv:2512. 24152v2 Announce Type: replace-cross Abstract: Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities.
By M. J. Wainwright
arXiv:2609.06327v2 Announce Type: replace-cross
Abstract: A query-oblivious coreset for a softmax-attention head is a subset of the key-value pairs whose attention output is within $\varepsilon$ of t...
By Ofek I. Cohen
arXiv:2605.13684v2 Announce Type: replace
Abstract: We study the optimal scale at which real-valued function classes exhibit uniform convergence and learnability. Our main result establishes a scale-...
By Shashaank Aiyer, Yishay Mansour, Shay Moran, Han Shao, Tom Waknine