arXiv:2602. 20376v3 Announce Type: replace-cross Abstract: We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity.
By Ria Stevens, Fangshuo Liao, Barbara Su, Thanasis Hadjidimoulas, Jianqiang Li, Anastasios Kyrillidis
arXiv:2607. 14304v1 Announce Type: cross Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold.
By Manuel Fernandez V, Yizhe Zhu
arXiv:2004. 05813v3 Announce Type: replace-cross Abstract: Suppose that we are given independent, identically distributed random samples $x_1,\cdots,x_n$ from a mixture at most $k$ many $d$-dimensional spherical Gaussian distributions $\mu_1,\cdots,\mu_{k_0}$ of identical and known variance $\sigma^2$ in each coordinate, such that the minimum $\ell^2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $2\Delta\sigma \min\{\sqrt{d},\sqrt k\}$, where $\Delta>C_0$, and $C_0$ is a sufficiently large universal constant.
By Somnath Chakraborty, Hariharan Narayanan
arXiv:2605. 03283v2 Announce Type: replace-cross Abstract: We provide a unified theoretical analysis of Linear Discriminant Analysis with simultaneous multilabel scatter matrix formulations and Stiefel orthogonality constraints.
By Brian Keith-Norambuena, Juan Bekios-Calfa
arXiv:2607. 24235v1 Announce Type: cross Abstract: Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence testing, among others.
By Jose Cribeiro-Ramallo, Florian Kalinke, Zolt\'an Szab\'o
arXiv:2607. 22620v1 Announce Type: cross Abstract: Yun, Sra, and Jadbabaie (COLT 2021, open question) conjectured the SS--RS--GD inequalities: for well-conditioned symmetric matrices $A_1,\dots,A_n$, the operators $W_{ss}$, $W_{rs}$, and $W_{gd}$ that encode the expected iterate of single-shuffle SGD, random-reshuffle SGD, and gradient descent on a quadratic finite sum should satisfy \[ \|W_{ss}\|\le \| W_{rs}\|\le \|W_{gd}\|.
By Binghui Peng