arXiv:2607. 09909v1 Announce Type: cross Abstract: We study nearest neighbor search from the perspective of data-driven algorithm design: given a dataset $P \subset \mathbb{R}^d$ of size $n$ and sample access to a query distribution over $\mathbb{R}^d$, the goal is to learn a data structure optimized for queries drawn from that specific distribution.
By Sanjeev Khanna, Ashwin Padaki, Erik Waingarten
arXiv:2509. 20848v2 Announce Type: replace-cross Abstract: In the classic point location problem, one is given an arbitrary dataset $X \subset \mathbb{R}^d$ of $n$ points with query access to an unknown halfspace $f : \mathbb{R}^d \to \{0,1\}$, and the goal is to learn the label of every point in $X$.
By Hadley Black, Kasper Green Larsen, Arya Mazumdar, Barna Saha, Geelon So
arXiv:2412. 16457v3 Announce Type: replace-cross Abstract: In this paper, we focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent vertex correspondence.
By Zhangsong Li
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:2607.17469v2 Announce Type: replace-cross
Abstract: How much does an algorithm's running-time distribution under independent randomness reveal about its behavior when independence is no longer...
By Yunbei Xu
The paper establishes the optimal incremental first‑order oracle (IFO) complexity for nonconvex finite‑sum optimization under individual smoothness, proving a matching lower bound that closes a previously missing √{n} factor. It also refines the analysis of the PAGE algorithm under the global Polyak‑Lojasiewicz condition, providing tighter guarantees for different ranges of the condition number. The authors introduce a novel dense weak hiding construction that yields these lower bounds and demonstrates the limits of existing methods.
By Yuxing Peng, Zhiqing Tang, Weijia Jia