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: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:2609. 02143v1 Announce Type: cross Abstract: Most vector databases rely on graph-based indexes, notably HNSW and Vamana, for approximate nearest neighbor search.
By Sajad Faghfoor Maghrebi, Navid Eslami, Niv Dayan
arXiv:2606. 11780v1 Announce Type: cross Abstract: We establish conditions for embedding a corpus of $N$ documents as $d$-dimensional vectors such that every $k$-subset $S \subseteq [N]$ is realizable as a result of top-$k$ retrieval by some query vector.
By Koki Okajima, Tsukasa Yoshida
arXiv:2605. 25303v3 Announce Type: replace-cross Abstract: The $2 \rightarrow q$ norm of a matrix $X \in \mathbb{R}^{n \times d}$ is defined as $\lVert X \rVert_{2 \rightarrow q} = \sup_{\lVert v \rVert_2 = 1} \lVert Xv \rVert_q$.
By Samuel B. Hopkins, Stefan Tiegel
CertEx introduces a GPU‑based exact k‑nearest‑neighbor search that relies on certified exclusion, a technique that conservatively eliminates vectors using low‑precision bounds before computing exact distances. By storing a half‑precision lower‑bounding projection and embedding a rounding certificate into the tensor‑core dot product, CertEx only evaluates distances for a small subset of candidates, guaranteeing exact results. Experiments on sixteen datasets with up to 100 million vectors show that CertEx achieves 7.1× to 18.0× the throughput of the fastest cuVS search on an H100 and outperforms quantized and graph indexes when exactness is required.
By Dongfang Zhao