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.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv AI.
arXiv:2601. 20844v3 Announce Type: replace-cross Abstract: This paper studies the Minimal Embeddable Dimension (MED): the least dimension in which there exists a configuration of $m$ object vectors so that every subset of size at most $k$ is exactly retrieved by score comparison.
arXiv:2602. 05790v2 Announce Type: replace-cross Abstract: Fast computation of a matrix product $W^\top X$ is a workhorse of modern LLMs.
arXiv:2606. 26373v1 Announce Type: cross Abstract: Dense embeddings power semantic search and retrieval-augmented generation, but embedding-inversion attacks can reconstruct source text from a vector: when a vector database leaks, the documents behind it leak too.
arXiv:2510. 04127v2 Announce Type: replace-cross Abstract: Approximate nearest neighbour (ANN) search underpins large-scale retrieval, increasingly within the retrieval-augmented generation pipelines that ground large language models, yet the methods that address it have multiplied across communities until they are seldom read as a single field.
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 $X$.
arXiv:2608. 02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$.