arXiv AI June 3, 2026 By Zihao Wang, Hang Yin, Lihui Liu, Hanghang Tong, Yangqiu Song, Ginny Wong, Simon See

$\mathbb{R}^{2k}$ is Theoretically Large Enough for Embedding-based Top-$k$ Retrieval

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

arXiv AI

Jun 11

What Limits Does Quantization Place on Dense Top-$k$ Retrieval? A Theoretical Study

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

rag efficiency

arXiv Machine Learning

Aug 20

Sharp Capacity Thresholds in Linear Associative Memory: From Top-1 Retrieval to Tail-Average Learning

arXiv:2605. 05189v2 Announce Type: replace-cross Abstract: How many key-value associations can a $d\times d$ linear memory store?

By Nicholas Barnfield, Juno Kim, Eshaan Nichani, Jason D. Lee, Yue M. Lu

rag

arXiv AI

Jun 30

High-Dimensional Concentration and Retrieval Instability in Embedding Spaces: Implications for Retrieval-Augmented Generation

arXiv:2606. 28330v1 Announce Type: cross Abstract: Embedding-based retrieval systems rely on the assumption that geometric proximity in highdimensional representation spaces reflects semantic relevance.

By Ernesto Lopez Fune (DE)

rag safety

arXiv Machine Learning

Jun 4

Distributional Approximate Nearest Neighbour Search for Uncertainty-Aware Retrieval

arXiv:2606. 04603v1 Announce Type: cross Abstract: Approximate Nearest Neighbour search indices form the backbone of real-world recommender systems, enabling real-time candidate retrieval over million-item catalogues.

By Olivier Jeunen

rag diffusion

arXiv AI

Jun 4

No More K-means: Single-Stage Sparse Coding for Efficient Multi-Vector Retrieval

arXiv:2605. 30120v3 Announce Type: replace-cross Abstract: Multi-vector retrieval (MVR) models, exemplified by ColBERT, have established new benchmarks in retrieval accuracy by preserving fine-grained token-level interactions.

By Lixuan Guo, Yifei Wang, Tiansheng Wen, Aosong Feng, Stefanie Jegelka, Chenyu You

rag efficiency benchmarks

arXiv Machine Learning

Jul 14

Retrieval with Multiple Query Vectors through Anomalous Pattern Detection

arXiv:2605. 01965v2 Announce Type: replace Abstract: A classical vector retrieval problem typically considers a \emph{single} query embedding vector as input and retrieves the most similar embedding vectors from a vector database.

By Allassan Tchangmena A Nken, Baimam Boukar Jean Jacques, Miriam Rateike, Celia Cintas, Skyler Speakman

rag

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What Limits Does Quantization Place on Dense Top-$k$ Retrieval? A Theoretical Study

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High-Dimensional Concentration and Retrieval Instability in Embedding Spaces: Implications for Retrieval-Augmented Generation

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