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: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.
arXiv:2605. 05189v2 Announce Type: replace-cross Abstract: How many key-value associations can a $d\times d$ linear memory store?
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.
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.
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.
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.
arXiv:2505. 17810v2 Announce Type: replace Abstract: Approximate nearest neighbor (ANN) search is a performance-critical component of many machine learning pipelines, and rigorous benchmarking is essential for assessing the performance of vector indexes for ANN search.
arXiv:2609. 02155v1 Announce Type: new Abstract: The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal.
arXiv:2606. 17910v1 Announce Type: cross Abstract: Dense retrieval has become the dominant paradigm in information retrieval, in which each document is scored against a query by the inner product of their vector embeddings, and the top-$k$ documents by score are retrieved for this query.
arXiv:2606. 16045v1 Announce Type: new Abstract: In the data selection problem, the objective is to choose a small, representative subset of data that can be used to efficiently train a machine learning model.
arXiv:2606. 13871v1 Announce Type: new Abstract: Tabular data embeddings have become a cornerstone of data profiling and data integration pipelines, enabling tasks such as entity annotation and resolution; schema matching; column type detection; and table search, among others.
arXiv:2606. 02765v1 Announce Type: cross Abstract: Model dimension ($d_{model}$) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored.