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

$\mathbb{R}^{2k}$ 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.

A Power Law in Logarithm's Clothing: On the Scalability of Graph-Based Vector Search

arXiv:2609. 02143v1 Announce Type: cross Abstract: Most vector databases rely on graph-based indexes, notably HNSW and Vamana, for approximate nearest neighbor search.

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?

Binary and Scalar Embedding Quantization for Significantly Faster & Cheaper Retrieval

Exact Limits of Random Projections for Preserving Geometry: Distance Recovery, Nearest-Neighbor Rankings, and Covariance Shape in Gaussian Models

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.

Price of metric universality in vector quantization is at most 0.11 bit

arXiv:2602. 05790v2 Announce Type: replace-cross Abstract: Fast computation of a matrix product $W^\top X$ is a workhorse of modern LLMs.

Hybrid privacy-aware semantic search: SVD-truncated document geometry and CKKS-encrypted query reranking under a restricted threat model

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.

Projection and Quantisation: A Unifying View of Learning to Hash, from Random Projections to the RAG Era

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.

Actively Learning Halfspaces without Synthetic Data

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 $X$.

Query-Oblivious Coresets for Softmax Attention: Improved Bounds and Efficient Constructions

arXiv:2609.06327v2 Announce Type: replace-cross Abstract: A query-oblivious coreset for a softmax-attention head is a subset of the key-value pairs whose attention output is within $\varepsilon$ of t...

Intrinsic Interaction Geometry Controls the Low-Rank Complexity of Softmax Attention

arXiv:2608.28150v2 Announce Type: replace Abstract: How much matrix rank is required to preserve every bounded value output of normalized softmax attention? We study the unrestricted maximum-row-\(\e...

Optimal Unambiguous DNFs and Alon-Saks-Seymour

arXiv:2608. 02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$.