Related papers: Vector search with small radiuses
In this note, we investigate how well we can reconstruct the best rank-$r$ approximation of a large matrix from a small number of its entries. We show that even if a data matrix is of full rank and cannot be approximated well by a low-rank…
Vector data is prevalent across business and scientific applications, and its popularity is growing with the proliferation of learned embeddings. Vector data collections often reach billions of vectors with thousands of dimensions, thus,…
Work in information retrieval has largely been centered around ranking and relevance: given a query, return some number of results ordered by relevance to the user. The problem of result list truncation, or where to truncate the ranked list…
Most approaches to cross-modal retrieval (CMR) focus either on object-centric datasets, meaning that each document depicts or describes a single object, or on scene-centric datasets, meaning that each image depicts or describes a complex…
Rank similarity measures provide a method for quantifying differences between search engine results without the need for relevance judgments. For example, the providers of a search service might use such measures to estimate the impact of a…
In a geometric $k$-clustering problem the goal is to partition a set of points in $\mathbb{R}^d$ into $k$ subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering…
A complex frame is a collection of vectors that span $\mathbb{C}^M$ and define measurements, called intensity measurements, on vectors in $\mathbb{C}^M$. In purely mathematical terms, the problem of phase retrieval is to recover a complex…
We consider the problem of finding the matching map between two sets of $d$-dimensional noisy feature-vectors. The distinctive feature of our setting is that we do not assume that all the vectors of the first set have their corresponding…
In large-scale metric localization, an incorrect result during retrieval will lead to an incorrect pose estimate or loop closure. Re-ranking methods propose to take into account all the top retrieval candidates and re-order them to increase…
We propose a method for metric-scale monocular depth estimation. Inferring depth from a single image is an ill-posed problem due to the loss of scale from perspective projection during the image formation process. Any scale chosen is a…
Computer science texts are particularly rich in both narrative content and illustrative charts, algorithms, images, annotated diagrams, etc. This study explores the extent to which vector-based multimodal retrieval, powered by…
Image retrieval can be formulated as a ranking problem where the goal is to order database images by decreasing similarity to the query. Recent deep models for image retrieval have outperformed traditional methods by leveraging…
Range-based set reconciliation is a simple approach to efficiently computing the union of two sets over a network, based on recursively partitioning the sets and comparing fingerprints of the partitions to probabilistically detect whether a…
Large language models (LLMs) frequently generate multiple candidate responses for a given prompt, yet selecting the most reliable one remains challenging, especially when correctness diverges from surface-level majority agreement. Existing…
Vector databases are critical infrastructure in AI systems, and average recall is the dominant metric for their evaluation. Both users and researchers rely on it to choose and optimize their systems. We show that relying on average recall…
This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…
Minimum error rate training (MERT) is a widely used training procedure for statistical machine translation. A general problem of this approach is that the search space is easy to converge to a local optimum and the acquired weight set is…
Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large…
Classification is a common AI problem, and vector search is a typical solution. This transforms a given body of text into a numerical representation, known as an embedding, and modern improvements to vector search focus on optimising speed…
Region search is widely used for object localization. Typically, the region search methods project the score of a classifier into an image plane, and then search the region with the maximal score. The recently proposed region search…