Foundations of Vector Retrieval

Type: Research paper / tutorial monograph
Author: Sebastian Bruch
Discipline: Computer Science – Data Structures and Algorithms; Information Retrieval
Year: 2024
DOI: https://doi.org/10.48550/arXiv.2401.09350
arXiv ID: arXiv:2401.09350

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Overview

“Foundations of Vector Retrieval” is a monograph that surveys and formalizes the principles and algorithms behind vector retrieval—finding vectors most similar to a query vector in large collections of high-dimensional data. It provides both theoretical and practical foundations relevant to modern vector databases and vector search engines, covering text, image, speech, and multimodal embeddings.

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Key Details

• Title: Foundations of Vector Retrieval
• Author: Sebastian Bruch
• First submission date: 17 January 2024
• Categories:
  • Data Structures and Algorithms (cs.DS)
  • Information Retrieval (cs.IR)
• Formats available:
  • PDF
  • HTML (experimental)
  • TeX Source
• Length: ~4.6 MB PDF (monograph-length survey/tutorial)

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Features

• Conceptual foundation for vector retrieval

  • Explains vectors as universal representations for text, images, speech, and multimodal data.
  • Covers both hand-crafted feature vectors and learned embeddings.
  • Formalizes the problem of retrieving vectors similar to a given query vector.

• Focus on similarity search in high-dimensional spaces

  • Centers on the task of finding nearest or most similar vectors in large collections.
  • Addresses the challenges that arise when the number of stored vectors is large.

• Coverage of fundamental concepts

  • Introduces the mathematical and algorithmic underpinnings of vector retrieval.
  • Lays out core ideas used in vector databases and vector search engines.

• Advanced data structures and algorithms

  • Surveys specialized data structures for efficient vector search.
  • Discusses advanced algorithms used in practice for scalable retrieval.

• Tutorial/monograph style

  • Designed to be accessible as an entry point into vector retrieval research.
  • Aims to “recap” and organize a broad body of work in one coherent treatment.
  • Helps lower the barrier to understanding modern vector search systems.

• Research integration and discoverability

  • Indexed in major scholarly tools (NASA ADS, Google Scholar, Semantic Scholar).
  • Linked to related resources via a related DOI (https://doi.org/10.1007/978-3-031-55182-6).
  • Connected to code/data discovery platforms (alphaXiv, CatalyzeX, DagsHub, etc.) via arXiv’s ecosystem.

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Access

• Abstract & metadata: https://arxiv.org/abs/2401.09350
• PDF: https://arxiv.org/pdf/2401.09350
• HTML (experimental): https://arxiv.org/html/2401.09350v1
• TeX source: https://arxiv.org/src/2401.09350

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Pricing

• Cost: Free to access and download via arXiv.org.