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© 2023, Amazon Web Services, Inc. or its affiliates.
© 2023, Amazon Web Services, Inc. or its affiliates.
Jonathan Katz
Principal Product Manager – Technical
Amazon RDS Open Source
Vectors are the new JSON
or "Going beyond the Page"
© 2023, Amazon Web Services, Inc. or its affiliates.
© 2023, Amazon Web Services, Inc. or its affiliates.
Vectors are the new JSON
2
© 2023, Amazon Web Services, Inc. or its affiliates.
© 2023, Amazon Web Services, Inc. or its affiliates.
Magnitude
© 2023, Amazon Web Services, Inc. or its affiliates.
Direction
© 2023, Amazon Web Services, Inc. or its affiliates.
Why use vectors?
• Math
• Physics
• Maps
• Artificial intelligence / machine learning
6
© 2023, Amazon Web Services, Inc. or its affiliates. 7
© 2023, Amazon Web Services, Inc. or its affiliates. 8
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5,0.9059704151167303,0.8129579833153429,0.8544592783288429,0.050935102703213886,0.6640650997798936,0.5830346238565767,0.8278167869285475,0.28298784896973217,0.450304101090115,0.41830426007102517,0.7626792333938361,0.516796149
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285042793155,0.20426355588516643,0.38923130948650453,0.19030229808697285,0.44731342822910136,0.5806663041043443,0.8305436981410423,0.49623415203229726
© 2023, Amazon Web Services, Inc. or its affiliates.
Dimensionality
• Machine learning algorithms create vector embeddings of "many
dimensionalities"
§ 256
§ 384
§ 768
§ 1536
§ 2048
§ 60K+
• Dimensionality keeps information about a particular attribute
9
© 2023, Amazon Web Services, Inc. or its affiliates.
Searching vector embeddings
• Vector normalization
§ Magnitude of 1
• Distance function
§ Euclidean distance (L2)
§ Cosine distance (cosine similarity)
§ Inner product
§ Taxicab / Manhattan (L1)
§ Chebyshev (L-inf)
10
© 2023, Amazon Web Services, Inc. or its affiliates.
K-nearest neighbor
SELECT *
FROM table
ORDER BY $VECTOR <-> embedding -- distance
LIMIT 5; -- k
11
© 2023, Amazon Web Services, Inc. or its affiliates. 12
100,000
© 2023, Amazon Web Services, Inc. or its affiliates. 13
1,000,000
© 2023, Amazon Web Services, Inc. or its affiliates. 14
100,000,000
© 2023, Amazon Web Services, Inc. or its affiliates. 15
1,000,000,000
© 2023, Amazon Web Services, Inc. or its affiliates.
Vector indexing methods
• ~20 years of modern research searching high dimensionality vectors
§ FAISS – open-source library of vector search algorithms
§ Leverage CPU/GPU acceleration
• "Approximate nearest neighbor" (ANN)
§ Tradeoff on performance / recall
• IVF FLAT (inverted indexes)
• HNSW (Hierarchical inverted small worlds)
16
© 2023, Amazon Web Services, Inc. or its affiliates.
pgvector
• Open source extension that provides vector data type, distance
operations, and indexing
• IVF FLAT index
• Can adjust performance / recall tradeoff through "probes"
• Connectors to interface with many programming languages
17
© 2023, Amazon Web Services, Inc. or its affiliates.
Quick recap on vectors in machine learning
• Vectors encode information about objects (text, images, videos)
• Vectors can have high dimensionality
• "Similarity search" is a popular operation
• Data sets can become very large
• Indexing techniques that can accelerate search at cost of "recall"
18
© 2023, Amazon Web Services, Inc. or its affiliates.
© 2023, Amazon Web Services, Inc. or its affiliates.
Going beyond the page
19
© 2023, Amazon Web Services, Inc. or its affiliates.
How big is a PostgreSQL page?
20
8192*
8192 – sizeof(page header)
© 2023, Amazon Web Services, Inc. or its affiliates.
How big is a 1536 dimensional vector?
21
1536 * 4 + 8 = 6152
© 2023, Amazon Web Services, Inc. or its affiliates.
How big is a 2048 dimensional vector?
22
2048 * 4 + 8 = 8200
X
© 2023, Amazon Web Services, Inc. or its affiliates. 23
But we can TOAST!
© 2023, Amazon Web Services, Inc. or its affiliates. 24
But we can TOAST (an index)!
X
© 2023, Amazon Web Services, Inc. or its affiliates.
What does this mean?
• PostgreSQL can only index vectors up to a certain dimensionality
without reduction
• Query plan costing becomes something developers need to worry
about
§ Cost of a sequential scan on a toasted column vs. index page
25
© 2023, Amazon Web Services, Inc. or its affiliates.
What can we do?
• Native support for vector operations in PostgreSQL – Functions / data types
• Mechanisms for managing vector data that goes beyond the page
• Performance: Indexing methods. Query plan costing. Parallelism (builds and
queries)
• Build on CPU acceleration work.
§ GPU acceleration – extension?
• Contribute to extensions (e.g. pgvector) / vice versa
26
© 2023, Amazon Web Services, Inc. or its affiliates.
© 2023, Amazon Web Services, Inc. or its affiliates.
Thank you!
27

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Vectors are the new JSON in PostgreSQL

  • 1. © 2023, Amazon Web Services, Inc. or its affiliates. © 2023, Amazon Web Services, Inc. or its affiliates. Jonathan Katz Principal Product Manager – Technical Amazon RDS Open Source Vectors are the new JSON or "Going beyond the Page"
  • 2. © 2023, Amazon Web Services, Inc. or its affiliates. © 2023, Amazon Web Services, Inc. or its affiliates. Vectors are the new JSON 2
  • 3. © 2023, Amazon Web Services, Inc. or its affiliates.
  • 4. © 2023, Amazon Web Services, Inc. or its affiliates. Magnitude
  • 5. © 2023, Amazon Web Services, Inc. or its affiliates. Direction
  • 6. © 2023, Amazon Web Services, Inc. or its affiliates. Why use vectors? • Math • Physics • Maps • Artificial intelligence / machine learning 6
  • 7. © 2023, Amazon Web Services, Inc. or its affiliates. 7
  • 8. © 2023, Amazon Web Services, Inc. or its affiliates. 8 0.003049829158165096,0.18639789248165428,0.25620939279058064,0.8474032584483915,0.728909751352397,0.5150510395040762,0.4462516533698704,0.5236709561811317,0.23075271031726885,0.2372686347975339,0.9375801900227572,0.9064239595 240302,0.4651187831953436,0.26254337449177356,0.8550190813318466,0.9841195123557434,0.8949629761265854,0.3042150462800528,0.057239707391303796,0.10891993000094757,0.6202587844948866,0.7137745836868454,0.06048318180182832,0.72 75440976627969,0.9478888345354122,0.8075292635669378,0.006104610242815056,0.723315680514812,0.8404533531441913,0.25125447598935935,0.7878795080344219,0.2611767393761504,0.7249823457880282,0.5664013738334184,0.6664423050495287 ,0.047870779146162334,0.6024105618756934,0.28159282587919066,0.2603034349390896,0.2542046099573376,0.3327296553204988,0.2429052644111387,0.06034160939414335,0.0704690858202035,0.07525846779974898,0.5113090488711158,0.17784307 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  • 9. © 2023, Amazon Web Services, Inc. or its affiliates. Dimensionality • Machine learning algorithms create vector embeddings of "many dimensionalities" § 256 § 384 § 768 § 1536 § 2048 § 60K+ • Dimensionality keeps information about a particular attribute 9
  • 10. © 2023, Amazon Web Services, Inc. or its affiliates. Searching vector embeddings • Vector normalization § Magnitude of 1 • Distance function § Euclidean distance (L2) § Cosine distance (cosine similarity) § Inner product § Taxicab / Manhattan (L1) § Chebyshev (L-inf) 10
  • 11. © 2023, Amazon Web Services, Inc. or its affiliates. K-nearest neighbor SELECT * FROM table ORDER BY $VECTOR <-> embedding -- distance LIMIT 5; -- k 11
  • 12. © 2023, Amazon Web Services, Inc. or its affiliates. 12 100,000
  • 13. © 2023, Amazon Web Services, Inc. or its affiliates. 13 1,000,000
  • 14. © 2023, Amazon Web Services, Inc. or its affiliates. 14 100,000,000
  • 15. © 2023, Amazon Web Services, Inc. or its affiliates. 15 1,000,000,000
  • 16. © 2023, Amazon Web Services, Inc. or its affiliates. Vector indexing methods • ~20 years of modern research searching high dimensionality vectors § FAISS – open-source library of vector search algorithms § Leverage CPU/GPU acceleration • "Approximate nearest neighbor" (ANN) § Tradeoff on performance / recall • IVF FLAT (inverted indexes) • HNSW (Hierarchical inverted small worlds) 16
  • 17. © 2023, Amazon Web Services, Inc. or its affiliates. pgvector • Open source extension that provides vector data type, distance operations, and indexing • IVF FLAT index • Can adjust performance / recall tradeoff through "probes" • Connectors to interface with many programming languages 17
  • 18. © 2023, Amazon Web Services, Inc. or its affiliates. Quick recap on vectors in machine learning • Vectors encode information about objects (text, images, videos) • Vectors can have high dimensionality • "Similarity search" is a popular operation • Data sets can become very large • Indexing techniques that can accelerate search at cost of "recall" 18
  • 19. © 2023, Amazon Web Services, Inc. or its affiliates. © 2023, Amazon Web Services, Inc. or its affiliates. Going beyond the page 19
  • 20. © 2023, Amazon Web Services, Inc. or its affiliates. How big is a PostgreSQL page? 20 8192* 8192 – sizeof(page header)
  • 21. © 2023, Amazon Web Services, Inc. or its affiliates. How big is a 1536 dimensional vector? 21 1536 * 4 + 8 = 6152
  • 22. © 2023, Amazon Web Services, Inc. or its affiliates. How big is a 2048 dimensional vector? 22 2048 * 4 + 8 = 8200 X
  • 23. © 2023, Amazon Web Services, Inc. or its affiliates. 23 But we can TOAST!
  • 24. © 2023, Amazon Web Services, Inc. or its affiliates. 24 But we can TOAST (an index)! X
  • 25. © 2023, Amazon Web Services, Inc. or its affiliates. What does this mean? • PostgreSQL can only index vectors up to a certain dimensionality without reduction • Query plan costing becomes something developers need to worry about § Cost of a sequential scan on a toasted column vs. index page 25
  • 26. © 2023, Amazon Web Services, Inc. or its affiliates. What can we do? • Native support for vector operations in PostgreSQL – Functions / data types • Mechanisms for managing vector data that goes beyond the page • Performance: Indexing methods. Query plan costing. Parallelism (builds and queries) • Build on CPU acceleration work. § GPU acceleration – extension? • Contribute to extensions (e.g. pgvector) / vice versa 26
  • 27. © 2023, Amazon Web Services, Inc. or its affiliates. © 2023, Amazon Web Services, Inc. or its affiliates. Thank you! 27