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Vector Index Comparison

Searching billions of vectors one at a time is too slow, so vector databases use specialized index structures that trade a little accuracy for a lot of speed. This MicroSim shows the same query running against three index types - Flat, IVF, and HNSW - side by side, so you can see how each one decides which vectors to examine.

Interactive Demo

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The red star is the query vector. Blue dots are vectors that get compared; gray dots are skipped. Toggle the checkbox to show or hide the skipped vectors.

To embed this MicroSim in another page, use the following iframe:

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<iframe src="main.html" width="100%" height="712" scrolling="no"></iframe>

Overview

Each panel is a conceptual 2D scatter plot of the same point cloud:

  • Flat (brute force) draws an arrow from the query to every vector - it compares all of them, guaranteeing 100% accuracy but with O(n) cost.
  • IVF (inverted file) groups vectors into clusters and only searches the nearest one or two clusters, skipping the rest for a large speedup.
  • HNSW (graph) builds a multi-layer navigable graph and walks from a sparse top layer down to the dense bottom layer, reaching the neighborhood in O(log n) hops.

How It Works

Real embeddings live in hundreds of dimensions, but the same ideas apply in 2D. The trade-off is always speed versus accuracy versus memory: Flat is exact but slow, IVF and HNSW are approximate but fast. The comparison table built into the MicroSim summarizes those trade-offs, including Product Quantization (PQ), which compresses vectors for very low memory use.

Lesson Plan

  • Warm up: Ask how long it would take to compare a query to one billion vectors one at a time, motivating approximate indexes.
  • Explore: Compare the arrows in the Flat panel to the clusters in IVF and the graph path in HNSW. Read each panel's search-time and accuracy metrics.
  • Discuss: Why does HNSW use more memory than IVF? When is the loss of a few percent of accuracy an acceptable trade for speed?
  • Extend: Using the table, have students choose an index for a real-time search service versus an offline batch job and justify the pick.

References