Week 3: Embeddings and Vector Search

Overview

Build SIMD-accelerated vector search with trueno and implement HNSW indexing.

Topics

#TypeTitlePlatformDuration
3.1VideoWhat Are Embeddings?Concept10 min
3.2VideoDatabricks Vector SearchDatabricks10 min
3.3LabCreate Vector Search IndexDatabricks35 min
3.4VideoSIMD Similarity: Cosine, Dot ProductSovereign10 min
3.5LabBuild SIMD Vector Search with truenoSovereign35 min
3.6VideoHNSW: Approximate Nearest NeighborsConcept10 min
3.7LabImplement HNSW IndexSovereign40 min
3.8VideoHybrid Search: BM25 + VectorSovereign8 min
3.9LabHybrid Retrieval with trueno-ragSovereign35 min
3.10QuizVector Search—15 min

Sovereign AI Stack Components

  • trueno for SIMD computation
  • trueno-rag for BM25 + HNSW
  • trueno-db for GPU analytics

Key Concepts

Similarity Metrics

  • Cosine similarity: dot(a, b) / (||a|| * ||b||)
  • Euclidean distance: sqrt(sum((a - b)^2))
  • Dot product: sum(a * b)

HNSW Algorithm

  • Hierarchical navigable small world graphs
  • O(log n) search complexity
  • Configurable M and ef parameters