“Vector Embeddings map semantic concepts into dense high-dimensional geometric spaces (e.g. OpenAI text-embedding-3-small with 1,536 dimensions), where semantically similar texts have high Cosine Similarity. Hierarchical Navigable Small World (HNSW) graphs organize vectors into multi-layer skip-list graph structures to achieve O(log N) nearest neighbor search over millions of embeddings.”
Transforming unstructured text into 1,536-dimensional floating point vectors and performing sub-millisecond approximate nearest neighbor (ANN) lookups with HNSW.
// Vector Similarity Calculation & Embedding Search
import { cosineSimilarity } from 'ai-vector-math';
export interface VectorDocument {
id: string;
text: string;
embedding: number[]; // 1536-dim vector
}
export class VectorStore {
private docs: VectorDocument[] = [];
add(doc: VectorDocument) { this.docs.push(doc); }
search(queryVector: number[], topK: number = 3): VectorDocument[] {
return [...this.docs]
.map(doc => ({
doc,
similarity: cosineSimilarity(queryVector, doc.embedding)
}))
.sort((a, b) => b.similarity - a.similarity)
.slice(0, topK)
.map(item => item.doc);
}
}Text Chunking: Split documents into 512-token chunks with 50-token semantic overlap
Vector Embedding: Model converts text chunk into 1,536-dimensional normalized float array
HNSW Graph Construction: Vector inserted into multi-layer graph with proximity edges (M=16, efConstruction=200)
Query Vectorization: User prompt converted into query vector
ANN Beam Search: Graph traversal hops across nearest nodes in Euclidean / Cosine space to return top-k matches
Scalar Quantization (SQ8) compresses 32-bit float vectors to 8-bit integers, reducing RAM usage by 75% with less than 1% recall loss.