Vector Embeddings Cheat Sheet

Generate, store, and search dense vector embeddings for semantic search, covering models, distance metrics, and vector databases.

2 PagesBeginnerJan 15, 2026

Generate an Embedding

Convert text into a fixed-length dense vector using a sentence embedding model.

python

from sentence_transformers import SentenceTransformermodel = SentenceTransformer("all-MiniLM-L6-v2")  # 384-dim vectorssentences = ["How do I reset my password?", "Password reset instructions"]embeddings = model.encode(sentences, normalize_embeddings=True)print(embeddings.shape)  # (2, 384)

Compute Similarity

Measure semantic closeness between two vectors with cosine similarity.

python

import numpy as npdef cosine_similarity(a, b):    return np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))score = cosine_similarity(embeddings[0], embeddings[1])print(f"similarity: {score:.4f}")  # closer to 1.0 = more similar

Store and Query in a Vector Database

Upsert embeddings into a vector database and run an approximate nearest-neighbor query.

python

import pineconepc = pinecone.Pinecone(api_key="...")index = pc.Index("docs")index.upsert(vectors=[    ("doc-1", embeddings[0].tolist(), {"text": sentences[0]}),    ("doc-2", embeddings[1].tolist(), {"text": sentences[1]}),])query_vec = model.encode("reset my login").tolist()results = index.query(vector=query_vec, top_k=3, include_metadata=True)

Distance Metrics

The most common ways to compare two vectors, and when to use each.

Cosine similarity- angle between vectors; ignores magnitude, most common for text
Dot product- fast, magnitude-sensitive; use with normalized embeddings for ranking
Euclidean (L2) distance- straight-line distance; common for image and general-purpose embeddings
Hamming distance- bit differences between binary/quantized vectors, very fast
HNSW index- graph-based ANN index trading recall for speed at scale

Popular Vector Databases

Common storage backends for production embedding search.

pgvector- Postgres extension, good when you already run Postgres
Pinecone- managed, serverless, low-ops vector search
Qdrant- open source, self-hostable, strong filtering support
Weaviate- open source with built-in hybrid search and modules
Chroma- lightweight, embedded, ideal for prototyping and small apps

Pro Tip

Normalize embeddings at generation time so you can use the cheaper dot-product metric in your vector index — it's mathematically equivalent to cosine similarity but avoids a normalization step on every query.

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