Embeddings Explained: Vector Representations for AI

What Are Vector Embeddings?

Vector embeddings are numerical representations of data points that express different types of data, including nonmathematical data such as words or images, as an array of numbers that machine learning (ML) models can process.

More specifically, vector embeddings are numerical representations that convert complex data—such as text, images, and documents—into multidimensional arrays of floating-point numbers. They are usually represented as a sequence of numbers in a multidimensional space, where the combination of all values characterizes the data input.

Why Embeddings Matter

These embeddings capture semantic relationships, allowing machines to process and compare data efficiently. The key insight: similar concepts are represented by vectors that are close together in the embedding space.

Types of Embeddings

Word Embeddings

Convert individual words into vectors. Classic models like Word2Vec and GloVe paved the way, while modern transformers generate contextual embeddings where the same word has different representations based on context.

Sentence Embeddings

Represent entire sentences as single vectors. Essential for semantic search, where you want to find sentences with similar meaning regardless of exact word matches.

Document Embeddings

Capture the meaning of entire documents. Used for document clustering, classification, and similarity search across large document collections.

Image Embeddings

Transform images into vector representations. Enable reverse image search, image classification, and finding visually similar images.

User and Product Embeddings

Represent users and products in the same embedding space. Power recommendation systems by finding products close to user preferences in vector space.

How Embeddings Are Created

Training Process

Embeddings are learned through neural networks trained on large datasets. The network learns to map inputs to vectors such that similar inputs produce similar vectors.

Dimensionality

Embeddings typically have hundreds to thousands of dimensions. Common sizes:

• Word2Vec: 300 dimensions
• BERT: 768 dimensions (base model)
• OpenAI text-embedding-3-large: 3072 dimensions (can be reduced)
• Sentence Transformers: 384-1024 dimensions

Applications of Embeddings

Semantic Search

Find documents by meaning, not just keyword matching. A search for "CEO" also returns results about "chief executive officer" and "company president."

RAG Systems

Retrieval-Augmented Generation relies on embeddings to find relevant context. Convert documents to embeddings, then retrieve those closest to the query embedding.

Recommendation Systems

Embed users and items in the same space. Recommend items close to the user's embedding. Powers Netflix, Spotify, and Amazon recommendations.

Clustering and Classification

Group similar items by clustering their embeddings. Classify new items by finding the nearest labeled examples in embedding space.

Anomaly Detection

Identify outliers by finding embeddings far from normal clusters. Used for fraud detection, quality control, and cybersecurity.

Measuring Similarity

Cosine Similarity

Most common metric for embedding similarity. Measures the angle between vectors, ranging from -1 (opposite) to 1 (identical). Insensitive to vector magnitude.

Euclidean Distance

Straight-line distance between points in embedding space. Simple and intuitive, but sensitive to vector magnitude.

Dot Product

Fast to compute and works well when embeddings are normalized. Used extensively in large-scale vector databases.

Popular Embedding Models (2025)

Best Practices

Choose the Right Model

Balance quality, speed, and cost. For prototypes, use OpenAI embeddings. For production at scale, consider open-source models you can self-host.

Normalize Embeddings

Normalize to unit length when using cosine similarity. This makes similarity computation faster and more numerically stable.

Cache Embeddings

Embeddings are expensive to compute. Cache them aggressively. Recompute only when source content changes.

Chunk Strategically

For long documents, chunk before embedding. Optimal chunk size depends on your model and use case, typically 200-500 tokens.

Use Vector Databases

Don't implement similarity search from scratch. Use specialized vector databases like Pinecone, Weaviate, or Qdrant for efficient large-scale retrieval.

Common Pitfalls