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Welcome! In the world of Large Language Models (LLMs), understanding text isn't just about words. It's about meaning.

Computers naturally work with numbers, not human language. How do we bridge this gap to help LLMs understand the meaning of text?

Vector embeddings are numerical representations of text (or images, audio, etc.). Think of them as a list of numbers that capture the 'essence' or 'meaning' of a piece of information.

• Each piece of text (a word, sentence, or document) gets its own unique vector.
• These vectors are usually long lists of floating-point numbers (e.g., [0.123, -0.456, 0.789, ...]).

How are these magical numbers created? Special machine learning models, often called embedding models, are trained to convert text into these vectors.

These models learn to map similar meanings to vectors that are numerically 'close' to each other in a high-dimensional space.

The core idea is that if two pieces of text have similar meanings, their vector embeddings will be close together.

For example, the embedding for "cat" would be closer to "kitten" than to "car". This 'closeness' is what allows computers to understand semantic similarity.

In a real RAG system, you'd use an API from a provider like OpenAI, Cohere, or an open-source model to generate embeddings for your text data.

You feed the text, and the API returns the vector. It's that simple from a usage perspective!

Here's a Python example showing how you might conceptually interact with an embedding function. In reality, get_embedding would make an API call.

Once you have all your documents (or chunks of documents) converted into embeddings, how do you find the most relevant ones when a user asks a question?

This is where similarity search comes in. It's the process of finding embeddings that are 'closest' to a given query embedding.

Similarity search mathematically measures the 'distance' or 'angle' between vectors. Common methods include:

• Cosine Similarity: Measures the angle between two vectors. A smaller angle (closer to 1) means higher similarity.
• Euclidean Distance: Measures the straight-line distance between two points (vectors). A smaller distance means higher similarity.

These calculations quickly identify the most semantically similar documents.

In RAG, when a user asks a question:

1. The question is converted into an embedding.
2. Similarity search is performed against a database of document embeddings.
3. The top N most similar document chunks are retrieved.

These retrieved chunks then provide context to the LLM, making its answers more accurate and grounded.

Vector embeddings are crucial for RAG. Let's test your understanding.

Great job! You've learned about the foundational concepts of vector embeddings and similarity search.

• Vector embeddings turn text into numbers, capturing meaning.
• Embedding models create these vectors.
• Similarity search uses mathematical distance to find the most relevant vectors (and thus documents) to a query.

These techniques are at the heart of how RAG systems find and provide relevant context to LLMs.