Chapter 3: Embedding Spaces and Representations

What are Embeddings?

Dense vector representations that capture semantic meaning:

from sentence_transformers import SentenceTransformer

model = SentenceTransformer('all-MiniLM-L6-v2')
embeddings = model.encode([
    "Machine learning is fascinating",
    "AI and ML are interesting topics",
    "I like pizza"
])

# First two are similar, third is different

Semantic Similarity

$$\text{similarity}(A, B) = \frac{A \cdot B}{||A|| \times ||B||}$$

from sklearn.metrics.pairwise import cosine_similarity
similarity = cosine_similarity([embeddings[0]], [embeddings[1]])
# High similarity for related sentences

Applications

Application	How Embeddings Help
Search	Find semantically similar documents
Clustering	Group related content
RAG	Retrieve relevant context
Classification	Feature vectors for ML

Key Takeaways

tip

1. Embeddings capture semantic meaning in vectors
2. Cosine similarity measures semantic relatedness
3. Essential for RAG and semantic search

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