RAG • Chapter 5

Semantic Search & Distance Metrics

RAG engineering module on Semantic Search & Distance Metrics.

6 note blocks4 exam topics

🎯 Exam Focus Areas

Evaluate chunking and embedding strategies.Understand Vector DB indexing architectures like HNSW.Analyze RAG prompts for injection vulnerabilities.Calculate and utilize RAGAS evaluation metrics.

Semantic search relies on mathematical distance metrics to determine how similar two vectors are. The retrieval engine compares the query vector against all document vectors in the database.

Advanced System Mechanics

The three most common metrics are Cosine Similarity (measures the angle between vectors, ignoring magnitude), Euclidean Distance (L2 norm, measures straight-line distance), and Dot Product (measures both angle and magnitude). In modern embedding models where vectors are normalized to a length of 1, Cosine Similarity and Dot Product yield effectively identical rankings.

1Understand the vector space implications of this concept.
2Identify potential hallucination risks.
3Optimize for low latency and high relevance.
4Ensure robust system prompts.

Implementation Blueprint

import numpy as np

def calculate_metrics(v1, v2):
    # Dot Product
    dot = np.dot(v1, v2)
    # Euclidean Distance
    l2 = np.linalg.norm(v1 - v2)
    # Cosine Similarity
    cosine = dot / (np.linalg.norm(v1) * np.linalg.norm(v2))
    return dot, l2, cosine

q = np.array([0.1, 0.8, 0.3])
d = np.array([0.2, 0.7, 0.4])
print("Metrics:", calculate_metrics(q, d))

📝 Quick Revision Points

1Review the differences between similarity metrics.
2Practice the LangChain/LlamaIndex code snippets.
3Understand the HyDE architecture deeply.
4Memorize the security guardrail implementations.

← PreviousDocument Chunking Strategies Next →Integrating LLMs (OpenAI, HuggingFace)

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import numpy as np def calculate_metrics(v1, v2): # Dot Product dot = np.dot(v1, v2) # Euclidean Distance l2 = np.linalg.norm(v1 - v2) # Cosine Similarity cosine = dot / (np.linalg.norm(v1) * np.linalg.norm(v2)) return dot, l2, cosine q = np.array([0.1, 0.8, 0.3]) d = np.array([0.2, 0.7, 0.4]) print("Metrics:", calculate_metrics(q, d))