Module 6: Embedding Operations

Introduction to Module 6: Embedding Operations

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Welcome

Embeddings aren't just compared - they can also be added, subtracted, interpolated, and composed. These operations enable analogies ("king - man + woman = queen"), semantic interpolation, and concept composition.

In this module you'll learn arithmetic operations, interpolation, dimensionality reduction, embedding composition, and practical applications. By the end, you'll master advanced operations with embeddings.

Objectives

  1. ✅ Arithmetic: A + B, A - B, analogies
  2. ✅ Interpolation: Semantic blending
  3. ✅ Composition: Combining multiple embeddings
  4. ✅ Dimensionality reduction: PCA, UMAP (visualization)
  5. ✅ Centroid: Representing clusters
  6. ✅ Outlier detection: Anomalies
  7. ✅ Applications: Query expansion, document summarization
  8. ✅ Project: Semantic Explorer Tool

Roadmap

Phase 1: Operations (Capsules 01-04)

  • Capsule 01: Introduction
  • Capsule 02: Arithmetic Operations
  • Capsule 03: Interpolation & Blending
  • Capsule 04: Composition Strategies

Phase 2: Analysis (Capsules 05-07)

  • Capsule 05: Dimensionality Reduction
  • Capsule 06: Centroid & Clustering
  • Capsule 07: Outlier Detection

Phase 3: Project (Capsule 08)

  • Capsule 08: Semantic Explorer Tool

Main operations

1. Addition (A + B):

emb_king = get_embedding("king")
emb_man = get_embedding("man")
emb_woman = get_embedding("woman")

# The famous analogy
result = emb_king - emb_man + emb_woman
# Result close to the embedding of "queen"

2. Interpolation:

# Blend between two concepts
alpha = 0.5
emb_blend = alpha * emb_a + (1 - alpha) * emb_b
# alpha=0.5 → semantic midpoint

3. Composition:

# Combine multiple embeddings
emb_doc = mean([emb_sent1, emb_sent2, emb_sent3])
# Represents the full document

Why operations matter

Query expansion:

# User searches for "Python"
query_emb = get_embedding("Python")

# Expand with related terms
related = get_embedding("programming language")
expanded_query = 0.7 * query_emb + 0.3 * related

# Retrieve with the expanded query (better recall)

Document summarization:

# Long document → multiple chunks
chunk_embs = [emb1, emb2, emb3, ..., emb10]

# Centroid = semantic summary
doc_summary_emb = np.mean(chunk_embs, axis=0)

Theory/practice balance (30/70)

Theory (30%):

  • Vector algebra
  • Mathematical properties
  • Semantic interpretation

Practice (70%):

  • numpy code
  • Real applications
  • Explorer tool project

In the next capsule

Capsule 02: Arithmetic Operations

You'll learn addition, subtraction, analogies (king-man+woman=queen), and practical code.

Module 6 - Embeddings Deep Dive Guide Embedding Operations: beyond comparison

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