Word Embeddings: The Foundation of Semantic Understanding

Summary

Word Embeddings are a fundamental component of Large Language Models (LLMs) and modern Natural Language Processing (NLP). They are dense, high-dimensional numerical vectors that represent words (or tokens) in a continuous vector space. The core idea is that words used in similar contexts should have similar embeddings, mathematically capturing their semantic (meaning) and syntactic (grammatical) relationships.

The Concept: Mapping Meaning to Math

• Dimensionality: Unlike simple one-hot encoding (where a vocabulary of 50,000 words requires 50,000 dimensions), modern word embeddings typically use vectors with 50 to 1,000 dimensions (e.g., a 768-dimension vector).
• The Proximity Principle: The spatial arrangement of these vectors is key. Words with related meanings (e.g., "king" and "prince," or "happy" and "joyful") are located closer to each other in the vector space.
• Contextualization: The most advanced embeddings used in LLMs (like those produced by the Transformer architecture) are contextual. The embedding for a word like "bank" will be different depending on whether it appears in the phrase "river bank" or "commercial bank."

How They Work: Training and Representation

Word embeddings are typically learned through unsupervised training on massive text corpora, often as a precursor to or as part of LLM pre-training.

Learning Objectives (Pre-Contextual Methods):

• Word2Vec (Skip-gram and CBOW):
  • Skip-gram: The model is trained to predict the surrounding context words given a target word.
  • CBOW (Continuous Bag of Words): The model is trained to predict a target word given its surrounding context words.
• GloVe (Global Vectors for Word Representation): This method learns embeddings by analyzing the co-occurrence statistics of words across the entire corpus.

Role in LLMs (Contextual Embeddings):

In Transformer-based LLMs, the initial Token Embedding is only the starting point. The final, powerful representation is created during the forward pass:

1. Initial Embeddings: The tokens are converted into basic, non-contextual input vectors.
2. Positional Encoding: A vector representing the token's position in the sequence is added to the initial embedding.
3. Transformer Layers: This combined vector is then passed through the Transformer's self-attention and feed-forward layers. The output of these layers is the highly contextualized word embedding—a refined numerical representation that captures the word's meaning in that specific sentence.

Practical Applications

The numerical nature of embeddings enables algebraic operations that capture linguistic relationships:

• Semantic Arithmetic: A famous example illustrates how vector arithmetic can capture analogies:

        Vector(King)−Vector(Man)+Vector(Woman)≈Vector(Queen)

• Similarity Search: By calculating the cosine similarity between two embedding vectors, we can quickly determine how semantically related two words, phrases, or documents are.

        CosineSimilarity(A,B)=∥A∥⋅∥B∥A⋅B​

Word embeddings transform text from an unstructured sequence of characters into a structured, numerical format that computers can process for tasks like translation, sentiment analysis, and question answering.

Word Embeddings Example

Word embeddings are vector representations of words that capture semantic meaning. Words with similar meanings appear close together in a high-dimensional vector space.

Simple Conceptual Example

Below is a simplified example using 3-dimensional embeddings.

From this table:

• king and queen are close to each other.
• man and woman are close.
• The difference between king→man is similar to queen→woman.

This allows the classic analogy:

    king - man + woman ≈ queen

Analogy Vector Example

Using the embeddings above:

    king       = [0.52, 0.89, 0.12]
    man        = [0.30, 0.20, 0.55]
    woman      = [0.29, 0.21, 0.56]

Compute the analogy vector:

    v = king - man + woman
      = [0.51, 0.90, 0.13]

The resulting vector is very close to:

    queen = [0.51, 0.90, 0.11]

Thus the model predicts queen.

Visual Intuition

If we project these embeddings to 2-D (e.g., via PCA or t-SNE), we may see:

    woman     queen
       \       /
        \     /
         man ---- king

Semantic clusters naturally form based on meaning.

Real-World Uses

• Finding similar words or documents
• Semantic search
• Text clustering and classification
• Language analogy tasks
• Inputs to machine learning models

Would you like a more detailed explanation of the Cosine Similarity calculation, or a deep dive into the Positional Encoding used in the Transformer?