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In modern natural language processing (NLP), word embeddings provide a dense, numerical representation of text. Whether it’s individual words, phrases, sentences, or entire documents, embeddings map semantically similar inputs to vectors that lie close together in high-dimensional space. Embeddings are generated by specialized models that convert text into one-dimensional arrays (vectors). When you feed related words or sentences into these models, the resulting vectors cluster based on meaning.
The image explains word embeddings, showing how text (phrases, sentences, words) is converted into vectors (arrays) with similar words/sentences having similar vectors.

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How Embeddings Power Language Models

Large language models (LLMs) use embeddings as a foundational building block. Before processing text, they tokenize the input and transform those tokens into dense vectors, capturing semantic and syntactic features.
The image explains word embeddings with three vectors, each containing related words: Vector 1 (Black, Inky, Dark), Vector 2 (Orange, Tangerine, Ginger), and Vector 3 (Powerful, Strong, Brawny).

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Embedding Workflow

  1. Prepare any text (a single word up to a large document).
  2. Send it to an embedding model API.
  3. Receive a numerical vector encoding its meaning.
The image illustrates the process of converting text into embeddings using a word embeddings model, showing how different sentences are transformed into numerical vectors.
Embeddings typically have hundreds to thousands of dimensions. Despite their size, they enable efficient similarity computations and downstream tasks such as clustering, recommendation, and semantic search.

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Measuring Similarity: Cosine Similarity

To compare two embedding vectors, we often use cosine similarity, which measures the cosine of the angle between them: cos(θ) = (A · B) / (||A|| ||B||)
The image illustrates the concept of cosine similarity using vectors representing different sentences, showing their angular relationships.
Similarity RangeInterpretation
0.9 – 1.0Nearly identical meaning
0.5 – 0.9Related concepts
0.0 – 0.5Weak or no relation
Negative valuesOpposing or dissimilar topics

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Semantic Search with Embeddings

Traditional keyword-based search can miss relevant results when phrasing differs. Semantic search converts both queries and documents into embeddings and retrieves items whose vectors lie closest to the query vector. Instead of exact string matches, semantic search finds content by meaning, powering applications like:
  • Document retrieval
  • FAQ matching
  • Contextual recommendation

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Generating Embeddings with OpenAI

Below is an example of how to generate embeddings using the OpenAI Python SDK: 
import openai

openai.api_key = "YOUR_API_KEY"

response = openai.Embedding.create(
    model="text-embedding-ada-002",
    input=["OpenAI embeddings are powerful", "Embeddings capture semantic meaning"]
)
vectors = [item["embedding"] for item in response["data"]]
print(vectors)
Or with cURL: 
curl https://api.openai.com/v1/embeddings \
  -H "Authorization: Bearer $OPENAI_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "model": "text-embedding-ada-002",
    "input": ["OpenAI embeddings are powerful", "Embeddings capture semantic meaning"]
  }'
Keep your API keys secure. Never expose them in client-side code or public repositories.

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References

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