AI Engineering Academy · Lesson

What Are Vector Embeddings?

Understand how neural networks map text to dense vectors in high-dimensional space, why semantically similar texts produce nearby vectors, and what cosine similarity measures.

What Are Vector Embeddings? is a free AI Engineering Academy lesson on CoddyKit — lesson 1 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the AI Engineering Academy learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.

The Meaning Behind Numbers

A vector embedding is a list of numbers (a vector) that represents the meaning of a piece of text. Instead of storing words as raw strings, neural networks learn to encode semantic meaning into dense numerical arrays. Two texts with similar meaning will produce vectors that are close together in this high-dimensional space.

High-Dimensional Vector Space

Modern embeddings typically have 768 to 3072 dimensions. Each dimension captures some latent feature of meaning — topics, sentiment, style, and relationships — without being explicitly programmed. The result is a rich geometric space where semantic relationships become measurable distances.

For example, text-embedding-3-small produces 1536-dimensional vectors, while text-embedding-3-large produces 3072-dimensional vectors.

How Neural Networks Learn Embeddings

Embedding models are trained on massive text corpora to predict missing words (masked language modeling) or to distinguish semantically similar from dissimilar pairs. During training, the network adjusts millions of weights until similar texts naturally cluster together in the learned vector space.

This is why embeddings are called dense representations — every dimension carries information, unlike sparse one-hot encodings where most values are zero.

Cosine Similarity: Measuring Closeness

Cosine similarity measures the angle between two vectors, returning a value between -1 and 1. A score of 1 means the vectors point in exactly the same direction (identical meaning), 0 means orthogonal (unrelated), and -1 means opposite directions.

It is preferred over Euclidean distance for text because it ignores vector magnitude and focuses purely on direction, making it robust to differences in text length.

import numpy as np

def cosine_similarity(vec_a, vec_b):
    dot_product = np.dot(vec_a, vec_b)
    norm_a = np.linalg.norm(vec_a)
    norm_b = np.linalg.norm(vec_b)
    return dot_product / (norm_a * norm_b)

# Example with tiny 3D vectors
v1 = np.array([0.8, 0.2, 0.5])
v2 = np.array([0.9, 0.1, 0.4])
print(cosine_similarity(v1, v2))  # Close to 1.0

Why Semantic Similarity Matters

Traditional keyword search breaks when users paraphrase: searching for automobile misses documents about cars. Vector embeddings solve this because semantically equivalent texts map to nearby vectors regardless of the exact words used.

This enables semantic search, where you find the most relevant result based on meaning rather than word overlap — a fundamental capability needed for RAG systems.

The Embedding Vector Visualized

Imagine plotting sentences in a 2D map (a simplified analogy). Sentences about machine learning cluster in one region, sentences about cooking cluster in another, and sentences about sports form a third cluster. Vector embeddings create this map in thousands of dimensions.

Famous relationships like king - man + woman ≈ queen are real arithmetic in this space — vector operations encode semantic analogies.

Generating a Simple Embedding

The OpenAI embeddings API accepts text and returns a list of floats. A single API call can embed one sentence or an entire paragraph. The returned vector has a fixed dimension regardless of input length.

Important: longer inputs do not produce larger vectors — they still produce the same fixed-size vector, but very long texts may lose fine-grained detail because the model compresses everything into that fixed space.

from openai import OpenAI

client = OpenAI()  # uses OPENAI_API_KEY from environment

response = client.embeddings.create(
    model='text-embedding-3-small',
    input='Vector embeddings capture semantic meaning.'
)

embedding = response.data[0].embedding
print(f'Dimensions: {len(embedding)}')  # 1536
print(f'First 5 values: {embedding[:5]}')

Embedding Multiple Texts at Once

You can embed multiple strings in a single API call by passing a list to the input parameter. This is much more efficient than making one request per text because it reduces network round-trips and lets the API batch the computation.

The response contains one embedding object per input, in the same order, so you can zip them together with your original texts.

from openai import OpenAI

client = OpenAI()

texts = [
    'Python is a programming language.',
    'Snakes are reptiles.',
    'Machine learning requires data.'
]

response = client.embeddings.create(
    model='text-embedding-3-small',
    input=texts
)

for text, result in zip(texts, response.data):
    print(f'{text[:30]}... -> {len(result.embedding)}D vector')

Dot Product vs Cosine Similarity

If your embeddings are L2-normalized (unit vectors with magnitude 1), the dot product equals cosine similarity. OpenAI's embedding models return normalized vectors, so you can use either metric — dot product is slightly faster to compute.

However, when combining embeddings from different models or sources that may not be normalized, always compute cosine similarity explicitly to avoid misleading results.

import numpy as np

def normalize(vec):
    return vec / np.linalg.norm(vec)

v1 = normalize(np.array([3.0, 4.0, 0.0]))
v2 = normalize(np.array([4.0, 3.0, 0.0]))

# For unit vectors: dot product == cosine similarity
dot = np.dot(v1, v2)
print(f'Dot product: {dot:.4f}')  # same as cosine sim

Embeddings vs One-Hot Encoding

One-hot encoding represents each word as a vector with exactly one 1 and all other values 0. A vocabulary of 50,000 words produces 50,000-dimensional vectors that are almost entirely zeros — very inefficient.

Dense embeddings use 768-3072 dimensions but every dimension carries real information. The space is 10-20x smaller yet captures far more nuance, including synonyms, analogies, and compositional meaning that one-hot encoding completely misses.

Common Use Cases for Embeddings

Beyond semantic search, embeddings power many practical applications:

Semantic search — find documents by meaning, not keywords
Recommendation systems — suggest items similar to ones the user liked
Clustering — group documents by topic automatically
Classification — feed embeddings to a linear classifier
Deduplication — detect near-duplicate content

All RAG systems depend on embeddings to match user queries with relevant document chunks.

Quick Check

Test your understanding of AI Engineering concepts from this lesson.

Lesson Recap

In this lesson you learned: vector embeddings encode semantic meaning as dense numerical arrays, cosine similarity measures semantic closeness by comparing vector directions, and OpenAI's embedding API converts text to fixed-size vectors in a single call. Next up we explore how to generate and compare embeddings using the OpenAI models in practice.

Frequently asked questions

Is the “What Are Vector Embeddings?” lesson free?

Yes — the full text of “What Are Vector Embeddings?” is free to read here on the web, and the AI Engineering Academy course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the AI Engineering Academy course, upgrade to CoddyKit PRO.

What will I learn in “What Are Vector Embeddings?”?

Understand how neural networks map text to dense vectors in high-dimensional space, why semantically similar texts produce nearby vectors, and what cosine similarity measures. You practise AI Engineering Academy with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.

Do I need any experience to start AI Engineering Academy?

No prior experience is required. AI Engineering Academy on CoddyKit is structured for beginners through advanced learners; this is — lesson 1 of 4, so you can start here or from the beginning and move at your own pace.

How long does the “What Are Vector Embeddings?” lesson take?

Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.

Can I write and run code in this AI Engineering Academy lesson?

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