What are embeddings in the OpenAI API and what are they used for?

from openai import OpenAI
import numpy as np

client = OpenAI()

# Generate embeddings
response = client.embeddings.create(
    model="text-embedding-3-large",    # 3072 dimensions
    # model="text-embedding-3-small",  # 1536 dimensions, cheaper
    input=[
        "OpenAI Codex is an agentic coding assistant.",
        "GitHub Copilot helps developers write code.",
        "The stock market rose 2% today.",
    ]
)

# Extract vectors
vectors = [item.embedding for item in response.data]

# Semantic similarity via cosine similarity
def cosine_similarity(a, b):
    return np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))

sim_coding = cosine_similarity(vectors[0], vectors[1])  # high - both about coding AI
sim_unrelated = cosine_similarity(vectors[0], vectors[2])  # low - different topic
print(f"Coding similarity: {sim_coding:.3f}")    # e.g. 0.89
print(f"Unrelated similarity: {sim_unrelated:.3f}")  # e.g. 0.21

# Dimension reduction (for storage/speed tradeoff):
response = client.embeddings.create(
    model="text-embedding-3-large",
    input="example text",
    dimensions=512,  # reduce from 3072 to 512
)