Semantic Similarity

Simple Example

Consider these two sentences:

Sentence A:

"I love learning Python."

Sentence B:

"Python programming is something I really enjoy."

The words are different, but the meaning is very similar.

Now compare:

Sentence C:

"The car needs new tires."

That's about something completely different.

A ↔ B → High similarity

A ↔ C → Low similarity

That's semantic similarity.

Example With Three Sentences

Suppose we have:

A = "I love Python programming."

B = "I enjoy coding with Python."

C = "The weather is very cold today."

After generating embeddings:

A → Vector A
B → Vector B
C → Vector C

We compare them.

A ↔ B
HIGH similarity

A ↔ C
LOW similarity

B ↔ C
LOW similarity

Why? Because A and B are about Python programming. C is about weather.

What Is a Similarity Score?

A similarity algorithm compares two vectors and produces a number.

For example, conceptually:

Sentence A:
"I love Python."

Sentence B:
"I enjoy Python programming."

Similarity:
0.91

And:

Sentence A:
"I love Python."

Sentence C:
"I bought a new car."

Similarity:
0.12

The exact score depends on the embedding model and similarity method.

Practical OpenAI Python Example

Using an embedding model:

from openai import OpenAI

client = OpenAI()

texts = [
    "I love learning Python.",
    "Python programming is very interesting."
]

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

vector_a = response.data[0].embedding
vector_b = response.data[1].embedding

Now calculate similarity:

import math


def cosine_similarity(a, b):

    dot_product = sum(
        x * y for x, y in zip(a, b)
    )

    magnitude_a = math.sqrt(
        sum(x * x for x in a)
    )

    magnitude_b = math.sqrt(
        sum(x * x for x in b)
    )

    return dot_product / (
        magnitude_a * magnitude_b
    )


score = cosine_similarity(
    vector_a,
    vector_b
)

print("Similarity:", score)