TDM 20100: Cosine Similarity
Cosine Similarity in LLMs
We made comparisons on the first ten numerical values to appear in the embedded vectors of some phrases. These vectors actually contain a lot more than ten values, and each is important for defining what has been embedded.
We could copy and paste the entire vector that outputs from running '/anvil/projects/tdm/bin/ollama run mxbai-embed-large-2 "The sky is blue"', but this is not very nice to do; it is long and messy, and some values could easily get left out.
Instead, we will use subprocess to run the mxbai-embed-large-2 model on each phrase, then we’ll save the vectors into a list that can easily be used for comparison.
import subprocess
import numpy as np
import ast
# run the Ollama mxbai-embed-large-2 model on "The sky is blue"
# capture the output as a string
result = subprocess.run(
['/anvil/projects/tdm/bin/ollama', 'run', 'mxbai-embed-large-2', "The sky is blue"],
capture_output=True,
text=True
)
# get the raw text
embedding_text = result.stdout.strip()
# convert the string representation of list into an actual Python list
vector_list = ast.literal_eval(embedding_text)
# convert list of vectors to NumPy array
vector1 = np.array(vector_list)
print("Vector shape:", vector1.shape)
print("First 5 values:", vector1[:5])|
Do this for each of the three phrases:
|
With the vectors of the phrases, you can now use cosine similarity to give a score from -1 to 1 on how similar each phrase is to the others.
# calculate cosine similarity
similarity = np.dot(first_vec, second_vec) / (np.linalg.norm(first_vec) * np.linalg.norm(second_vec))
print("Similarity score:", similarity)|
Cosine similarity ranges from -1 to 1:
|