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Embedding Cosine Similarity

Compute the cosine similarity between two embedding vectors.

Cosine similarity is defined as: $\text{cos\_sim}(a, b) = \frac{a \cdot b}{\|a\| \cdot \|b\|}$

Input:

Output: Cosine similarity rounded to 4 decimal places.

Input:

1.0 0.0 0.0
0.0 1.0 0.0

Output:

0.0

Reasoning:

First, we define the two embedding vectors: $a = (1.0, 0.0, 0.0)$ and $b = (0.0, 1.0, 0.0)$
Then, we calculate the dot product of $a$ and $b$ : $a \cdot b = (1.0)(0.0) + (0.0)(1.0) + (0.0)(0.0) = 0.0$
Next, we calculate the magnitudes of $a$ and $b$ : $\|a\| = \sqrt{(1.0)^2 + (0.0)^2 + (0.0)^2} = 1.0$ and $\|b\| = \sqrt{(0.0)^2 + (1.0)^2 + (0.0)^2} = 1.0$
The final output is the cosine similarity: $\text{cos\_sim}(a, b) = \frac{a \cdot b}{\|a\| \cdot \|b\|} = \frac{0.0}{1.0 \cdot 1.0} = 0.0$

Editor

Python 3.13.1

0/0

Run code to see test results.