Cosine Similarity vs Dot Product in Attention Mechanisms

Source: Dev.to

For comparing the hidden states between the encoder and decoder, we need a similarity score.
Two common approaches to calculate this are:

• Cosine similarity
• Dot product

Cosine Similarity

Cosine similarity performs a dot product on the vectors and then normalizes the result, yielding a score in the range ‑1 to 1.

Example

Encoder output:

[-0.76, 0.75]

Decoder output:

[0.91, 0.38]

Cosine similarity ≈ ‑0.39

• Close to 1 → very similar → strong attention
• Close to 0 → not related
• Negative → opposite → low attention

When to use

• Values can vary a lot in magnitude
• You want a consistent scale (‑1 to 1)

Note: Computing cosine similarity requires extra operations (division, square roots), which can be costly in attention mechanisms.

Dot Product

The dot product is simpler: multiply corresponding values and sum the results.

Example

(-0.76 × 0.91) + (0.75 × 0.38) = -0.41

Why it’s preferred in attention

• Fast and computationally cheap
• Simple to implement
• Provides good relative scores even without normalization

Even when the numbers are not normalized, the model can still infer:

• Which words are more important
• Which words to ignore

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