Dot-product similarity measures the similarity between two vectors by calculating their dot product.
Mathematically, it is defined as
\( A \cdot B = \sum_{i=1}^{n} a_i b_i \),
where \( A \) and \( B \) are two n-dimensional vectors, and \( a_i \) and \( b_i \) are their respective elements.
The result is a scalar value that reflects the extent to which the vectors point in the same direction.
In NLP, dot-product similarity is commonly used in attention mechanisms, where it helps determine the relevance of words in a sequence to each other. A higher dot product value indicates a stronger alignment or similarity between the vectors.
Dot-product similarity is computationally efficient but sensitive to vector magnitudes, which can affect similarity measurements if vectors are not normalized.
It is often used in conjunction with other similarity metrics, such as cosine similarity, for more nuanced comparisons.