In a self-attention mechanism, the key ($K$) is important because it defines the “features” that the model should attend to when computing the attention scores.
The key is also a learned parameter, just like the query vector, and it is used in conjunction with the query and value vectors to compute the output of the self-attention layer.
How to calculate
Here is the equation for the key matrix in a self-attention layer:
$$ K = XW_K $$
where $X$ is the input sequence of embeddings, and $W_K$ is a learned weight matrix that transforms the input embeddings into the key matrix.
- The key matrix is used to compute the attention scores between each pair of input elements and the query vector.
- The attention scores measure the similarity between the query vector and each key vector,
- indicating which input elements are most relevant to the current query.
- The attention scores are then used to weight the value matrix,
- which represents the input elements themselves, to compute the output of the self-attention layer.
By learning which features to attend to, the model can capture more complex relationships between the input elements and make more accurate predictions.
The key matrix allows the model to focus on the most informative aspects of the input sequence, and it is updated during training to optimize the performance of the model.