In a self-attention mechanism, the value ($V$) is important because it represents the input elements themselves and determines the output of the self-attention layer.
- The value matrix is also a learned parameter, just like the query and key matrices,
- and it is used in conjunction with the query and key matrices to compute the output of the self-attention layer.
How to calculate
Here is the equation for the value matrix in a self-attention layer:
$$ V = XW_V $$
where $X$ is the input sequence of embeddings, and $W_V$ is a learned weight matrix that transforms the input embeddings into the value matrix.
The value matrix is used to compute the output of the self-attention layer, which is a weighted sum of the input embeddings.
- The attention scores, which are computed by taking the dot product between the query and key matrices,
- are used to weight the value matrix, giving more weight to the input elements that are most relevant to the current query.
By learning which input elements to attend to, the model can better capture the relationships between the different parts of the input sequence and make more accurate predictions.
The value matrix allows the model to use the input elements themselves as the basis for the output of the self-attention layer, and it is updated during training to optimize the performance of the model.