Scaled dot-product attention

Attention Mechanism: Scaled dot-product attention

The Scaled Dot-Product Attention is a core part of the attention mechanism within the Transformer architecture. It's one of the main building blocks that allows the model to focus on different parts of the input sequence for different tasks. Here's a brief overview of how it fits into the overall process:

Scaled dot-product attention is a mechanism used in the multi-head self-attention layer of the Transformer model.

It is designed to capture the relationships between different elements in a sequence by computing attention scores that represent the importance of each element with respect to others. This mechanism is particularly useful for tasks that require understanding the context and dependencies between elements, such as language modeling or machine translation.

The scaled dot-product attention mechanism consists of the following steps:

Input

The attention mechanism takes three inputs: Query (Q), Key (K), and Value (V). These are derived from the input sequence, often through linear transformations. In the case of self-attention, Q, K, and V all come from the same input sequence, but they can also come from different sequences in the case of encoder-decoder attention.

Dot Product (Attention Score)

The attention scores are computed using the dot product between the Query (Q) and Key (K) matrices. For each token in the sequence, the dot product between its Query vector and all the Key vectors is calculated. This dot product measures the similarity or compatibility between the Query and the Keys. The higher the dot product, the more similar the Query is to a particular Key, indicating that the corresponding Value should be given more attention.

Scaling

Scale the dot product scores by dividing them by the square root of the key's dimension (d_k). This scaling step is done to prevent the softmax function from becoming too sensitive to small differences in the dot product values, which could lead to extremely small gradients during the backpropagation process.

In summary, scaled dot-product attention is a mechanism for computing the relevance of different elements in a sequence with respect to a given query. By calculating the dot product of the query and key vectors, scaling the result, applying the softmax function, and computing the weighted sum of the value vectors, the mechanism can effectively capture the contextual relationships and dependencies between elements in the input sequence.

Softmax Normalization

Once the dot products (attention score) are calculated, they are passed through a softmax function. The softmax function normalizes the attention score, converting them into a probability distribution that sums to 1. This ensures that the attention scores represent a relative weighting of the importance of each token in the sequence.

The resulting softmax output represents the attention weights, which indicate the importance of each value in the sequence concerning the query.

Weighted Sum of Values

Finally, the attention scores are used to weigh the Value (V) matrix. Each Value vector is multiplied by its corresponding attention score, and the results are summed to produce the output vector for the current token. This output vector is a context-aware representation of the input sequence, where each component of the Value matrix is weighted according to its relevance to the Query.

Now, let's simplify the explanation:

The Query matrix helps determine which components of the Value matrix to pay attention to by computing attention scores with the Key matrix.

These attention scores measure the similarity between the Query and the Keys.

The higher the similarity, the more attention the corresponding Value component should receive. The softmax function normalizes the attention scores, ensuring they represent a probability distribution. Finally, the attention scores are used to weigh the Value matrix, resulting in a context-aware output.