What is self-attention and how does it work in transformers?

 Self-attention is a mechanism that plays a central role in the operation of transformers. It allows the model to weigh the importance of different elements (or tokens) within a sequence and capture their relationships. In the context of transformers, self-attention is also known as scaled dot-product attention. Here's an overview of how self-attention works in transformers:

1. Input Embeddings:

   Before self-attention can be applied, the input sequence is typically transformed into vector representations called embeddings. Each element or token in the sequence, such as a word in natural language processing, is associated with an embedding vector that encodes its semantic information.

2. Query, Key, and Value:

   To perform self-attention, the input embeddings are linearly transformed into three different vectors: query (Q), key (K), and value (V). These transformations are parameterized weight matrices that map the input embeddings into lower-dimensional spaces. The query, key, and value vectors are computed independently for each token in the input sequence.

3. Attention Scores:

   The core of self-attention involves computing attention scores that measure the relevance or similarity between tokens in the sequence. The attention score between a query token and a key token is determined by the dot product between their corresponding query and key vectors. The dot product is then scaled by the square root of the dimensionality of the key vectors to alleviate the vanishing gradient problem.

4. Attention Weights:

   The attention scores are further processed using the softmax function to obtain attention weights. Softmax normalizes the attention scores across all key tokens for a given query token, ensuring that the attention weights sum up to 1. These attention weights represent the importance or relevance of each key token to the query token.

5. Weighted Sum of Values:

   The attention weights obtained in the previous step are used to compute a weighted sum of the value vectors. Each value vector is multiplied by its corresponding attention weight and the resulting weighted vectors are summed together. This weighted sum represents the attended representation of the query token, considering the contributions of the key tokens based on their relevance.

6. Multi-head Attention:

   Transformers typically employ multiple attention heads, which are parallel self-attention mechanisms operating on different learned linear projections of the input embeddings. Each attention head generates its own set of query, key, and value vectors and produces attention weights and attended representations independently. The outputs of multiple attention heads are concatenated and linearly transformed to obtain the final self-attention output.

7. Residual Connections and Layer Normalization:

   To facilitate the flow of information and alleviate the vanishing gradient problem, transformers employ residual connections. The output of the self-attention mechanism is added element-wise to the input embeddings, allowing the model to retain important information from the original sequence. Layer normalization is then applied to normalize the output before passing it to subsequent layers in the transformer architecture.

By applying self-attention, transformers can capture dependencies and relationships between tokens in a sequence. The attention mechanism enables the model to dynamically focus on different parts of the sequence, weighing the importance of each token based on its relationships with other tokens. This allows transformers to effectively model long-range dependencies and capture global context, making them powerful tools for various tasks such as natural language processing, image recognition, and time series analysis.