 Solution

A transformer block has two principal sublayers: multi-head attention and a positionwise feedforward neural network. Each sublayer has a residual connection and layer normalization. To make the components explicit, let $X\in {\mathbb{R}}^{L\times d_{\mathrm{model}}}$ contain the representations of $L$ sequence positions. For head $h$, learned projections formThe scaled dot-product attention output iswhere the softmax function acts along each row and $B$ is an optional attention mask. For causal self-attention, disallowed future positions receive $-\infty$ before the softmax function, giving zero attention weights. In self-attention, queries, keys, and values all come from the same input sequence. The multi-head attention output concatenates the heads and projects them:A standard post-normalization transformer block can then be writtenHere layer normalization normalizes the feature coordinates of each position separately, within each example, and applies learned scales and shifts. The positionwise feedforward neural network applies the same two affine maps and activation function at every position, for exampleThus attention mixes information between positions, while the feedforward sublayer transforms each position's features. The residual connections support propagation through a deep stack, and dropout is often used during training. Pre-normalization variants move layer normalization before the sublayer. A model's positional encoding supplies order information to the sequence representation or attention mechanism; a decoder in an encoder-decoder model also has a cross-attention sublayer between its self-attention and feedforward neural network sublayers.