Relative Position Encodings

Relative Position Encodings are a type of position embeddings for Transformer-based models that attempts to exploit pairwise, relative positional information. Relative positional information is supplied to the model on two levels: values and keys. This becomes apparent in the two modified self-attention equations shown below. First, relative positional information is supplied to the model as an additional component to the keys

$e\_{ij} = \frac{x\_{i}W^{Q}\left(x\_{j}W^{K} + a^{K}\_{ij}\right)^{T}}{\sqrt{d\_{z}}}$

Here $a$ is an edge representation for the inputs $x\_{i}$ and $x\_{j}$. The softmax operation remains unchanged from vanilla self-attention. Then relative positional information is supplied again as a sub-component of the values matrix:

$z\_{i} = \sum^{n}\_{j=1}\alpha\_{ij}\left(x\_{j}W^{V} + a\_{ij}^{V}\right)$

In other words, instead of simply combining semantic embeddings with absolute positional ones, relative positional information is added to keys and values on the fly during attention calculation.

Source: Jake Tae

Image Source: [Relative Positional Encoding for Transformers with Linear Complexity](https://www.youtube.com/watch?v=qajudaEHuq8