Absolute Position Encodings

Absolute Position Encodings are a type of position embeddings for [Transformer-based models] where positional encodings are added to the input embeddings at the bottoms of the encoder and decoder stacks. The positional encodings have the same dimension $d_{model}$ as the embeddings, so that the two can be summed. In the original implementation, sine and cosine functions of different frequencies are used:

$$ \text{PE}\left(pos, 2i\right) = \sin\left(pos/10000^{2i/d_{model}}\right) $$

$$ \text{PE}\left(pos, 2i+1\right) = \cos\left(pos/10000^{2i/d_{model}}\right) $$

where $pos$ is the position and $i$ is the dimension. That is, each dimension of the positional encoding corresponds to a sinusoid. The wavelengths form a geometric progression from $2\pi$ to $10000 \dot 2\pi$. This function was chosen because the authors hypothesized it would allow the model to easily learn to attend by relative positions, since for any fixed offset $k$, $\text{PE}_{pos+k}$ can be represented as a linear function of $\text{PE}_{pos}$.

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