Position Embeddings

Absolute Position Encodings

Introduced by Vaswani et al. in Attention Is All You Need

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 $\text{PE}_{pos}$.

Image Source: D2L.ai

Source: Attention Is All You Need


Paper Code Results Date Stars


Task Papers Share
Language Modelling 50 6.73%
Large Language Model 26 3.50%
Question Answering 20 2.69%
Retrieval 20 2.69%
Semantic Segmentation 17 2.29%
In-Context Learning 14 1.88%
Text Generation 14 1.88%
Decision Making 13 1.75%
Image Segmentation 11 1.48%


Component Type
3D Dynamic Scene Graph
3D Representations (optional)