{"url":"/method/absolute-position-encodings","slug":"absolute-position-encodings","name":"Absolute Position Encodings","full_name":"Absolute Position Encodings","full_name_withheld":false,"description_markdown":"**Absolute Position Encodings** are a type of position embeddings for [[Transformer](https://paperswithcode.com/method/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:\r\n\r\n$$ \\text{PE}\\left(pos, 2i\\right) = \\sin\\left(pos/10000^{2i/d\\_{model}}\\right) $$\r\n\r\n$$ \\text{PE}\\left(pos, 2i+1\\right) = \\cos\\left(pos/10000^{2i/d\\_{model}}\\right) $$\r\n\r\nwhere $pos$ 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 $\\text{PE}\\_{pos}$.\r\n\r\nImage Source: [D2L.ai](https://d2l.ai/chapter_attention-mechanisms/self-attention-and-positional-encoding.html)","description_state":"present","introduced_year":null,"introduced_by":{"title":"Attention Is All You Need","paper":"/paper/attention-is-all-you-need","first_author":"Ashish Vaswani","n_authors":8,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/attention-is-all-you-need"},"source":{"url":"https://arxiv.org/abs/1706.03762v7","title":"Attention Is All You Need","url_on_a_paper_host":true},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"General","area_id":"general","collection":"Position 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