positional-encodings 2.0.0

1D, 2D, and 3D Sinusodal Positional Encodings in PyTorch

1D, 2D, and 3D Sinusodal Postional Encoding Pytorch

This is an implemenation of 1D, 2D, and 3D sinusodal positional encoding, being able to encode on tensors of the form (batchsize, x, ch), (batchsize, x, y, ch), and (batchsize, x, y, z, ch), where the positional encodings will be added to the ch dimension. The Attention is All You Need allowed for positional encoding in only one dimension, however, this works to extend this to 2 and 3 dimensions.

New: This also works on tensors of the form (batchsize, x, ch), etc. For inputs of this type, include the word Permute before the number in the class; e.g. for a 1D input of size (batchsize, x, ch), do PositionalEncodingPermute1D instead of PositionalEncoding1D.

To install, simply run:

pip install positional-encodings

Specifically, the formula for inserting the positional encoding will be as follows:

1D:

PE(x,2i) = sin(x/10000^(2i/D))
PE(x,2i+1) = cos(x/10000^(2i/D))

Where:
x is a point in 2d space
i is in [0, D/2), where D is the size of the ch dimension

2D:

PE(x,y,2i) = sin(x/10000^(4i/D))
PE(x,y,2i+1) = cos(x/10000^(4i/D))
PE(x,y,2j+D/2) = sin(y/10000^(4j/D))
PE(x,y,2j+1+D/2) = cos(y/10000^(4j/D))

Where:
(x,y) is a point in 2d space
i,j is in [0, D/4), where D is the size of the ch dimension

3D:

PE(x,y,z,2i) = sin(x/10000^(6i/D))
PE(x,y,z,2i+1) = cos(x/10000^(6i/D))
PE(x,y,z,2j+D/3) = sin(y/10000^(6j/D))
PE(x,y,z,2j+1+D/3) = cos(y/10000^(6j/D))
PE(x,y,z,2k+2D/3) = sin(z/10000^(6k/D))
PE(x,y,z,2k+1+2D/3) = cos(z/10000^(6k/D))

Where:
(x,y,z) is a point in 3d space
i,j,k is in [0, D/6), where D is the size of the ch dimension

This is just a natural extension of the 2D positional encoding used in this paper.

Don't worry if the input is not divisible by 2 (1D), 4 (2D), or 6 (3D); all the necessary padding will be taken care of.

Usage:

import torch
from positional_encodings import PositionalEncoding1D, PositionalEncoding2D, PositionalEncoding3D

p_enc_1d = PositionalEncoding1D(10)
x = torch.zeros((1,6,10))
print(p_enc_1d(x).shape) # (1, 6, 10)

p_enc_2d = PositionalEncoding2D(8)
y = torch.zeros((1,6,2,8))
print(p_enc_2d(y).shape) # (1, 6, 2, 8)

p_enc_3d = PositionalEncoding3D(11)
z = torch.zeros((1,5,6,4,11))
print(p_enc_3d(z).shape) # (1, 5, 6, 4, 11)

And for tensors of the form (batchsize, ch, x), etc:

import torch
from positional_encodings import PositionalEncodingPermute1D, PositionalEncodingPermute2D, PositionalEncodingPermute3D

p_enc_1d = PositionalEncodingPermute1D(10)
x = torch.zeros((1,10,6))
print(p_enc_1d(x).shape) # (1, 10, 6)

p_enc_2d = PositionalEncodingPermute2D(8)
y = torch.zeros((1,8,6,2))
print(p_enc_2d(y).shape) # (1, 8, 6, 2)

p_enc_3d = PositionalEncodingPermute3D(11)
z = torch.zeros((1,11,5,6,4))
print(p_enc_3d(z).shape) # (1, 11, 5, 6, 4)

Thank you

Thank you for this repo for inspriration of this method.

Citations

1D:

@inproceedings{vaswani2017attention,
  title={Attention is all you need},
  author={Vaswani, Ashish and Shazeer, Noam and Parmar, Niki and Uszkoreit, Jakob and Jones, Llion and Gomez, Aidan N and Kaiser, {\L}ukasz and Polosukhin, Illia},
  booktitle={Advances in neural information processing systems},
  pages={5998--6008},
  year={2017}
}

2D:

@misc{wang2019translating,
    title={Translating Math Formula Images to LaTeX Sequences Using Deep Neural Networks with Sequence-level Training},
    author={Zelun Wang and Jyh-Charn Liu},
    year={2019},
    eprint={1908.11415},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}

3D: Coming soon!