1D, 2D, and 3D Sinusodal Positional Encodings in PyTorch
Project description
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, ch, x)
, 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, ch, x)
, 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 an integer 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 an integer 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 an integer 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!
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