CAPE 🌴 
PyTorch implementation of Continuous Augmented Positional Embeddings (CAPE), by Likhomanenko et al. Enhance your Transformer positional embeddings with easy-to-use augmentations!
Setup 🔧
Minimum requirements:
einops>=0.3.2
torch>=1.10.0
Install from source:
git clone https://github.com/gcambara/cape.git
cd cape
pip install --editable ./
Usage 📖
Ready to go along with PyTorch's official implementation of Transformers. Default initialization behaves identically as sinusoidal positional embeddings, summing them up to your content embeddings:
from torch import nn
from cape import CAPE1d
pos_emb = CAPE1d(d_model=512)
transformer = nn.Transformer(d_model=512)
x = torch.randn(10, 32, 512) # seq_len, batch_size, n_feats
x = pos_emb(x) # forward sums the positional embedding by default
x = transformer(x)Alternatively, you can get positional embeddings separately
x = torch.randn(10, 32, 512)
pos_emb = pos_emb.compute_pos_emb(x)
scale = 512**0.5
x = (scale * x) + pos_emb
x = transformer(x)Let's see a few examples of CAPE initialization for different modalities, inspired by the original paper experiments.
CAPE for text 🔤
CAPE1d is ready to be applied to text. Keep max_local_shift between 0 and 0.5 to shift local positions without disordering them.
from cape import CAPE1d
pos_emb = CAPE1d(d_model=512, max_global_shift=5.0,
max_local_shift=0.5, max_global_scaling=1.03,
normalize=False)
x = torch.randn(10, 32, 512) # seq_len, batch_size, n_feats
x = pos_emb(x)Padding is supported by indicating the length of samples in the forward method, with the x_lengths argument.
For example, the original length of samples is 7, although they have been padded to sequence length 10.
x = torch.randn(10, 32, 512) # seq_len, batch_size, n_feats
x_lengths = torch.ones(32)*7
x = pos_emb(x, x_lengths=x_lengths)CAPE for audio 🎙️
CAPE1d for audio is applied similarly to text.
Use positions_delta argument to set the separation in seconds
between time steps, and x_lengths for indicating sample
durations in case there is padding.
For instance, let's consider no padding and same hop size (30 ms) at every sample in the batch:
# Max global shift is 60 s.
# Max local shift is set to 0.5 to maintain positional order.
# Max global scaling is 1.1, according to WSJ recipe.
# Freq scale is 30 to ensure that 30 ms queries are possible with long audios
from cape import CAPE1d
pos_emb = CAPE1d(d_model=512, max_global_shift=60.0,
max_local_shift=0.5, max_global_scaling=1.1,
normalize=True, freq_scale=30.0)
x = torch.randn(100, 32, 512) # seq_len, batch_size, n_feats
positions_delta = 0.03 # 30 ms of stride
x = pos_emb(x, positions_delta=positions_delta)Now, let's imagine that the original duration of all samples is 2.5 s, although they have been padded to 3.0 s. Hop size is 30 ms for every sample in the batch.
x = torch.randn(100, 32, 512) # seq_len, batch_size, n_feats
duration = 2.5
positions_delta = 0.03
x_lengths = torch.ones(32)*duration
x = pos_emb(x, x_lengths=x_lengths, positions_delta=positions_delta)What if the hop size is different for every sample in the batch? E.g. first half of the samples have stride of 30 ms, and the second half of 50 ms.
positions_delta = 0.03
positions_delta = torch.ones(32)*positions_delta
positions_delta[16:] = 0.05
x = pos_emb(x, positions_delta=positions_delta)positions_delta
tensor([0.0300, 0.0300, 0.0300, 0.0300, 0.0300, 0.0300, 0.0300, 0.0300, 0.0300,
0.0300, 0.0300, 0.0300, 0.0300, 0.0300, 0.0300, 0.0300, 0.0500, 0.0500,
0.0500, 0.0500, 0.0500, 0.0500, 0.0500, 0.0500, 0.0500, 0.0500, 0.0500,
0.0500, 0.0500, 0.0500, 0.0500, 0.0500])Lastly, let's consider a very rare case, where hop size is different for every sample in the batch, and is not constant within some samples. E.g. stride of 30 ms for the first half of samples, and 50 ms for the second half. However, the hop size of the very first sample linearly increases for each time step.
from einops import repeat
positions_delta = 0.03
positions_delta = torch.ones(32)*positions_delta
positions_delta[16:] = 0.05
positions_delta = repeat(positions_delta, 'b -> b new_axis', new_axis=100)
positions_delta[0, :] *= torch.arange(1, 101)
x = pos_emb(x, positions_delta=positions_delta)positions_delta
tensor([[0.0300, 0.0600, 0.0900, ..., 2.9400, 2.9700, 3.0000],
[0.0300, 0.0300, 0.0300, ..., 0.0300, 0.0300, 0.0300],
[0.0300, 0.0300, 0.0300, ..., 0.0300, 0.0300, 0.0300],
...,
[0.0500, 0.0500, 0.0500, ..., 0.0500, 0.0500, 0.0500],
[0.0500, 0.0500, 0.0500, ..., 0.0500, 0.0500, 0.0500],
[0.0500, 0.0500, 0.0500, ..., 0.0500, 0.0500, 0.0500]])CAPE for ViT 🖼️
CAPE2d is used for embedding positions in image patches. Scaling of positions between [-1, 1] is done within the module, whether patches are square or non-square. Thus, set max_local_shift between 0 and 0.5, and the scale of local shifts will be adjusted according to the height and width of patches. Beyond values of 0.5 the order of positions might be altered, do this at your own risk!
from cape import CAPE2d
pos_emb = CAPE2d(d_model=512, max_global_shift=0.5,
max_local_shift=0.5, max_global_scaling=1.4)
# Case 1: square patches
x = torch.randn(16, 16, 32, 512) # height, width, batch_size, n_feats
x = pos_emb(x)
# Case 2: non-square patches
x = torch.randn(24, 16, 32, 512) # height, width, batch_size, n_feats
x = pos_emb(x)Citation ✍️
I just did this PyTorch implementation following the paper's Python code and the Flashlight recipe in C++. All the credit goes to the original authors, please cite them if you use this for your research project:
@inproceedings{likhomanenko2021cape,
title={{CAPE}: Encoding Relative Positions with Continuous Augmented Positional Embeddings},
author={Tatiana Likhomanenko and Qiantong Xu and Gabriel Synnaeve and Ronan Collobert and Alex Rogozhnikov},
booktitle={Thirty-Fifth Conference on Neural Information Processing Systems},
year={2021},
url={https://openreview.net/forum?id=n-FqqWXnWW}
}Acknowledgments 🙏
Many thanks to the paper's authors for code reviewing and clarifying doubts about the paper and the implementation. :)