entmax
This package provides a pytorch implementation of entmax and entmax losses: a sparse family of probability mappings and corresponding loss functions, generalizing softmax / cross-entropy.
Features:
- Exact partial-sort algorithms for 1.5-entmax and 2-entmax (sparsemax).
- A bisection-based algorithm for generic alpha-entmax.
- Gradients w.r.t. alpha for adaptive, learned sparsity!
Requirements: python 3, pytorch >= 1.0 (and pytest for unit tests)
Example
In [1]: import torch
In [2]: from torch.nn.functional import softmax
In [2]: from entmax import sparsemax, entmax15, entmax_bisect
In [4]: x = torch.tensor([-2, 0, 0.5])
In [5]: softmax(x, dim=0)
Out[5]: tensor([0.0486, 0.3592, 0.5922])
In [6]: sparsemax(x, dim=0)
Out[6]: tensor([0.0000, 0.2500, 0.7500])
In [7]: entmax15(x, dim=0)
Out[7]: tensor([0.0000, 0.3260, 0.6740])Gradients w.r.t. alpha (continued):
In [1]: from torch.autograd import grad
In [2]: x = torch.tensor([[-1, 0, 0.5], [1, 2, 3.5]])
In [3]: alpha = torch.tensor(1.33, requires_grad=True)
In [4]: p = entmax_bisect(x, alpha)
In [5]: p
Out[5]:
tensor([[0.0460, 0.3276, 0.6264],
[0.0026, 0.1012, 0.8963]], grad_fn=<EntmaxBisectFunctionBackward>)
In [6]: grad(p[0, 0], alpha)
Out[6]: (tensor(-0.2562),)Installation
pip install entmax
Citations
Sparse Sequence-to-Sequence Models
@inproceedings{entmax,
author = {Peters, Ben and Niculae, Vlad and Martins, Andr{\'e} FT},
title = {Sparse Sequence-to-Sequence Models},
booktitle = {Proc. ACL},
year = {2019},
url = {https://www.aclweb.org/anthology/P19-1146}
}
Adaptively Sparse Transformers
@inproceedings{correia19adaptively,
author = {Correia, Gon\c{c}alo M and Niculae, Vlad and Martins, Andr{\'e} FT},
title = {Adaptively Sparse Transformers},
booktitle = {Proc. EMNLP-IJCNLP (to appear)},
year = {2019},
}
Further reading:
- Blondel, Martins, and Niculae, 2019. Learning with Fenchel-Young Losses.
- Martins and Astudillo, 2016. From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification.
- Peters and Martins, 2019 IT-IST at the SIGMORPHON 2019 Shared Task: Sparse Two-headed Models for Inflection.