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Stochastic Positional Encoding (SPE)

This is the source code repository for the ICML 2021 paper Relative Positional Encoding for Transformers with Linear Complexity by Antoine Liutkus, Ondřej Cífka, Shih-Lun Wu, Umut Şimşekli, Yi-Hsuan Yang and Gaël Richard.

In this paper, we propose Stochastic Positional Encoding (SPE), which provably behaves like relative PE while being compatible with linear-complexity Transformers. We do this by drawing a connection between positional encoding and cross-covariance structures of correlated Gaussian processes.


Check out also the companion website with music examples.


  title = 	 {Relative Positional Encoding for {Transformers} with Linear Complexity},
  author =       {Liutkus, Antoine and C{\'i}fka, Ond{\v r}ej and Wu, Shih-Lun and {\c S}im{\c s}ekli, Umut and Yang, Yi-Hsuan and Richard, Ga{\"e}l},
  booktitle = 	 {Proceedings of the 38th International Conference on Machine Learning},
  pages = 	 {7067--7079},
  year = 	 {2021},
  editor = 	 {Meila, Marina and Zhang, Tong},
  volume = 	 {139},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {18--24 Jul},
  publisher =    {PMLR},
  pdf = 	 {},
  url = 	 {}

SPE implementation

We have implemented SPE in PyTorch and JAX/Flax. Each implementation is available as a separate Python package under src.


Each of the 3 experiments (LRA, pop piano generation, groove continuation) has a dedicated directory under experiments. See the README files there for how to set up the environment and prepare the datasets. To make sure you have the custom dependencies for each experiment, clone this repository with --recurse-submodules or run git submodule init && git submodule update after cloning.


Relative Positional Encoding for Transformers with Linear Complexity






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