LieTorch

This project provides a python package that expands the functionality of the PyTorch framework, the goals of this project are twofold:

1. Introduce Lie-group based geometrical tools to PyTorch in order to experiment with advanced geometrical machine learning.
2. Bring the capabilities of the Mathematica package LieAnalysis to python/pytorch.

The name

The name LieTorch is a reference to the Norwegian mathematician Sophus Lie, whose contributions to geometry are extensively used in this project. The name is pronounced /li:/ (as in Lee) and not /ˈlī/ (as in lie).

Milestones

• 0.1 : B-Spline based 𝕄₂ G-CNNs (2D roto-translation equivariant), see B-Spline CNNs on Lie Groups (arXiv).
• 0.2 : 𝕄₂ PDE-NNs, see PDE-based Group Equivariant Convolutional Neural Networks (arXiv).
• 0.3 : ℝ² PDE-NNs

Neural network modules

Modules are grouped according to the manifold they operate on. Most modules have a functional equivalant in the lietorch.nn.functional namespace.

Euclidean Space ℝ²

Basic operators:

Position and Orientation Space 𝕄₂

Basic operators:

High-level modules for implementing PDE-based networks:

Loss functions

Additional loss functions.

Generic

The modules in the generic category do not fit into any previous category and include operators that serve as C++/CUDA implementation examples.

Dependencies

The lietorch python package has the following dependencies.

• python 3.7+
• pytorch 1.6+
• torchvision 0.7+

The included experiments additionally depend on the following packages.

• scikit-learn
• tqdm
• numpy
• sty (PIP)
• mlflow (PIP)
• libtiff (PIP)

Structure

• /lietorch contains the main python package.
• /experiments contains various experiments, including those used in publications.
• /tests contains unit tests.
• /backend contains the source code of the C++/CUDA backend,
  • see ./backend/README.md if you wish to compile the extension yourself.
• /assets various files used in tests and documentation.

Cite

If you use this code in your own work please cite our paper:

Smets, B.M.N., Portegies, J., Bekkers, E.J., & Duits, R. (2021). PDE-based Group Equivariant Convolutional Neural Networks. arXiv preprint arXiv:2001.09046. Retrieved 10 August 2021, from https://arxiv.org/abs/2001.09046

@article{smets2021pde,
  title={PDE-based Group Equivariant Convolutional Neural Networks},
  author={Smets, Bart and Portegies, Jim and Bekkers, Erik and Duits, Remco},
  journal={arXiv preprint arXiv:2001.09046},
  year={2020}
}