LieTorch

This project provides a python package that expands the functionality of the PyTorch framework with PDE-based group equivariant CNN operators [1].

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).

Installation

The recommended installation method is using conda. The following commands will install PyTorch and the lietorch package in a new environment.

  conda create -n <environment name>
  conda activate <environment name>

  # install PyTorch the usual way
  conda install pytorch torchvision torchaudio pytorch-cuda=11.8 -c pytorch -c nvidia

  # install LieTorch with conda
  conda install -c lietorch lietorch

  # or install with pip
  pip install lietorch

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 current version of the lietorch python package has the following dependencies.

• python 3.9+
• pytorch 1.12+
• torchvision 0.13+

The included experiments additionally depend on the following packages.

• scikit-learn
• tqdm
• numpy
• sty
• mlflow
• libtiff

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:

[1] Smets, B.M.N., Portegies, J., Bekkers, E.J. et al. PDE-Based Group Equivariant Convolutional Neural Networks. J Math Imaging Vis (2022). https://doi.org/10.1007/s10851-022-01114-x

@article{smets2022pde,
  title={PDE-based Group Equivariant Convolutional Neural Networks},
  author={Smets, Bart and Portegies, Jim and Bekkers, Erik and Duits, Remco},
  journal={Journal of Mathematical Imaging and Vision},
  year={2022},
  doi={10.1007/s10851-022-01114-x},
  url={https://doi.org/10.1007/s10851-022-01114-x}
}