lie_learn is a python package that knows how to do various tricky computations related to Lie groups and manifolds (mainly the sphere S2 and rotation group SO3). This package was written to support various machine learning projects, such as Harmonic Exponential Families [2], (continuous) Group Equivariant Networks [3], Steerable CNNs [4] and Spherical CNNs [5].

This code was developed using an extremely agile, move-fast-and-break-things, extreme-programming software development workflow, and was extensively tested using the print command. Most of the code was written in the 72 hours preceding conference deadlines. In other words, this code is a bit of a mess, but we're releasing it anyway because it could be useful to others.

What this code can do


lie_learn can be installed from pypi using:

pip install lie_learn

Although cython is not a necessary dependency, if you have cython installed, cython will write new versions of the *.c files before compiling them into *.so during installation. To use lie_learn, you will need a c compiler which is available to python setuptools.


For questions and comments, feel free to contact Taco Cohen (


[1] Pinchon, D., & Hoggan, P. E. (2007). Rotation matrices for real spherical harmonics: general rotations of atomic orbitals in space-fixed axes. Journal of Physics A: Mathematical and Theoretical, 40(7), 1597–1610.

[2] Cohen, T. S., & Welling, M. (2015). Harmonic Exponential Families on Manifolds. In Proceedings of the 32nd International Conference on Machine Learning (ICML) (pp. 1757–1765).

[3] Cohen, T. S., & Welling, M. (2016). Group equivariant convolutional networks. In Proceedings of The 33rd International Conference on Machine Learning (ICML) (Vol. 48, pp. 2990–2999).

[4] Cohen, T. S., & Welling, M. (2017). Steerable CNNs. In ICLR.

[5] T.S. Cohen, M. Geiger, J. Koehler, M. Welling (2017). Convolutional Networks for Spherical Signals. In ICML Workshop on Principled Approaches to Deep Learning.