e3nn

E(3) is the Euclidean group in dimension 3. That is the group of rotations, translations and mirror. e3nn is a pytorch library that aims to create E(3) equivariant neural networks.

Example

from functools import partial

import torch

from e3nn.non_linearities.rescaled_act import swish
from e3nn.radial import GaussianRadialModel
from e3nn.kernel import Kernel
from e3nn.point.operations import Convolution
from e3nn.non_linearities.norm import Norm
from e3nn import rs

# Define the input and output representations
Rs_in = [(1, 0), (2, 1)]  # Input = One scalar plus two vectors
Rs_out = [(1, 1)]  # Output = One single vector

# Radial model:  R+ -> R^d
RadialModel = partial(GaussianRadialModel, max_radius=3.0, number_of_basis=3, h=100, L=1, act=swish)

# kernel: composed on a radial part that contains the learned parameters
#  and an angular part given by the spherical hamonics and the Clebsch-Gordan coefficients
K = partial(Kernel, RadialModel=RadialModel, normalization='norm')

# Use the kernel to define a convolution operation
C = partial(Convolution, K)

# Create the convolution module
conv = C(Rs_in, Rs_out)

# Module to compute the norm of each irreducible component
norm = Norm(Rs_out, normalization='norm')


n = 5  # number of input points
features = rs.randn(1, n, Rs_in, normalization='norm', requires_grad=True)
in_geometry = torch.randn(1, n, 3)
out_geometry = torch.zeros(1, 1, 3)  # One point at the origin


norm(conv(features, in_geometry, out_geometry)).backward()

print(features)
print(features.grad)

Hierarchy

• e3nn contains the library
  • e3nn/o3.py O(3) irreducible representations
  • e3nn/rsh.py real spherical harmonics
  • e3nn/rs.py geometrical tensor representations
  • e3nn/image contains voxels linear operations
  • e3nn/point contains points linear operations
  • e3nn/non_linearities non linearities operations
• examples simple scripts and experiments

Installation

pip install git+https://github.com/e3nn/e3nn

To get the CUDA kernels read the instructions in INSTALL.md.

Citing

@software{e3nn_2020_3723557,
  author       = {Mario Geiger and
                  Tess Smidt and
                  Benjamin K. Miller and
                  Wouter Boomsma and
                  Kostiantyn Lapchevskyi and
                  Maurice Weiler and
                  Michał Tyszkiewicz and
                  Jes Frellsen},
  title        = {github.com/e3nn/e3nn},
  month        = mar,
  year         = 2020,
  publisher    = {Zenodo},
  version      = {v0.3-alpha},
  doi          = {10.5281/zenodo.3723557},
  url          = {https://doi.org/10.5281/zenodo.3723557}
}