Equivariant convolutional neural networks for the group E(3) of 3 dimensional rotations, translations, and mirrors.

# 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.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

# 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

# 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)


## 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}
}


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