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A modular framework for neural networks with Euclidean symmetry
Python Cuda C++
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blondegeek add LearnableBispectrum (#56)
* add LearnableBispectrum

* add functools partial import

* remove lin to use learnabletensorproduct

* add input to final tensorproduct or dot product

* simplify dot product as LearnableTensorProduct
Latest commit 665d1e4 Apr 3, 2020


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The group E(3) is the group of 3 dimensional rotations, translations and mirror. This library aims to create E(3) equivariant convolutional neural networks.


from functools import partial
import torch
from e3nn.radial import CosineBasisModel
from e3nn.kernel import Kernel
from e3nn.point.operations import Convolution
from e3nn.util.plot import plot_sh_signal
import matplotlib.pyplot as plt

# Radial model:  R -> R^d
# Projection on cos^2 basis functions followed by a fully connected network
RadialModel = partial(CosineBasisModel, max_radius=3.0, number_of_basis=3, h=100, L=1, act=torch.relu)

# 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)

# Define input and output representations
Rs_in = [(1, 0)]  # one scalar
Rs_out = [(1, l) for l in range(10)]

# Use the kernel to define a convolution operation
conv = Convolution(K, Rs_in, Rs_out)

n = 3  # number of points
features = torch.ones(1, n, 1)
geometry = torch.randn(1, n, 3)

features = conv(features, geometry)


  • e3nn contains the library
    • e3nn/ defines all the needed mathematical functions
    • e3nn/image contains voxels linear operations
    • e3nn/point contains points linear operations
    • e3nn/non_linearities non linearities operations
  • examples simple scripts and experiments


  1. install pytorch
  2. pip install git+
  3. pip install git+



  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        = {},
  month        = mar,
  year         = 2020,
  publisher    = {Zenodo},
  version      = {v0.3-alpha},
  doi          = {10.5281/zenodo.3723557},
  url          = {}
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