Skip to main content

Implementation of the Spline-Based Convolution Operator of SplineCNN in PyTorch

Project description

Spline-Based Convolution Operator of SplineCNN

PyPI Version Testing Status Linting Status Code Coverage

This is a PyTorch implementation of the spline-based convolution operator of SplineCNN, as described in our paper:

Matthias Fey, Jan Eric Lenssen, Frank Weichert, Heinrich Müller: SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels (CVPR 2018)

The operator works on all floating point data types and is implemented both for CPU and GPU.



Update: You can now install pytorch-spline-conv via Anaconda for all major OS/PyTorch/CUDA combinations 🤗 Given that you have pytorch >= 1.8.0 installed, simply run

conda install pytorch-spline-conv -c pyg


We alternatively provide pip wheels for all major OS/PyTorch/CUDA combinations, see here.

PyTorch 2.0

To install the binaries for PyTorch 2.0.0, simply run

pip install torch-spline-conv -f${CUDA}.html

where ${CUDA} should be replaced by either cpu, cu117, or cu118 depending on your PyTorch installation.

cpu cu117 cu118

PyTorch 1.13

To install the binaries for PyTorch 1.13.0, simply run

pip install torch-spline-conv -f${CUDA}.html

where ${CUDA} should be replaced by either cpu, cu116, or cu117 depending on your PyTorch installation.

cpu cu116 cu117

Note: Binaries of older versions are also provided for PyTorch 1.4.0, PyTorch 1.5.0, PyTorch 1.6.0, PyTorch 1.7.0/1.7.1, PyTorch 1.8.0/1.8.1, PyTorch 1.9.0, PyTorch 1.10.0/1.10.1/1.10.2, PyTorch 1.11.0 and PyTorch 1.12.0/1.12.1 (following the same procedure). For older versions, you need to explicitly specify the latest supported version number or install via pip install --no-index in order to prevent a manual installation from source. You can look up the latest supported version number here.

From source

Ensure that at least PyTorch 1.4.0 is installed and verify that cuda/bin and cuda/include are in your $PATH and $CPATH respectively, e.g.:

$ python -c "import torch; print(torch.__version__)"
>>> 1.4.0

$ echo $PATH
>>> /usr/local/cuda/bin:...

$ echo $CPATH
>>> /usr/local/cuda/include:...

Then run:

pip install torch-spline-conv

When running in a docker container without NVIDIA driver, PyTorch needs to evaluate the compute capabilities and may fail. In this case, ensure that the compute capabilities are set via TORCH_CUDA_ARCH_LIST, e.g.:

export TORCH_CUDA_ARCH_LIST = "6.0 6.1 7.2+PTX 7.5+PTX"


from torch_spline_conv import spline_conv

out = spline_conv(x,

Applies the spline-based convolution operator

over several node features of an input graph. The kernel function is defined over the weighted B-spline tensor product basis, as shown below for different B-spline degrees.


  • x (Tensor) - Input node features of shape (number_of_nodes x in_channels).
  • edge_index (LongTensor) - Graph edges, given by source and target indices, of shape (2 x number_of_edges).
  • pseudo (Tensor) - Edge attributes, ie. pseudo coordinates, of shape (number_of_edges x number_of_edge_attributes) in the fixed interval [0, 1].
  • weight (Tensor) - Trainable weight parameters of shape (kernel_size x in_channels x out_channels).
  • kernel_size (LongTensor) - Number of trainable weight parameters in each edge dimension.
  • is_open_spline (ByteTensor) - Whether to use open or closed B-spline bases for each dimension.
  • degree (int, optional) - B-spline basis degree. (default: 1)
  • norm (bool, optional): Whether to normalize output by node degree. (default: True)
  • root_weight (Tensor, optional) - Additional shared trainable parameters for each feature of the root node of shape (in_channels x out_channels). (default: None)
  • bias (Tensor, optional) - Optional bias of shape (out_channels). (default: None)


  • out (Tensor) - Out node features of shape (number_of_nodes x out_channels).


import torch
from torch_spline_conv import spline_conv

x = torch.rand((4, 2), dtype=torch.float)  # 4 nodes with 2 features each
edge_index = torch.tensor([[0, 1, 1, 2, 2, 3], [1, 0, 2, 1, 3, 2]])  # 6 edges
pseudo = torch.rand((6, 2), dtype=torch.float)  # two-dimensional edge attributes
weight = torch.rand((25, 2, 4), dtype=torch.float)  # 25 parameters for in_channels x out_channels
kernel_size = torch.tensor([5, 5])  # 5 parameters in each edge dimension
is_open_spline = torch.tensor([1, 1], dtype=torch.uint8)  # only use open B-splines
degree = 1  # B-spline degree of 1
norm = True  # Normalize output by node degree.
root_weight = torch.rand((2, 4), dtype=torch.float)  # separately weight root nodes
bias = None  # do not apply an additional bias

out = spline_conv(x, edge_index, pseudo, weight, kernel_size,
                  is_open_spline, degree, norm, root_weight, bias)

torch.Size([4, 4])  # 4 nodes with 4 features each


Please cite our paper if you use this code in your own work:

  title={{SplineCNN}: Fast Geometric Deep Learning with Continuous {B}-Spline Kernels},
  author={Fey, Matthias and Lenssen, Jan Eric and Weichert, Frank and M{\"u}ller, Heinrich},
  booktitle={IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},

Running tests



torch-spline-conv also offers a C++ API that contains C++ equivalent of python models.

mkdir build
cd build
# Add -DWITH_CUDA=on support for the CUDA if needed
cmake ..
make install

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

torch_spline_conv-1.2.2.tar.gz (25.4 kB view hashes)

Uploaded source

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page