[pypi-image]: https://badge.fury.io/py/torch-spline-conv.svg [pypi-url]: https://pypi.python.org/pypi/torch-spline-conv [build-image]: https://travis-ci.org/rusty1s/pytorch_spline_conv.svg?branch=master [build-url]: https://travis-ci.org/rusty1s/pytorch_spline_conv [coverage-image]: https://codecov.io/gh/rusty1s/pytorch_spline_conv/branch/master/graph/badge.svg [coverage-url]: https://codecov.io/github/rusty1s/pytorch_spline_conv?branch=master # Spline-Based Convolution Operator of SplineCNN [![PyPI Version][pypi-image]][pypi-url] [![Build Status][build-image]][build-url] [![Code Coverage][coverage-image]][coverage-url] -------------------------------------------------------------------------------- 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](https://arxiv.org/abs/1711.08920) (CVPR 2018) The operator works on all floating point data types and is implemented both for CPU and GPU. ## Installation ### Binaries We provide pip wheels for all major OS/PyTorch/CUDA combinations, see [here](https://pytorch-geometric.com/whl). #### PyTorch 1.7.0 To install the binaries for PyTorch 1.7.0, simply run ``` pip install torch-spline-conv -f https://pytorch-geometric.com/whl/torch-1.7.0+${CUDA}.html ``` where `${CUDA}` should be replaced by either `cpu`, `cu92`, `cu101`, `cu102`, or `cu110` depending on your PyTorch installation. | | `cpu` | `cu92` | `cu101` | `cu102` | `cu110` | |-------------|-------|--------|---------|---------|---------| | **Linux** | ✅ | ✅ | ✅ | ✅ | ✅ | | **Windows** | ✅ | ❌ | ✅ | ✅ | ✅ | | **macOS** | ✅ | | | | | #### PyTorch 1.6.0 To install the binaries for PyTorch 1.6.0, simply run ``` pip install torch-spline-conv -f https://pytorch-geometric.com/whl/torch-1.6.0+${CUDA}.html ``` where `${CUDA}` should be replaced by either `cpu`, `cu92`, `cu101` or `cu102` depending on your PyTorch installation. | | `cpu` | `cu92` | `cu101` | `cu102` | |-------------|-------|--------|---------|---------| | **Linux** | ✅ | ✅ | ✅ | ✅ | | **Windows** | ✅ | ❌ | ✅ | ✅ | | **macOS** | ✅ | | | | **Note:** Binaries of older versions are also provided for PyTorch 1.4.0 and PyTorch 1.5.0 (following the same procedure). ### 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" ``` ## Usage ```python from torch_spline_conv import spline_conv out = spline_conv(x, edge_index, pseudo, weight, kernel_size, is_open_spline, degree=1, norm=True, root_weight=None, bias=None) ``` 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.

### Parameters * **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`) ### Returns * **out** *(Tensor)* - Out node features of shape `(number_of_nodes x out_channels)`. ### Example ```python 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) print(out.size()) torch.Size([4, 4]) # 4 nodes with 4 features each ``` ## Cite Please cite our paper if you use this code in your own work: ``` @inproceedings{Fey/etal/2018, 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)}, year={2018}, } ``` ## Running tests ``` python setup.py test ``` ## C++ API `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 make install ```