October 15, 2017

http://www.ntu.edu.sg/home/xbresson
https://github.com/xbresson
https://twitter.com/xbresson

Prototype implementation in PyTorch of the NIPS'16 paper:
Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
M Defferrard, X Bresson, P Vandergheynst
Advances in Neural Information Processing Systems, 3844-3852, 2016
ArXiv preprint: arXiv:1606.09375

The code provides a simple example of graph ConvNets for the MNIST classification task.
The graph is a 8-nearest neighbor graph of a 2D grid.
The signals on graph are the MNIST images vectorized as $28^2 \times 1$ vectors.

git clone https://github.com/xbresson/graph_convnets_pytorch.git
cd graph_convnets_pytorch
pip install -r requirements.txt # installation for python 3.6.2
python check_install.py
jupyter notebook # run the 2 notebooks

GPU Quadro M4000

• Standard ConvNets: 01_standard_convnet_lenet5_mnist_pytorch.ipynb, accuracy= 99.31, speed= 6.9 sec/epoch.
  
• Graph ConvNets: 02_graph_convnet_lenet5_mnist_pytorch.ipynb, accuracy= 99.19, speed= 100.8 sec/epoch
  

PyTorch has not yet implemented function torch.mm(sparse, dense) for variables: pytorch/pytorch#2389. It will be certainly implemented but in the meantime, I defined a new autograd function for sparse variables, called "my_sparse_mm", by subclassing torch.autograd.function and implementing the forward and backward passes.

class my_sparse_mm(torch.autograd.Function):
    """
    Implementation of a new autograd function for sparse variables, 
    called "my_sparse_mm", by subclassing torch.autograd.Function 
    and implementing the forward and backward passes.
    """
    
    def forward(self, W, x):  # W is SPARSE
        self.save_for_backward(W, x)
        y = torch.mm(W, x)
        return y
    
    def backward(self, grad_output):
        W, x = self.saved_tensors 
        grad_input = grad_output.clone()
        grad_input_dL_dW = torch.mm(grad_input, x.t()) 
        grad_input_dL_dx = torch.mm(W.t(), grad_input )
        return grad_input_dL_dW, grad_input_dL_dx

Any problem that can be cast as analyzing a set of signals on a fixed graph, and you want to use ConvNets for this analysis.