Source code for torch_geometric.nn.conv.arma_conv

from typing import Callable, Optional

import torch
import torch.nn.functional as F
from torch import Tensor, nn
from torch.nn import Parameter, ReLU

from torch_geometric.nn.conv import MessagePassing
from torch_geometric.nn.conv.gcn_conv import gcn_norm
from torch_geometric.nn.inits import glorot, zeros
from torch_geometric.typing import Adj, OptTensor, SparseTensor
from torch_geometric.utils import spmm

[docs]class ARMAConv(MessagePassing):
r"""The ARMA graph convolutional operator from the "Graph Neural Networks
with Convolutional ARMA Filters" <https://arxiv.org/abs/1901.01343>_
paper.

.. math::
\mathbf{X}^{\prime} = \frac{1}{K} \sum_{k=1}^K \mathbf{X}_k^{(T)},

with :math:\mathbf{X}_k^{(T)} being recursively defined by

.. math::
\mathbf{X}_k^{(t+1)} = \sigma \left( \mathbf{\hat{L}}
\mathbf{X}_k^{(t)} \mathbf{W} + \mathbf{X}^{(0)} \mathbf{V} \right),

where :math:\mathbf{\hat{L}} = \mathbf{I} - \mathbf{L} = \mathbf{D}^{-1/2}
\mathbf{A} \mathbf{D}^{-1/2} denotes the
modified Laplacian :math:\mathbf{L} = \mathbf{I} - \mathbf{D}^{-1/2}
\mathbf{A} \mathbf{D}^{-1/2}.

Args:
in_channels (int): Size of each input sample, or :obj:-1 to derive
the size from the first input(s) to the forward method.
out_channels (int): Size of each output sample
:math:\mathbf{x}^{(t+1)}.
num_stacks (int, optional): Number of parallel stacks :math:K.
(default: :obj:1).
num_layers (int, optional): Number of layers :math:T.
(default: :obj:1)
act (callable, optional): Activation function :math:\sigma.
(default: :meth:torch.nn.ReLU())
shared_weights (int, optional): If set to :obj:True the layers in
each stack will share the same parameters. (default: :obj:False)
dropout (float, optional): Dropout probability of the skip connection.
(default: :obj:0.)
bias (bool, optional): If set to :obj:False, the layer will not learn
an additive bias. (default: :obj:True)
:class:torch_geometric.nn.conv.MessagePassing.

Shapes:
- **input:**
node features :math:(|\mathcal{V}|, F_{in}),
edge indices :math:(2, |\mathcal{E}|),
edge weights :math:(|\mathcal{E}|) *(optional)*
- **output:** node features :math:(|\mathcal{V}|, F_{out})
"""
def __init__(self, in_channels: int, out_channels: int,
num_stacks: int = 1, num_layers: int = 1,
shared_weights: bool = False,
act: Optional[Callable] = ReLU(), dropout: float = 0.,
bias: bool = True, **kwargs):
super().__init__(**kwargs)

self.in_channels = in_channels
self.out_channels = out_channels
self.num_stacks = num_stacks
self.num_layers = num_layers
self.act = act
self.shared_weights = shared_weights
self.dropout = dropout

K, T, F_in, F_out = num_stacks, num_layers, in_channels, out_channels
T = 1 if self.shared_weights else T

self.weight = Parameter(torch.empty(max(1, T - 1), K, F_out, F_out))
if in_channels > 0:
self.init_weight = Parameter(torch.empty(K, F_in, F_out))
self.root_weight = Parameter(torch.empty(T, K, F_in, F_out))
else:
self.init_weight = torch.nn.parameter.UninitializedParameter()
self.root_weight = torch.nn.parameter.UninitializedParameter()
self._hook = self.register_forward_pre_hook(
self.initialize_parameters)

if bias:
self.bias = Parameter(torch.empty(T, K, 1, F_out))
else:
self.register_parameter('bias', None)

self.reset_parameters()

[docs]    def reset_parameters(self):
super().reset_parameters()
glorot(self.weight)
if not isinstance(self.init_weight, torch.nn.UninitializedParameter):
glorot(self.init_weight)
glorot(self.root_weight)
zeros(self.bias)

[docs]    def forward(self, x: Tensor, edge_index: Adj,
edge_weight: OptTensor = None) -> Tensor:

if isinstance(edge_index, Tensor):
edge_index, edge_weight = gcn_norm(  # yapf: disable
edge_index, edge_weight, x.size(self.node_dim),

elif isinstance(edge_index, SparseTensor):
edge_index = gcn_norm(  # yapf: disable
edge_index, edge_weight, x.size(self.node_dim),

x = x.unsqueeze(-3)
out = x
for t in range(self.num_layers):
if t == 0:
out = out @ self.init_weight
else:
out = out @ self.weight[0 if self.shared_weights else t - 1]

# propagate_type: (x: Tensor, edge_weight: OptTensor)
out = self.propagate(edge_index, x=out, edge_weight=edge_weight)

root = F.dropout(x, p=self.dropout, training=self.training)
root = root @ self.root_weight[0 if self.shared_weights else t]
out = out + root

if self.bias is not None:
out = out + self.bias[0 if self.shared_weights else t]

if self.act is not None:
out = self.act(out)

return out.mean(dim=-3)

def message(self, x_j: Tensor, edge_weight: Tensor) -> Tensor:
return edge_weight.view(-1, 1) * x_j

def initialize_parameters(self, module, input):
if isinstance(self.init_weight, nn.parameter.UninitializedParameter):
F_in, F_out = input[0].size(-1), self.out_channels
T, K = self.weight.size(0) + 1, self.weight.size(1)
self.init_weight.materialize((K, F_in, F_out))
self.root_weight.materialize((T, K, F_in, F_out))
glorot(self.init_weight)
glorot(self.root_weight)

module._hook.remove()
delattr(module, '_hook')

def __repr__(self) -> str:
return (f'{self.__class__.__name__}({self.in_channels}, '
f'{self.out_channels}, num_stacks={self.num_stacks}, '
f'num_layers={self.num_layers})')