import torch
from torch.nn import Parameter, Linear
import torch.nn.functional as F
from torch_geometric.nn.conv import MessagePassing
from torch_geometric.utils import remove_self_loops, add_self_loops, softmax
from ..inits import glorot, zeros
[docs]class GATConv(MessagePassing):
r"""The graph attentional operator from the `"Graph Attention Networks"
<https://arxiv.org/abs/1710.10903>`_ paper
.. math::
\mathbf{x}^{\prime}_i = \alpha_{i,i}\mathbf{\Theta}\mathbf{x}_{i} +
\sum_{j \in \mathcal{N}(i)} \alpha_{i,j}\mathbf{\Theta}\mathbf{x}_{j},
where the attention coefficients :math:`\alpha_{i,j}` are computed as
.. math::
\alpha_{i,j} =
\frac{
\exp\left(\mathrm{LeakyReLU}\left(\mathbf{a}^{\top}
[\mathbf{\Theta}\mathbf{x}_i \, \Vert \, \mathbf{\Theta}\mathbf{x}_j]
\right)\right)}
{\sum_{k \in \mathcal{N}(i) \cup \{ i \}}
\exp\left(\mathrm{LeakyReLU}\left(\mathbf{a}^{\top}
[\mathbf{\Theta}\mathbf{x}_i \, \Vert \, \mathbf{\Theta}\mathbf{x}_k]
\right)\right)}.
Args:
in_channels (int): Size of each input sample.
out_channels (int): Size of each output sample.
heads (int, optional): Number of multi-head-attentions.
(default: :obj:`1`)
concat (bool, optional): If set to :obj:`False`, the multi-head
attentions are averaged instead of concatenated.
(default: :obj:`True`)
negative_slope (float, optional): LeakyReLU angle of the negative
slope. (default: :obj:`0.2`)
dropout (float, optional): Dropout probability of the normalized
attention coefficients which exposes each node to a stochastically
sampled neighborhood during training. (default: :obj:`0`)
bias (bool, optional): If set to :obj:`False`, the layer will not learn
an additive bias. (default: :obj:`True`)
**kwargs (optional): Additional arguments of
:class:`torch_geometric.nn.conv.MessagePassing`.
"""
def __init__(self, in_channels, out_channels, heads=1, concat=True,
negative_slope=0.2, dropout=0, bias=True, **kwargs):
super(GATConv, self).__init__(aggr='add', **kwargs)
self.in_channels = in_channels
self.out_channels = out_channels
self.heads = heads
self.concat = concat
self.negative_slope = negative_slope
self.dropout = dropout
self.__alpha__ = None
self.lin = Linear(in_channels, heads * out_channels, bias=False)
self.att_i = Parameter(torch.Tensor(1, heads, out_channels))
self.att_j = Parameter(torch.Tensor(1, heads, out_channels))
if bias and concat:
self.bias = Parameter(torch.Tensor(heads * out_channels))
elif bias and not concat:
self.bias = Parameter(torch.Tensor(out_channels))
else:
self.register_parameter('bias', None)
self.reset_parameters()
[docs] def reset_parameters(self):
glorot(self.lin.weight)
glorot(self.att_i)
glorot(self.att_j)
zeros(self.bias)
[docs] def forward(self, x, edge_index, return_attention_weights=False):
""""""
if torch.is_tensor(x):
x = self.lin(x)
x = (x, x)
else:
x = (self.lin(x[0]), self.lin(x[1]))
edge_index, _ = remove_self_loops(edge_index)
edge_index, _ = add_self_loops(edge_index,
num_nodes=x[1].size(self.node_dim))
out = self.propagate(edge_index, x=x,
return_attention_weights=return_attention_weights)
if self.concat:
out = out.view(-1, self.heads * self.out_channels)
else:
out = out.mean(dim=1)
if self.bias is not None:
out = out + self.bias
if return_attention_weights:
alpha, self.__alpha__ = self.__alpha__, None
return out, (edge_index, alpha)
else:
return out
def message(self, x_i, x_j, edge_index_i, size_i,
return_attention_weights):
# Compute attention coefficients.
x_i = x_i.view(-1, self.heads, self.out_channels)
x_j = x_j.view(-1, self.heads, self.out_channels)
alpha = (x_i * self.att_i).sum(-1) + (x_j * self.att_j).sum(-1)
alpha = F.leaky_relu(alpha, self.negative_slope)
alpha = softmax(alpha, edge_index_i, size_i)
if return_attention_weights:
self.__alpha__ = alpha
# Sample attention coefficients stochastically.
alpha = F.dropout(alpha, p=self.dropout, training=self.training)
return x_j * alpha.view(-1, self.heads, 1)
def __repr__(self):
return '{}({}, {}, heads={})'.format(self.__class__.__name__,
self.in_channels,
self.out_channels, self.heads)