# Source code for torch_geometric.nn.conv.gat_conv

from typing import Optional, Tuple, Union

import torch
import torch.nn.functional as F
from torch import Tensor
from torch.nn import Parameter
from torch_sparse import SparseTensor, set_diag

from torch_geometric.nn.conv import MessagePassing
from torch_geometric.nn.dense.linear import Linear
from torch_geometric.typing import NoneType  # noqa
from torch_geometric.typing import Adj, OptPairTensor, OptTensor, Size
from torch_geometric.utils import add_self_loops, remove_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)}.

If the graph has multi-dimensional edge features :math:\mathbf{e}_{i,j},
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
\, \Vert \, \mathbf{\Theta}_{e} \mathbf{e}_{i,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
\, \Vert \, \mathbf{\Theta}_{e} \mathbf{e}_{i,k}]\right)\right)}.

Args:
in_channels (int or tuple): Size of each input sample, or :obj:-1 to
derive the size from the first input(s) to the forward method.
A tuple corresponds to the sizes of source and target
dimensionalities.
out_channels (int): Size of each output sample.
(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)
add_self_loops (bool, optional): If set to :obj:False, will not add
self-loops to the input graph. (default: :obj:True)
edge_dim (int, optional): Edge feature dimensionality (in case
there are any). (default: :obj:None)
fill_value (float or Tensor or str, optional): The way to generate
edge features of self-loops (in case :obj:edge_dim != None).
If given as :obj:float or :class:torch.Tensor, edge features of
self-loops will be directly given by :obj:fill_value.
If given as :obj:str, edge features of self-loops are computed by
aggregating all features of edges that point to the specific node,
according to a reduce operation. (:obj:"add", :obj:"mean",
:obj:"min", :obj:"max", :obj:"mul"). (default: :obj:"mean")
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}) or
:math:((|\mathcal{V_s}|, F_{s}), (|\mathcal{V_t}|, F_{t}))
if bipartite,
edge indices :math:(2, |\mathcal{E}|),
edge features :math:(|\mathcal{E}|, D) *(optional)*
- **output:** node features :math:(|\mathcal{V}|, H * F_{out}) or
:math:((|\mathcal{V}_t|, H * F_{out}) if bipartite.
If :obj:return_attention_weights=True, then
:math:((|\mathcal{V}|, H * F_{out}),
((2, |\mathcal{E}|), (|\mathcal{E}|, H)))
or :math:((|\mathcal{V_t}|, H * F_{out}), ((2, |\mathcal{E}|),
(|\mathcal{E}|, H))) if bipartite
"""
def __init__(
self,
in_channels: Union[int, Tuple[int, int]],
out_channels: int,
concat: bool = True,
negative_slope: float = 0.2,
dropout: float = 0.0,
edge_dim: Optional[int] = None,
fill_value: Union[float, Tensor, str] = 'mean',
bias: bool = True,
**kwargs,
):
super().__init__(node_dim=0, **kwargs)

self.in_channels = in_channels
self.out_channels = out_channels
self.concat = concat
self.negative_slope = negative_slope
self.dropout = dropout
self.edge_dim = edge_dim
self.fill_value = fill_value

# In case we are operating in bipartite graphs, we apply separate
# transformations 'lin_src' and 'lin_dst' to source and target nodes:
if isinstance(in_channels, int):
self.lin_src = Linear(in_channels, heads * out_channels,
bias=False, weight_initializer='glorot')
self.lin_dst = self.lin_src
else:
self.lin_src = Linear(in_channels[0], heads * out_channels, False,
weight_initializer='glorot')
self.lin_dst = Linear(in_channels[1], heads * out_channels, False,
weight_initializer='glorot')

# The learnable parameters to compute attention coefficients:

if edge_dim is not None:
self.lin_edge = Linear(edge_dim, heads * out_channels, bias=False,
weight_initializer='glorot')
else:
self.lin_edge = None
self.register_parameter('att_edge', None)

if bias and concat:
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):
self.lin_src.reset_parameters()
self.lin_dst.reset_parameters()
if self.lin_edge is not None:
self.lin_edge.reset_parameters()
glorot(self.att_src)
glorot(self.att_dst)
glorot(self.att_edge)
zeros(self.bias)

[docs]    def forward(self, x: Union[Tensor, OptPairTensor], edge_index: Adj,
edge_attr: OptTensor = None, size: Size = None,
return_attention_weights=None):
# type: (Union[Tensor, OptPairTensor], Tensor, OptTensor, Size, NoneType) -> Tensor  # noqa
# type: (Union[Tensor, OptPairTensor], SparseTensor, OptTensor, Size, NoneType) -> Tensor  # noqa
# type: (Union[Tensor, OptPairTensor], Tensor, OptTensor, Size, bool) -> Tuple[Tensor, Tuple[Tensor, Tensor]]  # noqa
# type: (Union[Tensor, OptPairTensor], SparseTensor, OptTensor, Size, bool) -> Tuple[Tensor, SparseTensor]  # noqa
r"""
Args:
return_attention_weights (bool, optional): If set to :obj:True,
:obj:(edge_index, attention_weights), holding the computed
attention weights for each edge. (default: :obj:None)
"""
# NOTE: attention weights will be returned whenever
# return_attention_weights is set to a value, regardless of its
# actual value (might be True or False). This is a current somewhat
# hacky workaround to allow for TorchScript support via the
# torch.jit._overload decorator, as we can only change the output
# arguments conditioned on type (None or bool), not based on its
# actual value.

# We first transform the input node features. If a tuple is passed, we
# transform source and target node features via separate weights:
if isinstance(x, Tensor):
assert x.dim() == 2, "Static graphs not supported in 'GATConv'"
x_src = x_dst = self.lin_src(x).view(-1, H, C)
else:  # Tuple of source and target node features:
x_src, x_dst = x
assert x_src.dim() == 2, "Static graphs not supported in 'GATConv'"
x_src = self.lin_src(x_src).view(-1, H, C)
if x_dst is not None:
x_dst = self.lin_dst(x_dst).view(-1, H, C)

x = (x_src, x_dst)

# Next, we compute node-level attention coefficients, both for source
# and target nodes (if present):
alpha_src = (x_src * self.att_src).sum(dim=-1)
alpha_dst = None if x_dst is None else (x_dst * self.att_dst).sum(-1)
alpha = (alpha_src, alpha_dst)

if isinstance(edge_index, Tensor):
# We only want to add self-loops for nodes that appear both as
# source and target nodes:
num_nodes = x_src.size(0)
if x_dst is not None:
num_nodes = min(num_nodes, x_dst.size(0))
num_nodes = min(size) if size is not None else num_nodes
edge_index, edge_attr = remove_self_loops(
edge_index, edge_attr)
edge_index, edge_attr, fill_value=self.fill_value,
num_nodes=num_nodes)
elif isinstance(edge_index, SparseTensor):
if self.edge_dim is None:
edge_index = set_diag(edge_index)
else:
raise NotImplementedError(
"The usage of 'edge_attr' and 'add_self_loops' "
"simultaneously is currently not yet supported for "
"'edge_index' in a 'SparseTensor' form")

# edge_updater_type: (alpha: OptPairTensor, edge_attr: OptTensor)
alpha = self.edge_updater(edge_index, alpha=alpha, edge_attr=edge_attr)

# propagate_type: (x: OptPairTensor, alpha: Tensor)
out = self.propagate(edge_index, x=x, alpha=alpha, size=size)

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 isinstance(return_attention_weights, bool):
if isinstance(edge_index, Tensor):
return out, (edge_index, alpha)
elif isinstance(edge_index, SparseTensor):
return out, edge_index.set_value(alpha, layout='coo')
else:
return out

[docs]    def edge_update(self, alpha_j: Tensor, alpha_i: OptTensor,
edge_attr: OptTensor, index: Tensor, ptr: OptTensor,
size_i: Optional[int]) -> Tensor:
# Given edge-level attention coefficients for source and target nodes,
# we simply need to sum them up to "emulate" concatenation:
alpha = alpha_j if alpha_i is None else alpha_j + alpha_i

if edge_attr is not None and self.lin_edge is not None:
if edge_attr.dim() == 1:
edge_attr = edge_attr.view(-1, 1)
edge_attr = self.lin_edge(edge_attr)
alpha_edge = (edge_attr * self.att_edge).sum(dim=-1)
alpha = alpha + alpha_edge

alpha = F.leaky_relu(alpha, self.negative_slope)
alpha = softmax(alpha, index, ptr, size_i)
alpha = F.dropout(alpha, p=self.dropout, training=self.training)
return alpha

def message(self, x_j: Tensor, alpha: Tensor) -> Tensor:
return alpha.unsqueeze(-1) * x_j

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