def add_self_loops(
edge_index: Tensor,
edge_attr: OptTensor = None,
fill_value: Union[float, Tensor, str] = None,
num_nodes: Optional[int] = None) -> Tuple[Tensor, OptTensor]:
r"""Adds a self-loop :math:`(i,i) \in \mathcal{E}` to every node
:math:`i \in \mathcal{V}` in the graph given by :attr:`edge_index`.
In case the graph is weighted or has multi-dimensional edge features
(:obj:`edge_attr != None`), edge features of self-loops will be added
according to :obj:`fill_value`.
Args:
edge_index (LongTensor): The edge indices.
edge_attr (Tensor, optional): Edge weights or multi-dimensional edge
features. (default: :obj:`None`)
fill_value (float or Tensor or str, optional): The way to generate
edge features of self-loops (in case :obj:`edge_attr != 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:`1.`)
num_nodes (int, optional): The number of nodes, *i.e.*
:obj:`max_val + 1` of :attr:`edge_index`. (default: :obj:`None`)
:rtype: (:class:`LongTensor`, :class:`Tensor`)
"""
N = maybe_num_nodes(edge_index, num_nodes)
loop_index = torch.arange(0, N, dtype=torch.long, device=edge_index.device)
loop_index = loop_index.unsqueeze(0).repeat(2, 1)
if edge_attr is not None:
if fill_value is None:
loop_attr = edge_attr.new_full((N, ) + edge_attr.size()[1:], 1.)
elif isinstance(fill_value, float) or isinstance(fill_value, int):
loop_attr = edge_attr.new_full((N, ) + edge_attr.size()[1:],
fill_value)
elif isinstance(fill_value, Tensor):
loop_attr = fill_value.to(edge_attr.device, edge_attr.dtype)
if edge_attr.dim() != loop_attr.dim():
loop_attr = loop_attr.unsqueeze(0)
sizes = [N] + [1] * (loop_attr.dim() - 1)
loop_attr = loop_attr.repeat(*sizes)
elif isinstance(fill_value, str):
loop_attr = scatter(edge_attr,
edge_index[1],
dim=0,
dim_size=N,
reduce=fill_value)
else:
raise AttributeError("No valid 'fill_value' provided")
edge_attr = torch.cat([edge_attr, loop_attr], dim=0)
edge_index = torch.cat([edge_index, loop_index], dim=1)
return edge_index, edge_attr
def message(self, x_j: Tensor, x_i: Tensor, edge_attr: OptTensor,
index: Tensor, ptr: OptTensor,
size_i: Optional[int]) -> Tensor:
x = x_i + x_j
if edge_attr is not None:
if edge_attr.dim() == 1:
edge_attr = edge_attr.view(-1, 1)
assert self.lin_edge is not None
edge_attr = self.lin_edge(edge_attr)
edge_attr = edge_attr.view(-1, self.heads, self.out_channels)
x += edge_attr
x = F.leaky_relu(x, self.negative_slope)
alpha = (x * self.att).sum(dim=-1)
alpha = softmax(alpha, index, ptr, size_i)
self._alpha = alpha
alpha = F.dropout(alpha, p=self.dropout, training=self.training)
return x_j * alpha.unsqueeze(-1)
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)
edge_attr = edge_attr.view(-1, self.heads, self.out_channels)
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_i: Tensor, x_j: Tensor, edge_type: Tensor,
edge_attr: OptTensor, index: Tensor, ptr: OptTensor,
size_i: Optional[int]) -> Tensor:
if self.num_bases is not None: # Basis-decomposition =================
w = torch.matmul(self.att, self.basis.view(self.num_bases, -1))
w = w.view(self.num_relations, self.in_channels,
self.heads * self.out_channels)
if self.num_blocks is not None: # Block-diagonal-decomposition =======
if (x_i.dtype == torch.long and x_j.dtype == torch.long
and self.num_blocks is not None):
raise ValueError('Block-diagonal decomposition not supported '
'for non-continuous input features.')
w = self.weight
x_i = x_i.view(-1, 1, w.size(1), w.size(2))
x_j = x_j.view(-1, 1, w.size(1), w.size(2))
w = torch.index_select(w, 0, edge_type)
outi = torch.einsum('abcd,acde->ace', x_i, w)
outi = outi.contiguous().view(-1, self.heads * self.out_channels)
outj = torch.einsum('abcd,acde->ace', x_j, w)
outj = outj.contiguous().view(-1, self.heads * self.out_channels)
else: # No regularization/Basis-decomposition ========================
if self.num_bases is None:
w = self.weight
w = torch.index_select(w, 0, edge_type)
outi = torch.bmm(x_i.unsqueeze(1), w).squeeze(-2)
outj = torch.bmm(x_j.unsqueeze(1), w).squeeze(-2)
qi = torch.matmul(outi, self.q)
kj = torch.matmul(outj, self.k)
alpha_edge, alpha = 0, torch.tensor([0])
if edge_attr is not None:
if edge_attr.dim() == 1:
edge_attr = edge_attr.view(-1, 1)
assert self.lin_edge is not None, (
"Please set 'edge_dim = edge_attr.size(-1)' while calling the "
"RGATConv layer")
edge_attributes = self.lin_edge(edge_attr).view(
-1, self.heads * self.out_channels)
if edge_attributes.size(0) != edge_attr.size(0):
edge_attributes = torch.index_select(edge_attributes, 0,
edge_type)
alpha_edge = torch.matmul(edge_attributes, self.e)
if self.attention_mode == "additive-self-attention":
if edge_attr is not None:
alpha = torch.add(qi, kj) + alpha_edge
else:
alpha = torch.add(qi, kj)
alpha = F.leaky_relu(alpha, self.negative_slope)
elif self.attention_mode == "multiplicative-self-attention":
if edge_attr is not None:
alpha = (qi * kj) * alpha_edge
else:
alpha = qi * kj
if self.attention_mechanism == "within-relation":
across_out = torch.zeros_like(alpha)
for r in range(self.num_relations):
mask = edge_type == r
across_out[mask] = softmax(alpha[mask], index[mask])
alpha = across_out
elif self.attention_mechanism == "across-relation":
alpha = softmax(alpha, index, ptr, size_i)
self._alpha = alpha
if self.mod == "additive":
if self.attention_mode == "additive-self-attention":
ones = torch.ones_like(alpha)
h = (outj.view(-1, self.heads, self.out_channels) *
ones.view(-1, self.heads, 1))
h = torch.mul(self.w, h)
return (outj.view(-1, self.heads, self.out_channels) *
alpha.view(-1, self.heads, 1) + h)
elif self.attention_mode == "multiplicative-self-attention":
ones = torch.ones_like(alpha)
h = (outj.view(-1, self.heads, 1, self.out_channels) *
ones.view(-1, self.heads, self.dim, 1))
h = torch.mul(self.w, h)
return (outj.view(-1, self.heads, 1, self.out_channels) *
alpha.view(-1, self.heads, self.dim, 1) + h)
elif self.mod == "scaled":
if self.attention_mode == "additive-self-attention":
ones = alpha.new_ones(index.size())
degree = scatter_add(ones, index,
dim_size=size_i)[index].unsqueeze(-1)
degree = torch.matmul(degree, self.l1) + self.b1
degree = self.activation(degree)
degree = torch.matmul(degree, self.l2) + self.b2
return torch.mul(
outj.view(-1, self.heads, self.out_channels) *
alpha.view(-1, self.heads, 1),
degree.view(-1, 1, self.out_channels))
elif self.attention_mode == "multiplicative-self-attention":
ones = alpha.new_ones(index.size())
degree = scatter_add(ones, index,
dim_size=size_i)[index].unsqueeze(-1)
degree = torch.matmul(degree, self.l1) + self.b1
degree = self.activation(degree)
degree = torch.matmul(degree, self.l2) + self.b2
return torch.mul(
outj.view(-1, self.heads, 1, self.out_channels) *
alpha.view(-1, self.heads, self.dim, 1),
degree.view(-1, 1, 1, self.out_channels))
elif self.mod == "f-additive":
alpha = torch.where(alpha > 0, alpha + 1, alpha)
elif self.mod == "f-scaled":
ones = alpha.new_ones(index.size())
degree = scatter_add(ones, index,
dim_size=size_i)[index].unsqueeze(-1)
alpha = alpha * degree
elif self.training and self.dropout > 0:
alpha = F.dropout(alpha, p=self.dropout, training=True)
else:
alpha = alpha # original
if self.attention_mode == "additive-self-attention":
return alpha.view(-1, self.heads, 1) * outj.view(
-1, self.heads, self.out_channels)
else:
return (alpha.view(-1, self.heads, self.dim, 1) *
outj.view(-1, self.heads, 1, self.out_channels))
