from typing import Optional import torch from torch import Tensor from torch.nn import Parameter from torch_geometric.nn.conv import MessagePassing from torch_geometric.nn.dense.linear import Linear from torch_geometric.nn.inits import zeros from torch_geometric.typing import ( Adj, OptPairTensor, OptTensor, SparseTensor, torch_sparse, ) from torch_geometric.utils import add_remaining_self_loops from torch_geometric.utils import add_self_loops as add_self_loops_fn from torch_geometric.utils import ( is_torch_sparse_tensor, scatter, spmm, to_edge_index, ) from torch_geometric.utils.num_nodes import maybe_num_nodes from torch_geometric.utils.sparse import set_sparse_value @torch.jit._overload def gcn_norm( # noqa: F811 edge_index, edge_weight, num_nodes, improved, add_self_loops, flow, dtype): # type: (Tensor, OptTensor, Optional[int], bool, bool, str, Optional[int]) -> OptPairTensor # noqa pass @torch.jit._overload def gcn_norm( # noqa: F811 edge_index, edge_weight, num_nodes, improved, add_self_loops, flow, dtype): # type: (SparseTensor, OptTensor, Optional[int], bool, bool, str, Optional[int]) -> SparseTensor # noqa pass def gcn_norm( # noqa: F811 edge_index: Adj, edge_weight: OptTensor = None, num_nodes: Optional[int] = None, improved: bool = False, add_self_loops: bool = True, flow: str = "source_to_target", dtype: Optional[torch.dtype] = None, ): fill_value = 2. if improved else 1. if isinstance(edge_index, SparseTensor): assert edge_index.size(0) == edge_index.size(1) adj_t = edge_index if not adj_t.has_value(): adj_t = adj_t.fill_value(1., dtype=dtype) if add_self_loops: adj_t = torch_sparse.fill_diag(adj_t, fill_value) deg = torch_sparse.sum(adj_t, dim=1) deg_inv_sqrt = deg.pow_(-0.5) deg_inv_sqrt.masked_fill_(deg_inv_sqrt == float('inf'), 0.) adj_t = torch_sparse.mul(adj_t, deg_inv_sqrt.view(-1, 1)) adj_t = torch_sparse.mul(adj_t, deg_inv_sqrt.view(1, -1)) return adj_t if is_torch_sparse_tensor(edge_index): assert edge_index.size(0) == edge_index.size(1) if edge_index.layout == torch.sparse_csc: raise NotImplementedError("Sparse CSC matrices are not yet " "supported in 'gcn_norm'") adj_t = edge_index if add_self_loops: adj_t, _ = add_self_loops_fn(adj_t, None, fill_value, num_nodes) edge_index, value = to_edge_index(adj_t) col, row = edge_index[0], edge_index[1] deg = scatter(value, col, 0, dim_size=num_nodes, reduce='sum') deg_inv_sqrt = deg.pow_(-0.5) deg_inv_sqrt.masked_fill_(deg_inv_sqrt == float('inf'), 0) value = deg_inv_sqrt[row] * value * deg_inv_sqrt[col] return set_sparse_value(adj_t, value), None assert flow in ['source_to_target', 'target_to_source'] num_nodes = maybe_num_nodes(edge_index, num_nodes) if add_self_loops: edge_index, edge_weight = add_remaining_self_loops( edge_index, edge_weight, fill_value, num_nodes) if edge_weight is None: edge_weight = torch.ones((edge_index.size(1), ), dtype=dtype, device=edge_index.device) row, col = edge_index[0], edge_index[1] idx = col if flow == 'source_to_target' else row deg = scatter(edge_weight, idx, dim=0, dim_size=num_nodes, reduce='sum') deg_inv_sqrt = deg.pow_(-0.5) deg_inv_sqrt.masked_fill_(deg_inv_sqrt == float('inf'), 0) edge_weight = deg_inv_sqrt[row] * edge_weight * deg_inv_sqrt[col] return edge_index, edge_weight class GCNConv(MessagePassing): r"""The graph convolutional operator from the `"Semi-supervised Classification with Graph Convolutional Networks" `_ paper. .. math:: \mathbf{X}^{\prime} = \mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2} \mathbf{X} \mathbf{\Theta}, where :math:`\mathbf{\hat{A}} = \mathbf{A} + \mathbf{I}` denotes the adjacency matrix with inserted self-loops and :math:`\hat{D}_{ii} = \sum_{j=0} \hat{A}_{ij}` its diagonal degree matrix. The adjacency matrix can include other values than :obj:`1` representing edge weights via the optional :obj:`edge_weight` tensor. Its node-wise formulation is given by: .. math:: \mathbf{x}^{\prime}_i = \mathbf{\Theta}^{\top} \sum_{j \in \mathcal{N}(i) \cup \{ i \}} \frac{e_{j,i}}{\sqrt{\hat{d}_j \hat{d}_i}} \mathbf{x}_j with :math:`\hat{d}_i = 1 + \sum_{j \in \mathcal{N}(i)} e_{j,i}`, where :math:`e_{j,i}` denotes the edge weight from source node :obj:`j` to target node :obj:`i` (default: :obj:`1.0`) 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. improved (bool, optional): If set to :obj:`True`, the layer computes :math:`\mathbf{\hat{A}}` as :math:`\mathbf{A} + 2\mathbf{I}`. (default: :obj:`False`) cached (bool, optional): If set to :obj:`True`, the layer will cache the computation of :math:`\mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2}` on first execution, and will use the cached version for further executions. This parameter should only be set to :obj:`True` in transductive learning scenarios. (default: :obj:`False`) add_self_loops (bool, optional): If set to :obj:`False`, will not add self-loops to the input graph. By default, self-loops will be added in case :obj:`normalize` is set to :obj:`True`, and not added otherwise. (default: :obj:`None`) normalize (bool, optional): Whether to add self-loops and compute symmetric normalization coefficients on-the-fly. (default: :obj:`True`) 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`. Shapes: - **input:** node features :math:`(|\mathcal{V}|, F_{in})`, edge indices :math:`(2, |\mathcal{E}|)` or sparse matrix :math:`(|\mathcal{V}|, |\mathcal{V}|)`, edge weights :math:`(|\mathcal{E}|)` *(optional)* - **output:** node features :math:`(|\mathcal{V}|, F_{out})` """ _cached_edge_index: Optional[OptPairTensor] _cached_adj_t: Optional[SparseTensor] def __init__( self, in_channels: int, out_channels: int, improved: bool = False, cached: bool = False, add_self_loops: Optional[bool] = None, normalize: bool = True, bias: bool = True, **kwargs, ): kwargs.setdefault('aggr', 'add') super().__init__(**kwargs) if add_self_loops is None: add_self_loops = normalize if add_self_loops and not normalize: raise ValueError(f"'{self.__class__.__name__}' does not support " f"adding self-loops to the graph when no " f"on-the-fly normalization is applied") self.in_channels = in_channels self.out_channels = out_channels self.improved = improved self.cached = cached self.add_self_loops = add_self_loops self.normalize = normalize self._cached_edge_index = None self._cached_adj_t = None self.lin = Linear(in_channels, out_channels, bias=False, weight_initializer='glorot') if bias: self.bias = Parameter(torch.empty(out_channels)) else: self.register_parameter('bias', None) self.reset_parameters() def reset_parameters(self): super().reset_parameters() self.lin.reset_parameters() zeros(self.bias) self._cached_edge_index = None self._cached_adj_t = None def forward(self, x: Tensor, edge_index: Adj, edge_weight: OptTensor = None) -> Tensor: if isinstance(x, (tuple, list)): raise ValueError(f"'{self.__class__.__name__}' received a tuple " f"of node features as input while this layer " f"does not support bipartite message passing. " f"Please try other layers such as 'SAGEConv' or " f"'GraphConv' instead") if self.normalize: if isinstance(edge_index, Tensor): cache = self._cached_edge_index if cache is None: edge_index, edge_weight = gcn_norm( # yapf: disable edge_index, edge_weight, x.size(self.node_dim), self.improved, self.add_self_loops, self.flow, x.dtype) if self.cached: self._cached_edge_index = (edge_index, edge_weight) else: edge_index, edge_weight = cache[0], cache[1] elif isinstance(edge_index, SparseTensor): cache = self._cached_adj_t if cache is None: edge_index = gcn_norm( # yapf: disable edge_index, edge_weight, x.size(self.node_dim), self.improved, self.add_self_loops, self.flow, x.dtype) if self.cached: self._cached_adj_t = edge_index else: edge_index = cache x = self.lin(x) # propagate_type: (x: Tensor, edge_weight: OptTensor) out = self.propagate(edge_index, x=x, edge_weight=edge_weight) if self.bias is not None: out = out + self.bias return out def message(self, x_j: Tensor, edge_weight: OptTensor) -> Tensor: return x_j if edge_weight is None else edge_weight.view(-1, 1) * x_j def message_and_aggregate(self, adj_t: Adj, x: Tensor) -> Tensor: return spmm(adj_t, x, reduce=self.aggr)