from typing import Optional, Tuple
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.typing import Adj, SparseTensor
from torch_geometric.utils import is_torch_sparse_tensor, spmm
[docs]class PANConv(MessagePassing):
r"""The path integral based convolutional operator from the
`"Path Integral Based Convolution and Pooling for Graph Neural Networks"
<https://arxiv.org/abs/2006.16811>`_ paper.
.. math::
\mathbf{X}^{\prime} = \mathbf{M} \mathbf{X} \mathbf{W}
where :math:`\mathbf{M}` denotes the normalized and learned maximal entropy
transition (MET) matrix that includes neighbors up to :obj:`filter_size`
hops:
.. math::
\mathbf{M} = \mathbf{Z}^{-1/2} \sum_{n=0}^L e^{-\frac{E(n)}{T}}
\mathbf{A}^n \mathbf{Z}^{-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.
filter_size (int): The filter size :math:`L`.
**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}|)`,
- **output:** node features :math:`(|\mathcal{V}|, F_{out})`
"""
def __init__(self, in_channels: int, out_channels: int, filter_size: int,
**kwargs):
kwargs.setdefault('aggr', 'add')
super().__init__(**kwargs)
self.in_channels = in_channels
self.out_channels = out_channels
self.filter_size = filter_size
self.lin = Linear(in_channels, out_channels)
self.weight = Parameter(torch.empty(filter_size + 1))
self.reset_parameters()
[docs] def reset_parameters(self):
super().reset_parameters()
self.lin.reset_parameters()
self.weight.data.fill_(0.5)
[docs] def forward(
self,
x: Tensor,
edge_index: Adj,
) -> Tuple[Tensor, SparseTensor]:
adj_t: Optional[SparseTensor] = None
if isinstance(edge_index, Tensor):
if is_torch_sparse_tensor(edge_index):
# TODO Handle PyTorch sparse tensor directly.
if edge_index.layout == torch.sparse_coo:
adj_t = SparseTensor.from_torch_sparse_coo_tensor(
edge_index)
elif edge_index.layout == torch.sparse_csr:
adj_t = SparseTensor.from_torch_sparse_csr_tensor(
edge_index)
else:
raise ValueError(f"Unexpected sparse tensor layout "
f"(got '{edge_index.layout}')")
else:
adj_t = SparseTensor(row=edge_index[1], col=edge_index[0],
sparse_sizes=(x.size(0), x.size(0)))
elif isinstance(edge_index, SparseTensor):
adj_t = edge_index.set_value(None)
adj_t = self.panentropy(adj_t, dtype=x.dtype)
deg = adj_t.storage.rowcount().to(x.dtype)
deg_inv_sqrt = deg.pow_(-0.5)
deg_inv_sqrt[deg_inv_sqrt == float('inf')] = 0.
M = deg_inv_sqrt.view(1, -1) * adj_t * deg_inv_sqrt.view(-1, 1)
out = self.propagate(M, x=x, edge_weight=None)
out = self.lin(out)
return out, M
def message(self, x_j: Tensor, edge_weight: Tensor) -> Tensor:
return 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)
def panentropy(self, adj_t: SparseTensor,
dtype: Optional[int] = None) -> SparseTensor:
if not adj_t.has_value():
adj_t = adj_t.fill_value(1.0)
tmp = SparseTensor.eye(adj_t.size(0), adj_t.size(1), has_value=True,
dtype=dtype, device=adj_t.device())
tmp = tmp.mul_nnz(self.weight[0], layout='coo')
outs = [tmp]
for i in range(1, self.filter_size + 1):
tmp = tmp @ adj_t
tmp = tmp.mul_nnz(self.weight[i], layout='coo')
outs += [tmp]
row = torch.cat([out.storage.row() for out in outs], dim=0)
col = torch.cat([out.storage.col() for out in outs], dim=0)
value = torch.cat([out.storage.value() for out in outs], dim=0)
out = SparseTensor(row=row, col=col, value=value,
sparse_sizes=adj_t.sparse_sizes()).coalesce()
return out
def __repr__(self) -> str:
return (f'{self.__class__.__name__}({self.in_channels}, '
f'{self.out_channels}, filter_size={self.filter_size})')