import warnings
from typing import List, Tuple, Union
import torch
from torch import Tensor, nn
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, OptPairTensor, OptTensor, Size
from torch_geometric.utils.repeat import repeat
from ..inits import uniform, zeros
try:
from torch_spline_conv import spline_basis, spline_weighting
except ImportError:
spline_basis = None
spline_weighting = None
[docs]class SplineConv(MessagePassing):
r"""The spline-based convolutional operator from the `"SplineCNN: Fast
Geometric Deep Learning with Continuous B-Spline Kernels"
<https://arxiv.org/abs/1711.08920>`_ paper
.. math::
\mathbf{x}^{\prime}_i = \frac{1}{|\mathcal{N}(i)|} \sum_{j \in
\mathcal{N}(i)} \mathbf{x}_j \cdot
h_{\mathbf{\Theta}}(\mathbf{e}_{i,j}),
where :math:`h_{\mathbf{\Theta}}` denotes a kernel function defined
over the weighted B-Spline tensor product basis.
.. note::
Pseudo-coordinates must lay in the fixed interval :math:`[0, 1]` for
this method to work as intended.
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.
dim (int): Pseudo-coordinate dimensionality.
kernel_size (int or [int]): Size of the convolving kernel.
is_open_spline (bool or [bool], optional): If set to :obj:`False`, the
operator will use a closed B-spline basis in this dimension.
(default :obj:`True`)
degree (int, optional): B-spline basis degrees. (default: :obj:`1`)
aggr (string, optional): The aggregation operator to use
(:obj:`"add"`, :obj:`"mean"`, :obj:`"max"`).
(default: :obj:`"mean"`)
root_weight (bool, optional): If set to :obj:`False`, the layer will
not add transformed root node features to the output.
(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`.
"""
def __init__(
self,
in_channels: Union[int, Tuple[int, int]],
out_channels: int,
dim: int,
kernel_size: Union[int, List[int]],
is_open_spline: bool = True,
degree: int = 1,
aggr: str = 'mean',
root_weight: bool = True,
bias: bool = True,
**kwargs,
):
super().__init__(aggr=aggr, **kwargs)
if spline_basis is None:
raise ImportError("'SplineConv' requires 'torch-spline-conv'")
self.in_channels = in_channels
self.out_channels = out_channels
self.dim = dim
self.degree = degree
self.root_weight = root_weight
kernel_size = torch.tensor(repeat(kernel_size, dim), dtype=torch.long)
self.register_buffer('kernel_size', kernel_size)
is_open_spline = repeat(is_open_spline, dim)
is_open_spline = torch.tensor(is_open_spline, dtype=torch.uint8)
self.register_buffer('is_open_spline', is_open_spline)
if isinstance(in_channels, int):
in_channels = (in_channels, in_channels)
self.K = kernel_size.prod().item()
if in_channels[0] > 0:
self.weight = Parameter(
torch.Tensor(self.K, in_channels[0], out_channels))
else:
self.weight = torch.nn.parameter.UninitializedParameter()
self._hook = self.register_forward_pre_hook(
self.initialize_parameters)
if root_weight:
self.lin = Linear(in_channels[1], out_channels, bias=False,
weight_initializer='uniform')
if bias:
self.bias = Parameter(torch.Tensor(out_channels))
else:
self.register_parameter('bias', None)
self.reset_parameters()
[docs] def reset_parameters(self):
if not isinstance(self.weight, nn.UninitializedParameter):
size = self.weight.size(0) * self.weight.size(1)
uniform(size, self.weight)
if self.root_weight:
self.lin.reset_parameters()
zeros(self.bias)
[docs] def forward(self, x: Union[Tensor, OptPairTensor], edge_index: Adj,
edge_attr: OptTensor = None, size: Size = None) -> Tensor:
""""""
if isinstance(x, Tensor):
x: OptPairTensor = (x, x)
if not x[0].is_cuda:
warnings.warn(
'We do not recommend using the non-optimized CPU version of '
'`SplineConv`. If possible, please move your data to GPU.')
# propagate_type: (x: OptPairTensor, edge_attr: OptTensor)
out = self.propagate(edge_index, x=x, edge_attr=edge_attr, size=size)
x_r = x[1]
if x_r is not None and self.root_weight:
out += self.lin(x_r)
if self.bias is not None:
out += self.bias
return out
def message(self, x_j: Tensor, edge_attr: Tensor) -> Tensor:
data = spline_basis(edge_attr, self.kernel_size, self.is_open_spline,
self.degree)
return spline_weighting(x_j, self.weight, *data)
@torch.no_grad()
def initialize_parameters(self, module, input):
if isinstance(self.weight, torch.nn.parameter.UninitializedParameter):
x = input[0][0] if isinstance(input, tuple) else input[0]
in_channels = x.size(-1)
self.weight.materialize((self.K, in_channels, self.out_channels))
size = self.weight.size(0) * self.weight.size(1)
uniform(size, self.weight)
module._hook.remove()
delattr(module, '_hook')
def __repr__(self) -> str:
return (f'{self.__class__.__name__}({self.in_channels}, '
f'{self.out_channels}, dim={self.dim})')