import warnings
import torch
import torch_geometric
from torch.nn import Parameter
from torch_geometric.nn.conv import MessagePassing
from torch_geometric.utils.repeat import repeat
from ..inits import uniform, zeros
try:
from torch_spline_conv import SplineBasis, SplineWeighting
except ImportError:
SplineBasis = None
SplineWeighting = 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): Size of each input sample.
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, out_channels, dim, kernel_size,
is_open_spline=True, degree=1, aggr='mean', root_weight=True,
bias=True, **kwargs):
super(SplineConv, self).__init__(aggr=aggr, **kwargs)
if SplineBasis 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
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)
K = kernel_size.prod().item()
self.weight = Parameter(torch.Tensor(K, in_channels, out_channels))
if root_weight:
self.root = Parameter(torch.Tensor(in_channels, out_channels))
else:
self.register_parameter('root', None)
if bias:
self.bias = Parameter(torch.Tensor(out_channels))
else:
self.register_parameter('bias', None)
self.reset_parameters()
[docs] def reset_parameters(self):
size = self.in_channels * self.weight.size(0)
uniform(size, self.weight)
uniform(size, self.root)
zeros(self.bias)
[docs] def forward(self, x, edge_index, pseudo):
""""""
x = x.unsqueeze(-1) if x.dim() == 1 else x
pseudo = pseudo.unsqueeze(-1) if pseudo.dim() == 1 else pseudo
if not x.is_cuda:
warnings.warn('We do not recommend using the non-optimized CPU '
'version of SplineConv. If possible, please convert '
'your data to the GPU.')
if torch_geometric.is_debug_enabled():
if x.size(1) != self.in_channels:
raise RuntimeError(
'Expected {} node features, but found {}'.format(
self.in_channels, x.size(1)))
if pseudo.size(1) != self.dim:
raise RuntimeError(
('Expected pseudo-coordinate dimensionality of {}, but '
'found {}').format(self.dim, pseudo.size(1)))
min_index, max_index = edge_index.min(), edge_index.max()
if min_index < 0 or max_index > x.size(0) - 1:
raise RuntimeError(
('Edge indices must lay in the interval [0, {}]'
' but found them in the interval [{}, {}]').format(
x.size(0) - 1, min_index, max_index))
min_pseudo, max_pseudo = pseudo.min(), pseudo.max()
if min_pseudo < 0 or max_pseudo > 1:
raise RuntimeError(
('Pseudo-coordinates must lay in the fixed interval [0, 1]'
' but found them in the interval [{}, {}]').format(
min_pseudo, max_pseudo))
return self.propagate(edge_index, x=x, pseudo=pseudo)
def message(self, x_j, pseudo):
data = SplineBasis.apply(pseudo, self._buffers['kernel_size'],
self._buffers['is_open_spline'], self.degree)
return SplineWeighting.apply(x_j, self.weight, *data)
def update(self, aggr_out, x):
if self.root is not None:
aggr_out = aggr_out + torch.mm(x, self.root)
if self.bias is not None:
aggr_out = aggr_out + self.bias
return aggr_out
def __repr__(self):
return '{}({}, {}, dim={})'.format(self.__class__.__name__,
self.in_channels, self.out_channels,
self.dim)