"""Torch Module for Graph Convolutional Network via Initial residual
and Identity mapping (GCNII) layer"""
# pylint: disable= no-member, arguments-differ, invalid-name
import math
import torch as th
from torch import nn
from .... import function as fn
from ....base import DGLError
from .graphconv import EdgeWeightNorm
[docs]class GCN2Conv(nn.Module):
r"""Graph Convolutional Network via Initial residual
and Identity mapping (GCNII) from `Simple and Deep Graph Convolutional
Networks <https://arxiv.org/abs/2007.02133>`__
It is mathematically is defined as follows:
.. math::
\mathbf{h}^{(l+1)} =\left( (1 - \alpha)(\mathbf{D}^{-1/2} \mathbf{\hat{A}}
\mathbf{D}^{-1/2})\mathbf{h}^{(l)} + \alpha {\mathbf{h}^{(0)}} \right)
\left( (1 - \beta_l) \mathbf{I} + \beta_l \mathbf{W} \right)
where :math:`\mathbf{\hat{A}}` is the adjacency matrix with self-loops,
:math:`\mathbf{D}_{ii} = \sum_{j=0} \mathbf{A}_{ij}` is its diagonal degree matrix,
:math:`\mathbf{h}^{(0)}` is the initial node features,
:math:`\mathbf{h}^{(l)}` is the feature of layer :math:`l`,
:math:`\alpha` is the fraction of initial node features, and
:math:`\beta_l` is the hyperparameter to tune the strength of identity mapping.
It is defined by :math:`\beta_l = \log(\frac{\lambda}{l}+1)\approx\frac{\lambda}{l}`,
where :math:`\lambda` is a hyperparameter. :math:`\beta` ensures that the decay of
the weight matrix adaptively increases as we stack more layers.
Parameters
----------
in_feats : int
Input feature size; i.e, the number of dimensions of :math:`h_j^{(l)}`.
layer : int
the index of current layer.
alpha : float
The fraction of the initial input features. Default: ``0.1``
lambda_ : float
The hyperparameter to ensure the decay of the weight matrix
adaptively increases. Default: ``1``
project_initial_features : bool
Whether to share a weight matrix between initial features and
smoothed features. Default: ``True``
bias : bool, optional
If True, adds a learnable bias to the output. Default: ``True``.
activation : callable activation function/layer or None, optional
If not None, applies an activation function to the updated node features.
Default: ``None``.
allow_zero_in_degree : bool, optional
If there are 0-in-degree nodes in the graph, output for those nodes will be invalid
since no message will be passed to those nodes. This is harmful for some applications
causing silent performance regression. This module will raise a DGLError if it detects
0-in-degree nodes in input graph. By setting ``True``, it will suppress the check
and let the users handle it by themselves. Default: ``False``.
Note
----
Zero in-degree nodes will lead to invalid output value. This is because no message
will be passed to those nodes, the aggregation function will be appied on empty input.
A common practice to avoid this is to add a self-loop for each node in the graph if
it is homogeneous, which can be achieved by:
>>> g = ... # a DGLGraph
>>> g = dgl.add_self_loop(g)
Calling ``add_self_loop`` will not work for some graphs, for example, heterogeneous graph
since the edge type can not be decided for self_loop edges. Set ``allow_zero_in_degree``
to ``True`` for those cases to unblock the code and handle zero-in-degree nodes manually.
A common practise to handle this is to filter out the nodes with zero-in-degree when use
after conv.
Examples
--------
>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GCN2Conv
>>> # Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 3)
>>> g = dgl.add_self_loop(g)
>>> conv1 = GCN2Conv(3, layer=1, alpha=0.5, \
... project_initial_features=True, allow_zero_in_degree=True)
>>> conv2 = GCN2Conv(3, layer=2, alpha=0.5, \
... project_initial_features=True, allow_zero_in_degree=True)
>>> res = feat
>>> res = conv1(g, res, feat)
>>> res = conv2(g, res, feat)
>>> print(res)
tensor([[1.3803, 3.3191, 2.9572],
[1.3803, 3.3191, 2.9572],
[1.3803, 3.3191, 2.9572],
[1.4770, 3.8326, 3.2451],
[1.3623, 3.2102, 2.8679],
[1.3803, 3.3191, 2.9572]], grad_fn=<AddBackward0>)
"""
def __init__(
self,
in_feats,
layer,
alpha=0.1,
lambda_=1,
project_initial_features=True,
allow_zero_in_degree=False,
bias=True,
activation=None,
):
super().__init__()
self._in_feats = in_feats
self._project_initial_features = project_initial_features
self.alpha = alpha
self.beta = math.log(lambda_ / layer + 1)
self._bias = bias
self._activation = activation
self._allow_zero_in_degree = allow_zero_in_degree
self.weight1 = nn.Parameter(th.Tensor(self._in_feats, self._in_feats))
if self._project_initial_features:
self.register_parameter("weight2", None)
else:
self.weight2 = nn.Parameter(
th.Tensor(self._in_feats, self._in_feats)
)
if self._bias:
self.bias = nn.Parameter(th.Tensor(self._in_feats))
else:
self.register_parameter("bias", None)
self.reset_parameters()
[docs] def reset_parameters(self):
r"""
Description
-----------
Reinitialize learnable parameters.
"""
nn.init.normal_(self.weight1)
if not self._project_initial_features:
nn.init.normal_(self.weight2)
if self._bias:
nn.init.zeros_(self.bias)
def set_allow_zero_in_degree(self, set_value):
r"""
Description
-----------
Set allow_zero_in_degree flag.
Parameters
----------
set_value : bool
The value to be set to the flag.
"""
self._allow_zero_in_degree = set_value
[docs] def forward(self, graph, feat, feat_0, edge_weight=None):
r"""
Description
-----------
Compute graph convolution.
Parameters
----------
graph : DGLGraph
The graph.
feat : torch.Tensor
The input feature of shape
:math:`(N, D_{in})`
where :math:`D_{in}` is the size of input feature and :math:`N` is the number of nodes.
feat_0 : torch.Tensor
The initial feature of shape :math:`(N, D_{in})`
edge_weight: torch.Tensor, optional
edge_weight to use in the message passing process. This is equivalent to
using weighted adjacency matrix in the equation above, and
:math:`\tilde{D}^{-1/2}\tilde{A} \tilde{D}^{-1/2}`
is based on :class:`dgl.nn.pytorch.conv.graphconv.EdgeWeightNorm`.
Returns
-------
torch.Tensor
The output feature
Raises
------
DGLError
If there are 0-in-degree nodes in the input graph, it will raise DGLError
since no message will be passed to those nodes. This will cause invalid output.
The error can be ignored by setting ``allow_zero_in_degree`` parameter to ``True``.
Note
----
* Input shape: :math:`(N, *, \text{in_feats})` where * means any number of additional
dimensions, :math:`N` is the number of nodes.
* Output shape: :math:`(N, *, \text{out_feats})` where all but the last dimension are
the same shape as the input.
* Weight shape: :math:`(\text{in_feats}, \text{out_feats})`.
"""
with graph.local_scope():
if not self._allow_zero_in_degree:
if (graph.in_degrees() == 0).any():
raise DGLError(
"There are 0-in-degree nodes in the graph, "
"output for those nodes will be invalid. "
"This is harmful for some applications, "
"causing silent performance regression. "
"Adding self-loop on the input graph by "
"calling `g = dgl.add_self_loop(g)` will resolve "
"the issue. Setting ``allow_zero_in_degree`` "
"to be `True` when constructing this module will "
"suppress the check and let the code run."
)
# normalize to get smoothed representation
if edge_weight is None:
degs = graph.in_degrees().to(feat).clamp(min=1)
norm = th.pow(degs, -0.5)
norm = norm.to(feat.device).unsqueeze(1)
else:
edge_weight = EdgeWeightNorm("both")(graph, edge_weight)
if edge_weight is None:
feat = feat * norm
graph.ndata["h"] = feat
msg_func = fn.copy_u("h", "m")
if edge_weight is not None:
graph.edata["_edge_weight"] = edge_weight
msg_func = fn.u_mul_e("h", "_edge_weight", "m")
graph.update_all(msg_func, fn.sum("m", "h"))
feat = graph.ndata.pop("h")
if edge_weight is None:
feat = feat * norm
# scale
feat = feat * (1 - self.alpha)
# initial residual connection to the first layer
feat_0 = feat_0[: feat.size(0)] * self.alpha
feat_sum = feat + feat_0
if self._project_initial_features:
feat_proj_sum = feat_sum @ self.weight1
else:
feat_proj_sum = feat @ self.weight1 + feat_0 @ self.weight2
rst = (1 - self.beta) * feat_sum + self.beta * feat_proj_sum
if self._bias:
rst = rst + self.bias
if self._activation is not None:
rst = self._activation(rst)
return rst
def extra_repr(self):
"""Set the extra representation of the module,
which will come into effect when printing the model.
"""
summary = "in={_in_feats}"
summary += ", share_weight={_share_weights}, alpha={alpha}, beta={beta}"
if "self._bias" in self.__dict__:
summary += ", bias={bias}"
if "self._activation" in self.__dict__:
summary += ", activation={_activation}"
return summary.format(**self.__dict__)