"""Torch Module for Graph Isomorphism Network layer"""
# pylint: disable= no-member, arguments-differ, invalid-name
import torch as th
from torch import nn
from .... import function as fn
from ....utils import expand_as_pair
[docs]class GINConv(nn.Module):
r"""
Description
-----------
Graph Isomorphism Network layer from paper `How Powerful are Graph
Neural Networks? <https://arxiv.org/pdf/1810.00826.pdf>`__.
.. math::
h_i^{(l+1)} = f_\Theta \left((1 + \epsilon) h_i^{l} +
\mathrm{aggregate}\left(\left\{h_j^{l}, j\in\mathcal{N}(i)
\right\}\right)\right)
If a weight tensor on each edge is provided, the weighted graph convolution is defined as:
.. math::
h_i^{(l+1)} = f_\Theta \left((1 + \epsilon) h_i^{l} +
\mathrm{aggregate}\left(\left\{e_{ji} h_j^{l}, j\in\mathcal{N}(i)
\right\}\right)\right)
where :math:`e_{ji}` is the weight on the edge from node :math:`j` to node :math:`i`.
Please make sure that `e_{ji}` is broadcastable with `h_j^{l}`.
Parameters
----------
apply_func : callable activation function/layer or None
If not None, apply this function to the updated node feature,
the :math:`f_\Theta` in the formula.
aggregator_type : str
Aggregator type to use (``sum``, ``max`` or ``mean``).
init_eps : float, optional
Initial :math:`\epsilon` value, default: ``0``.
learn_eps : bool, optional
If True, :math:`\epsilon` will be a learnable parameter. Default: ``False``.
Example
-------
>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import GINConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> lin = th.nn.Linear(10, 10)
>>> conv = GINConv(lin, 'max')
>>> res = conv(g, feat)
>>> res
tensor([[-0.4821, 0.0207, -0.7665, 0.5721, -0.4682, -0.2134, -0.5236, 1.2855,
0.8843, -0.8764],
[-0.4821, 0.0207, -0.7665, 0.5721, -0.4682, -0.2134, -0.5236, 1.2855,
0.8843, -0.8764],
[-0.4821, 0.0207, -0.7665, 0.5721, -0.4682, -0.2134, -0.5236, 1.2855,
0.8843, -0.8764],
[-0.4821, 0.0207, -0.7665, 0.5721, -0.4682, -0.2134, -0.5236, 1.2855,
0.8843, -0.8764],
[-0.4821, 0.0207, -0.7665, 0.5721, -0.4682, -0.2134, -0.5236, 1.2855,
0.8843, -0.8764],
[-0.1804, 0.0758, -0.5159, 0.3569, -0.1408, -0.1395, -0.2387, 0.7773,
0.5266, -0.4465]], grad_fn=<AddmmBackward>)
"""
def __init__(self,
apply_func,
aggregator_type,
init_eps=0,
learn_eps=False):
super(GINConv, self).__init__()
self.apply_func = apply_func
self._aggregator_type = aggregator_type
if aggregator_type == 'sum':
self._reducer = fn.sum
elif aggregator_type == 'max':
self._reducer = fn.max
elif aggregator_type == 'mean':
self._reducer = fn.mean
else:
raise KeyError('Aggregator type {} not recognized.'.format(aggregator_type))
# to specify whether eps is trainable or not.
if learn_eps:
self.eps = th.nn.Parameter(th.FloatTensor([init_eps]))
else:
self.register_buffer('eps', th.FloatTensor([init_eps]))
[docs] def forward(self, graph, feat, edge_weight=None):
r"""
Description
-----------
Compute Graph Isomorphism Network layer.
Parameters
----------
graph : DGLGraph
The graph.
feat : torch.Tensor or pair of torch.Tensor
If a torch.Tensor is given, the input feature of shape :math:`(N, D_{in})` where
:math:`D_{in}` is size of input feature, :math:`N` is the number of nodes.
If a pair of torch.Tensor is given, the pair must contain two tensors of shape
:math:`(N_{in}, D_{in})` and :math:`(N_{out}, D_{in})`.
If ``apply_func`` is not None, :math:`D_{in}` should
fit the input dimensionality requirement of ``apply_func``.
edge_weight : torch.Tensor, optional
Optional tensor on the edge. If given, the convolution will weight
with regard to the message.
Returns
-------
torch.Tensor
The output feature of shape :math:`(N, D_{out})` where
:math:`D_{out}` is the output dimensionality of ``apply_func``.
If ``apply_func`` is None, :math:`D_{out}` should be the same
as input dimensionality.
"""
with graph.local_scope():
aggregate_fn = fn.copy_src('h', 'm')
if edge_weight is not None:
assert edge_weight.shape[0] == graph.number_of_edges()
graph.edata['_edge_weight'] = edge_weight
aggregate_fn = fn.u_mul_e('h', '_edge_weight', 'm')
feat_src, feat_dst = expand_as_pair(feat, graph)
graph.srcdata['h'] = feat_src
graph.update_all(aggregate_fn, self._reducer('m', 'neigh'))
rst = (1 + self.eps) * feat_dst + graph.dstdata['neigh']
if self.apply_func is not None:
rst = self.apply_func(rst)
return rst