"""Torch Module for Relational graph convolution layer"""
# pylint: disable= no-member, arguments-differ, invalid-name
import torch as th
from torch import nn
from .... import function as fn
from ..linear import TypedLinear
[docs]class RelGraphConv(nn.Module):
r"""Relational graph convolution layer from `Modeling Relational Data with Graph
Convolutional Networks <https://arxiv.org/abs/1703.06103>`__
It can be described in as below:
.. math::
h_i^{(l+1)} = \sigma(\sum_{r\in\mathcal{R}}
\sum_{j\in\mathcal{N}^r(i)}e_{j,i}W_r^{(l)}h_j^{(l)}+W_0^{(l)}h_i^{(l)})
where :math:`\mathcal{N}^r(i)` is the neighbor set of node :math:`i` w.r.t. relation
:math:`r`. :math:`e_{j,i}` is the normalizer. :math:`\sigma` is an activation
function. :math:`W_0` is the self-loop weight.
The basis regularization decomposes :math:`W_r` by:
.. math::
W_r^{(l)} = \sum_{b=1}^B a_{rb}^{(l)}V_b^{(l)}
where :math:`B` is the number of bases, :math:`V_b^{(l)}` are linearly combined
with coefficients :math:`a_{rb}^{(l)}`.
The block-diagonal-decomposition regularization decomposes :math:`W_r` into :math:`B`
number of block diagonal matrices. We refer :math:`B` as the number of bases.
The block regularization decomposes :math:`W_r` by:
.. math::
W_r^{(l)} = \oplus_{b=1}^B Q_{rb}^{(l)}
where :math:`B` is the number of bases, :math:`Q_{rb}^{(l)}` are block
bases with shape :math:`R^{(d^{(l+1)}/B)*(d^{l}/B)}`.
Parameters
----------
in_feat : int
Input feature size; i.e, the number of dimensions of :math:`h_j^{(l)}`.
out_feat : int
Output feature size; i.e., the number of dimensions of :math:`h_i^{(l+1)}`.
num_rels : int
Number of relations.
regularizer : str, optional
Which weight regularizer to use ("basis", "bdd" or ``None``):
- "basis" is for basis-decomposition.
- "bdd" is for block-diagonal-decomposition.
- ``None`` applies no regularization.
Default: ``None``.
num_bases : int, optional
Number of bases. It comes into effect when a regularizer is applied.
If ``None``, it uses number of relations (``num_rels``). Default: ``None``.
Note that ``in_feat`` and ``out_feat`` must be divisible by ``num_bases``
when applying "bdd" regularizer.
bias : bool, optional
True if bias is added. Default: ``True``.
activation : callable, optional
Activation function. Default: ``None``.
self_loop : bool, optional
True to include self loop message. Default: ``True``.
dropout : float, optional
Dropout rate. Default: ``0.0``
layer_norm: bool, optional
True to add layer norm. Default: ``False``
Examples
--------
>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import RelGraphConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = RelGraphConv(10, 2, 3, regularizer='basis', num_bases=2)
>>> etype = th.tensor([0,1,2,0,1,2])
>>> res = conv(g, feat, etype)
>>> res
tensor([[ 0.3996, -2.3303],
[-0.4323, -0.1440],
[ 0.3996, -2.3303],
[ 2.1046, -2.8654],
[-0.4323, -0.1440],
[-0.1309, -1.0000]], grad_fn=<AddBackward0>)
"""
def __init__(self,
in_feat,
out_feat,
num_rels,
regularizer=None,
num_bases=None,
bias=True,
activation=None,
self_loop=True,
dropout=0.0,
layer_norm=False):
super().__init__()
if regularizer is not None and num_bases is None:
num_bases = num_rels
self.linear_r = TypedLinear(in_feat, out_feat, num_rels, regularizer, num_bases)
self.bias = bias
self.activation = activation
self.self_loop = self_loop
self.layer_norm = layer_norm
# bias
if self.bias:
self.h_bias = nn.Parameter(th.Tensor(out_feat))
nn.init.zeros_(self.h_bias)
# TODO(minjie): consider remove those options in the future to make
# the module only about graph convolution.
# layer norm
if self.layer_norm:
self.layer_norm_weight = nn.LayerNorm(out_feat, elementwise_affine=True)
# weight for self loop
if self.self_loop:
self.loop_weight = nn.Parameter(th.Tensor(in_feat, out_feat))
nn.init.xavier_uniform_(self.loop_weight, gain=nn.init.calculate_gain('relu'))
self.dropout = nn.Dropout(dropout)
def message(self, edges):
"""Message function."""
m = self.linear_r(edges.src['h'], edges.data['etype'], self.presorted)
if 'norm' in edges.data:
m = m * edges.data['norm']
return {'m' : m}
[docs] def forward(self, g, feat, etypes, norm=None, *, presorted=False):
"""Forward computation.
Parameters
----------
g : DGLGraph
The graph.
feat : torch.Tensor
A 2D tensor of node features. Shape: :math:`(|V|, D_{in})`.
etypes : torch.Tensor or list[int]
An 1D integer tensor of edge types. Shape: :math:`(|E|,)`.
norm : torch.Tensor, optional
An 1D tensor of edge norm value. Shape: :math:`(|E|,)`.
presorted : bool, optional
Whether the edges of the input graph have been sorted by their types.
Forward on pre-sorted graph may be faster. Graphs created
by :func:`~dgl.to_homogeneous` automatically satisfy the condition.
Also see :func:`~dgl.reorder_graph` for sorting edges manually.
Returns
-------
torch.Tensor
New node features. Shape: :math:`(|V|, D_{out})`.
"""
self.presorted = presorted
with g.local_scope():
g.srcdata['h'] = feat
if norm is not None:
g.edata['norm'] = norm
g.edata['etype'] = etypes
# message passing
g.update_all(self.message, fn.sum('m', 'h'))
# apply bias and activation
h = g.dstdata['h']
if self.layer_norm:
h = self.layer_norm_weight(h)
if self.bias:
h = h + self.h_bias
if self.self_loop:
h = h + feat[:g.num_dst_nodes()] @ self.loop_weight
if self.activation:
h = self.activation(h)
h = self.dropout(h)
return h