RelGraphConv

class dgl.nn.mxnet.conv.RelGraphConv(in_feat, out_feat, num_rels, regularizer='basis', num_bases=None, bias=True, activation=None, self_loop=True, low_mem=False, dropout=0.0, layer_norm=False)

Bases: mxnet.gluon.block.Block

Relational graph convolution layer from Modeling Relational Data with Graph Convolutional Networks

It can be described as below:

\[h_i^{(l+1)} = \sigma(\sum_{r\in\mathcal{R}} \sum_{j\in\mathcal{N}^r(i)}\frac{1}{c_{i,r}}W_r^{(l)}h_j^{(l)}+W_0^{(l)}h_i^{(l)})\]

where \(\mathcal{N}^r(i)\) is the neighbor set of node \(i\) w.r.t. relation \(r\). \(c_{i,r}\) is the normalizer equal to \(|\mathcal{N}^r(i)|\). \(\sigma\) is an activation function. \(W_0\) is the self-loop weight.

The basis regularization decomposes \(W_r\) by:

\[W_r^{(l)} = \sum_{b=1}^B a_{rb}^{(l)}V_b^{(l)}\]

where \(B\) is the number of bases, \(V_b^{(l)}\) are linearly combined with coefficients \(a_{rb}^{(l)}\).

The block-diagonal-decomposition regularization decomposes \(W_r\) into \(B\) number of block diagonal matrices. We refer \(B\) as the number of bases.

The block regularization decomposes \(W_r\) by:

\[W_r^{(l)} = \oplus_{b=1}^B Q_{rb}^{(l)}\]

where \(B\) is the number of bases, \(Q_{rb}^{(l)}\) are block bases with shape \(R^{(d^{(l+1)}/B)*(d^{l}/B)}\).

Parameters

• in_feat (int) – Input feature size; i.e, the number of dimensions of \(h_j^{(l)}\).

• out_feat (int) – Output feature size; i.e., the number of dimensions of \(h_i^{(l+1)}\).

• num_rels (int) – Number of relations. .

• regularizer (str) – Which weight regularizer to use “basis” or “bdd”. “basis” is short for basis-diagonal-decomposition. “bdd” is short for block-diagonal-decomposition.

• num_bases (int, optional) – Number of bases. If is none, use number of relations. Default: None.

• 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.

• low_mem (bool, optional) – True to use low memory implementation of relation message passing function. Default: False. This option trades speed with memory consumption, and will slowdown the forward/backward. Turn it on when you encounter OOM problem during training or evaluation. Default: False.

• dropout (float, optional) – Dropout rate. Default: 0.0

• layer_norm (float, optional) – Add layer norm. Default: False

Examples

>>> import dgl
>>> import numpy as np
>>> import mxnet as mx
>>> from mxnet import gluon
>>> from dgl.nn import RelGraphConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = mx.nd.ones((6, 10))
>>> conv = RelGraphConv(10, 2, 3, regularizer='basis', num_bases=2)
>>> conv.initialize(ctx=mx.cpu(0))
>>> etype = mx.nd.array(np.array([0,1,2,0,1,2]).astype(np.int64))
>>> res = conv(g, feat, etype)
[[ 0.561324    0.33745846]
[ 0.61585337  0.09992217]
[ 0.561324    0.33745846]
[-0.01557937  0.01227859]
[ 0.61585337  0.09992217]
[ 0.056508   -0.00307822]]
<NDArray 6x2 @cpu(0)>

forward(g, x, etypes, norm=None)

Forward computation

Parameters

• g (DGLGraph) – The graph.

• feat (mx.ndarray.NDArray) –

  Input node features. Could be either

  • \((|V|, D)\) dense tensor

  • \((|V|,)\) int64 vector, representing the categorical values of each node. It then treat the input feature as an one-hot encoding feature.

• etypes (mx.ndarray.NDArray) – Edge type tensor. Shape: \((|E|,)\)

• norm (mx.ndarray.NDArray) – Optional edge normalizer tensor. Shape: \((|E|, 1)\).

Returns

New node features.

Return type

mx.ndarray.NDArray