# Source code for dgl.nn.mxnet.conv.relgraphconv

"""MXNet module for RelGraphConv"""
# pylint: disable= no-member, arguments-differ, invalid-name
import math
import numpy as np

import mxnet as mx
from mxnet import gluon, nd
from mxnet.gluon import nn
from .... import function as fn
from .. import utils

[docs]class RelGraphConv(gluon.Block): r"""Relational graph convolution layer from Modeling Relational Data with Graph Convolutional Networks <https://arxiv.org/abs/1703.06103>__ It can be described as below: .. math:: 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 :math:\mathcal{N}^r(i) is the neighbor set of node :math:i w.r.t. relation :math:r. :math:c_{i,r} is the normalizer equal to :math:|\mathcal{N}^r(i)|. :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 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)> """ def __init__(self, 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): super(RelGraphConv, self).__init__() self.in_feat = in_feat self.out_feat = out_feat self.num_rels = num_rels self.regularizer = regularizer self.num_bases = num_bases if self.num_bases is None or self.num_bases > self.num_rels or self.num_bases < 0: self.num_bases = self.num_rels self.bias = bias self.activation = activation self.self_loop = self_loop assert low_mem is False, 'MXNet currently does not support low-memory implementation.' assert layer_norm is False, 'MXNet currently does not support layer norm.' if regularizer == "basis": # add basis weights self.weight = self.params.get( 'weight', shape=(self.num_bases, self.in_feat, self.out_feat), init=mx.init.Xavier(magnitude=math.sqrt(2.0))) if self.num_bases < self.num_rels: # linear combination coefficients self.w_comp = self.params.get( 'w_comp', shape=(self.num_rels, self.num_bases), init=mx.init.Xavier(magnitude=math.sqrt(2.0))) # message func self.message_func = self.basis_message_func elif regularizer == "bdd": if in_feat % num_bases != 0 or out_feat % num_bases != 0: raise ValueError('Feature size must be a multiplier of num_bases.') # add block diagonal weights self.submat_in = in_feat // self.num_bases self.submat_out = out_feat // self.num_bases # assuming in_feat and out_feat are both divisible by num_bases self.weight = self.params.get( 'weight', shape=(self.num_rels, self.num_bases * self.submat_in * self.submat_out), init=mx.init.Xavier(magnitude=math.sqrt(2.0))) # message func self.message_func = self.bdd_message_func else: raise ValueError("Regularizer must be either 'basis' or 'bdd'") # bias if self.bias: self.h_bias = self.params.get('bias', shape=(out_feat,), init=mx.init.Zero()) # weight for self loop if self.self_loop: self.loop_weight = self.params.get( 'W_0', shape=(in_feat, out_feat), init=mx.init.Xavier(magnitude=math.sqrt(2.0))) self.dropout = nn.Dropout(dropout) def basis_message_func(self, edges): """Message function for basis regularizer""" ctx = edges.src['h'].context if self.num_bases < self.num_rels: # generate all weights from bases weight = self.weight.data(ctx).reshape( self.num_bases, self.in_feat * self.out_feat) weight = nd.dot(self.w_comp.data(ctx), weight).reshape( self.num_rels, self.in_feat, self.out_feat) else: weight = self.weight.data(ctx) msg = utils.bmm_maybe_select(edges.src['h'], weight, edges.data['type']) if 'norm' in edges.data: msg = msg * edges.data['norm'] return {'msg': msg} def bdd_message_func(self, edges): """Message function for block-diagonal-decomposition regularizer""" ctx = edges.src['h'].context if edges.src['h'].dtype in (np.int32, np.int64) and len(edges.src['h'].shape) == 1: raise TypeError('Block decomposition does not allow integer ID feature.') weight = self.weight.data(ctx)[edges.data['type'], :].reshape( -1, self.submat_in, self.submat_out) node = edges.src['h'].reshape(-1, 1, self.submat_in) msg = nd.batch_dot(node, weight).reshape(-1, self.out_feat) if 'norm' in edges.data: msg = msg * edges.data['norm'] return {'msg': msg}
[docs] def forward(self, g, x, etypes, norm=None): """ Description ----------- Forward computation Parameters ---------- g : DGLGraph The graph. feat : mx.ndarray.NDArray Input node features. Could be either * :math:(|V|, D) dense tensor * :math:(|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: :math:(|E|,) norm : mx.ndarray.NDArray Optional edge normalizer tensor. Shape: :math:(|E|, 1). Returns ------- mx.ndarray.NDArray New node features. """ assert g.is_homogeneous, \ "not a homogeneous graph; convert it with to_homogeneous " \ "and pass in the edge type as argument" with g.local_scope(): g.ndata['h'] = x g.edata['type'] = etypes if norm is not None: g.edata['norm'] = norm if self.self_loop: loop_message = utils.matmul_maybe_select(x, self.loop_weight.data(x.context)) # message passing g.update_all(self.message_func, fn.sum(msg='msg', out='h')) # apply bias and activation node_repr = g.ndata['h'] if self.bias: node_repr = node_repr + self.h_bias.data(x.context) if self.self_loop: node_repr = node_repr + loop_message if self.activation: node_repr = self.activation(node_repr) node_repr = self.dropout(node_repr) return node_repr