wehub-resource-sync
288 lines
9.8 KiB
Python
288 lines
9.8 KiB
Python
"""MXNet module for RelGraphConv"""
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# pylint: disable= no-member, arguments-differ, invalid-name
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import math
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import mxnet as mx
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import numpy as np
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from mxnet import gluon, nd
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from mxnet.gluon import nn
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from .... import function as fn
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from .. import utils
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class RelGraphConv(gluon.Block):
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r"""Relational graph convolution layer from `Modeling Relational Data with Graph
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Convolutional Networks <https://arxiv.org/abs/1703.06103>`__
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It can be described as below:
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.. math::
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h_i^{(l+1)} = \sigma(\sum_{r\in\mathcal{R}}
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\sum_{j\in\mathcal{N}^r(i)}\frac{1}{c_{i,r}}W_r^{(l)}h_j^{(l)}+W_0^{(l)}h_i^{(l)})
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where :math:`\mathcal{N}^r(i)` is the neighbor set of node :math:`i` w.r.t. relation
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:math:`r`. :math:`c_{i,r}` is the normalizer equal
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to :math:`|\mathcal{N}^r(i)|`. :math:`\sigma` is an activation function. :math:`W_0`
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is the self-loop weight.
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The basis regularization decomposes :math:`W_r` by:
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.. math::
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W_r^{(l)} = \sum_{b=1}^B a_{rb}^{(l)}V_b^{(l)}
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where :math:`B` is the number of bases, :math:`V_b^{(l)}` are linearly combined
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with coefficients :math:`a_{rb}^{(l)}`.
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The block-diagonal-decomposition regularization decomposes :math:`W_r` into :math:`B`
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number of block diagonal matrices. We refer :math:`B` as the number of bases.
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The block regularization decomposes :math:`W_r` by:
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.. math::
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W_r^{(l)} = \oplus_{b=1}^B Q_{rb}^{(l)}
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where :math:`B` is the number of bases, :math:`Q_{rb}^{(l)}` are block
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bases with shape :math:`R^{(d^{(l+1)}/B)*(d^{l}/B)}`.
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Parameters
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----------
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in_feat : int
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Input feature size; i.e, the number of dimensions of :math:`h_j^{(l)}`.
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out_feat : int
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Output feature size; i.e., the number of dimensions of :math:`h_i^{(l+1)}`.
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num_rels : int
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Number of relations. .
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regularizer : str
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Which weight regularizer to use "basis" or "bdd".
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"basis" is short for basis-diagonal-decomposition.
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"bdd" is short for block-diagonal-decomposition.
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num_bases : int, optional
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Number of bases. If is none, use number of relations. Default: ``None``.
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bias : bool, optional
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True if bias is added. Default: ``True``.
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activation : callable, optional
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Activation function. Default: ``None``.
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self_loop : bool, optional
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True to include self loop message. Default: ``True``.
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low_mem : bool, optional
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True to use low memory implementation of relation message passing function. Default: False.
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This option trades speed with memory consumption, and will slowdown the forward/backward.
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Turn it on when you encounter OOM problem during training or evaluation. Default: ``False``.
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dropout : float, optional
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Dropout rate. Default: ``0.0``
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layer_norm: float, optional
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Add layer norm. Default: ``False``
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Examples
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--------
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>>> import dgl
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>>> import numpy as np
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>>> import mxnet as mx
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>>> from mxnet import gluon
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>>> from dgl.nn import RelGraphConv
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>>>
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>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
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>>> feat = mx.nd.ones((6, 10))
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>>> conv = RelGraphConv(10, 2, 3, regularizer='basis', num_bases=2)
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>>> conv.initialize(ctx=mx.cpu(0))
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>>> etype = mx.nd.array(np.array([0,1,2,0,1,2]).astype(np.int64))
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>>> res = conv(g, feat, etype)
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[[ 0.561324 0.33745846]
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[ 0.61585337 0.09992217]
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[ 0.561324 0.33745846]
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[-0.01557937 0.01227859]
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[ 0.61585337 0.09992217]
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[ 0.056508 -0.00307822]]
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<NDArray 6x2 @cpu(0)>
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"""
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def __init__(
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self,
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in_feat,
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out_feat,
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num_rels,
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regularizer="basis",
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num_bases=None,
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bias=True,
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activation=None,
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self_loop=True,
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low_mem=False,
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dropout=0.0,
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layer_norm=False,
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):
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super(RelGraphConv, self).__init__()
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self.in_feat = in_feat
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self.out_feat = out_feat
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self.num_rels = num_rels
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self.regularizer = regularizer
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self.num_bases = num_bases
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if (
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self.num_bases is None
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or self.num_bases > self.num_rels
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or self.num_bases < 0
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):
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self.num_bases = self.num_rels
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self.bias = bias
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self.activation = activation
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self.self_loop = self_loop
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assert (
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low_mem is False
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), "MXNet currently does not support low-memory implementation."
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assert (
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layer_norm is False
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), "MXNet currently does not support layer norm."
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if regularizer == "basis":
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# add basis weights
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self.weight = self.params.get(
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"weight",
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shape=(self.num_bases, self.in_feat, self.out_feat),
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init=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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)
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if self.num_bases < self.num_rels:
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# linear combination coefficients
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self.w_comp = self.params.get(
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"w_comp",
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shape=(self.num_rels, self.num_bases),
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init=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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)
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# message func
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self.message_func = self.basis_message_func
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elif regularizer == "bdd":
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if in_feat % num_bases != 0 or out_feat % num_bases != 0:
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raise ValueError(
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"Feature size must be a multiplier of num_bases."
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)
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# add block diagonal weights
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self.submat_in = in_feat // self.num_bases
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self.submat_out = out_feat // self.num_bases
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# assuming in_feat and out_feat are both divisible by num_bases
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self.weight = self.params.get(
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"weight",
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shape=(
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self.num_rels,
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self.num_bases * self.submat_in * self.submat_out,
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),
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init=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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)
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# message func
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self.message_func = self.bdd_message_func
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else:
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raise ValueError("Regularizer must be either 'basis' or 'bdd'")
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# bias
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if self.bias:
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self.h_bias = self.params.get(
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"bias", shape=(out_feat,), init=mx.init.Zero()
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)
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# weight for self loop
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if self.self_loop:
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self.loop_weight = self.params.get(
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"W_0",
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shape=(in_feat, out_feat),
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init=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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)
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self.dropout = nn.Dropout(dropout)
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def basis_message_func(self, edges):
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"""Message function for basis regularizer"""
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ctx = edges.src["h"].context
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if self.num_bases < self.num_rels:
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# generate all weights from bases
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weight = self.weight.data(ctx).reshape(
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self.num_bases, self.in_feat * self.out_feat
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)
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weight = nd.dot(self.w_comp.data(ctx), weight).reshape(
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self.num_rels, self.in_feat, self.out_feat
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)
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else:
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weight = self.weight.data(ctx)
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msg = utils.bmm_maybe_select(edges.src["h"], weight, edges.data["type"])
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if "norm" in edges.data:
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msg = msg * edges.data["norm"]
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return {"msg": msg}
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def bdd_message_func(self, edges):
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"""Message function for block-diagonal-decomposition regularizer"""
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ctx = edges.src["h"].context
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if (
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edges.src["h"].dtype in (np.int32, np.int64)
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and len(edges.src["h"].shape) == 1
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):
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raise TypeError(
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"Block decomposition does not allow integer ID feature."
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)
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weight = self.weight.data(ctx)[edges.data["type"], :].reshape(
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-1, self.submat_in, self.submat_out
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)
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node = edges.src["h"].reshape(-1, 1, self.submat_in)
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msg = nd.batch_dot(node, weight).reshape(-1, self.out_feat)
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if "norm" in edges.data:
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msg = msg * edges.data["norm"]
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return {"msg": msg}
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def forward(self, g, x, etypes, norm=None):
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"""
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Description
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-----------
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Forward computation
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Parameters
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----------
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g : DGLGraph
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The graph.
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feat : mx.ndarray.NDArray
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Input node features. Could be either
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* :math:`(|V|, D)` dense tensor
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* :math:`(|V|,)` int64 vector, representing the categorical values of each
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node. It then treat the input feature as an one-hot encoding feature.
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etypes : mx.ndarray.NDArray
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Edge type tensor. Shape: :math:`(|E|,)`
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norm : mx.ndarray.NDArray
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Optional edge normalizer tensor. Shape: :math:`(|E|, 1)`.
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Returns
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-------
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mx.ndarray.NDArray
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New node features.
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"""
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assert g.is_homogeneous, (
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"not a homogeneous graph; convert it with to_homogeneous "
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"and pass in the edge type as argument"
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)
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with g.local_scope():
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g.ndata["h"] = x
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g.edata["type"] = etypes
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if norm is not None:
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g.edata["norm"] = norm
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if self.self_loop:
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loop_message = utils.matmul_maybe_select(
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x, self.loop_weight.data(x.context)
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)
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# message passing
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g.update_all(self.message_func, fn.sum(msg="msg", out="h"))
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# apply bias and activation
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node_repr = g.ndata["h"]
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if self.bias:
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node_repr = node_repr + self.h_bias.data(x.context)
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if self.self_loop:
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node_repr = node_repr + loop_message
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if self.activation:
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node_repr = self.activation(node_repr)
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node_repr = self.dropout(node_repr)
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return node_repr
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