wehub-resource-sync
342 lines
14 KiB
Python
342 lines
14 KiB
Python
"""MXNet modules for graph attention networks(GAT)."""
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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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from mxnet.gluon import nn
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from mxnet.gluon.contrib.nn import Identity
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from .... import function as fn
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from ....base import DGLError
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from ....utils import expand_as_pair
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from ...functional import edge_softmax
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# pylint: enable=W0235
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class GATConv(nn.Block):
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r"""Graph attention layer from `Graph Attention Network
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<https://arxiv.org/pdf/1710.10903.pdf>`__
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.. math::
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h_i^{(l+1)} = \sum_{j\in \mathcal{N}(i)} \alpha_{i,j} W^{(l)} h_j^{(l)}
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where :math:`\alpha_{ij}` is the attention score bewteen node :math:`i` and
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node :math:`j`:
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.. math::
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\alpha_{ij}^{l} &= \mathrm{softmax_i} (e_{ij}^{l})
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e_{ij}^{l} &= \mathrm{LeakyReLU}\left(\vec{a}^T [W h_{i} \| W h_{j}]\right)
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Parameters
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----------
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in_feats : int, or pair of ints
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Input feature size; i.e, the number of dimensions of :math:`h_i^{(l)}`.
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GATConv can be applied on homogeneous graph and unidirectional
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`bipartite graph <https://docs.dgl.ai/generated/dgl.bipartite.html?highlight=bipartite>`__.
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If the layer is to be applied to a unidirectional bipartite graph, ``in_feats``
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specifies the input feature size on both the source and destination nodes. If
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a scalar is given, the source and destination node feature size would take the
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same value.
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out_feats : 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_heads : int
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Number of heads in Multi-Head Attention.
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feat_drop : float, optional
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Dropout rate on feature. Defaults: ``0``.
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attn_drop : float, optional
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Dropout rate on attention weight. Defaults: ``0``.
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negative_slope : float, optional
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LeakyReLU angle of negative slope. Defaults: ``0.2``.
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residual : bool, optional
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If True, use residual connection. Defaults: ``False``.
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activation : callable activation function/layer or None, optional.
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If not None, applies an activation function to the updated node features.
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Default: ``None``.
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allow_zero_in_degree : bool, optional
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If there are 0-in-degree nodes in the graph, output for those nodes will be invalid
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since no message will be passed to those nodes. This is harmful for some applications
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causing silent performance regression. This module will raise a DGLError if it detects
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0-in-degree nodes in input graph. By setting ``True``, it will suppress the check
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and let the users handle it by themselves. Defaults: ``False``.
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Note
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----
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Zero in-degree nodes will lead to invalid output value. This is because no message
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will be passed to those nodes, the aggregation function will be appied on empty input.
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A common practice to avoid this is to add a self-loop for each node in the graph if
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it is homogeneous, which can be achieved by:
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>>> g = ... # a DGLGraph
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>>> g = dgl.add_self_loop(g)
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Calling ``add_self_loop`` will not work for some graphs, for example, heterogeneous graph
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since the edge type can not be decided for self_loop edges. Set ``allow_zero_in_degree``
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to ``True`` for those cases to unblock the code and handle zero-in-degree nodes manually.
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A common practise to handle this is to filter out the nodes with zero-in-degree when use
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after conv.
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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 GATConv
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>>>
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>>> # Case 1: Homogeneous graph
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>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
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>>> g = dgl.add_self_loop(g)
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>>> feat = mx.nd.ones((6, 10))
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>>> gatconv = GATConv(10, 2, num_heads=3)
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>>> gatconv.initialize(ctx=mx.cpu(0))
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>>> res = gatconv(g, feat)
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>>> res
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[[[ 0.32368395 -0.10501936]
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[ 1.0839728 0.92690575]
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[-0.54581136 -0.84279203]]
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[[ 0.32368395 -0.10501936]
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[ 1.0839728 0.92690575]
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[-0.54581136 -0.84279203]]
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[[ 0.32368395 -0.10501936]
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[ 1.0839728 0.92690575]
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[-0.54581136 -0.84279203]]
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[[ 0.32368395 -0.10501937]
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[ 1.0839728 0.9269058 ]
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[-0.5458114 -0.8427921 ]]
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[[ 0.32368395 -0.10501936]
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[ 1.0839728 0.92690575]
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[-0.54581136 -0.84279203]]
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[[ 0.32368395 -0.10501936]
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[ 1.0839728 0.92690575]
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[-0.54581136 -0.84279203]]]
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<NDArray 6x3x2 @cpu(0)>
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>>> # Case 2: Unidirectional bipartite graph
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>>> u = [0, 1, 0, 0, 1]
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>>> v = [0, 1, 2, 3, 2]
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>>> g = dgl.heterograph({('A', 'r', 'B'): (u, v)})
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>>> u_feat = mx.nd.random.randn(2, 5)
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>>> v_feat = mx.nd.random.randn(4, 10)
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>>> gatconv = GATConv((5,10), 2, 3)
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>>> gatconv.initialize(ctx=mx.cpu(0))
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>>> res = gatconv(g, (u_feat, v_feat))
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>>> res
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[[[-1.01624 1.8138596 ]
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[ 1.2322129 -0.8410206 ]
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[-1.9325689 1.3824553 ]]
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[[ 0.9915016 -1.6564168 ]
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[-0.32610354 0.42505783]
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[ 1.5278397 -0.92114615]]
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[[-0.32592064 0.62067866]
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[ 0.6162219 -0.3405491 ]
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[-1.356375 0.9988818 ]]
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[[-1.01624 1.8138596 ]
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[ 1.2322129 -0.8410206 ]
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[-1.9325689 1.3824553 ]]]
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<NDArray 4x3x2 @cpu(0)>
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"""
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def __init__(
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self,
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in_feats,
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out_feats,
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num_heads,
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feat_drop=0.0,
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attn_drop=0.0,
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negative_slope=0.2,
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residual=False,
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activation=None,
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allow_zero_in_degree=False,
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):
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super(GATConv, self).__init__()
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self._num_heads = num_heads
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self._in_src_feats, self._in_dst_feats = expand_as_pair(in_feats)
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self._in_feats = in_feats
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self._out_feats = out_feats
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self._allow_zero_in_degree = allow_zero_in_degree
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with self.name_scope():
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if isinstance(in_feats, tuple):
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self.fc_src = nn.Dense(
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out_feats * num_heads,
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use_bias=False,
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weight_initializer=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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in_units=self._in_src_feats,
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)
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self.fc_dst = nn.Dense(
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out_feats * num_heads,
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use_bias=False,
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weight_initializer=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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in_units=self._in_dst_feats,
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)
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else:
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self.fc = nn.Dense(
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out_feats * num_heads,
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use_bias=False,
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weight_initializer=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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in_units=in_feats,
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)
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self.attn_l = self.params.get(
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"attn_l",
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shape=(1, num_heads, out_feats),
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init=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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)
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self.attn_r = self.params.get(
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"attn_r",
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shape=(1, num_heads, out_feats),
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init=mx.init.Xavier(magnitude=math.sqrt(2.0)),
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)
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self.feat_drop = nn.Dropout(feat_drop)
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self.attn_drop = nn.Dropout(attn_drop)
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self.leaky_relu = nn.LeakyReLU(negative_slope)
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if residual:
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if in_feats != out_feats:
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self.res_fc = nn.Dense(
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out_feats * num_heads,
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use_bias=False,
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weight_initializer=mx.init.Xavier(
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magnitude=math.sqrt(2.0)
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),
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in_units=in_feats,
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)
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else:
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self.res_fc = Identity()
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else:
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self.res_fc = None
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self.activation = activation
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def set_allow_zero_in_degree(self, set_value):
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r"""
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Description
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-----------
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Set allow_zero_in_degree flag.
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Parameters
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----------
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set_value : bool
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The value to be set to the flag.
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"""
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self._allow_zero_in_degree = set_value
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def forward(self, graph, feat, get_attention=False):
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r"""
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Description
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-----------
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Compute graph attention network layer.
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Parameters
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----------
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graph : DGLGraph
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The graph.
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feat : mxnet.NDArray or pair of mxnet.NDArray
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If a mxnet.NDArray is given, the input feature of shape :math:`(N, *, D_{in})` where
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:math:`D_{in}` is size of input feature, :math:`N` is the number of nodes.
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If a pair of mxnet.NDArray is given, the pair must contain two tensors of shape
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:math:`(N_{in}, *, D_{in_{src}})` and :math:`(N_{out}, *, D_{in_{dst}})`.
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get_attention : bool, optional
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Whether to return the attention values. Default to False.
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Returns
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-------
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mxnet.NDArray
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The output feature of shape :math:`(N, *, H, D_{out})` where :math:`H`
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is the number of heads, and :math:`D_{out}` is size of output feature.
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mxnet.NDArray, optional
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The attention values of shape :math:`(E, *, H, 1)`, where :math:`E` is the number of
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edges. This is returned only when :attr:`get_attention` is ``True``.
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Raises
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------
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DGLError
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If there are 0-in-degree nodes in the input graph, it will raise DGLError
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since no message will be passed to those nodes. This will cause invalid output.
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The error can be ignored by setting ``allow_zero_in_degree`` parameter to ``True``.
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"""
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with graph.local_scope():
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if not self._allow_zero_in_degree:
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if graph.in_degrees().min() == 0:
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raise DGLError(
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"There are 0-in-degree nodes in the graph, "
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"output for those nodes will be invalid. "
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"This is harmful for some applications, "
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"causing silent performance regression. "
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"Adding self-loop on the input graph by "
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"calling `g = dgl.add_self_loop(g)` will resolve "
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"the issue. Setting ``allow_zero_in_degree`` "
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"to be `True` when constructing this module will "
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"suppress the check and let the code run."
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)
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if isinstance(feat, tuple):
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src_prefix_shape = feat[0].shape[:-1]
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dst_prefix_shape = feat[1].shape[:-1]
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feat_dim = feat[0].shape[-1]
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h_src = self.feat_drop(feat[0])
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h_dst = self.feat_drop(feat[1])
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if not hasattr(self, "fc_src"):
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self.fc_src, self.fc_dst = self.fc, self.fc
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feat_src = self.fc_src(h_src.reshape(-1, feat_dim)).reshape(
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*src_prefix_shape, self._num_heads, self._out_feats
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)
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feat_dst = self.fc_dst(h_dst.reshape(-1, feat_dim)).reshape(
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*dst_prefix_shape, self._num_heads, self._out_feats
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)
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else:
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src_prefix_shape = dst_prefix_shape = feat.shape[:-1]
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feat_dim = feat[0].shape[-1]
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h_src = h_dst = self.feat_drop(feat)
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feat_src = feat_dst = self.fc(
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h_src.reshape(-1, feat_dim)
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).reshape(*src_prefix_shape, self._num_heads, self._out_feats)
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if graph.is_block:
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feat_dst = feat_src[: graph.number_of_dst_nodes()]
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h_dst = h_dst[: graph.number_of_dst_nodes()]
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dst_prefix_shape = (
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graph.number_of_dst_nodes(),
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) + dst_prefix_shape[1:]
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# NOTE: GAT paper uses "first concatenation then linear projection"
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# to compute attention scores, while ours is "first projection then
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# addition", the two approaches are mathematically equivalent:
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# We decompose the weight vector a mentioned in the paper into
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# [a_l || a_r], then
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# a^T [Wh_i || Wh_j] = a_l Wh_i + a_r Wh_j
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# Our implementation is much efficient because we do not need to
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# save [Wh_i || Wh_j] on edges, which is not memory-efficient. Plus,
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# addition could be optimized with DGL's built-in function u_add_v,
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# which further speeds up computation and saves memory footprint.
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el = (
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(feat_src * self.attn_l.data(feat_src.context))
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.sum(axis=-1)
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.expand_dims(-1)
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)
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er = (
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(feat_dst * self.attn_r.data(feat_src.context))
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.sum(axis=-1)
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.expand_dims(-1)
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)
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graph.srcdata.update({"ft": feat_src, "el": el})
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graph.dstdata.update({"er": er})
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# compute edge attention, el and er are a_l Wh_i and a_r Wh_j respectively.
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graph.apply_edges(fn.u_add_v("el", "er", "e"))
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e = self.leaky_relu(graph.edata.pop("e"))
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# compute softmax
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graph.edata["a"] = self.attn_drop(edge_softmax(graph, e))
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graph.update_all(fn.u_mul_e("ft", "a", "m"), fn.sum("m", "ft"))
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rst = graph.dstdata["ft"]
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# residual
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if self.res_fc is not None:
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resval = self.res_fc(h_dst.reshape(-1, feat_dim)).reshape(
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*dst_prefix_shape, -1, self._out_feats
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)
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rst = rst + resval
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# activation
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if self.activation:
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rst = self.activation(rst)
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if get_attention:
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return rst, graph.edata["a"]
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else:
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return rst
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