wehub-resource-sync
181 lines
6.2 KiB
Python
181 lines
6.2 KiB
Python
"""MXNet Module for NNConv layer"""
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# pylint: disable= no-member, arguments-differ, invalid-name
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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 ....utils import expand_as_pair
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class NNConv(nn.Block):
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r"""Graph Convolution layer from `Neural Message Passing
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for Quantum Chemistry <https://arxiv.org/pdf/1704.01212.pdf>`__
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.. math::
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h_{i}^{l+1} = h_{i}^{l} + \mathrm{aggregate}\left(\left\{
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f_\Theta (e_{ij}) \cdot h_j^{l}, j\in \mathcal{N}(i) \right\}\right)
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where :math:`e_{ij}` is the edge feature, :math:`f_\Theta` is a function
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with learnable parameters.
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Parameters
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----------
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in_feats : int
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Input feature size; i.e, the number of dimensions of :math:`h_j^{(l)}`.
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NN 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 on 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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edge_func : callable activation function/layer
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Maps each edge feature to a vector of shape
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``(in_feats * out_feats)`` as weight to compute
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messages.
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Also is the :math:`f_\Theta` in the formula.
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aggregator_type : str
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Aggregator type to use (``sum``, ``mean`` or ``max``).
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residual : bool, optional
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If True, use residual connection. Default: ``False``.
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bias : bool, optional
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If True, adds a learnable bias to the output. Default: ``True``.
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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 NNConv
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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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>>> lin = gluon.nn.Dense(20)
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>>> lin.initialize(ctx=mx.cpu(0))
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>>> def edge_func(efeat):
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>>> return lin(efeat)
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>>> efeat = mx.nd.ones((12, 5))
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>>> conv = NNConv(10, 2, edge_func, 'mean')
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>>> conv.initialize(ctx=mx.cpu(0))
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>>> res = conv(g, feat, efeat)
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>>> res
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[[0.39946803 0.32098457]
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[0.39946803 0.32098457]
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[0.39946803 0.32098457]
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[0.39946803 0.32098457]
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[0.39946803 0.32098457]
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[0.39946803 0.32098457]]
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<NDArray 6x2 @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({('_N', '_E', '_N'):(u, v)})
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>>> u_feat = mx.nd.random.randn(2, 10)
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>>> v_feat = mx.nd.random.randn(4, 10)
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>>> conv = NNConv(10, 2, edge_func, 'mean')
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>>> conv.initialize(ctx=mx.cpu(0))
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>>> efeat = mx.nd.ones((5, 5))
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>>> res = conv(g, (u_feat, v_feat), efeat)
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>>> res
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[[ 0.24425688 0.3238042 ]
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[-0.11651017 -0.01738572]
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[ 0.06387337 0.15320925]
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[ 0.24425688 0.3238042 ]]
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<NDArray 4x2 @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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edge_func,
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aggregator_type,
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residual=False,
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bias=True,
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):
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super(NNConv, self).__init__()
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self._in_src_feats, self._in_dst_feats = expand_as_pair(in_feats)
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self._out_feats = out_feats
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if aggregator_type == "sum":
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self.reducer = fn.sum
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elif aggregator_type == "mean":
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self.reducer = fn.mean
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elif aggregator_type == "max":
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self.reducer = fn.max
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else:
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raise KeyError(
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"Aggregator type {} not recognized: ".format(aggregator_type)
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)
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self._aggre_type = aggregator_type
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with self.name_scope():
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self.edge_nn = edge_func
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if residual:
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if self._in_dst_feats != out_feats:
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self.res_fc = nn.Dense(
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out_feats,
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in_units=self._in_dst_feats,
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use_bias=False,
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weight_initializer=mx.init.Xavier(),
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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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if bias:
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self.bias = self.params.get(
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"bias", shape=(out_feats,), init=mx.init.Zero()
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)
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else:
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self.bias = None
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def forward(self, graph, feat, efeat):
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r"""Compute MPNN Graph Convolution 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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The input feature of shape :math:`(N, D_{in})` where :math:`N`
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is the number of nodes of the graph and :math:`D_{in}` is the
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input feature size.
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efeat : mxnet.NDArray
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The edge feature of shape :math:`(N, *)`, should fit the input
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shape requirement of ``edge_nn``.
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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, D_{out})` where :math:`D_{out}`
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is the output feature size.
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"""
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with graph.local_scope():
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feat_src, feat_dst = expand_as_pair(feat, graph)
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# (n, d_in, 1)
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graph.srcdata["h"] = feat_src.expand_dims(-1)
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# (n, d_in, d_out)
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graph.edata["w"] = self.edge_nn(efeat).reshape(
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-1, self._in_src_feats, self._out_feats
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)
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# (n, d_in, d_out)
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graph.update_all(
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fn.u_mul_e("h", "w", "m"), self.reducer("m", "neigh")
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)
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rst = graph.dstdata.pop("neigh").sum(axis=1) # (n, d_out)
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# residual connection
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if self.res_fc is not None:
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rst = rst + self.res_fc(feat_dst)
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# bias
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if self.bias is not None:
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rst = rst + self.bias.data(feat_dst.context)
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return rst
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