dmlc--dgl
Minjie Wang
8a07ab7737
* reorg * change titles * rm some stale API doc; minor fix * fix docs * add warning * rm new-tutorial run in ci * lint
110 行
3.6 KiB
Python
110 行
3.6 KiB
Python
"""dgl edge_softmax operator module."""
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from ..backend import edge_softmax as edge_softmax_internal
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from ..backend import astype
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from ..base import ALL, is_all
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__all__ = ['edge_softmax']
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def edge_softmax(graph, logits, eids=ALL, norm_by='dst'):
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r"""Compute softmax over weights of incoming edges for every node.
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For a node :math:`i`, edge softmax is an operation that computes
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.. math::
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a_{ij} = \frac{\exp(z_{ij})}{\sum_{j\in\mathcal{N}(i)}\exp(z_{ij})}
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where :math:`z_{ij}` is a signal of edge :math:`j\rightarrow i`, also
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called logits in the context of softmax. :math:`\mathcal{N}(i)` is
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the set of nodes that have an edge to :math:`i`.
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By default edge softmax is normalized by destination nodes(i.e. :math:`ij`
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are incoming edges of `i` in the formula above). We also support edge
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softmax normalized by source nodes(i.e. :math:`ij` are outgoing edges of
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`i` in the formula). The former case corresponds to softmax in GAT and
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Transformer, and the latter case corresponds to softmax in Capsule network.
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An example of using edge softmax is in
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`Graph Attention Network <https://arxiv.org/pdf/1710.10903.pdf>`__ where
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the attention weights are computed with this operation.
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Other non-GNN examples using this are
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`Transformer <https://papers.nips.cc/paper/7181-attention-is-all-you-need.pdf>`__,
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`Capsule <https://arxiv.org/pdf/1710.09829.pdf>`__, etc.
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Parameters
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----------
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graph : DGLGraph
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The graph over which edge softmax will be performed.
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logits : torch.Tensor
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The input edge feature.
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eids : torch.Tensor or ALL, optional
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The IDs of the edges to apply edge softmax. If ALL, it will apply edge
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softmax to all edges in the graph. Default: ALL.
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norm_by : str, could be `src` or `dst`
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Normalized by source nodes or destination nodes. Default: `dst`.
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Returns
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-------
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Tensor
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Softmax value.
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Notes
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-----
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* Input shape: :math:`(E, *, 1)` where * means any number of
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additional dimensions, :math:`E` equals the length of eids.
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If the `eids` is ALL, :math:`E` equals the number of edges in
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the graph.
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* Return shape: :math:`(E, *, 1)`
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Examples
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--------
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The following example uses PyTorch backend.
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>>> from dgl.nn.functional import edge_softmax
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>>> import dgl
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>>> import torch as th
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Create a :code:`DGLGraph` object and initialize its edge features.
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>>> g = dgl.graph((th.tensor([0, 0, 0, 1, 1, 2]), th.tensor([0, 1, 2, 1, 2, 2])))
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>>> edata = th.ones(6, 1).float()
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>>> edata
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tensor([[1.],
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[1.],
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[1.],
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[1.],
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[1.],
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[1.]])
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Apply edge softmax over g:
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>>> edge_softmax(g, edata)
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tensor([[1.0000],
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[0.5000],
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[0.3333],
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[0.5000],
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[0.3333],
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[0.3333]])
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Apply edge softmax over g normalized by source nodes:
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>>> edge_softmax(g, edata, norm_by='src')
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tensor([[0.3333],
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[0.3333],
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[0.3333],
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[0.5000],
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[0.5000],
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[1.0000]])
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Apply edge softmax to first 4 edges of g:
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>>> edge_softmax(g, edata[:4], th.Tensor([0,1,2,3]))
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tensor([[1.0000],
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[0.5000],
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[1.0000],
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[0.5000]])
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"""
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if not is_all(eids):
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eids = astype(eids, graph.idtype)
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return edge_softmax_internal(graph._graph, logits,
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eids=eids, norm_by=norm_by)
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