# DotGatConv¶

class dgl.nn.pytorch.conv.DotGatConv(in_feats, out_feats, num_heads, allow_zero_in_degree=False)[source]

Bases: torch.nn.modules.module.Module

Apply dot product version of self attention in Graph Attention Network

$h_i^{(l+1)} = \sum_{j\in \mathcal{N}(i)} \alpha_{i, j} h_j^{(l)}$

where $$\alpha_{ij}$$ is the attention score bewteen node $$i$$ and node $$j$$:

\begin{align}\begin{aligned}\alpha_{i, j} &= \mathrm{softmax_i}(e_{ij}^{l})\\e_{ij}^{l} &= ({W_i^{(l)} h_i^{(l)}})^T \cdot {W_j^{(l)} h_j^{(l)}}\end{aligned}\end{align}

where $$W_i$$ and $$W_j$$ transform node $$i$$’s and node $$j$$’s features into the same dimension, so that when compute note features’ similarity, it can use dot-product.

Parameters
• in_feats (int, or pair of ints) – Input feature size; i.e, the number of dimensions of $$h_i^{(l)}$$. DotGatConv can be applied on homogeneous graph and unidirectional bipartite graph. If the layer is to be applied to a unidirectional bipartite graph, in_feats specifies the input feature size on both the source and destination nodes. If a scalar is given, the source and destination node feature size would take the same value.

• out_feats (int) – Output feature size; i.e, the number of dimensions of $$h_i^{(l+1)}$$.

• allow_zero_in_degree (bool, optional) – If there are 0-in-degree nodes in the graph, output for those nodes will be invalid since no message will be passed to those nodes. This is harmful for some applications causing silent performance regression. This module will raise a DGLError if it detects 0-in-degree nodes in input graph. By setting True, it will suppress the check and let the users handle it by themselves. Default: False.

Note

Zero in-degree nodes will lead to invalid output value. This is because no message will be passed to those nodes, the aggregation function will be appied on empty input. A common practice to avoid this is to add a self-loop for each node in the graph if it is homogeneous, which can be achieved by:

>>> g = ... # a DGLGraph


Calling add_self_loop will not work for some graphs, for example, heterogeneous graph since the edge type can not be decided for self_loop edges. Set allow_zero_in_degree to True for those cases to unblock the code and handle zero-in-degree nodes manually. A common practise to handle this is to filter out the nodes with zero-in-degree when use after conv.

Examples

>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import DotGatConv

>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> dotgatconv = DotGatConv(10, 2, num_heads=3)
>>> res = dotgatconv(g, feat)
>>> res
tensor([[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],
[ 1.0390, -1.1479]],
[[ 3.4570,  1.8634],
[ 1.3805, -0.0762],

>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.bipartite((u, v))
>>> u_feat = th.tensor(np.random.rand(2, 5).astype(np.float32))
>>> v_feat = th.tensor(np.random.rand(4, 10).astype(np.float32))
>>> dotgatconv = DotGatConv((5,10), 2, 3)
>>> res = dotgatconv(g, (u_feat, v_feat))
>>> res
tensor([[[-0.6066,  1.0268],
[-0.5945, -0.4801],
[ 0.1594,  0.3825]],
[[ 0.0268,  1.0783],
[ 0.5041, -1.3025],
[ 0.6568,  0.7048]],
[[-0.2688,  1.0543],
[-0.0315, -0.9016],
[ 0.3943,  0.5347]],
[[-0.6066,  1.0268],
[-0.5945, -0.4801],

forward(graph, feat, get_attention=False)[source]

Apply dot product version of self attention in GCN.

Parameters
• graph (DGLGraph or bi_partities graph) – The graph

• feat (torch.Tensor or pair of torch.Tensor) – If a torch.Tensor is given, the input feature of shape $$(N, D_{in})$$ where $$D_{in}$$ is size of input feature, $$N$$ is the number of nodes. If a pair of torch.Tensor is given, the pair must contain two tensors of shape $$(N_{in}, D_{in_{src}})$$ and $$(N_{out}, D_{in_{dst}})$$.

• get_attention (bool, optional) – Whether to return the attention values. Default to False.

Returns

• torch.Tensor – The output feature of shape $$(N, D_{out})$$ where $$D_{out}$$ is size of output feature.

• torch.Tensor, optional – The attention values of shape $$(E, 1)$$, where $$E$$ is the number of edges. This is returned only when get_attention is True.

Raises

DGLError – If there are 0-in-degree nodes in the input graph, it will raise DGLError since no message will be passed to those nodes. This will cause invalid output. The error can be ignored by setting allow_zero_in_degree parameter to True.