gammagl.layers.conv.HardGATConv

class HardGATConv(in_channels, out_channels, k=8, heads=1, concat=True, negative_slope=0.2, dropout_rate=0.0, add_bias=True)[source]

The graph hard attentional operator from the “Graph Representation Learning via Hard and Channel-Wise Attention Networks” paper

\[\begin{split}\begin{aligned} &y=\frac{\left|X^T p\right|}{\|p\|}\\ &\text { for } i=1,2, \cdots, N \text { do }\\ &\quad\quad id x_i=\text { Ranking }_k\left(A_{: i} \circ y\right) \quad \in \mathbb{R}^k\\ &\quad\quad\hat{X}_i=X\left(:, i d x_i\right) \quad \in \mathbb{R}^{d \times k}\\ &\quad\quad\tilde{y}_i=\operatorname{sigmoid}\left(y\left(i d x_i\right)\right) \quad \in \mathbb{R}^k\\ &\quad\quad\tilde{X}_i=\hat{X}_i \operatorname{diag}\left(\tilde{y}_i\right) \quad \in \mathbb{R}^{d \times k}\\ &\quad\quad z_i=\operatorname{attn}\left(x_i, \tilde{X}_i, \tilde{X}_i\right) \quad \in \mathbb{R}^d\\ &Z=\left[z_1, z_2, \ldots, z_N\right]\in \mathbb{R}^{d \times N} \end{aligned}\end{split}\]

where the attn operation is the same as GAT, and the process is as follows.

\[\mathbf{x}^{\prime}_i = \alpha_{i,i}\mathbf{\Theta}\mathbf{x}_{i} + \sum_{j \in \mathcal{N}(i)} \alpha_{i,j}\mathbf{\Theta}\mathbf{x}_{j},\]

where the attention coefficients \(\alpha_{i,j}\) are computed as

\[\alpha_{i,j} = \frac{ \exp\left(\mathrm{LeakyReLU}\left(\mathbf{a}^{\top} [\mathbf{\Theta}\mathbf{x}_i \, \Vert \, \mathbf{\Theta}\mathbf{x}_j] \right)\right)} {\sum_{k \in \mathcal{N}(i) \cup \{ i \}} \exp\left(\mathrm{LeakyReLU}\left(\mathbf{a}^{\top} [\mathbf{\Theta}\mathbf{x}_i \, \Vert \, \mathbf{\Theta}\mathbf{x}_k] \right)\right)}.\]
Parameters:

  • in_channels (int, tuple) – Size of each input sample, or -1 to derive the size from the first input(s) to the forward method. A tuple corresponds to the sizes of source and target dimensionalities.

  • out_channels (int) – Size of each output sample.

  • heads (int, optional) – Number of multi-head-attentions. (default: 1)

  • k (int, optional) – Number of neighbors to attention (default: 8)

  • concat (bool, optional) – If set to False, the multi-head attentions are averaged instead of concatenated. (default: True)

  • negative_slope (float, optional) – LeakyReLU angle of the negative slope. (default: 0.2)

  • dropout_rate (float, optional) – Dropout probability of the normalized attention coefficients which exposes each node to a stochastically sampled neighborhood during training. (default: 0)

  • add_self_loops (bool, optional) – If set to False, will not add self-loops to the input graph. (default: True)

  • add_bias (bool, optional) – If set to False, the layer will not learn an additive bias. (default: True)

select_topk(edge_index, value)[source]
message(x, edge_index, edge_weight=None, num_nodes=None)[source]

Function that construct message from source nodes to destination nodes.

Parameters:

  • x (tensor) – input node feature.

  • edge_index (tensor) – edges from src to dst.

  • edge_weight (tensor, optional) – weight of each edge.

Returns:

  • tensor – output message

  • Returns – the message matrix, and the shape is [num_edges, message_dim]

forward(x, edge_index, num_nodes)[source]