gammagl.layers.conv.GCNIIConv

class GCNIIConv(in_channels, out_channels, alpha, beta, variant=False)

The graph convolutional operator with initial residual connections and identity mapping (GCNII) from the “Simple and Deep Graph Convolutional Networks” paper

\[\mathbf{X}^{\prime} = \left( (1 - \alpha) \mathbf{\hat{P}}\mathbf{X} + \alpha \mathbf{X^{(0)}}\right) \left( (1 - \beta) \mathbf{I} + \beta \mathbf{\Theta} \right)\]

with \(\mathbf{\hat{P}} = \mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2}\), where \(\mathbf{\hat{A}} = \mathbf{A} + \mathbf{I}\) denotes the adjacency matrix with inserted self-loops and \(\hat{D}_{ii} = \sum_{j=0} \hat{A}_{ij}\) its diagonal degree matrix, and \(\mathbf{X}^{(0)}\) being the initial feature representation. Here, \(\alpha\) models the strength of the initial residual connection, while \(\beta\) models the strength of the identity mapping. The adjacency matrix can include other values than 1 representing edge weights via the optional edge_weight tensor.

Parameters:

• in_channels (int) – Size of each input sample.

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

• alpha (float) – The strength of the initial residual connection \(\alpha\).

• beta (float) – The hyperparameter \(\beta\) to compute the strength of the identity mapping \(\beta = \log \left( \frac{\beta}{\ell} + 1 \right)\). (default: None)

• variant (bool, optional) –

  use GCNII*, which can be fomuliazed as following:

  \[\begin{split}\mathbf{H}^{(\ell+1)}= \sigma\left(\left(1-\alpha_{\ell}\right) \tilde{\mathbf{P}} \mathbf{H}^{(\ell)}\left(\left(1-\beta_{\ell}\right) \mathbf{I}_{n}+\beta_{\ell} \mathbf{W}_{1}^{(\ell)}\right)+\right.\\ \left.+\alpha_{\ell} \mathbf{H}^{(0)}\left(\left(1-\beta_{\ell}\right) \mathbf{I}_{n}+\beta_{\ell} \mathbf{W}_{2}^{(\ell)}\right)\right)\end{split}\]

forward(x0, x, edge_index, edge_weight, num_nodes)

Define the computation performed at every call.

Should be overridden by all subclasses.

Note

Although the recipe for forward pass needs to be defined within this function, one should call the Module instance afterwards instead of this since the former takes care of running the registered hooks while the latter silently ignores them.