class GCN2Conv(channels: int, alpha: float, theta: Optional[float] = None, layer: Optional[int] = None, shared_weights: bool = True, cached: bool = False, add_self_loops: bool = True, normalize: bool = True, **kwargs)[source]

Bases: MessagePassing

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.

  • channels (int) – Size of each input and output sample.

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

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

  • layer (int, optional) – The layer \(\ell\) in which this module is executed. (default: None)

  • shared_weights (bool, optional) – If set to False, will use different weight matrices for the smoothed representation and the initial residual (“GCNII*”). (default: True)

  • cached (bool, optional) – If set to True, the layer will cache the computation of \(\mathbf{\hat{D}}^{-1/2} \mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2}\) on first execution, and will use the cached version for further executions. This parameter should only be set to True in transductive learning scenarios. (default: False)

  • normalize (bool, optional) – Whether to add self-loops and apply symmetric normalization. (default: True)

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

  • **kwargs (optional) – Additional arguments of torch_geometric.nn.conv.MessagePassing.

  • input: node features \((|\mathcal{V}|, F)\), initial node features \((|\mathcal{V}|, F)\), edge indices \((2, |\mathcal{E}|)\), edge weights \((|\mathcal{E}|)\) (optional)

  • output: node features \((|\mathcal{V}|, F)\)

forward(x: Tensor, x_0: Tensor, edge_index: Union[Tensor, SparseTensor], edge_weight: Optional[Tensor] = None) Tensor[source]

Runs the forward pass of the module.


Resets all learnable parameters of the module.