class FAConv(channels: int, eps: float = 0.1, dropout: float = 0.0, cached: bool = False, add_self_loops: bool = True, normalize: bool = True, **kwargs)[source]

Bases: MessagePassing

The Frequency Adaptive Graph Convolution operator from the “Beyond Low-Frequency Information in Graph Convolutional Networks” paper

\[\mathbf{x}^{\prime}_i= \epsilon \cdot \mathbf{x}^{(0)}_i + \sum_{j \in \mathcal{N}(i)} \frac{\alpha_{i,j}}{\sqrt{d_i d_j}} \mathbf{x}_{j}\]

where \(\mathbf{x}^{(0)}_i\) and \(d_i\) denote the initial feature representation and node degree of node \(i\), respectively. The attention coefficients \(\alpha_{i,j}\) are computed as

\[\mathbf{\alpha}_{i,j} = \textrm{tanh}(\mathbf{a}^{\top}[\mathbf{x}_i, \mathbf{x}_j])\]

based on the trainable parameter vector \(\mathbf{a}\).

  • channels (int) – Size of each input sample, or -1 to derive the size from the first input(s) to the forward method.

  • eps (float, optional) – \(\epsilon\)-value. (default: 0.1)

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

  • cached (bool, optional) – If set to True, the layer will cache the computation of \(\sqrt{d_i d_j}\) 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)

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

  • normalize (bool, optional) – Whether to add self-loops (if add_self_loops is True) and compute symmetric normalization coefficients on the fly. If set to False, edge_weight needs to be provided in the layer’s forward() method. (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 \((|\mathcal{V}|, F)\) or \(((|\mathcal{V}|, F), ((2, |\mathcal{E}|), (|\mathcal{E}|)))\) if return_attention_weights=True

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

Runs the forward pass of the module.


return_attention_weights (bool, optional) – If set to True, will additionally return the tuple (edge_index, attention_weights), holding the computed attention weights for each edge. (default: None)


Resets all learnable parameters of the module.