class GATConv(in_channels: Union[int, Tuple[int, int]], out_channels: int, heads: int = 1, concat: bool = True, negative_slope: float = 0.2, dropout: float = 0.0, add_self_loops: bool = True, edge_dim: Optional[int] = None, fill_value: Union[float, Tensor, str] = 'mean', bias: bool = True, **kwargs)[source]

Bases: MessagePassing

The graph attentional operator from the “Graph Attention Networks” paper.

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

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

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

If the graph has multi-dimensional edge features \(\mathbf{e}_{i,j}\), the attention coefficients \(\alpha_{i,j}\) are computed as

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

If the graph is not bipartite, \(\mathbf{\Theta}_{s} = \mathbf{\Theta}_{t}\).

  • in_channels (int or 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 in case of a bipartite graph.

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

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

  • 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 (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)

  • edge_dim (int, optional) – Edge feature dimensionality (in case there are any). (default: None)

  • fill_value (float or torch.Tensor or str, optional) – The way to generate edge features of self-loops (in case edge_dim != None). If given as float or torch.Tensor, edge features of self-loops will be directly given by fill_value. If given as str, edge features of self-loops are computed by aggregating all features of edges that point to the specific node, according to a reduce operation. ("add", "mean", "min", "max", "mul"). (default: "mean")

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

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

  • input: node features \((|\mathcal{V}|, F_{in})\) or \(((|\mathcal{V_s}|, F_{s}), (|\mathcal{V_t}|, F_{t}))\) if bipartite, edge indices \((2, |\mathcal{E}|)\), edge features \((|\mathcal{E}|, D)\) (optional)

  • output: node features \((|\mathcal{V}|, H * F_{out})\) or \(((|\mathcal{V}_t|, H * F_{out})\) if bipartite. If return_attention_weights=True, then \(((|\mathcal{V}|, H * F_{out}), ((2, |\mathcal{E}|), (|\mathcal{E}|, H)))\) or \(((|\mathcal{V_t}|, H * F_{out}), ((2, |\mathcal{E}|), (|\mathcal{E}|, H)))\) if bipartite

forward(x: Union[Tensor, Tuple[Tensor, Optional[Tensor]]], edge_index: Union[Tensor, SparseTensor], edge_attr: Optional[Tensor] = None, size: Optional[Tuple[int, int]] = None, return_attention_weights=None)[source]

Runs the forward pass of the module.

  • x (torch.Tensor or (torch.Tensor, torch.Tensor)) – The input node features.

  • edge_index (torch.Tensor or SparseTensor) – The edge indices.

  • edge_attr (torch.Tensor, optional) – The edge features. (default: None)

  • size ((int, int), optional) – The shape of the adjacency matrix. (default: None)

  • 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.