class GMMConv(in_channels: Union[int, Tuple[int, int]], out_channels: int, dim: int, kernel_size: int, separate_gaussians: bool = False, aggr: str = 'mean', root_weight: bool = True, bias: bool = True, **kwargs)[source]

Bases: MessagePassing

The gaussian mixture model convolutional operator from the “Geometric Deep Learning on Graphs and Manifolds using Mixture Model CNNs” paper.

\[\mathbf{x}^{\prime}_i = \frac{1}{|\mathcal{N}(i)|} \sum_{j \in \mathcal{N}(i)} \frac{1}{K} \sum_{k=1}^K \mathbf{w}_k(\mathbf{e}_{i,j}) \odot \mathbf{\Theta}_k \mathbf{x}_j,\]


\[\mathbf{w}_k(\mathbf{e}) = \exp \left( -\frac{1}{2} {\left( \mathbf{e} - \mathbf{\mu}_k \right)}^{\top} \Sigma_k^{-1} \left( \mathbf{e} - \mathbf{\mu}_k \right) \right)\]

denotes a weighting function based on trainable mean vector \(\mathbf{\mu}_k\) and diagonal covariance matrix \(\mathbf{\Sigma}_k\).


The edge attribute \(\mathbf{e}_{ij}\) is usually given by \(\mathbf{e}_{ij} = \mathbf{p}_j - \mathbf{p}_i\), where \(\mathbf{p}_i\) denotes the position of node \(i\) (see torch_geometric.transform.Cartesian).

  • 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.

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

  • dim (int) – Pseudo-coordinate dimensionality.

  • kernel_size (int) – Number of kernels \(K\).

  • separate_gaussians (bool, optional) – If set to True, will learn separate GMMs for every pair of input and output channel, inspired by traditional CNNs. (default: False)

  • aggr (str, optional) – The aggregation operator to use ("add", "mean", "max"). (default: "mean")

  • root_weight (bool, optional) – If set to False, the layer will not add transformed root node features to the output. (default: True)

  • 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 \((|\mathcal{V}|, F_{out})\) or \((|\mathcal{V}_t|, F_{out})\) 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)[source]

Runs the forward pass of the module.


Resets all learnable parameters of the module.