torch_geometric.nn.dense.dense_diff_pool
- dense_diff_pool(x: Tensor, adj: Tensor, s: Tensor, mask: Optional[Tensor] = None, normalize: bool = True) Tuple[Tensor, Tensor, Tensor, Tensor] [source]
The differentiable pooling operator from the “Hierarchical Graph Representation Learning with Differentiable Pooling” paper.
\[ \begin{align}\begin{aligned}\mathbf{X}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot \mathbf{X}\\\mathbf{A}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot \mathbf{A} \cdot \mathrm{softmax}(\mathbf{S})\end{aligned}\end{align} \]based on dense learned assignments \(\mathbf{S} \in \mathbb{R}^{B \times N \times C}\). Returns the pooled node feature matrix, the coarsened adjacency matrix and two auxiliary objectives: (1) The link prediction loss
\[\mathcal{L}_{LP} = {\| \mathbf{A} - \mathrm{softmax}(\mathbf{S}) {\mathrm{softmax}(\mathbf{S})}^{\top} \|}_F,\]and (2) the entropy regularization
\[\mathcal{L}_E = \frac{1}{N} \sum_{n=1}^N H(\mathbf{S}_n).\]- Parameters:
x (torch.Tensor) – Node feature tensor \(\mathbf{X} \in \mathbb{R}^{B \times N \times F}\), with batch-size \(B\), (maximum) number of nodes \(N\) for each graph, and feature dimension \(F\).
adj (torch.Tensor) – Adjacency tensor \(\mathbf{A} \in \mathbb{R}^{B \times N \times N}\).
s (torch.Tensor) – Assignment tensor \(\mathbf{S} \in \mathbb{R}^{B \times N \times C}\) with number of clusters \(C\). The softmax does not have to be applied before-hand, since it is executed within this method.
mask (torch.Tensor, optional) – Mask matrix \(\mathbf{M} \in {\{ 0, 1 \}}^{B \times N}\) indicating the valid nodes for each graph. (default:
None
)normalize (bool, optional) – If set to
False
, the link prediction loss is not divided byadj.numel()
. (default:True
)
- Return type: