Unigcnii_Layer#
UniGCNII layer implementation.
- class topomodelx.nn.hypergraph.unigcnii_layer.UniGCNIILayer(in_channels, hidden_channels, alpha: float, beta: float, use_norm=False, **kwargs)[source]#
Implementation of the UniGCNII layer [1].
- Parameters:
- in_channelsint
Dimension of the input features.
- hidden_channelsint
Dimension of the hidden features.
- alphafloat
The alpha parameter determining the importance of the self-loop (theta_2).
- betafloat
The beta parameter determining the importance of the learned matrix (theta_1).
- use_normbool, default=False
Whether to apply row normalization after the layer.
- **kwargsoptional
Additional arguments for the layer modules.
References
[1]Huang and Yang. UniGNN: a unified framework for graph and hypergraph neural networks. IJCAI 2021. https://arxiv.org/pdf/2105.00956.pdf
- forward(x_0, incidence_1, x_skip=None)[source]#
Forward pass of the UniGCNII layer.
The forward pass consists of: - two messages, and - a skip connection with a learned update function.
First every hyper-edge sums up the features of its constituent edges:
\[\begin{split}\begin{align*} & 🟥 \quad m_{y \rightarrow z}^{(0 \rightarrow 1)} = (B^T_1)\_{zy} \cdot h^{t,(0)}_y \\ & 🟧 \quad m_z^{(0\rightarrow1)} = \sum_{y \in \mathcal{B}(z)} m_{y \rightarrow z}^{(0 \rightarrow 1)} \end{align*}\end{split}\]Second, the second message is normalized with the node and edge degrees:
\[\begin{split}\begin{align*} & 🟥 \quad m_{z \rightarrow x}^{(1 \rightarrow 0)} = B_1 \cdot m_z^{(0 \rightarrow 1)} \\ & 🟧 \quad m_{x}^{(1\rightarrow0)} = \frac{1}{\sqrt{d_x}}\sum_{z \in \mathcal{C}(x)} \frac{1}{\sqrt{d_z}}m_{z \rightarrow x}^{(1\rightarrow0)} \\ \end{align*}\end{split}\]Third, the computed message is combined with skip connections and a linear transformation using hyperparameters alpha and beta:
\[\begin{split}\begin{align*} & 🟩 \quad m_x^{(0)} = m_x^{(1 \rightarrow 0)} \\ & 🟦 \quad m_x^{(0)} = ((1-\beta)I + \beta W)((1-\alpha)m_x^{(0)} + \alpha \cdot h_x^{t,(0)}) \\ \end{align*}\end{split}\]- Parameters:
- x_0torch.Tensor, shape = (num_nodes, in_channels)
Input features of the nodes of the hypergraph.
- incidence_1torch.Tensor, shape = (num_nodes, num_edges)
Incidence matrix of the hypergraph. It is expected that the incidence matrix contains self-loops for all nodes.
- x_skiptorch.Tensor, shape = (num_nodes, in_channels)
Original node features of the hypergraph used for the skip connections. If not provided, the input to the layer is used as a skip connection.
- Returns:
- x_0torch.Tensor
Output node features.
- x_1torch.Tensor
Output hyperedge features.