Implementation of UniGIN layer from Huang et. al.: UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks.

class topomodelx.nn.hypergraph.unigin_layer.UniGINLayer(in_channels, eps: float = 0.0, train_eps: bool = False, use_norm: bool = False, **kwargs)

Layer of UniGIN.

Implementation of UniGIN layer proposed in [1].

Parameters:

in_channelsint

Dimension of input features.

epsfloat, default=0.0

Constant in GIN Update equation.

train_epsbool, default=False

Whether to make eps a trainable parameter.

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

[2]

Papillon, Sanborn, Hajij, Miolane. Equations of topological neural networks (2023). awesome-tnns/awesome-tnns

[3]

Papillon, Sanborn, Hajij, Miolane. Architectures of topological deep learning: a survey on topological neural networks (2023). https://arxiv.org/abs/2304.10031

forward(x_0, incidence_1)

[1]_ initially proposed the forward pass.

Its equations are given in [2]_ and graphically illustrated in [3]_.

The forward pass of this layer is composed of three steps.

1. Every hyper-edge sums up the features of its constituent edges:

\[\begin{split}\begin{align*} &🟥 \quad m_{y \rightarrow z}^{(0 \rightarrow 1)} = B_1^T \cdot h_y^{t, (0)}\\ &🟧 \quad m_z^{(0 \rightarrow 1)} = \sum_{y \in \mathcal{B}(z)} m_{y \rightarrow z}^{(0 \rightarrow 1)}\\ \end{align*}\end{split}\]

2. The message to the nodes is the sum of the messages from the incident hyper-edges.

\[\begin{split}\begin{align*} &🟥 \quad m_{z \rightarrow x}^{(1 \rightarrow 0)} = B_1 \cdot m_z^{(0 \rightarrow 1)}\\ &🟧 \quad m_{x}^{(1\rightarrow0)} = \sum_{z \in \mathcal{C}(x)} m_{z \rightarrow x}^{(1\rightarrow0)}\\ \end{align*}\end{split}\]

3. The node features are then updated using the GIN update equation:

\[\begin{split}\begin{align*} &🟩 \quad m_x^{(0)} = m_{x}^{(1\rightarrow0)}\\ &🟦 \quad h_x^{t+1,(0)} = \Theta^t \cdot ((1+\eps)\cdot h_x^{t,(0)}+m_x^{(0)}) \end{align*}\end{split}\]

Parameters:

x_0torch.Tensor, shape = (n_nodes, in_channels)

Input features on the nodes of the hypergraph.

incidence_1torch.sparse, shape = (n_nodes, n_edges)

Incidence matrix mapping edges to nodes (B_1).

Returns:

x_0torch.Tensor

Output node features.

x_1torch.Tensor

Output hyperedge features.