HNHN_Layer#
Template Layer with two conv passing steps.
- class topomodelx.nn.hypergraph.hnhn_layer.HNHNLayer(in_channels, hidden_channels, incidence_1=None, use_bias: bool = True, use_normalized_incidence: bool = True, alpha: float = -1.5, beta: float = -0.5, bias_gain: float = 1.414, bias_init: Literal['xavier_uniform', 'xavier_normal'] = 'xavier_uniform', **kwargs)[source]#
Layer of a Hypergraph Networks with Hyperedge Neurons (HNHN).
Implementation of a simplified version of the HNHN layer proposed in [1].
This layer is composed of two convolutional layers: 1. A convolutional layer sending messages from edges to nodes. 2. A convolutional layer sending messages from nodes to edges. The incidence matrices can be normalized usign the node and edge cardinality. Two hyperparameters alpha and beta, control the normalization strenght. The convolutional layers support the training of a bias term.
- Parameters:
- in_channelsint
Dimension of node features.
- hidden_channelsint
Dimension of hidden features.
- incidence_1torch.sparse, shape = (n_nodes, n_edges)
Incidence matrix mapping edges to nodes (B_1).
- use_biasbool
Flag controlling whether to use a bias term in the convolution.
- use_normalized_incidencebool
Flag controlling whether to normalize the incidence matrices.
- alphafloat
Scalar controlling the importance of edge cardinality.
- betafloat
Scalar controlling the importance of node cardinality.
- bias_gainfloat
Gain for the bias initialization.
- bias_initLiteral[“xavier_uniform”, “xavier_normal”], default=”xavier_uniform”
Controls the bias initialization method.
- **kwargsoptional
Additional arguments for the layer modules.
Notes
This is the architecture proposed for node classification.
References
[1]Dong, Sawin, Bengio. HNHN: hypergraph networks with hyperedge neurons. Graph Representation Learning and Beyond Workshop at ICML 2020. https://grlplus.github.io/papers/40.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.
- compute_normalization_matrices() None[source]#
Compute the normalization matrices for the incidence matrices.
- forward(x_0, incidence_1=None)[source]#
Forward computation.
The forward pass was initially proposed in [1]_. Its equations are given in [2]_ and graphically illustrated in [3]_.
The equations of one layer of this neural network are given by:
\[\begin{split}\begin{align*} &🟥 \quad m_{y \rightarrow x}^{(0 \rightarrow 1)} = \sigma((B_1^T \cdot W^{(0)})_{xy} \cdot h_y^{t,(0)} \cdot \Theta^{t,(0)} + b^{t,(0)})\\ &🟥 \quad m_{y \rightarrow x}^{(1 \rightarrow 0)} = \sigma((B_1 \cdot W^{(1)})_{xy} \cdot h_y^{t,(1)} \cdot \Theta^{t,(1)} + b^{t,(1)})\\ &🟧 \quad m_x^{(0 \rightarrow 1)} = \sum_{y \in \mathcal{B}(x)} m_{y \rightarrow x}^{(0 \rightarrow 1)}\\ &🟧 \quad m_x^{(1 \rightarrow 0)} = \sum_{y \in \mathcal{C}(x)} m_{y \rightarrow x}^{(1 \rightarrow 0)}\\ &🟩 \quad m_x^{(0)} = m_x^{(1 \rightarrow 0)}\\ &🟩 \quad m_x^{(1)} = m_x^{(0 \rightarrow 1)}\\ &🟦 \quad h_x^{t+1,(0)} = m_x^{(0)}\\ &🟦 \quad h_x^{t+1,(1)} = m_x^{(1)} \end{align*}\end{split}\]- Parameters:
- x_0torch.Tensor, shape = (n_nodes, channels_node)
Input features on the hypernodes.
- incidence_1torch.Tensor, shape = (n_nodes, n_edges)
Incidence matrix mapping edges to nodes (B_1).
- Returns:
- x_0torch.Tensor, shape = (n_nodes, channels_node)
Output features on the hypernodes.
- x_1torch.Tensor, shape = (n_edges, channels_edge)
Output features on the hyperedges.