Simplical Complex Autoencoder Layer.
- class topomodelx.nn.simplicial.sca_cmps_layer.SCACMPSLayer(channels_list, complex_dim, att: bool = False)[source]#
Layer of a Simplicial Complex Autoencoder (SCA) using the Coadjacency Message Passing Scheme (CMPS).
Implementation of the SCA layer proposed in [1].
- Parameters:
- channels_listlist[int]
Dimension of features at each dimension.
- complex_dimint
Highest dimension of chains on the input simplicial complexes.
- attbool, default=False
Whether to use attention.
Notes
This is the architecture proposed for complex classification.
References
[1]Hajij, Zamzmi, Papamarkou, Maroulas, Cai. Simplicial complex autoencoder (2022). https://arxiv.org/pdf/2103.04046.pdf
[2]Papillon, Sanborn, Hajij, Miolane. Architectures of topological deep learning: a survey on topological neural networks (2023). https://arxiv.org/abs/2304.10031.
[3]Papillon, Sanborn, Hajij, Miolane. Equations of topological neural networks (2023). awesome-tnns/awesome-tnns
- forward(x_list, down_lap_list, incidencet_list)[source]#
Forward pass.
The forward pass was initially proposed in [1]_. Its equations are given in [3]_ and graphically illustrated in [2]_.
Coadjacency message passing scheme:
\[\begin{split}\begin{align*} &🟥 \quad m_{y \rightarrow x}^{(r \rightarrow r'' \rightarrow r)} = M(h_{x}^{t, (r)}, h_{y}^{t, (r)},att(h_{x}^{t, (r)}, h_{y}^{t, (r)}),x,y,{\Theta^t}) \qquad \text{where } r'' < r < r'\\ &🟥 \quad m_{y \rightarrow x}^{(r'' \rightarrow r)} = M(h_{x}^{t, (r)}, h_{y}^{t, (r'')},att(h_{x}^{t, (r)}, h_{y}^{t, (r'')}),x,y,{\Theta^t})\\ &🟧 \quad m_x^{(r \rightarrow r)} = AGG_{y \in \mathcal{L}\_\downarrow(x)} m_{y \rightarrow x}^{(r \rightarrow r)}\\ &🟧 \quad m_x^{(r'' \rightarrow r)} = AGG_{y \in \mathcal{B}(x)} m_{y \rightarrow x}^{(r'' \rightarrow r)}\\ &🟩 \quad m_x^{(r)} = \text{AGG}\_{\mathcal{N}\_k \in \mathcal{N}}(m_x^{(k)})\\ &🟦 \quad h_{x}^{t+1, (r)} = U(h_x^{t, (r)}, m_{x}^{(r)}) \end{align*}\end{split}\]- Parameters:
- x_listlist[torch.Tensor]
List of tensors holding the features of each chain at each level.
- down_lap_listlist[torch.Tensor]
List of down laplacian matrices for skeletons from 1 dimension to the dimension of the simplicial complex.
- incidencet_listlist[torch.Tensor]
List of transpose incidence matrices for skeletons from 1 dimension to the dimension of the simplicial complex.
- Returns:
- list[torch.Tensor]
Output for skeletons of each dimension (the node features are left untouched: x_list[0]).