class dgl.nn.pytorch.conv.EGNNConv(in_size, hidden_size, out_size, edge_feat_size=0)[source]

Bases: torch.nn.modules.module.Module

Equivariant Graph Convolutional Layer from E(n) Equivariant Graph Neural Networks

\[ \begin{align}\begin{aligned}m_{ij}=\phi_e(h_i^l, h_j^l, ||x_i^l-x_j^l||^2, a_{ij})\\x_i^{l+1} = x_i^l + C\sum_{j\in\mathcal{N}(i)}(x_i^l-x_j^l)\phi_x(m_{ij})\\m_i = \sum_{j\in\mathcal{N}(i)} m_{ij}\\h_i^{l+1} = \phi_h(h_i^l, m_i)\end{aligned}\end{align} \]

where \(h_i\), \(x_i\), \(a_{ij}\) are node features, coordinate features, and edge features respectively. \(\phi_e\), \(\phi_h\), and \(\phi_x\) are two-layer MLPs. \(C\) is a constant for normalization, computed as \(1/|\mathcal{N}(i)|\).

  • in_size (int) – Input feature size; i.e. the size of \(h_i^l\).

  • hidden_size (int) – Hidden feature size; i.e. the size of hidden layer in the two-layer MLPs in \(\phi_e, \phi_x, \phi_h\).

  • out_size (int) – Output feature size; i.e. the size of \(h_i^{l+1}\).

  • edge_feat_size (int, optional) – Edge feature size; i.e. the size of \(a_{ij}\). Default: 0.


>>> import dgl
>>> import torch as th
>>> from dgl.nn import EGNNConv
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> node_feat, coord_feat, edge_feat = th.ones(6, 10), th.ones(6, 3), th.ones(6, 2)
>>> conv = EGNNConv(10, 10, 10, 2)
>>> h, x = conv(g, node_feat, coord_feat, edge_feat)
forward(graph, node_feat, coord_feat, edge_feat=None)[source]

Compute EGNN layer.

  • graph (DGLGraph) – The graph.

  • node_feat (torch.Tensor) – The input feature of shape \((N, h_n)\). \(N\) is the number of nodes, and \(h_n\) must be the same as in_size.

  • coord_feat (torch.Tensor) – The coordinate feature of shape \((N, h_x)\). \(N\) is the number of nodes, and \(h_x\) can be any positive integer.

  • edge_feat (torch.Tensor, optional) – The edge feature of shape \((M, h_e)\). \(M\) is the number of edges, and \(h_e\) must be the same as edge_feat_size.


  • node_feat_out (torch.Tensor) – The output node feature of shape \((N, h_n')\) where \(h_n'\) is the same as out_size.

  • coord_feat_out (torch.Tensor) – The output coordinate feature of shape \((N, h_x)\) where \(h_x\) is the same as the input coordinate feature dimension.