Graph Isomorphism Network Layer (Xu et al. 2019)

Implements the Graph Isomorphism Network (GIN) layer:

$$\mathbf{h}_i^{(k)} = \text{MLP}^{(k)}\left((1 + \epsilon^{(k)}) \cdot \mathbf{h}_i^{(k-1)} + \sum_{j \in \mathcal{N}(i)} \mathbf{h}_j^{(k-1)}\right)$$

This layer:

1. Aggregates neighbor features via summation

2. Adds weighted self features using learnable epsilon

3. Applies MLP transformation

Parameters:

• MLP: Multi-layer perceptron (typically 2 layers)

• epsilon: Learnable or fixed weight for self features

Usage

layer_gin(in_features, out_features, eps = 0, learn_eps = FALSE)

Arguments

in_features

Integer. Number of input features per node

out_features

Integer. Number of output features per node

eps

Numeric. Initial value for epsilon. Default: 0

learn_eps

Logical. Whether to learn epsilon parameter. Default: FALSE

Value

Tensor n_nodes x out_features. Transformed node features

Details

The MLP is constructed as a sequence of Linear-BatchNorm-ReLU-Linear layers. The epsilon parameter can be learned or fixed at 0.

Forward pass

layer(x, adj)

• x: Tensor n_nodes x in_features. Node feature matrix.

• adj: Sparse COO tensor n_nodes x n_nodes. Adjacency matrix defining graph structure.

References

Xu, K., Hu, W., Leskovec, J., & Jegelka, S. (2019). How Powerful are Graph Neural Networks? International Conference on Learning Representations. doi:10.48550/arXiv.1810.00826

Examples

if (FALSE) { # torch::torch_is_installed()
adj <- adj_from_edgelist(from = c(1, 2, 3, 4), to = c(2, 3, 4, 1))
x <- torch::torch_randn(4, 8)

layer <- layer_gin(8, 4)
layer(x, adj)

# Learn the weight given to a node's own features
layer <- layer_gin(8, 4, learn_eps = TRUE)
layer(x, adj)
}