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GraphSAGE Layer (Hamilton et al. 2017)

layer_sage.Rd

Implements the GraphSAGE (Graph Sample and Aggregate) layer:

$$\mathbf{h}_{\mathcal{N}(v)}^{(k)} = \text{AGGREGATE}\left(\{\mathbf{h}_u^{(k-1)} : u \in \mathcal{N}(v)\}\right)$$

$$\mathbf{h}_v^{(k)} = \sigma\left(\mathbf{W}^{(k)} \cdot \text{CONCAT}\left(\mathbf{h}_v^{(k-1)}, \mathbf{h}_{\mathcal{N}(v)}^{(k)}\right)\right)$$

This layer:

  1. Aggregates neighbor features using the specified aggregator

  2. Concatenates node's own features with aggregated neighbor features

  3. Applies linear transformation and optional normalization

Parameters:

  • \(W\): (in_features + aggregated_features) x out_features learnable weight matrix

  • \(b\): out_features learnable bias term (optional)

Usage

layer_sage(
  in_features,
  out_features,
  aggregator = MeanAggregator(),
  bias = TRUE,
  concat = TRUE
)

Arguments

in_features

Integer. Number of input features per node

out_features

Integer. Number of output features per node

aggregator

Aggregator S7 object. Default: MeanAggregator()

bias

Logical. Add learnable bias. Default: TRUE

concat

Logical. If TRUE, concatenates self and neighbor features. If FALSE, adds them. Default: TRUE

x

Tensor n_nodes x in_features. Node feature matrix (dense or sparse)

adj

Sparse torch tensor n_nodes x n_nodes. Adjacency matrix defining graph structure. Must be a sparse COO tensor.

Value

Tensor n_nodes x out_features. Transformed node features

Details

The aggregator should be an S7 Aggregator object (e.g., MeanAggregator(), MaxAggregator()). Each aggregator is responsible for its own normalization. For example, MeanAggregator() applies row normalization internally, while MaxAggregator() uses the adjacency structure without normalization.

Forward pass

References

Hamilton, W., Ying, Z., & Leskovec, J. (2017). Inductive representation learning on large graphs. Advances in Neural Information Processing Systems, 30. doi:10.48550/arXiv.1706.02216