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Residual connection

As explained in Knowledge Graphs and LLMs in Action

A residual connection is a neural-network connection that combines a layer's input with its transformed output to facilitate information and gradient propagation.

A residual connection creates a shortcut around one or more neural-network layers, combining earlier node information with transformed neighborhood information. In graph neural networks, it preserves node features, improves gradient flow, and helps prevent over-smoothing as message passing becomes deeper. section 11.6 section 11.6.4

In a GNN update, a residual connection can:

  • Preserve access to original node features while incorporating aggregated neighbor features. section 11.6.4
  • Provide additional backpropagation paths that support deeper architectures. section 11.6
  • Reduce feature homogenization caused by repeated message passing. section 11.6

GraphSAGE-style update

Concatenate each node’s current features with its aggregated neighbor features, transform the combined vector with a linear layer, and apply ReLU. This preserves both information sources for the next representation.

How Knowledge Graphs and LLMs in Action covers it

How deep it goes
Explains shortcut motivation and a concatenation-based update, while deferring detailed residual variants and broader architecture design.
Examples
Uses a GraphSAGE update function that concatenates node and aggregated-neighbor features before applying a linear transformation and ReLU.
What it assumes
Assumes familiarity with node representations, neighborhood aggregation, message passing, and neural-network training.
What you can do after
Apply residual-style updates in GNNs to preserve features and support deeper message-passing models.
How it connects
Connects residual connections with message passing, GraphSAGE, over-smoothing, gated updates, attention mechanisms, and normalization layers.

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This explainer was generated by Manning's knowledge graph from the text of Knowledge Graphs and LLMs in Action. The section links point to the parts of the book it draws on.