Update rule

As explained in Graph Neural Networks in Action

The update step is the message-passing stage in which each node’s features are replaced or revised with its newly computed representation.

The update rule is the final stage of message passing. It replaces or revises each node’s or edge’s features with a representation that includes the newly computed message, combining local data with information from the graph. section 3.4.2 section 1.5.3

Treat one message-passing layer as a short pipeline:

• Aggregate information from each node’s neighborhood using an order-invariant operation such as sum, mean, or max. section 3.4.2
• Transform the aggregated messages with a neural network to produce new embeddings or features. section 3.4.2 section 1.5.3
• Update each node or edge by incorporating that transformed message into its stored features. section 3.4.2

Completing the update finishes one round of message passing. Stacking layers repeats the process, allowing representations to encode information from progressively more hops away in the graph. section 3.4.2 section 1.5.3

Figure 3.15 Elements of our message-passing layer. Each message-passing layer consists of an aggregation, a transformation, and an update step.

Use the message-passing diagram to track the update rule as the third stage after aggregation and transformation. section 3.4.2

How Graph Neural Networks in Action covers it

How deep it goes

Traces the update as the final operation in a message-passing pipeline and relates repeated layers to graph hops.

Examples

Uses node and edge features alongside the Aggregate → Transform → Update diagram as concrete representations of the rule.

What you can do after

Apply the update stage to complete one message-passing round and produce revised node or edge representations.

How it connects

Connects update rules to message passing, aggregation, transformation, embeddings, and graph neural network layers.

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Related concepts

• simulated annealingused by · Simulated annealing is a stochastic optimization method that gradually reduces the probability of accepting worse solutions to escape local optima.
• message passingpart of · A communication or computation technique in which entities exchange messages to transmit or propagate information, coordinate work, or update state.

This explainer was generated by Manning's knowledge graph from the text of Graph Neural Networks in Action. The section links point to the parts of the book it draws on.