Editing Graph Neural Networks (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
The key insight of GNNs is: '''a node's representation should depend on both its own features and the features of its neighborhood.''' This mirrors how we understand entities in relation to their context — a person's role in society depends partly on who they're connected to.

'''Message passing''' is the universal GNN framework:

For each layer l and each node v:
1. '''Message''': compute a message from each neighbor u: m''{u→v} = M(h''u^l, h''v^l, e''{uv})
2. '''Aggregate''': combine all incoming messages: a''v^l = AGG({m''{u→v} : u ∈ N(v)})
3. '''Update''': compute new node representation: h''v^{l+1} = U(h''v^l, a_v^l)

Where M is a message function, AGG is an aggregation function (sum, mean, max, attention-weighted), and U is an update function (typically a neural network). After L layers, each node's representation encodes information from its L-hop neighborhood.

Think of it like rumor spreading: after 1 layer, each node knows about its direct neighbors; after 2 layers, about neighbors' neighbors; and so on.

'''Why not just use a standard neural network?''' Graphs are irregular — nodes have different numbers of neighbors, and there's no canonical ordering of neighbors. GNNs handle this through permutation-invariant aggregation (sum, mean, max produce the same result regardless of neighbor ordering).

'''Expressiveness limits''': The Weisfeiler-Leman (WL) graph isomorphism test provides a theoretical upper bound on GNN expressiveness. Standard message-passing GNNs cannot distinguish certain graph structures — for example, regular graphs of the same degree look identical from any node's perspective, even if the graphs have different global structure.
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