Decoding GNNs

A GNN is a neural network architecture designed to operate on graph-structured data. It learns a function that maps a graph and its associated features to a set of node-level, edge-level, or graph-level outputs. The following is a formal mathematical definition of a GNN.

Given a graph , where is the set of nodes and is the set of edges, let be the node feature matrix, where each row represents the features of node .

A GNN is a function parameterized by learnable weights , which maps the graph and its node features to a new set of node representations , where is the dimensionality of the output node representations.

The function is computed through a series of message passing and aggregation steps, typically organized into layers. At each layer , the node representations are updated as follows:

Let’s break this down:

• is the representation of node at layer with . Here, represents a real-valued vector space of dimension .
• The...