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...
