Physics-Inspired Graph Neural Networks (PI-GNNs) reformulate
MAX-CUT as QUBO energy minimization, training a GNN
to produce soft binary node assignments without labeled data.
The baseline PI-GCN uses static, degree-normalized aggregation,
while its attention-augmented counterpart PI-GAT—built on
GATv2—introduces additional hyperparameters whose effects
remain uncharacterized. This paper addresses that gap through
controlled experiments on five Gset benchmark graphs (800–10,000
nodes) and five real-world graphs from communication, social,
and scientific collaboration networks (500–1,590 nodes). The first
experiment examines how attention dropout pattn affects solution
quality and convergence stability across 25 seeds per configuration.
The second sweeps depth from 1 to 20 layers with 5 independent
seeds, quantifying oversmoothing via Dirichlet energy, cosine
similarity, and mean absolute deviation. On dense graphs (average
degree ≥ 10), dropout in [0.10, 0.20] reduces inter-run variance
by 30–41% while improving best-cut value; on the sparse graph
G70 (average degree∼2), any dropout is detrimental. PI-GAT
delays oversmoothing onset by one to two layers versus PI-GCN, at
1.5–1.8× computational overhead per layer. Real-world validation
confirms that depth advantage persists across all five diverse
network families, with PI-GAT retaining 25× more solution quality
than PI-GCN at depth K = 10 on a communication network
(avg. degree 9.61). These findings indicate that graph density
and diameter are strong empirical predictors of whether dynamic
attention benefits the PI-GNN framework.