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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, diameter∼34), 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 establish graph density and diameter as the primary structural determinants of whether dynamic attention benefits the PI-GNN framework.
The Maximum Cut (Max-Cut) problem is a classic NP-hard combinatorial optimization challenge involved in areas such as circuit layout, data segmentation, and statistical physics. Recent developments have emerged with Physics-Inspired Graph Neural Networks (PI-GNNs), providing promising unsupervised methods through the combination of differentiable message passing and energy-based objectives derived from Quadratic Unconstrained Binary Optimization (QUBO) models. This study explores hyperparameter sensitivity with respect to learning and dropout rates and assesses depth resilience using Dirichlet energy, global cosine similarity, and cut-value metrics. Our experiments on five standard graphs (G14, G15, G22, G49, G70) show that dropout significantly impacts solution quality, while PI-GATv2 demonstrates greater stability in deeper network layers. The results suggest that PI-GATv2 is a competitive and often more robust option for unsupervised Max- Cut tasks involving deeper networks.
Энэхүү судалгаанд бид физикээс сэдсэн Граф Нейрал Сүлжээ (GNN)-ний гүйцэтгэлийг комбинаторик оновчлолын MaxCut бодлогыг шийдвэрлэхэд үнэлж, харьцуулав. Тодруулбал, бид шинээр санал болгож буй Физикээс Сэдсэн Граф Анхаарлын Сүлжээ (PI-GAT), түүний хувилбар PI-GATv2 болон Физикээс Сэдсэн GraphSAGE (PI-SAGE) гэсэн архитектуруудыг Физикээс Сэдсэн GNN (PI-GCN) загвартай харьцуулсан туршилтын үр дүнг танилцуулж байна. Судалгаа нь шийдийн чанар (огтлолын хэмжээ) болон тооцооллын өртөг (сургалтын хугацаа, сургалтын үеийн тоо) хоорондын харилцан хамаарал, мөн хасалтын коэффициент болон суралцах хурд зэрэг хайперпараметрүүдийн эдгээр физикээс сэдсэн загваруудад үзүүлэх нөлөөг шинжилсэн. PI-GAT, PI-GATv2 болон PI-SAGE загварууд нь том графуудад илүү сайн үр дүн үзүүлж байна.
