arXiv:2602.15239v2 Announce Type: replace 
Abstract: Transformers have achieved remarkable success across domains, motivating the rise of Graph Transformers (GTs) as attention-based architectures for graph-structured data. A key design choice in GTs is the use of Graph Neural Network (GNN)-based positional encodings to incorporate structural information. In this work, we study GTs through the lens of manifold limit models for graph sequences and establish a theoretical connection between GTs with GNN positional encodings and Manifold Neural Networks (MNNs). Building on transferability results for GNNs under manifold convergence, we show that GTs inherit transferability guarantees from their positional encodings. In particular, GTs trained on small graphs provably generalize to larger graphs under mild assumptions. We complement our theory with extensive experiments on standard graph benchmarks, demonstrating that GTs exhibit scalable behavior on par with GNNs. To further show the efficiency in a real-world scenario, we implement GTs for shortest path distance estimation over terrains to better illustrate the efficiency of the transferable GTs. Our results provide new insights into the understanding of GTs and suggest practical directions for efficient training of GTs in large-scale settings.

أظهرت الأبحاث الحديثة وجود ارتباط نظري بين المحولات الرسومية (GT) مع الترميزات الموضعية لشبكات الأعصاب الرسومية (GNN) والشبكات العصبية المتعددة الأبعاد (MNN)، مما يثبت أن GT المدربة على الرسوم البيانية الأصغر يمكن أن تعمم على الرسوم البيانية الأكبر تحت ظروف معينة. يبرز هذا العمل أهمية الترميزات الموضعية في تعزيز قابلية النقل لـ GT.

Investigaciones recientes han establecido una conexión teórica entre los Transformadores de Grafos (GT) con codificaciones posicionales de Redes Neuronales de Grafos (GNN) y Redes Neuronales de Variedad (MNN), demostrando que los GT entrenados en grafos más pequeños pueden generalizar a grafos más grandes bajo ciertas condiciones. Este trabajo enfatiza la importancia de las codificaciones posicionales en la mejora de la transferibilidad de los GT.

Des recherches récentes ont établi une connexion théorique entre les Graph Transformers (GT) avec des encodages positionnels de Graph Neural Network (GNN) et les Manifold Neural Networks (MNN), démontrant que les GT formés sur de plus petits graphes peuvent se généraliser à des graphes plus grands sous certaines conditions. Ce travail souligne l'importance des encodages positionnels pour améliorer la transférabilité des GT.

Recent research has established a theoretical connection between Graph Transformers (GTs) with Graph Neural Network (GNN) positional encodings and Manifold Neural Networks (MNNs), demonstrating that GTs trained on smaller graphs can generalize to larger graphs under certain conditions. This work emphasizes the importance of positional encodings in enhancing the transferability of GTs.