arXiv:2406.12841v4 Announce Type: replace 
Abstract: Higher-order graph neural networks (HOGNNs) and the related architectures from Topological Deep Learning are an important class of GNN models that harness polyadic relations between vertices beyond plain edges. They have been used to eliminate issues such as over-smoothing or over-squashing, to significantly enhance the accuracy of GNN predictions, to improve the expressiveness of GNN architectures, and for numerous other goals. A plethora of HOGNN models have been introduced, and they come with diverse neural architectures, and even with different notions of what the "higher-order" means. This richness makes it very challenging to appropriately analyze and compare HOGNN models, and to decide in what scenario to use specific ones. To alleviate this, we first design an in-depth taxonomy and a blueprint for HOGNNs. This facilitates designing models that maximize performance. Then, we use our taxonomy to analyze and compare the available HOGNN models. The outcomes of our analysis are synthesized in a set of insights that help to select the most beneficial GNN model in a given scenario, and a comprehensive list of challenges and opportunities for further research into more powerful HOGNNs.

تمثل الشبكات العصبية الرسومية من الدرجة العليا (HOGNN) تقدمًا كبيرًا في نماذج الشبكات العصبية الرسومية (GNN)، حيث تستخدم العلاقات متعددة الأطراف بين الرؤوس لمعالجة التحديات مثل الإفراط في التنعيم أو الضغط الزائد. يعزز هذا التطور دقة وتعبير تنبؤات GNN، حيث يوفر تصنيفًا شاملًا ومخططًا لـ HOGNN لتسهيل تصميم النماذج وتعظيم الأداء.

Las redes neuronales gráficas de orden superior (HOGNN) representan un avance significativo en los modelos de redes neuronales gráficas (GNN), utilizando relaciones poliadicas entre los vértices para abordar desafíos como el sobreajuste y la sobrecompresión. Este desarrollo mejora la precisión y expresividad de las predicciones de GNN, proporcionando una taxonomía y un plano detallado para HOGNN que facilitan el diseño de modelos y la maximización del rendimiento.

Les réseaux de neurones graphiques d'ordre supérieur (HOGNN) représentent une avancée significative dans les modèles de réseaux de neurones graphiques (GNN), utilisant des relations polyadiques entre les sommets pour relever des défis tels que le sur-lissage et le sur-compressage. Ce développement améliore la précision et l'expressivité des prédictions GNN, fournissant une taxonomie et un plan détaillé pour les HOGNN afin de faciliter la conception de modèles et la maximisation des performances.

Higher-order graph neural networks (HOGNNs) represent a significant advancement in graph neural network (GNN) models, utilizing polyadic relations among vertices to address challenges like over-smoothing and over-squashing. This development enhances the accuracy and expressiveness of GNN predictions, providing a comprehensive taxonomy and blueprint for HOGNNs to facilitate model design and performance maximization.

Demystifying Higher-Order Graph Neural Networks

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