تحليل انحنا در شبكه‌هاي عصبي گراف

A graph is a mathematical structure that has various manifestations in the real world. Connections in social networks, road maps, molecular structures, an‎d relationships between drugs an‎d proteins are different examples of how graphs are used in real life. To analyze, model, an‎d predict the behavior of graphs using artificial intelligence, Graph Neural Networks are employed. However, these networks face challenges such as low accuracy on certain datasets, over-smoothing, an‎d over-squashing. Previous studies have shown that there is a close relationship between the phenomena of over-smoothing an‎d over-squashing an‎d the concept of graph curvature. In this research, we first provide a critical eva‎luation of the claimed relationship between graph curvature an‎d the over-squashing problem. Then, we theoretically examine the over-squashing phenomenon in a specific case using a synthetic designed dataset created for this purpose. In addition, we study the application of graph curvature to improve the accuracy of dynamic graph neural networks through the use of local curvature profiles, an‎d we demonstrate that employing curvature can enhance the performance of these networks. Furthermore, we critique methods such as hyperbolic graph convolutional networks, which utilize Riemannian manifolds in the structure of graph neural networks. Finally, we introduce a new architecture called the Graph Convolution Network with Kernel Points, which performs the convolution operation by embedding graph nodes into a continuous space.

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