Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across a broad spectrum of disciplines, from life to social and engineering sciences. Despite their practical success, our theoretical understanding of the properties of GNNs remains highly incomplete. Recent theoretical advancements primarily focus on elucidating the coarse-grained expressive power of GNNs, predominantly employing combinatorial techniques. However, these studies do not perfectly align with practice, particularly in understanding the generalization behavior of GNNs when trained with stochastic first-order optimization techniques. In this position paper, we argue that the graph machine learning community needs to shift its attention to developing a more balanced theory of graph machine learning, focusing on a more thorough understanding of the interplay of expressive power, generalization, and optimization.

机器学习与图神经网络，尤其是使用图神经网络（GNN）的机器学习，在各个领域的图数据广泛应用中受到了广泛关注。然而，对于GNN的性质仍存在理论上的不完备性。最近的理论进展主要集中于阐明GNN的粗粒度表达能力，主要使用组合技巧。然而，这些研究与实践并不完全一致，特别是在理解使用随机一阶优化技术训练时GNN的泛化行为方面。在本文中，我们将论证图机器学习社区需要将关注点转向发展一个更加平衡的图机器学习理论，重点研究表达能力、泛化和优化的相互作用。

图机器学习基础的未来方向