Graph Neural Networks (GNNs) have advanced relational data analysis but lack invariance learning techniques common in image classification. In node classification with GNNs, it is actually the ego-graph of the center node that is classified. This research extends the scale invariance concept to node classification by drawing an analogy to image processing: just as scale invariance being used in image classification to capture multi-scale features, we propose the concept of ``scaled ego-graphs''. Scaled ego-graphs generalize traditional ego-graphs by replacing undirected single-edges with ``scaled-edges'', which are ordered sequences of multiple directed edges. We empirically assess the performance of the proposed scale invariance in graphs on seven benchmark datasets, across both homophilic and heterophilic structures. Our scale-invariance-based graph learning outperforms inception models derived from random walks by being simpler, faster, and more accurate. The scale invariance explains inception models' success on homophilic graphs and limitations on heterophilic graphs. To ensure applicability of inception model to heterophilic graphs as well, we further present ScaleNet, an architecture that leverages multi-scaled features. ScaleNet achieves state-of-the-art results on five out of seven datasets (four homophilic and one heterophilic) and matches top performance on the remaining two, demonstrating its excellent applicability. This represents a significant advance in graph learning, offering a unified framework that enhances node classification across various graph types. Our code is available at https://github.com/Qin87/ScaleNet/tree/July25.

翻译：图神经网络（GNNs）在关系数据分析方面取得了进展，但缺乏图像分类中常见的不变性学习技术。在使用GNNs进行节点分类时，实际被分类的是中心节点的自我图。本研究通过类比图像处理，将尺度不变性概念扩展到节点分类：正如尺度不变性在图像分类中用于捕获多尺度特征，我们提出了“尺度化自我图”的概念。尺度化自我图通过将无向单边替换为“尺度边”（即多条有向边的有序序列）来推广传统的自我图。我们在七个基准数据集上，针对同配性和异配性图结构，对所提出的图尺度不变性性能进行了实证评估。基于尺度不变性的图学习方法比基于随机游走的初始模型更简单、更快且更准确，从而表现更优。尺度不变性解释了初始模型在同配性图上的成功及其在异配性图上的局限性。为确保初始模型同样适用于异配性图，我们进一步提出了ScaleNet，一种利用多尺度特征的架构。ScaleNet在七个数据集中的五个（四个同配性图和一个异配性图）上取得了最先进的结果，并在其余两个数据集上达到了顶级性能，展示了其出色的适用性。这代表了图学习领域的重大进展，提供了一个统一的框架，可增强跨不同图类型的节点分类性能。我们的代码可在 https://github.com/Qin87/ScaleNet/tree/July25 获取。