我们是否正确地测量图神经网络中的过度平滑现象？
Are We Measuring Oversmoothing in Graph Neural Networks Correctly?
AI总结：
本文提出通过特征表示的数值或有效秩来测量图神经网络中的过度平滑现象，而非传统基于能量的指标，并通过实验和理论分析证明了该方法的有效性。
摘要：
过度平滑是图神经网络（GNNs）中的一个基本挑战：随着层数的增加，节点嵌入变得越来越相似，模型性能急剧下降。传统上，过度平滑通过测量邻居节点特征相似性的指标来量化，例如狄利克雷能量。我们认为这些指标有关键的局限性，并且无法可靠地捕捉到现实场景中的过度平滑。例如，它们只在非常深的网络中提供有意义的见解，而典型的GNN在仅有的10层时就已经出现性能下降。作为替代方案，我们提出通过检查特征表示的数值或有效秩来测量过度平滑。我们提供了广泛的数值评估，涵盖了多样化的图架构和数据集，以证明基于秩的指标能够一致地捕捉到过度平滑，而基于能量的指标往往失败。值得注意的是，我们发现秩的下降与性能下降紧密相关，即使在能量指标保持不变的情况下也是如此。除了实验评估外，我们还为此方法提供了理论支持，阐明了为什么狄利克雷类度量可能无法捕捉到性能下降，并证明了特征表示的数值秩对于广泛的一类GNN架构会坍缩为一。
英文摘要：
Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drops sharply. Traditionally, oversmoothing has been quantified using metrics that measure the similarity of neighbouring node features, such as the Dirichlet energy. We argue that these metrics have critical limitations and fail to reliably capture oversmoothing in realistic scenarios. For instance, they provide meaningful insights only for very deep networks, while typical GNNs show a performance drop already with as few as 10 layers. As an alternative, we propose measuring oversmoothing by examining the numerical or effective rank of the feature representations. We provide extensive numerical evaluation across diverse graph architectures and datasets to show that rank-based metrics consistently capture oversmoothing, whereas energy-based metrics often fail. Notably, we reveal that drops in the rank align closely with performance degradation, even in scenarios where energy metrics remain unchanged. Along with the experimental evaluation, we provide theoretical support for this approach, clarifying why Dirichlet-like measures may fail to capture performance drop and proving that the numerical rank of feature representations collapses to one for a broad family of GNN architectures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
