论文标题
关于图形卷积神经网络的稳定性在边缘重新布线
On the Stability of Graph Convolutional Neural Networks under Edge Rewiring
论文作者
论文摘要
图形神经网络由于能够适应非欧几里得领域和灌输归纳偏见，因此在机器学习社区中经历了流行。尽管如此，它们的稳定性，即它们对输入中小扰动的稳健性尚不清楚。尽管存在一些结果显示图形神经网络的稳定性，但大多数人以图形拓扑扰动引起的变化大小的上限形式。但是，以现有界限捕获的图形拓扑的变化往往不会以结构属性表示，从而限制了我们对模型鲁棒性属性的理解。在这项工作中，我们开发了一种可解释的上限阐明，即图神经网络在高度节点之间重新布线稳定。相似类型界限的这种结合和进一步的研究提供了对图神经网络的稳定性特性的进一步理解。
Graph neural networks are experiencing a surge of popularity within the machine learning community due to their ability to adapt to non-Euclidean domains and instil inductive biases. Despite this, their stability, i.e., their robustness to small perturbations in the input, is not yet well understood. Although there exists some results showing the stability of graph neural networks, most take the form of an upper bound on the magnitude of change due to a perturbation in the graph topology. However, the change in the graph topology captured in existing bounds tend not to be expressed in terms of structural properties, limiting our understanding of the model robustness properties. In this work, we develop an interpretable upper bound elucidating that graph neural networks are stable to rewiring between high degree nodes. This bound and further research in bounds of similar type provide further understanding of the stability properties of graph neural networks.
