Graph Neural Networks (GNNs) are de facto solutions to structural data learning. However, it is susceptible to low-quality and unreliable structure, which has been a norm rather than an exception in real-world graphs. Existing graph structure learning (GSL) frameworks still lack robustness and interpretability. This paper proposes a general GSL framework, SE-GSL, through structural entropy and the graph hierarchy abstracted in the encoding tree. Particularly, we exploit the one-dimensional structural entropy to maximize embedded information content when auxiliary neighbourhood attributes are fused to enhance the original graph. A new scheme of constructing optimal encoding trees is proposed to minimize the uncertainty and noises in the graph whilst assuring proper community partition in hierarchical abstraction. We present a novel sample-based mechanism for restoring the graph structure via node structural entropy distribution. It increases the connectivity among nodes with larger uncertainty in lower-level communities. SE-GSL is compatible with various GNN models and enhances the robustness towards noisy and heterophily structures. Extensive experiments show significant improvements in the effectiveness and robustness of structure learning and node representation learning.

翻译：图神经网络（GNNs）是处理结构性数据学习的事实解决方案。然而，它们容易受到低质量和不可靠结构的影响，这在现实世界的图中已成为常态而非例外。现有的图结构学习（GSL）框架仍然缺乏鲁棒性和可解释性。本文通过结构熵和编码树中抽象出的图层次，提出了一种通用的GSL框架SE-GSL。特别地，我们利用一维结构熵最大化嵌入信息量，同时融合辅助邻域属性以增强原始图。提出了一种构建最优编码树的新方案以最小化图中的不确定性和噪声，同时确保层次抽象中适当的社区划分。我们提出了一种新颖的基于样本的机制，通过节点结构熵分布恢复图结构。该机制增加了下层社区中不确定性较大节点之间的连通性。SE-GSL与各类GNN模型兼容，并增强了对噪声和异质结构的鲁棒性。大量实验表明，其在结构学习和节点表示学习的效果与鲁棒性方面均有显著提升。