Although recent network representation learning (NRL) works in text-attributed networks demonstrated superior performance for various graph inference tasks, learning network representations could always raise privacy concerns when nodes represent people or human-related variables. Moreover, standard NRLs that leverage structural information from a graph proceed by first encoding pairwise relationships into learned representations and then analysing its properties. This approach is fundamentally misaligned with problems where the relationships involve multiple points, and topological structure must be encoded beyond pairwise interactions. Fortunately, the machinery of topological data analysis (TDA) and, in particular, simplicial neural networks (SNNs) offer a mathematically rigorous framework to learn higher-order interactions between nodes. It is critical to investigate if the representation outputs from SNNs are more vulnerable compared to regular representation outputs from graph neural networks (GNNs) via pairwise interactions. In my dissertation, I will first study learning the representations with text attributes for simplicial complexes (RT4SC) via SNNs. Then, I will conduct research on two potential attacks on the representation outputs from SNNs: (1) membership inference attack, which infers whether a certain node of a graph is inside the training data of the GNN model; and (2) graph reconstruction attacks, which infer the confidential edges of a text-attributed network. Finally, I will study a privacy-preserving deterministic differentially private alternating direction method of multiplier to learn secure representation outputs from SNNs that capture multi-scale relationships and facilitate the passage from local structure to global invariant features on text-attributed networks.

翻译：尽管近年来在文本属性网络中的网络表示学习（NRL）工作在各种图推理任务中展现出卓越性能，但当节点代表人员或与人相关的变量时，学习网络表示总会引发隐私问题。此外，利用图结构信息的标准NRL通常先通过编码成对关系生成表示，再分析其属性。这种方法与涉及多节点关系的问题根本不相适应，因为此时拓扑结构必须超越成对交互进行编码。幸运的是，拓扑数据分析（TDA）工具，特别是单纯神经网络（SNN），提供了数学上严谨的框架来学习节点间的高阶交互。关键问题在于，与通过成对交互的图神经网络（GNN）的常规表示输出相比，SNN的表示输出是否更容易受到攻击。在我的论文中，我将首先通过SNN研究带有文本属性的单纯复形表示学习（RT4SC）。接着，我将针对SNN表示输出可能面临的两种攻击展开研究：（1）成员推断攻击，即推断图中某节点是否属于GNN模型的训练数据；（2）图重建攻击，即推断文本属性网络中机密边的存在。最后，我将研究一种隐私保护的确定性差分隐私交替方向乘子法，以从SNN中学习安全的表示输出，该输出能捕捉文本属性网络中的多尺度关系，并促进从局部结构到全局不变特征的过渡。