The standard approach to representation learning on attributed graphs -- i.e., simultaneously reconstructing node attributes and graph structure -- is geometrically flawed, as it merges two potentially incompatible metric spaces. This forces a destructive alignment that erodes information about the graph's underlying generative process. To recover this lost signal, we introduce a custom variational autoencoder that separates manifold learning from structural alignment. By quantifying the metric distortion needed to map the attribute manifold onto the graph's Heat Kernel, we transform geometric conflict into an interpretable structural descriptor. Experiments show our method uncovers connectivity patterns and anomalies undetectable by conventional approaches, proving both their theoretical inadequacy and practical limitations.

翻译：属性图表示学习的标准方法——即同时重构节点属性与图结构——在几何上存在缺陷，因为它合并了两个可能不兼容的度量空间。这迫使一种破坏性的对齐，从而侵蚀了关于图底层生成过程的信息。为了恢复这一丢失的信号，我们引入了一种定制化的变分自编码器，将流形学习与结构对齐分离开来。通过量化将属性流形映射到图热核所需的度量畸变，我们将几何冲突转化为可解释的结构描述符。实验表明，我们的方法能够揭示传统方法无法检测的连接模式与异常，从而证明了它们在理论上的不足与实践上的局限性。