论文标题
图形拓扑特征的神经近似
Neural Approximation of Graph Topological Features
论文作者
论文摘要
基于持续同源性的拓扑特征捕获高阶结构信息，以增强图形神经网络方法。但是，计算扩展的持续同源性摘要对于大而密集的图表仍然很慢，对于学习管道来说，可能是一个严重的瓶颈。受神经算法推理的成功启发，我们提出了一个新颖的图神经网络，以有效地估算图表上的扩展持久图（EPDS）。我们的模型建立在算法的见解上，并受益于更好的监督和与EPD计算算法更紧密的一致性。我们通过在近似EPD和下游图表示学习任务上具有令人信服的经验结果来验证我们的方法。我们的方法也很有效。在大图图上，我们将计算加速近100倍。
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and can be a serious bottleneck for the learning pipeline. Inspired by recent success in neural algorithmic reasoning, we propose a novel graph neural network to estimate extended persistence diagrams (EPDs) on graphs efficiently. Our model is built on algorithmic insights, and benefits from better supervision and closer alignment with the EPD computation algorithm. We validate our method with convincing empirical results on approximating EPDs and downstream graph representation learning tasks. Our method is also efficient; on large and dense graphs, we accelerate the computation by nearly 100 times.
