论文标题
从滑轮和神经切线内核的角度来看图形卷积网络
Graph Convolutional Networks from the Perspective of Sheaves and the Neural Tangent Kernel
论文作者
论文摘要
图形卷积网络是一类流行的深神经网络算法，在许多关系学习任务中都表现出成功。尽管取得了成功，但图形卷积网络仍表现出许多特殊的特征，包括偏向学习超平滑和同质函数的偏见，由于这些算法的复杂性质，这些功能不容易被诊断出来。我们建议通过研究捆卷卷积网络的神经切线内核来弥合这一差距，这是图形卷积网络的拓扑概括。为此，我们得出了捆卷卷网络的神经切线内核的参数化，该卷积网络将函数分为两个部分：一个由图形确定的正向扩散过程驱动，另一个由节点在输出层上激活的复合效应确定。这种以几何为重点的派生产生了许多直接见解，我们会详细讨论这些见解。
Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features, including a bias towards learning oversmoothed and homophilic functions, which are not easily diagnosed due to the complex nature of these algorithms. We propose to bridge this gap in understanding by studying the neural tangent kernel of sheaf convolutional networks--a topological generalization of graph convolutional networks. To this end, we derive a parameterization of the neural tangent kernel for sheaf convolutional networks which separates the function into two parts: one driven by a forward diffusion process determined by the graph, and the other determined by the composite effect of nodes' activations on the output layer. This geometrically-focused derivation produces a number of immediate insights which we discuss in detail.
