论文标题
简单的神经网络
Simplicial Neural Networks
论文作者
论文摘要
我们提出了简单的神经网络（SNN），这是图形神经网络对生活在一类称为简单复合物的拓扑空间上的数据的概括。这些是图形的自然多维扩展，不仅编码成对关系，而且还编码顶点之间的高阶交互 - 使我们可以考虑更丰富的数据，包括向量字段和$ n $ fold-fold合作网络。我们定义了一个适当的卷积概念，即我们利用构建所需的卷积神经网络。我们测试了SNN的任务，该任务是将丢失的数据归为合作综合体。
We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not only pairwise relationships but also higher-order interactions between vertices - allowing us to consider richer data, including vector fields and $n$-fold collaboration networks. We define an appropriate notion of convolution that we leverage to construct the desired convolutional neural networks. We test the SNNs on the task of imputing missing data on coauthorship complexes.
