论文标题
置换模棱两可的神经网络和高阶图形编码器的一般理论
The general theory of permutation equivarant neural networks and higher order graph variational encoders
论文作者
论文摘要
以前的对称群体等效神经网络的工作通常仅考虑通过将单个向量的元素置于元素来起作用的情况。在本文中，我们得出了一般置换量表层的公式，包括该层通过同时置换其行和列来对矩阵作用的情况。这种情况自然出现在图形学习和关系学习应用中。作为高阶置换量表网络的特定情况，我们提出了一个二阶图形编码器，并表明模型的潜在分布必须可以交换。我们证明了这种体系结构对引文图和分子图生成中链接预测任务的功效。
Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers, including the case where the layer acts on matrices by permuting their rows and columns simultaneously. This case arises naturally in graph learning and relation learning applications. As a specific case of higher order permutation equivariant networks, we present a second order graph variational encoder, and show that the latent distribution of equivariant generative models must be exchangeable. We demonstrate the efficacy of this architecture on the tasks of link prediction in citation graphs and molecular graph generation.
