论文标题
隐式图形神经表示
Implicit Graphon Neural Representation
论文作者
论文摘要
图形是一般且强大的模型，用于生成不同大小的图形。在本文中，我们建议使用神经网络直接对图形进行建模，从而获得隐式图形神经表示（IGNR）。现有在建模和重建图形中的工作通常通过固定分辨率的恒定表示形式近似目标图形。我们的IGNR的好处是它可以将图形表示为任意分辨率，并在学习模型后，可以自然，有效地生成具有所需结构的任意大小的图形。此外，我们通过利用Gromov-Wasserstein距离来允许输入图数据不一致，并具有不同的尺寸。我们首先通过在Graphon学习任务上显示出卓越的性能来证明我们的模型的有效性。然后，我们提出了可以将IGNR扩展的扩展，该扩展可以将其纳入自动编码器框架中，并在更一般的Graphon学习环境下演示其良好的性能。我们还表明，我们的模型适用于图表的学习和图形生成。
Graphons are general and powerful models for generating graphs of varying size. In this paper, we propose to directly model graphons using neural networks, obtaining Implicit Graphon Neural Representation (IGNR). Existing work in modeling and reconstructing graphons often approximates a target graphon by a fixed resolution piece-wise constant representation. Our IGNR has the benefit that it can represent graphons up to arbitrary resolutions, and enables natural and efficient generation of arbitrary sized graphs with desired structure once the model is learned. Furthermore, we allow the input graph data to be unaligned and have different sizes by leveraging the Gromov-Wasserstein distance. We first demonstrate the effectiveness of our model by showing its superior performance on a graphon learning task. We then propose an extension of IGNR that can be incorporated into an auto-encoder framework, and demonstrate its good performance under a more general setting of graphon learning. We also show that our model is suitable for graph representation learning and graph generation.
