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.
翻译:图形是生成不同大小的图形的一般和强大的模型。 在本文中, 我们提议直接使用神经网络来模拟图形, 获取隐形图形神经代表( INGR) 。 建模和重建图形的现有工作往往以固定分辨率的笔记式常态表示方式近似目标图形。 我们的IGNR的好处是, 它可以代表图解, 达到任意分辨率, 并且一旦了解模型, 就可以自然和高效地生成任意大小的图解, 并有理想的结构。 此外, 我们允许输入图数据不匹配, 并且通过利用 Gromov- Wasserstein 的距离, 具有不同的大小。 我们首先通过在图形学习任务上展示模型的优异性表现来展示模型的有效性 。 我们然后提议扩展IGNR, 并将其纳入自动编码框架, 并在更一般的图形学习设置下展示其良好性能 。 我们还表明, 我们的模型适合于图形代表学习和图形生成。