Implicit Graphon Neural Representation
This work addresses the challenge of flexible and efficient graph modeling for researchers and practitioners in machine learning, though it appears incremental as it builds on existing graphon approximation methods.
The authors tackled the problem of modeling graphons, which are general models for generating graphs of varying sizes, by proposing Implicit Graphon Neural Representation (IGNR) that can represent graphons up to arbitrary resolutions and enable efficient generation of arbitrary-sized graphs, demonstrating superior performance on graphon learning tasks and good performance in graph representation learning and generation.
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.