Implicit Graphon Neural Representation
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.
Code (1)
Tasks
Graph GenerationGraph Representation LearningRepresentation LearningSimilar Papers 제목 키워드 기반
Scalable Implicit Graphon Learning
Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit ne…
Data AugmentationThe Graphon Limit Hypothesis: Understanding Neural Network Pruning via Infinite Width Analysis
Sparse neural networks promise efficiency, yet training them effectively remains a fundamental challenge. Despite advances in pruning methods that create sparse architectures, understanding why some sparse structures are…
Network PruningLearning Graphon Autoencoders for Generative Graph Modeling
Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called \textit{graphon autoencoder} to buil…
DecoderEfficient Evolutionary Models with Digraphons
We present two main contributions which help us in leveraging the theory of graphons for modeling evolutionary processes. We show a generative model for digraphons using a finite basis of subgraphs, which is representati…
Pruning at Initialisation through the lens of Graphon Limit: Convergence, Expressivity, and Generalisation
Pruning at Initialisation methods discover sparse, trainable subnetworks before training, but their theoretical mechanisms remain elusive. Existing analyses are often limited to finite-width statistics, lacking a rigorou…