Despite advances in generative methods, accurately modeling the distribution of graphs remains a challenging task primarily because of the absence of predefined or inherent unique graph representation. Two main strategies have emerged to tackle this issue: 1) restricting the number of possible representations by sorting the nodes, or 2) using permutation-invariant/equivariant functions, specifically Graph Neural Networks (GNNs). In this paper, we introduce a new framework named Discrete Graph Auto-Encoder (DGAE), which leverages the strengths of both strategies and mitigate their respective limitations. In essence, we propose a strategy in 2 steps. We first use a permutation-equivariant auto-encoder to convert graphs into sets of discrete latent node representations, each node being represented by a sequence of quantized vectors. In the second step, we sort the sets of discrete latent representations and learn their distribution with a specifically designed auto-regressive model based on the Transformer architecture. Through multiple experimental evaluations, we demonstrate the competitive performances of our model in comparison to the existing state-of-the-art across various datasets. Various ablation studies support the interest of our method.

翻译：尽管生成方法取得了进展，准确建模图的分布仍然是一项具有挑战性的任务，主要原因是缺乏预定义的或固有的唯一图表示。为了解决这一问题，出现了两种主要策略：1）通过对节点进行排序来限制可能表示的数量；2）使用置换不变/等变函数，特别是图神经网络（GNNs）。在本文中，我们提出了一种名为离散图自编码器（DGAE）的新框架，它结合了这两种策略的优势并缓解了各自的局限性。本质上，我们提出了一种两步策略。首先，我们使用置换等变自编码器将图转换为离散潜在节点表示的集合，每个节点由一系列量化向量表示。在第二步中，我们对离散潜在表示的集合进行排序，并使用基于Transformer架构的专门设计的自回归模型学习其分布。通过多次实验评估，我们在各种数据集上证明了我们的模型与现有最先进方法相比具有竞争力的性能。多项消融研究支持了我们方法的有效性。