标题： 基于得分的生成建模的排列不变图生成 显示英文标题

标题： Permutation Invariant Graph Generation via Score-Based Generative Modeling

摘要： 学习图结构数据的生成模型具有挑战性，因为图是离散的、组合的，且底层数据分布对节点顺序是不变的。 然而，现有的大多数图生成模型并不对所选顺序具有不变性，这可能导致学习到的分布出现不良偏差。 为了解决这个困难，我们提出了一种排列不变的方法来建模图，使用了基于分数的生成建模的最新框架。 具体来说，我们设计了一个排列等变的多通道图神经网络，以对输入图的数据分布梯度（即分数函数）进行建模。 这种梯度的排列等变模型隐式地定义了一个图的排列不变分布。 我们通过分数匹配训练这个图神经网络，并通过退火的朗之万动力学进行采样。 在实验中，我们首先展示了这种新架构在学习离散图算法方面的能力。 对于图生成，我们发现我们的学习方法在基准数据集上取得了优于或与现有模型相当的结果。 显示英文摘要

摘要： Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for graphs are not invariant to the chosen ordering, which might lead to an undesirable bias in the learned distribution. To address this difficulty, we propose a permutation invariant approach to modeling graphs, using the recent framework of score-based generative modeling. In particular, we design a permutation equivariant, multi-channel graph neural network to model the gradient of the data distribution at the input graph (a.k.a., the score function). This permutation equivariant model of gradients implicitly defines a permutation invariant distribution for graphs. We train this graph neural network with score matching and sample from it with annealed Langevin dynamics. In our experiments, we first demonstrate the capacity of this new architecture in learning discrete graph algorithms. For graph generation, we find that our learning approach achieves better or comparable results to existing models on benchmark datasets.