Chenhao Niu

Ziwei Zhang, Chenhao Niu, Peng Cui et al.

Graph neural networks (GNNs) are emerging machine learning models on graphs. Permutation-equivariance and proximity-awareness are two important properties highly desirable for GNNs. Both properties are needed to tackle some challenging graph problems, such as finding communities and leaders. In this paper, we first analytically show that the existing GNNs, mostly based on the message-passing mechanism, cannot simultaneously preserve the two properties. Then, we propose Stochastic Message Passing (SMP) model, a general and simple GNN to maintain both proximity-awareness and permutation-equivariance. In order to preserve node proximities, we augment the existing GNNs with stochastic node representations. We theoretically prove that the mechanism can enable GNNs to preserve node proximities, and at the same time, maintain permutation-equivariance with certain parametrization. We report extensive experimental results on ten datasets and demonstrate the effectiveness and efficiency of SMP for various typical graph mining tasks, including graph reconstruction, node classification, and link prediction.

Chenhao Niu, Yang Song, Jiaming Song et al.

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.