Permute Me Softly: Learning Soft Permutations for Graph Representations

TL;DR

This paper introduces $$-GNN, a novel graph neural network that learns soft permutation matrices to create a common vector space for graphs, enabling effective graph classification and regression.

Contribution

The paper proposes $$-GNN, a new architecture that learns soft permutations for graphs, providing an alternative to message passing neural networks.

Findings

Achieves competitive performance on graph classification tasks.

Efficiently handles large graphs with relaxed stochastic matrices.

Provides a new perspective on graph representation learning.

Abstract

Graph neural networks (GNNs) have recently emerged as a dominant paradigm for machine learning with graphs. Research on GNNs has mainly focused on the family of message passing neural networks (MPNNs). Similar to the Weisfeiler-Leman (WL) test of isomorphism, these models follow an iterative neighborhood aggregation procedure to update vertex representations, and they next compute graph representations by aggregating the representations of the vertices. Although very successful, MPNNs have been studied intensively in the past few years. Thus, there is a need for novel architectures which will allow research in the field to break away from MPNNs. In this paper, we propose a new graph neural network model, so-called $\pi$-GNN which learns a "soft" permutation (i.e., doubly stochastic) matrix for each graph, and thus projects all graphs into a common vector space. The learned matrices impose a "soft" ordering on the vertices of the input graphs, and based on this ordering, the adjacency matrices are mapped into vectors. These vectors can be fed into fully-connected or convolutional layers to deal with supervised learning tasks. In case of large graphs, to make the model more efficient in terms of running time and memory, we further relax the doubly stochastic matrices to row stochastic matrices. We empirically evaluate the model on graph classification and graph regression datasets and show that it achieves performance competitive with state-of-the-art models.