Article Source

• On Recoverability of Graph Neural Network Representation

On Recoverability of Graph Neural Network Representation

• Paper “On Recoverability of Graph Neural Network Representation, Maxim Fisherman”: https://arxiv.org/abs/2201.12843
• Authors: Maxim Fishman, Chaim Baskin, Evgenii Zheltonozhskii, Almog David, Ron Banner, Avi Mendelson

Abstract

Despite their growing popularity, graph neural networks (GNNs) still have multiple unsolved problems, including finding more expressive aggregation methods, propagation of information to distant nodes, and training on large-scale graphs. Understanding and solving such problems require developing analytic tools and techniques. In this work, we propose the notion of recoverability, which is tightly related to information aggregation in GNNs, and based on this concept, develop the method for GNN embedding analysis. We define recoverability theoretically and propose a method for its efficient empirical estimation. We demonstrate, through extensive experimental results on various datasets and different GNN architectures, that estimated recoverability correlates with aggregation method expressivity and graph sparsification quality. Therefore, we believe that the proposed method could provide an essential tool for understanding the roots of the aforementioned problems, and potentially lead to a GNN design that overcomes them.