ON RECOVERABILITY OF GRAPH NEURAL NETWORK REPRESENTATIONS

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 \textit{recoverability}, which is tightly related to information aggregation in GNNs,and based on this concept, develop the method for GNN embedding analysis.Through extensive experimental results on various datasets and different GNN architectures, we demonstrate that estimated recoverability correlates with aggregation method expressivity and graph sparsification quality.The code to reproduce our experiments is available at \url{https://github.com/Anonymous1252022/Recoverability}.