Faster Inference Time for GNNs using coarsening

Graph Neural Networks (GNNs) have shown remarkable success in various graph-based tasks, including node classification, node regression, graph classification, and graph regression. However, their scalability remains a significant challenge, particularly when dealing with large-scale graphs. To tackle this challenge, coarsening-based methods are used to reduce the graph into a smaller one, resulting in faster computation. However, no previous research has tackled the computation cost during the inference. This motivated us to ponder whether we can trade off the improvement in training time of coarsening-based approaches with inference time. This paper presents a novel approach to improve the scalability of GNNs through subgraph-based techniques. We reduce the computational burden during the training and inference phases by using the coarsening algorithm to partition large graphs into smaller, manageable subgraphs. Previously, graph-level tasks had not been explored using this approach. We propose a novel approach for using the coarsening algorithm for graph-level tasks such as graph classification and graph regression. We conduct extensive experiments on multiple benchmark datasets to evaluate the performance of our approach. The results demonstrate that our subgraph-based GNN method achieves competitive results in node classification, node regression, graph classification, and graph regression tasks compared to traditional GNN models. Furthermore, our approach significantly reduces the inference time, enabling the practical application of GNNs to large-scale graphs.

Improving Expressivity of Graph Neural Networks using Localization

In this paper, we propose localized versions of Weisfeiler-Leman (WL) algorithms in an effort to both increase the expressivity, as well as decrease the computational overhead. We focus on the specific problem of subgraph counting and give localized versions of $k-$WL for any $k$. We analyze the power of Local $k-$WL and prove that it is more expressive than $k-$WL and at most as expressive as $(k+1)-$WL. We give a characterization of patterns whose count as a subgraph and induced subgraph are invariant if two graphs are Local $k-$WL equivalent. We also introduce two variants of $k-$WL: Layer $k-$WL and recursive $k-$WL. These methods are more time and space efficient than applying $k-$WL on the whole graph. We also propose a fragmentation technique that guarantees the exact count of all induced subgraphs of size at most 4 using just $1-$WL. The same idea can be extended further for larger patterns using $k>1$. We also compare the expressive power of Local $k-$WL with other GNN hierarchies and show that given a bound on the time-complexity, our methods are more expressive than the ones mentioned in Papp and Wattenhofer[2022a].