Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. However, they still encounter several challenges: 1) Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization and should be incorporated into the model design. Existing simulators either consider insufficient symmetry, or enforce excessive equivariance in practice when symmetry is partially broken by gravity.

Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes for this task, overtaking classical methods based on fixed molecular kernels. However, they still appear very limited from a theoretical perspective, since regular GNNs cannot distinguish certain types of graphs. In this work we close this gap between theory and practice. We show that GNNs with directed edge embeddings and two-hop message passing are indeed universal approximators for predictions that are invariant to translation, and equivariant to permutation and rotation. We then leverage these insights and multiple structural improvements to propose the geometric message passing neural network (GemNet). We demonstrate the benefits of the proposed changes in multiple ablation studies. GemNet outperforms previous models on the COLL, MD17, and OC20 datasets by 34 %, 41 %, and 20 %, respectively, and performs especially well on the most challenging molecules. Our implementation is available online. 1

The most popular design paradigm for Graph Neural Networks (GNNs) is 1-hop message passing--aggregating information from 1-hop neighbors repeatedly. However, the expressive power of 1-hop message passing is bounded by the WeisfeilerLehman (1-WL) test. Recently, researchers extended 1-hop message passing to K-hop message passing by aggregating information from K-hop neighbors of nodes simultaneously. However, there is no work on analyzing the expressive power of K-hop message passing. In this work, we theoretically characterize the expressive power of K-hop message passing.

Inductive relation prediction (IRP)--where entities can be different during training and inference--has shown great power for completing evolving knowledge graphs. Existing works mainly focus on using graph neural networks (GNNs) to learn the representation of the subgraph induced from the target link, which can be seen as an implicit rule-mining process to measure the plausibility of the target link. However, these methods cannot differentiate the target link and other links during message passing, hence the final subgraph representation will contain irrelevant rule information to the target link, which reduces the reasoning performance and severely hinders the applications for real-world scenarios. To tackle this problem, we propose a novel single-source edge-wise GNN model to learn the Rule-inducEd Subgraph represenTations (REST), which encodes relevant rules and eliminates irrelevant rules within the subgraph. Specifically, we propose a single-source initialization approach to initialize edge features only for the target link, which guarantees the relevance of mined rules and target link. Then we propose several RNN-based functions for edge-wise message passing to model the sequential property of mined rules. REST is a simple and effective approach with theoretical support to learn the rule-induced subgraph representation. Moreover, REST does not need node labeling, which significantly accelerates the subgraph preprocessing time by up to 11.66 . Experiments on inductive relation prediction benchmarks demonstrate the effectiveness of our REST2.

Dna demethylation is associated with malignant progression oflower-grade gliomas.Scientific reports,9(1):1-12, 2019.

Recently,researchers extended 1-hop message passing to K-hop message passing by aggregating information fromK-hop neighbors of nodes simultaneously. However, there is no work on analyzing the expressive powerofK-hopmessagepassing.

A common approach to create more expressive GNNs is to change the message passing function of MPNNs. If a GNN is more expressive than MPNNs by adapting the message passing function, we call this non-standard message passing . Examples of this are message passing variants that operate on subgraphs [Frasca et al., 2022, Bevilacqua