Graph neural networks (GNNs) appear to be powerful tools to learn state representations for agents in distributed, decentralized multi-agent systems, but generate catastrophically incorrect predictions when nodes update asynchronously during inference. This failure under asynchrony effectively excludes these architectures from many potential applications where synchrony is difficult or impossible to enforce, e.g., robotic swarms or sensor networks. In this work we identify ''implicitly-defined'' GNNs as a class of architectures which is provably robust to asynchronous ''hogwild'' inference, adapting convergence guarantees from work in asynchronous and distributed optimization. We then propose a novel implicitly-defined GNN architecture, which we call an energy GNN. We show that this architecture outperforms other GNNs from this class on a variety of synthetic tasks inspired by multi-agent systems.

SUMMARY: The Pseudomonas aeruginosa Interaction Database, PaIntDB, is an intuitive web-based tool for network-based systems biology analyses using protein-protein interactions (PPI) in this medically important pathogen. It enables the integration and visualization of omics analyses including RNA-Seq and Tn-Seq. High-throughput datasets can be mapped onto PPI networks, which can be explored visually and filtered to uncover novel putative molecular pathways related to the conditions of study. PaIntDB contains the most comprehensive P.aeruginosa interactome to date, collected from a variety of resources, including interactions predicted computationally to further expand analysis capabilities. The web server implementation makes it easily extendable to other bacterial species. AVAILABILITY AND IMPLEMENTATION: PaIntDB is freely available at https://www.paintdb.ca, the source code and database file are available at https://github.com/yavyx/PaIntDB. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.