[2604.02615] Complex-Valued GNNs for Distributed Basis-Invariant Control of Planar Systems

Computer Science > Machine Learning arXiv:2604.02615 (cs) [Submitted on 3 Apr 2026] Title:Complex-Valued GNNs for Distributed Basis-Invariant Control of Planar Systems Authors:Samuel Honor, Mohamed Abdelnaby, Kevin Leahy View a PDF of the paper titled Complex-Valued GNNs for Distributed Basis-Invariant Control of Planar Systems, by Samuel Honor and 2 other authors View PDF HTML (experimental) Abstract:Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in the network collect geometric observations in compatible bases, which limits the usefulness of such controllers in GPS-denied and compass-denied environments. This paper presents a GNN parametrization that is globally invariant to choice of local basis. 2D geometric features and transformations between bases are expressed in the complex domain. Inside each GNN layer, complex-valued linear layers with phase-equivariant activation functions are used. When viewed from a fixed global frame, all policies learned by this architecture are strictly invariant to choice of local frames. This architecture is shown to increase the data efficiency, tracking performance, and generalization of learned control when compared to a real-valued baseline on an imitation learning flocking task. Comments: Subjects: Machine Learning (cs.LG) Cite as: arXiv:2604.02615...