On the Expressive Power of Geometric Graph Neural Networks

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL's discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at https://github.com/chaitjo/geometric-gnn-dojoComment: NeurIPS 2022 Workshop on Symmetry and Geometry in Neural Representation

From Hypergraph Energy Functions to Hypergraph Neural Networks

Hypergraphs are a powerful abstraction for representing higher-order interactions between entities of interest. To exploit these relationships in making downstream predictions, a variety of hypergraph neural network architectures have recently been proposed, in large part building upon precursors from the more traditional graph neural network (GNN) literature. Somewhat differently, in this paper we begin by presenting an expressive family of parameterized, hypergraph-regularized energy functions. We then demonstrate how minimizers of these energies effectively serve as node embeddings that, when paired with a parameterized classifier, can be trained end-to-end via a supervised bilevel optimization process. Later, we draw parallels between the implicit architecture of the predictive models emerging from the proposed bilevel hypergraph optimization, and existing GNN architectures in common use. Empirically, we demonstrate state-of-the-art results on various hypergraph node classification benchmarks. Code is available at https://github.com/yxzwang/PhenomNN.Comment: Accepted to ICML 202

Learning and comparing functional connectomes across subjects

Functional connectomes capture brain interactions via synchronized fluctuations in the functional magnetic resonance imaging signal. If measured during rest, they map the intrinsic functional architecture of the brain. With task-driven experiments they represent integration mechanisms between specialized brain areas. Analyzing their variability across subjects and conditions can reveal markers of brain pathologies and mechanisms underlying cognition. Methods of estimating functional connectomes from the imaging signal have undergone rapid developments and the literature is full of diverse strategies for comparing them. This review aims to clarify links across functional-connectivity methods as well as to expose different steps to perform a group study of functional connectomes

Near Real-Time Distributed State Estimation via AI/ML-Empowered 5G Networks

Fifth-Generation (5G) networks have a potential to accelerate power system transition to a flexible, softwarized, data-driven, and intelligent grid. With their evolving support for Machine Learning (ML)/Artificial Intelligence (AI) functions, 5G networks are expected to enable novel data-centric Smart Grid (SG) services. In this paper, we explore how data-driven SG services could be integrated with ML/AI-enabled 5G networks in a symbiotic relationship. We focus on the State Estimation (SE) function as a key element of the energy management system and focus on two main questions. Firstly, in a tutorial fashion, we present an overview on how distributed SE can be integrated with the elements of the 5G core network and radio access network architecture. Secondly, we present and compare two powerful distributed SE methods based on: i) graphical models and belief propagation, and ii) graph neural networks. We discuss their performance and capability to support a near real-time distributed SE via 5G network, taking into account communication delays