Link Prediction with Relational Hypergraphs

Link prediction with knowledge graphs has been thoroughly studied in graph machine learning, leading to a rich landscape of graph neural network architectures with successful applications. Nonetheless, it remains challenging to transfer the success of these architectures to link prediction with relational hypergraphs. The presence of relational hyperedges makes link prediction a task between $k$ nodes for varying choices of $k$, which is substantially harder than link prediction with knowledge graphs, where every relation is binary ($k=2$). In this paper, we propose two frameworks for link prediction with relational hypergraphs and conduct a thorough analysis of the expressive power of the resulting model architectures via corresponding relational Weisfeiler-Leman algorithms, and also via some natural logical formalisms. Through extensive empirical analysis, we validate the power of the proposed model architectures on various relational hypergraph benchmarks. The resulting model architectures substantially outperform every baseline for inductive link prediction, and lead to state-of-the-art results for transductive link prediction. Our study therefore unlocks applications of graph neural networks to fully relational structures.

Cooperative Graph Neural Networks

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either 'listen', 'broadcast', 'listen and broadcast', or to 'isolate'. The standard message propagation scheme can then be viewed as a special case of this framework where every node 'listens and broadcasts' to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic dataset and on real-world datasets.

A Theory of Link Prediction via Relational Weisfeiler-Leman

Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains highly incomplete in the context of knowledge graphs. The goal of this work is to provide a systematic understanding of the landscape of graph neural networks for knowledge graphs pertaining the prominent task of link prediction. Our analysis entails a unifying perspective on seemingly unrelated models, and unlocks a series of other models. The expressive power of various models is characterized via a corresponding relational Weisfeiler-Leman algorithm with different initialization regimes. This analysis is extended to provide a precise logical characterization of the class of functions captured by a class of graph neural networks. Our theoretical findings explain the benefits of some widely employed practical design choices, which are validated empirically.