Thomas Bailie

Thomas Bailie, Yun Sing Koh, Karthik Mukkavilli

Graphs model latent variable relationships in many real-world systems, and Message Passing Neural Networks (MPNNs) are widely used to learn such structures for downstream tasks. While edge-based MPNNs effectively capture local interactions, their expressive power is theoretically bounded, limiting the discovery of higher-order relationships. We introduce the Higher-Order Graph Attention (HoGA) module, which constructs a k-order attention matrix by sampling subgraphs to maximize diversity among feature vectors. Unlike existing higher-order attention methods that greedily resample similar k-order relationships, HoGA targets diverse modalities in higher-order topology, reducing redundancy and expanding the range of captured substructures. Applied to two single-hop attention models, HoGA achieves at least a 5% accuracy gain on all benchmark node classification datasets and outperforms recent baselines on six of eight datasets. Code is available at https://github.com/TB862/Higher_Order.

Thomas Bailie, Yun Sing Koh, S. Karthik Mukkavilli et al.

Graphical forecasting models learn the structure of time series data via projecting onto a graph, with recent techniques capturing spatial-temporal associations between variables via edge weights. Hierarchical variants offer a distinct advantage by analysing the time series across multiple resolutions, making them particularly effective in tasks like global weather forecasting, where low-resolution variable interactions are significant. A critical challenge in hierarchical models is information loss during forward or backward passes through the hierarchy. We propose the Hierarchical Graph Flow (HiGFlow) network, which introduces a memory buffer variable of dynamic size to store previously seen information across variable resolutions. We theoretically show two key results: HiGFlow reduces smoothness when mapping onto new feature spaces in the hierarchy and non-strictly enhances the utility of message-passing by improving Weisfeiler-Lehman (WL) expressivity. Empirical results demonstrate that HiGFlow outperforms state-of-the-art baselines, including transformer models, by at least an average of 6.1% in MAE and 6.2% in RMSE. Code is available at https://github.com/TB862/ HiGFlow.git.