Illustration of simplices, boundary operators, and simplex downsampling. Credit: IEEE Transactions on Pattern Analysis and Machine Intelligence (2025). DOI: 10.1109/tpami.2025.3594226

As an emerging technology in the field of artificial intelligence (AI), graph neural networks (GNNs) are deep learning models designed to process graph-structured data. Currently, GNNs are effective at capturing relationships between nodes and edges in data, but often overlook higher-order, complex connections. To address this challenge, a research team at The Hong Kong Polytechnic University (PolyU) has developed a new heterogeneous graph attention network, revolutionizing the modeling of complex relationships in graph-structured data. This innovation is poised to break through AI application limitations in fields such as neuroscience, logistics, computer vision and biology.

In simple terms, traditional GNNs mainly consider pairwise relationships such as the connections of "A to B" and "B to C," having difficulties in understanding group interactions among A, B and C. Developed by Prof. Anqi QIU, Professor of the PolyU Department of Health Technology and Informatics and Global STEM Scholar, and her research team, the new "Hodge-Laplacian Heterogeneous Graph Attention Network" (HL-HGAT) can learn and analyze heterogeneous signals at different levels, capturing complex associations among various graph structures.

Mathematically, k-simplices are fundamental elements of higher-dimensional geometry that capture higher-order relationships among multiple nodes: a 0-simplex is a single node, a 1-simplex is an edge connecting two nodes, a 2-simplex is a triangle formed by three nodes and so on. The HL-HGAT model interprets graphs as simplicial complexes, enabling it to simultaneously capture complex interactions among nodes, edges, triangles and other multi-level structures, greatly enhancing the model’s ability to understand intricate data relationships.

At the core of HL-HGAT is the Hodge-Laplacian (HL) operator, which provides a mathematical framework for modeling and propagating signals on simplicial complexes. This allows the network to break through the limitations of pairwise relationships and construct more precise models for complex, multi-level interactions in structured data. In the field of dynamic graphs, HL-HGAT’s major breakthrough lies in its ability to extend high-order topological representations into the temporal domain, combining efficient HL filtering, adaptive attention mechanisms and heterogeneous signal decomposition to reveal complex time-varying motifs that traditional static GNNs cannot capture.

Prof. Qiu said, "The HL-HGAT model demonstrates broad efficacy and versatility across diverse graph-based scenarios, from theoretical optimization problems to real-world biomedical applications. It has been comprehensively evaluated across diverse graph applications, and the results demonstrate the model’s adaptability as a unified framework capable of handling optimization, classification, regression and multimodal learning tasks across disciplines."

The research team conducted comprehensive tests in multiple fields. In logistics, HL-HGAT effectively solved the classic Traveling Salesman Problem (how to plan the shortest delivery route), helping logistics companies save significant time and costs. In computer vision, HL-HGAT analyzes images by converting them into graph structures, outperforming traditional GNNs in the CIFAR-10 image classification task by capturing image details with greater precision. In chemistry, HL-HGAT has achieved superior accuracy in predicting molecular properties, accelerating the development of new drugs.

In neuroscience and medical diagnostics, HL-HGAT also demonstrates high application value. The team applied it to functional magnetic resonance imaging data analysis, accurately predicting intelligence and brain age, and even discovering abnormal "tripartite synapses" in the default mode and limbic networks of depression patients—subtle changes that traditional methods cannot detect. Additionally, HL-HGAT can identify early cortical thinning and disrupted neural connectivity in Alzheimer’s disease patients, enabling more timely detection of symptoms.

This innovative HL-HGAT model not only achieves remarkable results in tackling complex graph-based tasks in scientific and industrial applications, but also marks a significant advancement in graph neural network technology. The research, in a paper titled "HL-HGAT: Heterogeneous Graph Attention Network via Hodge-Laplacian Operator," has been published in IEEE Transactions on Pattern Analysis and Machine Intelligence.

More information: Jinghan Huang et al, HL-HGAT: Heterogeneous Graph Attention Network via Hodge-Laplacian Operator, IEEE Transactions on Pattern Analysis and Machine Intelligence (2025). DOI: 10.1109/tpami.2025.3594226

Citation: New graph attention network models higher-order relationships in complex graph data (2026, January 28) retrieved 28 January 2026 from https://techxplore.com/news/2026-01-graph-attention-network-higher-relationships.html

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