# Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data

arXiv: https://arxiv.org/abs/2403.06687 · HTML: https://mlsanity.com/paper/2403.06687/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 75 references that are in the map.
- First posted on arXiv 11 Mar 2024.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [BrainGB: A Benchmark for Brain Network Analysis with Graph Neural Networks](https://mlsanity.com/paper/2204.07054/) (2022)
- [Knowledge-aware Coupled Graph Neural Network for Social Recommendation](https://mlsanity.com/paper/2110.03987/) (2021)
- [Topology-Aware Graph Pooling Networks](https://mlsanity.com/paper/2010.09834/) (2020)
- [Edge Representation Learning with Hypergraphs](https://mlsanity.com/paper/2106.15845/) (2021)
- [Generalized Simplicial Attention Neural Networks](https://mlsanity.com/paper/2309.02138/) (2023)
- [Dual-Primal Graph Convolutional Networks](https://mlsanity.com/paper/1806.00770/) (2018)
- [Fast Polynomial Approximation of Heat Kernel Convolution on Manifolds and Its Application to Brain Sulcal and Gyral Graph Pattern Analysis](https://mlsanity.com/paper/1911.02721/) (2019)
- [Revisiting convolutional neural network on graphs with polynomial approximations of Laplace-Beltrami spectral filtering](https://mlsanity.com/paper/2010.13269/) (2020)

## Built on by (most cited first, 1 of 1)

- [TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selection](https://mlsanity.com/paper/2605.08870/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have proven effective in capturing relationships among nodes in a graph. This study introduces a novel perspective by considering a graph as a simplicial complex, encompassing nodes, edges, triangles, and k-simplices, enabling the definition of graph-structured data on any k-simplices. Our contribution is the Hodge-Laplacian heterogeneous graph attention network (HL-HGAT), designed to learn heterogeneous signal representations across k-simplices. The HL-HGAT incorporates three key components: HL convolutional filters (HL-filters), simplicial projection (SP), and simplicial attention pooling (SAP) operators, applied to k-simplices. HL-filters leverage the unique topology of k-simplices encoded by the Hodge-Laplacian (HL) operator, operating within the spectral domain of the k-th HL operator. To address computation challenges, we introduce a polynomial approximation for HL-filters, exhibiting spatial localization properties. Additionally, we propose a pooling operator to coarsen k-simplices, combining features through simplicial attention mechanisms of self-attention and cross-attention via transformers and SP operators, capturing topological interconnections across multiple dimensions of simplices. The HL-HGAT is comprehensively evaluated across diverse graph applications, including NP-hard problems, graph multi-label and classification challenges, and graph regression tasks in logistics, computer vision, biology, chemistry, and neuroscience. The results demonstrate the model's efficacy and versatility in handling a wide range of graph-based scenarios.