# Rhomboid Tiling for Geometric Graph Deep Learning

arXiv: https://arxiv.org/abs/2505.09586 · HTML: https://mlsanity.com/paper/2505.09586/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 14 May 2025.

## Builds on (most cited first, 19 of 19)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [On Valid Optimal Assignment Kernels and Applications to Graph Classification](https://mlsanity.com/paper/1606.01141/) (2016)
- [SkipGNN: Predicting Molecular Interactions with Skip-Graph Networks](https://mlsanity.com/paper/2004.14949/) (2020)
- [Faster Kernels for Graphs with Continuous Attributes via Hashing](https://mlsanity.com/paper/1610.00064/) (2016)
- [FP-GNN: a versatile deep learning architecture for enhanced molecular property prediction](https://mlsanity.com/paper/2205.03834/) (2022)
- [Deep Graph Mapper: Seeing Graphs through the Neural Lens](https://mlsanity.com/paper/2002.03864/) (2020)
- [Molecular geometric deep learning](https://mlsanity.com/paper/2306.15065/) (2023)
- [Topological Pooling on Graphs](https://mlsanity.com/paper/2303.14543/) (2023)
- [Computing the Multicover Bifiltration](https://mlsanity.com/paper/2103.07823/) (2021)

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

- [Multi-Scale Harmonic Encoding for Feature-Wise Graph Message Passing](https://mlsanity.com/paper/2505.15015/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have proven effective for learning from graph-structured data through their neighborhood-based message passing framework. Many hierarchical graph clustering pooling methods modify this framework by introducing clustering-based strategies, enabling the construction of more expressive and powerful models. However, all of these message passing framework heavily rely on the connectivity structure of graphs, limiting their ability to capture the rich geometric features inherent in geometric graphs. To address this, we propose Rhomboid Tiling (RT) clustering, a novel clustering method based on the rhomboid tiling structure, which performs clustering by leveraging the complex geometric information of the data and effectively extracts its higher-order geometric structures. Moreover, we design RTPool, a hierarchical graph clustering pooling model based on RT clustering for graph classification tasks. The proposed model demonstrates superior performance, outperforming 21 state-of-the-art competitors on all the 7 benchmark datasets.