# DeepHGCN: Toward Deeper Hyperbolic Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2310.02027 · HTML: https://mlsanity.com/paper/2310.02027/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 57 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [Graph Geometry Interaction Learning](https://mlsanity.com/paper/2010.12135/) (2020)

## Built on by (most cited first, 4 of 4)

- [Continuous Geometry-Aware Graph Diffusion via Hyperbolic Neural PDE](https://mlsanity.com/paper/2406.01282/) (2024)
- [Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs](https://mlsanity.com/paper/2506.15464/) (2025)
- [HANS-Net: Hyperbolic Convolution and Adaptive Temporal Attention for Accurate and Generalizable Liver and Tumor Segmentation in CT Imaging](https://mlsanity.com/paper/2507.11325/) (2025)
- [Demystifying Oversmoothing in Sheaf Neural Networks: An Index-Theoretic Criterion](https://mlsanity.com/paper/2608.16180/) (2026)

## Abstract (arXiv)

Hyperbolic graph convolutional networks (HGCNs) have demonstrated significant potential in extracting information from hierarchical graphs. However, existing HGCNs are limited to shallow architectures due to the computational expense of hyperbolic operations and the issue of over-smoothing as depth increases. Although treatments have been applied to alleviate over-smoothing in GCNs, developing a hyperbolic solution presents distinct challenges since operations must be carefully designed to fit the hyperbolic nature. Addressing these challenges, we propose DeepHGCN, the first deep multi-layer HGCN architecture with dramatically improved computational efficiency and substantially reduced over-smoothing. DeepHGCN features two key innovations: (1) a novel hyperbolic feature transformation layer that enables fast and accurate linear mappings, and (2) techniques such as hyperbolic residual connections and regularization for both weights and features, facilitated by an efficient hyperbolic midpoint method. Extensive experiments demonstrate that DeepHGCN achieves significant improvements in link prediction and node classification tasks compared to both Euclidean and shallow hyperbolic GCN variants.