# Hyperbolic Convolution via Kernel Point Aggregation

arXiv: https://arxiv.org/abs/2306.08862 · HTML: https://mlsanity.com/paper/2306.08862/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 54 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 30 of 40)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Dynamic Convolution: Attention over Convolution Kernels](https://mlsanity.com/paper/1912.03458/) (2019)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (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)
- [Scaling Neural Machine Translation](https://mlsanity.com/paper/1806.00187/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Point Convolutional Neural Networks by Extension Operators](https://mlsanity.com/paper/1803.10091/) (2018)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)

## Built on by (most cited first, 2 of 2)

- [Cross-Modal Fusion and Attention Mechanism for Weakly Supervised Video Anomaly Detection](https://mlsanity.com/paper/2412.20455/) (2024)
- [Robust Hyperbolic Learning with Curvature-Aware Optimization](https://mlsanity.com/paper/2405.13979/) (2024)

## Abstract (arXiv)

Learning representations according to the underlying geometry is of vital importance for non-Euclidean data. Studies have revealed that the hyperbolic space can effectively embed hierarchical or tree-like data. In particular, the few past years have witnessed a rapid development of hyperbolic neural networks. However, it is challenging to learn good hyperbolic representations since common Euclidean neural operations, such as convolution, do not extend to the hyperbolic space. Most hyperbolic neural networks do not embrace the convolution operation and ignore local patterns. Others either only use non-hyperbolic convolution, or miss essential properties such as equivariance to permutation. We propose HKConv, a novel trainable hyperbolic convolution which first correlates trainable local hyperbolic features with fixed kernel points placed in the hyperbolic space, then aggregates the output features within a local neighborhood. HKConv not only expressively learns local features according to the hyperbolic geometry, but also enjoys equivariance to permutation of hyperbolic points and invariance to parallel transport of a local neighborhood. We show that neural networks with HKConv layers advance state-of-the-art in various tasks.