# L^2GC:Lorentzian Linear Graph Convolutional Networks for Node Classification

arXiv: https://arxiv.org/abs/2403.06064 · HTML: https://mlsanity.com/paper/2403.06064/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 10 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Graph Convolutional Networks for Text Classification](https://mlsanity.com/paper/1809.05679/) (2018)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [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)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [GAMENet: Graph Augmented MEmory Networks for Recommending Medication Combination](https://mlsanity.com/paper/1809.01852/) (2018)
- [Elastic Graph Neural Networks](https://mlsanity.com/paper/2107.06996/) (2021)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space](https://mlsanity.com/paper/1602.06522/) (2016)
- [Enhancing Hyperbolic Graph Embeddings via Contrastive Learning](https://mlsanity.com/paper/2201.08554/) (2022)

## Built on by (most cited first, 5 of 5)

- [AutoP2C: An LLM-Based Agent Framework for Code Repository Generation from Multimodal Content in Academic Papers](https://mlsanity.com/paper/2504.20115/) (2025)
- [Hierarchical Mamba Meets Hyperbolic Geometry: A New Paradigm for Structured Language Embeddings](https://mlsanity.com/paper/2505.18973/) (2025)
- [A Compressive Memory-based Retrieval Approach for Event Argument Extraction](https://mlsanity.com/paper/2409.09322/) (2024)
- [Fully Hyperbolic Rotation for Knowledge Graph Embedding](https://mlsanity.com/paper/2411.03622/) (2024)
- [MAC-Tuning: LLM Multi-Compositional Problem Reasoning with Enhanced Knowledge Boundary Awareness](https://mlsanity.com/paper/2504.21773/) (2025)

## Abstract (arXiv)

Linear Graph Convolutional Networks (GCNs) are used to classify the node in the graph data. However, we note that most existing linear GCN models perform neural network operations in Euclidean space, which do not explicitly capture the tree-like hierarchical structure exhibited in real-world datasets that modeled as graphs. In this paper, we attempt to introduce hyperbolic space into linear GCN and propose a novel framework for Lorentzian linear GCN. Specifically, we map the learned features of graph nodes into hyperbolic space, and then perform a Lorentzian linear feature transformation to capture the underlying tree-like structure of data. Experimental results on standard citation networks datasets with semi-supervised learning show that our approach yields new state-of-the-art results of accuracy 74.7% on Citeseer and 81.3% on PubMed datasets. Furthermore, we observe that our approach can be trained up to two orders of magnitude faster than other nonlinear GCN models on PubMed dataset. Our code is publicly available at https://github.com/llqy123/LLGC-master.