# Can we ease the Injectivity Bottleneck on Lorentzian Manifolds for Graph Neural Networks?

arXiv: https://arxiv.org/abs/2504.00142 · HTML: https://mlsanity.com/paper/2504.00142/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 31 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [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)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [Neural Injective Functions for Multisets, Measures and Graphs via a Finite Witness Theorem](https://mlsanity.com/paper/2306.06529/) (2023)
- [Improving Attention Mechanism in Graph Neural Networks via Cardinality Preservation](https://mlsanity.com/paper/1907.02204/) (2019)
- [Hyperbolic Graph Neural Networks at Scale: A Meta Learning Approach](https://mlsanity.com/paper/2310.18918/) (2023)
- [Contextualized Messages Boost Graph Representations](https://mlsanity.com/paper/2403.12529/) (2024)
- [A Unification Framework for Euclidean and Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/2206.04285/) (2022)

## Abstract (arXiv)

While hyperbolic GNNs show promise for hierarchical data, they often have limited discriminative power compared to Euclidean counterparts or the WL test, due to non-injective aggregation. To address this expressivity gap, we propose the Lorentzian Graph Isomorphic Network (LGIN), a novel HGNN designed for enhanced discrimination within the Lorentzian model. LGIN introduces a new update rule that preserves the Lorentzian metric while effectively capturing richer structural information. This marks a significant step towards more expressive GNNs on Riemannian manifolds. Extensive evaluations across nine benchmark datasets demonstrate LGIN's superior performance, consistently outperforming or matching state-of-the-art hyperbolic and Euclidean baselines, showcasing its ability to capture complex graph structures. LGIN is the first to adapt principles of powerful, highly discriminative GNN architectures to a Riemannian manifold. The code for our paper can be found at https://github.com/Deceptrax123/LGIN