# Adversarial Attacks on Hyperbolic Networks

arXiv: https://arxiv.org/abs/2412.01495 · HTML: https://mlsanity.com/paper/2412.01495/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 87 references that are in the map.
- First posted on arXiv 2 Dec 2024.

## Builds on (most cited first, 30 of 61)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networks](https://mlsanity.com/paper/1704.01155/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Feature Denoising for Improving Adversarial Robustness](https://mlsanity.com/paper/1812.03411/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [Shadows can be Dangerous: Stealthy and Effective Physical-world Adversarial Attack by Natural Phenomenon](https://mlsanity.com/paper/2203.03818/) (2022)
- [Improving Adversarial Robustness via Channel-wise Activation Suppressing](https://mlsanity.com/paper/2103.08307/) (2021)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Hyperbolic Graph Attention Network](https://mlsanity.com/paper/1912.03046/) (2019)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)

## Built on by (most cited first, 3 of 3)

- [Fast and Geometrically Grounded Lorentz Neural Networks](https://mlsanity.com/paper/2601.21529/) (2026)
- [Geometry-Aware Backdoor Attacks: Leveraging Curvature in Hyperbolic Embeddings](https://mlsanity.com/paper/2510.06397/) (2025)
- [Curvature Under Attack in hZACH-ViT: Gauge Symmetry, Boundary Saturation, and Adversarial Failure](https://mlsanity.com/paper/2610.00680/) (2026)

## Abstract (arXiv)

As hyperbolic deep learning grows in popularity, so does the need for adversarial robustness in the context of such a non-Euclidean geometry. To this end, this paper proposes hyperbolic alternatives to the commonly used FGM and PGD adversarial attacks. Through interpretable synthetic benchmarks and experiments on existing datasets, we show how the existing and newly proposed attacks differ. Moreover, we investigate the differences in adversarial robustness between Euclidean and fully hyperbolic networks. We find that these networks suffer from different types of vulnerabilities and that the newly proposed hyperbolic attacks cannot address these differences. Therefore, we conclude that the shifts in adversarial robustness are due to the models learning distinct patterns resulting from their different geometries.