# Geometry-Aware Backdoor Attacks: Leveraging Curvature in Hyperbolic Embeddings

arXiv: https://arxiv.org/abs/2510.06397 · HTML: https://mlsanity.com/paper/2510.06397/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 28 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 19 of 19)

- [BadNets: Identifying Vulnerabilities in the Machine Learning Model Supply Chain](https://mlsanity.com/paper/1708.06733/) (2017)
- [Targeted Backdoor Attacks on Deep Learning Systems Using Data Poisoning](https://mlsanity.com/paper/1712.05526/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Fine-Pruning: Defending Against Backdooring Attacks on Deep Neural Networks](https://mlsanity.com/paper/1805.12185/) (2018)
- [Detecting Backdoor Attacks on Deep Neural Networks by Activation Clustering](https://mlsanity.com/paper/1811.03728/) (2018)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Backdoor Learning: A Survey](https://mlsanity.com/paper/2007.08745/) (2020)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Blind Backdoors in Deep Learning Models](https://mlsanity.com/paper/2005.03823/) (2020)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Dynamic Backdoor Attacks Against Machine Learning Models](https://mlsanity.com/paper/2003.03675/) (2020)
- [Certifiable Robustness to Graph Perturbations](https://mlsanity.com/paper/1910.14356/) (2019)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [Certified Patch Robustness via Smoothed Vision Transformers](https://mlsanity.com/paper/2110.07719/) (2021)
- [Backdoor Attacks against Hybrid Classical-Quantum Neural Networks](https://mlsanity.com/paper/2407.16273/) (2024)
- [Graph Neural Backdoor: Fundamentals, Methodologies, Applications, and Future Directions](https://mlsanity.com/paper/2406.10573/) (2024)
- [Adversarial Attacks on Hyperbolic Networks](https://mlsanity.com/paper/2412.01495/) (2024)

## Abstract (arXiv)

Non-Euclidean foundation models increasingly place representations in curved spaces such as hyperbolic geometry. We show that this geometry creates a boundary-driven asymmetry that backdoor triggers can exploit. Near the boundary, small input changes appear subtle to standard input-space detectors but produce disproportionately large shifts in the model's representation space. Our analysis formalizes this effect and also reveals a limitation for defenses: methods that act by pulling points inward along the radius can suppress such triggers, but only by sacrificing useful model sensitivity in that same direction. Building on these insights, we propose a simple geometry-adaptive trigger and evaluate it across tasks and architectures. Empirically, attack success increases toward the boundary, whereas conventional detectors weaken, mirroring the theoretical trends. Together, these results surface a geometry-specific vulnerability in non-Euclidean models and offer analysis-backed guidance for designing and understanding the limits of defenses.