# Angular Gradient Sign Method: Uncovering Vulnerabilities in Hyperbolic Networks

arXiv: https://arxiv.org/abs/2511.12985 · HTML: https://mlsanity.com/paper/2511.12985/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 20 of 20)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [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)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models](https://mlsanity.com/paper/1505.04870/) (2015)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [The Space of Transferable Adversarial Examples](https://mlsanity.com/paper/1704.03453/) (2017)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Meta Gradient Adversarial Attack](https://mlsanity.com/paper/2108.04204/) (2021)
- [Mind the box: l1-APGD for sparse adversarial attacks on image classifiers](https://mlsanity.com/paper/2103.01208/) (2021)
- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [Learning Structured Representations with Hyperbolic Embeddings](https://mlsanity.com/paper/2412.01023/) (2024)
- [HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules](https://mlsanity.com/paper/2504.08912/) (2025)

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

- [Direct Product Flow Matching: Decoupling Radial and Angular Dynamics for Few-Shot Adaptation](https://mlsanity.com/paper/2605.05054/) (2026)
- [PoLAR: Factorizing Extent and Mode in Latent Actions for Robot Policy Learning](https://mlsanity.com/paper/2606.21139/) (2026)

## Abstract (arXiv)

Adversarial examples in neural networks have been extensively studied in Euclidean geometry, but recent advances in textithyperbolic networks call for a reevaluation of attack strategies in non-Euclidean geometries. Existing methods such as FGSM and PGD apply perturbations without regard to the underlying hyperbolic structure, potentially leading to inefficient or geometrically inconsistent attacks. In this work, we propose a novel adversarial attack that explicitly leverages the geometric properties of hyperbolic space. Specifically, we compute the gradient of the loss function in the tangent space of hyperbolic space, decompose it into a radial (depth) component and an angular (semantic) component, and apply perturbation derived solely from the angular direction. Our method generates adversarial examples by focusing perturbations in semantically sensitive directions encoded in angular movement within the hyperbolic geometry. Empirical results on image classification, cross-modal retrieval tasks and network architectures demonstrate that our attack achieves higher fooling rates than conventional adversarial attacks, while producing high-impact perturbations with deeper insights into vulnerabilities of hyperbolic embeddings. This work highlights the importance of geometry-aware adversarial strategies in curved representation spaces and provides a principled framework for attacking hierarchical embeddings.