Geometry-Aware Backdoor Attacks: Leveraging Curvature in Hyperbolic Embeddings

2025/10/07 by Ali Baheri, Baheri, Ali
Computer Science · #Artificial Intelligence (cs.AI) #Digital and Cyber Forensics #FOS: Computer and information sciences #Image Processing and 3D Reconstruction #Machine Learning (cs.LG) #Security and Verification in Computing

paper · pdf · doi:10.48550/arxiv.2510.06397

openalex publication_date 2025/10/07 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Adversarial Attacks on Hyperbolic Networks
• Backdoor Attacks against Hybrid Classical-Quantum Neural Networks
• Graph Neural Backdoor: Fundamentals, Methodologies, Applications, and Future Directions
• Certified Patch Robustness via Smoothed Vision Transformers
• Backdoor Learning: A Survey
• Blind Backdoors in Deep Learning Models
• Dynamic Backdoor Attacks Against Machine Learning Models
• Certifiable Robustness to Graph Perturbations
• Hyperbolic Graph Convolutional Neural Networks
• Hyperbolic Image Embeddings
• EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs
• Detecting Backdoor Attacks on Deep Neural Networks by Activation Clustering
• Poincaré GloVe: Hyperbolic Word Embeddings
• Fine-Pruning: Defending Against Backdooring Attacks on Deep Neural Networks
• Hyperbolic Neural Networks
• Targeted Backdoor Attacks on Deep Learning Systems Using Data Poisoning
• BadNets: Identifying Vulnerabilities in the Machine Learning Model Supply Chain
• Poincaré Embeddings for Learning Hierarchical Representations

Related

• Angular Gradient Sign Method: Uncovering Vulnerabilities in Hyperbolic Networks
• Adversarial Attacks on Hyperbolic Networks
• GeoDetect: Geometric Adversarial Detection for VLPs
• Stealthy Patch-Wise Backdoor Attack in 3D Point Cloud via Curvature Awareness
• STONE: Pioneering the One-to-N Universal Backdoor Threat in 3D Point Cloud