Angular Gradient Sign Method: Uncovering Vulnerabilities in Hyperbolic Networks

Adversarial examples in neural networks have been extensively studied in Euclidean geometry, but recent advances in \textit{hyperbolic 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.

CL3DOR: Contrastive Learning for 3D Large Multimodal Models via Odds Ratio on High-Resolution Point Clouds

Recent research has demonstrated that Large Language Models (LLMs) are not limited to text-only tasks but can also function as multimodal models across various modalities, including audio, images, and videos. In particular, research on 3D Large Multimodal Models (3D LMMs) is making notable strides, driven by the potential of processing higher-dimensional data like point clouds. However, upon closer examination, we find that the visual and textual content within each sample of existing training datasets lacks both high informational granularity and clarity, which serve as a bottleneck for precise cross-modal understanding. To address these issues, we propose CL3DOR, Contrastive Learning for 3D large multimodal models via Odds ratio on high-Resolution point clouds, designed to ensure greater specificity and clarity in both visual and textual content. Specifically, we increase the density of point clouds per object and construct informative hard negative responses in the training dataset to penalize unwanted responses. To leverage hard negative responses, we incorporate the odds ratio as an auxiliary term for contrastive learning into the conventional language modeling loss. CL3DOR achieves state-of-the-art performance in 3D scene understanding and reasoning benchmarks. Additionally, we demonstrate the effectiveness of CL3DOR's key components through extensive experiments.