arXiv：cs.LG（机器学习，全量分类）· Athanasios Angelakis, Marta Gomez-Barrero·· 15 小时前AI 评分35
hZACH-ViT 曲率对抗攻击研究：规范对称性、边界饱和与对抗失效
Curvature Under Attack in hZACH-ViT: Gauge Symmetry, Boundary Saturation, and Adversarial Failure
AI 导读
研究在 hZACH-ViT 紧凑 Vision Transformer 上考察曲率与对抗鲁棒性的关系，该模型含欧几里得、Poincare 和球面原型头，在三个 MedMNIST 数据集和五个种子上匹配训练。
正文
Abstract:Curvature is often treated as an intrinsic property of a representation, although its empirical effect also depends on coordinate scale, learned logit temperature, and numerical safeguards. We study this interaction in hZACH-ViT, a compact Vision Transformer with Euclidean, Poincare, and spherical prototype heads. The backbone architecture, seed-specific initialization, 50-per-class training subset, and optimization protocol are matched across three MedMNIST datasets and five seeds. At the fixed comparison curvature $c=1$, Poincare has the lowest class-macro PGD attack-success rate in all 12 dataset-budget cells and under a stronger CE+DLR multi-restart attack on all three datasets, but it also has the lowest clean MacroF1. An end-to-end curvature intervention changes the interpretation. Reducing Poincare curvature to $c=0.1$ improves clean MacroF1 in every one of the 15 paired seed-dataset comparisons and removes hard boundary clipping, yet on OrganAMNIST it increases strong attack success from $89.7\%$ to $99.3\%$ (paired difference $+9.57$ points; 95\% hierarchical bootstrap CI $[+5.52,+14.03]$). At $c=1$, $40$-$47\%$ of clean Poincare features are hard-clipped, the radial Jacobian of the inherited map is nearly zero, and dimensionless attack trajectories are unusually long and inefficient. The spherical head provides a control: its curvature change is an exact scale gauge to floating-point precision and produces much smaller attack differences. These results do not establish intrinsic hyperbolic robustness. They identify an implementation-sensitive regime in which curvature, scale, and proximity to the Poincare boundary jointly organize clean recognition and adversarial representation motion.
| Comments: | 12 pages, 3 figures, 4 tables. Accepted at NeurReps 2026: Symmetry and Geometry in Neural Representations, NeurIPS 2026 |
| Subjects: | Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV) |
| Cite as: | arXiv:2610.00680 [cs.LG] |
| (or arXiv:2610.00680v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.00680 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Athanasios Angelakis [view email]
[v1]
Wed, 30 Sep 2026 20:20:13 UTC (79 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org