{"slug": "geometry-is-not-robustness-a-trajectory-level-study-of-pgd-evaluation", "title": "Geometry Is Not Robustness: A Trajectory-Level Study of PGD Evaluation", "summary": "A new study from arXiv (arXiv:2608.14594v1) finds that trajectory-level diagnostics from Projected Gradient Descent (PGD) attacks, such as loss evolution and gradient alignment, do not independently measure adversarial robustness, while steps-to-failure distributions provide clearer separation of robustness regimes. The researchers evaluated clean-trained and adversarially-trained convolutional neural networks on Fashion-MNIST using 20-step PGD attacks with random initialization and multiple restarts, recording full trajectories across 3000 clean-correct samples per model. The findings suggest trajectory-level analysis should complement, not replace, standard robustness measurements.", "body_md": "arXiv:2608.14594v1 Announce Type: new\nAbstract: Projected Gradient Descent (PGD) is widely used to evaluate adversarial robustness, typically via final adversarial accuracy, which does not capture model behaviour throughout the attack. Recent work proposes trajectory-level diagnostics, such as loss evolution, gradient alignment, and steps-to-failure, for deeper insight into adversarial optimisation dynamics. However, whether these diagnostics reliably indicate robustness strength remains unclear. We conduct a trajectory-level investigation of PGD attacks on convolutional neural networks trained on Fashion-MNIST. We compare clean-trained and adversarially-trained models across multiple robustness regimes, using rigorous 20-step PGD evaluations with random initialisation and multiple restarts for robustness measurement, and single-initialisation trajectory recording for diagnostics. We record full PGD trajectories across 3000 clean-correct samples per model and analyse loss evolution, gradient alignment, and failure timing across attack iterations. Our results reveal a clear robustness hierarchy across models; however, trajectory metrics do not contribute equally to its identification. Mean loss trajectories and gradient alignment patterns appear quantitatively similar across adversarially-trained models with substantially different robust accuracies. In contrast, steps-to-failure distributions provide a clearer separation of robustness regimes, directly reflecting functional resistance to adversarial perturbation. These findings indicate that trajectory-level diagnostics describe optimisation geometry but do not independently measure adversarial robustness. Their interpretability depends on robustness regime, attack strength, and multi-metric evaluation. Trajectory-level analysis should be a complementary diagnostic tool, interpreted in context, rather than a replacement for standard robustness measurements.", "url": "https://wpnews.pro/news/geometry-is-not-robustness-a-trajectory-level-study-of-pgd-evaluation", "canonical_source": "https://arxiv.org/abs/2608.14594", "published_at": "2026-08-18 04:00:00+00:00", "updated_at": "2026-08-18 04:12:25.051658+00:00", "lang": "en", "topics": ["artificial-intelligence", "machine-learning", "ai-safety"], "entities": ["arXiv", "Projected Gradient Descent (PGD)", "Fashion-MNIST"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/geometry-is-not-robustness-a-trajectory-level-study-of-pgd-evaluation", "markdown": "https://wpnews.pro/news/geometry-is-not-robustness-a-trajectory-level-study-of-pgd-evaluation.md", "text": "https://wpnews.pro/news/geometry-is-not-robustness-a-trajectory-level-study-of-pgd-evaluation.txt", "jsonld": "https://wpnews.pro/news/geometry-is-not-robustness-a-trajectory-level-study-of-pgd-evaluation.jsonld"}}