Geometry Is Not Robustness: A Trajectory-Level Study of PGD Evaluation

[2608.14594] Geometry Is Not Robustness: A Trajectory-Level Study of PGD Evaluation Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.14594 (cs) [Submitted on 26 Jun 2026] Title: Geometry Is Not Robustness: A Trajectory-Level Study of PGD Evaluation Authors: Dhairysheel Durgule View a PDF of the paper titled Geometry Is Not Robustness: A Trajectory-Level Study of PGD Evaluation, by Dhairysheel Durgule View PDF HTML (experimental) Abstract: 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. Comments: 16 pages, 3 figures Subjects: Machine Learning (cs.LG) Cite as: arXiv:2608.14594 [cs.LG] (or arXiv:2608.14594v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.14594 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Dhairysheel Durgule [ view email ] [v1] Fri, 26 Jun 2026 05:28:33 UTC (90 KB) Full-text links: Access Paper: View a PDF of the paper titled Geometry Is Not Robustness: A Trajectory-Level Study of PGD Evaluation, by Dhairysheel Durgule View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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