Grassmann Flows Under Adversarial and Distribution Shift: A Robustness Perspective

TL;DR: Could the geometric regularity of Grassmann flows yield greater robustness to adversarial perturbations or distribution shifts compared to Transformers? Test this by subjecting Grassmann-based and attention-based models to adversarial attacks and out-of-distribution inputs on SNLI and Wikitext-2.

Research Question: Do Grassmann flow-based architectures offer increased robustness to adversarial attacks and distribution shifts relative to self-attention-based models, and can their geometric structure be exploited for further defenses?

Hypothesis: The structured, low-rank subspace evolution in Grassmann models will make them less susceptible to off-manifold perturbations, resulting in higher adversarial and OOD robustness.

Experiment Plan: Train matched Grassmann and Transformer models. Apply standard adversarial attacks (FGSM, PGD) and create OOD splits (e.g., novel vocabulary, shuffled syntax). Measure performance drop and visualize subspace trajectories during attacks. Explore adding explicit geometric regularization to further enhance robustness.

References:

• [Original paper]
• Zhang, D. (2025). The Neural Differential Manifold: An Architecture with Explicit Geometric Structure. arXiv.org.