The Geometry of Robustness: Optimizing Loss Landscape Curvature and Feature Manifold Alignment for Robust Finetuning of Vision-Language Models

Abstract: Fine-tuning approaches for Vision-LLMs (VLMs) face a critical three-way trade-off between In-Distribution (ID) accuracy, Out-of-Distribution (OOD) generalization, and adversarial robustness. Existing robust fine-tuning strategies resolve at most two axes of this trade-off. Generalization-preserving methods retain ID/OOD performance but leave models vulnerable to adversarial attacks, while adversarial training improves robustness to targeted attacks but degrades ID/OOD accuracy. Our key insight is that the robustness trade-off stems from two geometric failures: sharp, anisotropic minima in parameter space and unstable feature representations that deform under perturbation. To address this, we propose GRACE (Gram-aligned Robustness via Adaptive Curvature Estimation), a unified fine-tuning framework that jointly regularizes the parameter-space curvature and feature-space invariance for VLMs. Grounded in Robust PAC-Bayes theory, GRACE employs adaptive weight perturbations scaled by local curvature to promote flatter minima, combined with a feature alignment loss that maintains representation consistency across clean, adversarial, and OOD inputs. On ImageNet fine-tuning of CLIP models, GRACE simultaneously improves ID accuracy by 10.8%, and adversarial accuracy by 13.5% while maintaining 57.0% OOD accuracy (vs. 57.4% zero-shot baseline). Geometric analysis confirms that GRACE converges to flatter minima without feature distortion across distribution shifts, providing a principled step toward generalized robustness in foundation VLMs.