Anticipating Domain Shifts Via Geometry-Guided Functional Probing

Domain generalization (DG) aims to learn a model from multiple source domains that remains reliable on unseen target domains. Recent studies have sought flat minima in the loss landscape to enhance robustness to diverse input variations, thereby mitigating domain shift in classification tasks. However, these methods typically rely on generic parameter-space perturbations to explore flatness, which not only lacks explicit grounding in class-relevant predictive variations but also suffers from additional perturbation-searching overhead. This motivates us to leverage the learned geometry of the classifier's decision boundary to randomly construct diverse predictive variations in anticipation of unseen domain shifts. To this end, we propose Anticipating Shifts via Functional Probing (ASFP), a lightweight framework that promotes local flatness along the explored functional directions by jointly optimizing a family of perturbed predictive functions. Specifically, ASFP constructs perturbation directions that evolve with the classifier by randomly combining pairwise differences between its class-weight vectors, enabling structured functional exploration without costly perturbation search. *Theoretically*, with the SmoothMax objective, we characterize the induced curvature and sensitivity regularization and establish a local bound on loss increases under unseen-domain perturbations covered by this geometry. *Empirically*, we demonstrate through extensive experiments on five benchmarks that ASFP consistently outperforms strong baselines while maintaining low training overhead.