Perturbations in the Orthogonal Complement Subspace for Efficient Out-of-Distribution Detection

Out-of-distribution (OOD) detection is essential for deploying deep learning models in open-world environments. Existing approaches, such as energy-based scoring and gradient-projection methods, typically rely on high-dimensional representations to separate in-distribution (ID) and OOD samples. We introduce P-OCS (Perturbations in the Orthogonal Complement Subspace), a lightweight and theoretically grounded method that operates in the orthogonal complement of the principal subspace defined by ID features. P-OCS applies a single projected perturbation restricted to this complementary subspace, enhancing subtle ID-OOD distinctions while preserving the geometry of ID representations. We show that a one-step update is sufficient in the small-perturbation regime and provide convergence guarantees for the resulting detection score. Experiments across multiple architectures and datasets demonstrate that P-OCS achieves state-of-the-art OOD detection with negligible computational cost and without requiring model retraining, access to OOD data, or changes to model architecture.