Spectral Projection Profiles for Out-of-distribution Detection

Out-of-distribution (OOD) detection is essential for the safe deployment of deep models. However, the accuracy of OOD detection methods varies strongly across backbone models. We analyze this dependence through spectral projection profiles, measuring how in-distribution (ID) and OOD samples spread across the right singular vectors of the classifier's weight matrix. We find that in “well-behaved” models, which are accurate and robust across multiple dimensions, ID samples spread across the spectrum, whereas OOD inputs concentrate on the leading directions with large singular values. Less well-behaved models lack this distinction. This helps explain why logit-based and activation-shaping methods degrade on well-behaved models: the concentration of OOD inputs on the leading directions with larger singular values inflates the resulting logits, breaking the assumption that logits yield a reliable confidence measure. We further find that leading directions mainly encode local texture cues, whereas trailing directions encode global structure. Building on these insights, we propose OMASHU, a post-hoc OOD detection score with two complementary components that target the limitations of existing methods in well-behaved models. OMA normalizes the logits with a spectrally weighted norm that attenuates the effect of the leading directions. SHU exploits the fact that under patch shuffling, which destroys global structure but preserves local cues, the trailing projections of ID samples change more than those of OOD samples. On the OpenOOD benchmark, OMASHU and its variant OMASHU++, which also uses training statistics, achieve state-of-the-art OOD detection accuracy among methods without and with training data, respectively, for well-behaved transformer and convolutional backbones.