Out-of-Distribution (OOD) data poses a significant threat to machine learning models, often leading to model failure during deployment. All existing OOD detection methods are post-hoc, relying on evaluation metrics such as accuracy and AUC-ROC during inference to indirectly assess the model's response to OOD data by measuring deviations. In contrast to existing approaches, the proposed work shifts the paradigm from OOD detection to OOD prediction by proposing a pre-hoc anticipatory framework called PLSP for OOD prediction. We make several key contributions: (a) a dataset-independent metric called the CREDibility Score (CREDS) is proposed for OOD prediction; (b) credibility curves are introduced to study the maximum credibility a model can attain; and (c) credibility heat maps (and volume under surface) are introduced to characterize pre-hoc model behavior across different datasets. This work provides a novel perspective on signal processing under distributional shifts. Experiments across multiple datasets demonstrate that the proposed metric serves as a valuable measure for improving the robustness of machine learning models toward OOD prediction.
Out-of-distribution (OOD) detection is essential for deploying machine learning models in open-world and safety-critical scenarios, where test inputs may deviate from the training distribution and overconfident predictions on unknown samples can lead to unreliable decisions. Outlier Exposure (OE) has emerged as a promising OOD detection paradigm by introducing auxiliary outliers during training to enlarge the margin between in-distribution (ID) and OOD samples. Existing OE-based methods typically enlarge this margin by employing uniform labels to maximize the entropy of OOD samples over ID categories. However, we theoretically show that uniform labels inevitably disregard the relations between OOD samples and ID categories, termed the over-softening effect, leading to a suboptimal margin bound. Our theoretical analysis further reveals that explicitly exploiting such relations can instead yield improved OOD detection performance. Motivated by this insight, we propose \underline{A}daptive Confidence \underline{OE} (AOE), a simple yet effective method that leverages temperature scaling to recalibrate outlier labels. Specifically, AOE generates adaptive soft targets from temperature-scaled model predictions for OOD samples, where the learnable temperature smooths the prediction distribution without fully erasing class-wise relational information. By supervising OOD samples with these adaptive soft targets, AOE preserves the semantic proximity between OOD samples and ID categories while encouraging the softened targets to approach a high-entropy distribution, thereby suppressing overconfident OOD predictions and enlarging the separation margin. Extensive experiments across diverse benchmarks demonstrate the effectiveness of AOE.
Detecting out-of-distribution (OOD) data is crucial for reliable machine learning deployment. Among detection strategies, post-hoc methods are particularly attractive due to their efficiency, as they operate directly on pre-trained networks without requiring retraining. Within this paradigm, one promising direction exploits loss-landscape curvature to estimate model uncertainty; however, such methods incur substantial computational cost and rely on implicit assumptions about how landscape flatness differs between in-distribution (ID) and OOD data. In this work, we provide the first systematic investigation of this curvature discrepancy and show that OOD inputs exhibit larger Hessian curvature than ID data, with the gap widening under stronger distributional shifts. Motivated by these observations, we propose Fold, a lightweight flatness-modulated OOD detector that leverages the feature Hessian and partial feature normalization to improve ID-OOD separability while avoiding costly parameter-space curvature approximations. To optimally adapt this normalization across diverse datasets, we further introduce AutoFold, a self-supervised tuning scheme that synthesizes pseudo-OOD samples via ID logit masking for automatic calibration without requiring external data. Experiments on OOD benchmarks show that Fold outperforms prior methods, improving the average AUROC by 1.63% and reducing FPR95 by 2.30%, while maintaining computational efficiency comparable to a standard forward pass. Supported by theoretical analysis and extensive ablations, Fold provides a principled and practical solution for robust real-world deployment.
Probabilistic Circuits (PCs) are tractable generative models whose internal nodes encode a hierarchy of probabilistic sum- maries over different variable scopes. Existing PC-based out- of-distribution (OOD) detection methods ignore this hierar- chy, reducing the entire circuit to the scalar likelihood (or its uncertainty) computed at the root. We introduce Hierar- chical Likelihood Vector (HLV), a representation whose en- tries are the likelihoods associated with selected PC nodes and define the Hierarchical Likelihood Distance (HLD), a PC-induced pseudo-metric that compares the probability dis- tributions through the expectations of their HLVs. We show that HLD is an integral probability metric over a function class naturally induced by the PC and develop a principled goodness-of-fit hypothesis test for unsupervised OOD detec- tion. Unlike existing approaches, the trained PC alone serves as the representation of the in-distribution: no held-out in- distribution data are required at deployment. We further show that the quantities required by the hypothesis test can be com- puted exactly, directly from the trained circuit, yielding an ap- proximate analytic decision threshold. Experiments on tabular and MNIST datasets demonstrate that exploiting the hierarchi- cal probabilistic summaries encoded through the PC improve OOD detection over root-likelihood, uncertainty-, typicality- and kernel-based baselines, while naturally localizing distri- bution shifts to the PC nodes responsible for the shift.