Deep generative models that can tractably compute input likelihoods, including normalizing flows, often assign unexpectedly high likelihoods to out-of-distribution (OOD) inputs. We mitigate this paradox from an entropic perspective with Semantic Proportional Entropy Manipulation (SPEM), a training-free procedure that applies stronger perturbations to inputs less similar to an in-distribution (ID) memory bank. We derive theoretical lower bounds showing that this entropy gap increases the expected log-likelihood difference in favor of the ID, and experiments on standard benchmarks show that this manipulation realigns the likelihood ordering with human intuition. Strikingly, this realignment persists even when the flow is given only visually meaningless noise instead of the original input, and we analyze this phenomenon theoretically to characterize the conditions under which it occurs.
Out-of-distribution (OOD) detection is recognized as a critical problem in AI safety. SCALE is an effective post-hoc OOD detection method in the activation-shaping family that requires no training data and rescales penultimate activations using a percentile-based magnitude ratio. However, this ratio is ill-defined when negative activations are present, since positive and negative contributions cancel within the underlying sum, causing SCALE to degenerate on backbones such as ViT. We address this with an Absolute Fix that computes the ratio over absolute-valued activations rather than discarding negative activations through ReLU. Building on this corrected scale, we propose Anti-coherence regularization, which penalizes the scaling factor by the fraction of a sample's max-logit contributions to the max logit that are sign-mismatched and thereby suppresses unreliable evidence for the predicted class. Despite requiring no access to training data or training labels, our method ties or outperforms activation-shaping methods that rely on training data in terms of AUROC and FPR@95 on CIFAR-10 and ImageNet under the OpenOOD v1.5 protocol.
Deep generative models with tractable likelihoods, exemplified by normalizing flows, offer an effective basis for anomaly detection through likelihood-based scoring. We demonstrate that, unlike in the image domain where deep generative models frequently assign higher likelihoods to anomalous data, such counterintuitive behavior occurs rarely in tabular settings. We first introduce a domain-agnostic formulation that enables consistent detection and evaluation of the counterintuitive phenomenon, addressing the lack of a precise definition in prior work. Through extensive experiments on 47 tabular datasets benchmarked against 13 baseline models and on 10 CV/NLP embedding datasets from ADBench, we show that the phenomenon is consistently rare in general tabular data and that normalizing flow likelihood achieves competitive anomaly detection performance. We further provide theoretical and empirical analyses attributing this disparity to differences in dimensionality and feature correlation between tabular and image data. Therefore, our results indicate that likelihood-based detection with normalizing flows is a practical approach for tabular anomaly detection.
Out-of-distribution (OOD) detection is a critical component for ensuring the reliability of deep neural networks in safety-critical applications. In this work, we present a key empirical observation: for in-distribution (ID) samples, class-wise Mahalanobis distances exhibit a pronounced sharp minimum structure, where the distance to the nearest class is small while distances to all other classes remain large, resulting in high variance across classes. In contrast, OOD samples tend to exhibit a less pronounced sharp minimum structure, producing comparatively lower variance across classes. We further provide a theoretical analysis grounding this observation in Neural Collapse geometry: under relaxed Neural Collapse assumptions on within-class compactness and inter-class separation, ID samples are shown to structurally exhibit high class-wise distance variance, offering a theoretical basis for its use as an OOD score. Motivated by this observation and its theoretical backing, we propose MahaVar, a simple and effective post-hoc OOD detector that augments the Mahalanobis distance with a class-wise distance variance term. Following the OpenOOD v1.5 benchmark protocol, MahaVar achieves state-of-the-art performance on CIFAR-100 and ImageNet, with consistent improvements in both AUROC and FPR@95 over existing Mahalanobis-based methods across all benchmarks.