MahaVar: OOD Detection via Class-wise Mahalanobis Distance Variance under Neural Collapse

TL;DR

MahaVar is a novel OOD detection method that leverages class-wise Mahalanobis distance variance, supported by a theoretical analysis rooted in Neural Collapse geometry, achieving state-of-the-art results.

Contribution

The paper introduces MahaVar, a simple post-hoc OOD detector that incorporates class-wise Mahalanobis distance variance, with theoretical grounding and superior empirical performance.

Findings

MahaVar outperforms existing Mahalanobis-based methods on CIFAR-100 and ImageNet.

ID samples show high class-wise distance variance, OOD samples show lower variance.

Theoretical analysis links class-wise distance variance to Neural Collapse geometry.

Abstract

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.