FEVER-OOD: Free Energy Vulnerability Elimination for Robust Out-of-Distribution Detection

TL;DR

FEVER-OOD analyzes fundamental vulnerabilities in free energy–based OOD detection, showing that null-space directions and least-singular-vector directions can cause in-distribution and OOD samples to yield indistinguishable energies. It proposes NSR to reduce null space and two regularisers—Least Singular Value Regulariser and a Condition Number Regulariser—to maximize energy separation across feature-space directions. Empirical results demonstrate state-of-the-art OOD detection on Imagenet-100 with Dream-OOD and consistent gains on CIFAR-10/100 and object-detection benchmarks, validating robustness improvements across classification and detection tasks. The work advances reliable open-set recognition by strengthening energy-based uncertainty measures and offers practical pathways for deploying more robust OOD detectors in real-world systems.

Abstract

Modern machine learning models, that excel on computer vision tasks such as classification and object detection, are often overconfident in their predictions for Out-of-Distribution (OOD) examples, resulting in unpredictable behaviour for open-set environments. Recent works have demonstrated that the free energy score is an effective measure of uncertainty for OOD detection given its close relationship to the data distribution. However, despite free energy-based methods representing a significant empirical advance in OOD detection, our theoretical analysis reveals previously unexplored and inherent vulnerabilities within the free energy score formulation such that in-distribution and OOD instances can have distinct feature representations yet identical free energy scores. This phenomenon occurs when the vector direction representing the feature space difference between the in-distribution and OOD sample lies within the null space of the last layer of a neural-based classifier. To mitigate these issues, we explore lower-dimensional feature spaces to reduce the null space footprint and introduce novel regularisation to maximize the least singular value of the final linear layer, hence enhancing inter-sample free energy separation. We refer to these techniques as Free Energy Vulnerability Elimination for Robust Out-of-Distribution Detection (FEVER-OOD). Our experiments show that FEVER-OOD techniques achieve state of the art OOD detection in Imagenet-100, with average OOD false positive rate (at 95% true positive rate) of 35.83% when used with the baseline Dream-OOD model.

Figures (15)

• Figure 1: FEVER-OOD (right, green) improves baseline Free Energy-based OOD detection methods (left, blue).
• Figure 2: Vulnerabilities of Free Energy-based OOD detection. Directions in the Null Space do not change the energy, while the LSV direction has minimal change, compared to other directions.
• Figure 3: Null space reduction. We add an extra layer $g'$ to create $r$-dimensional features, reducing the size of the null space.
• Figure 4: MS-COCO objects detected on OOD images by VOS baseline duvos (first row) and Fever-OOD (second row). Blue: OOD objects detected and mis-classified as being in-distribution. Green: the same OOD objects correctly detected as OOD by FEVER-OOD (ours).
• Figure 5: Feature Space UMAP Projection for models trained on CIFAR-10. Top row corresponds to the VOS duvos model while the bottom shows the FEVER-OOD VOS (Ours) projections. (a) In-distribution vs OOD feature space projection, (b) Free Energy visualization of the feature space, and (c) different important directions, including Null Space directions, the LSV direction and a random direction.