Title: Out-of-Distribution Detection with Relative Angles
Venue: NeurIPS 2025
Accepted: yes
Keywords: out-of-distribution

out-of-distribution detection

decision boundaries
Abstract: Deep learning systems deployed in real-world applications often encounter data that is different from their in-distribution (ID). A reliable model should ideally abstain from making decisions in this out-of-distribution (OOD) setting. Existing state-of-the-art methods primarily focus on feature distances, such as k-th nearest neighbors and distances to decision boundaries, either overlooking or ineffectively using in-distribution statistics. In this work, we propose a novel angle-based metric for OOD detection that is computed relative to the in-distribution structure. We demonstrate that the angles between feature representations and decision boundaries, viewed from the mean of in-distribution features, serve as an effective discriminative factor between ID and OOD data. We evaluate our method on nine ImageNet-pretrained models. Our approach achieves the lowest FPR in 5 out of 9 ImageNet models, obtains the best average FPR overall, and consistently ranking among the top 3 across all evaluated models. Furthermore, we highlight the benefits of contrastive representations by showing strong performance with ResNet SCL and CLIP architectures. Finally, we demonstrate that the scale-invariant nature of our score enables an ensemble strategy via simple score summation.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a new OOD detection metric called ORA, which uses relative angles between two vectors: (1) the vector from the mean of in-distribution dataset features to the feature point, and (2) the vector from the mean of in-distribution dataset features to the feature point's projection onto the decision boundary. The authors argue that the angular distance provides better discrimination between ID and OOD samples compared to previous distance-based approaches, particularly the closely related fDBD method. They evaluate their method extensively across various pretrained architectures, including convolutional and transformer-based models, reporting modest improvements over existing methods.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n1. The paper is clearly written.\n\n2. Extensive experiments have been conducted.\n\n3. The interpretation of fDBD from a geometric perspective is highly interesting. Specifically, leveraging the law of sines to accurately highlight the connection between fDBD and the proposed method is insightful and appealing.\n\n**Weaknesses**\n\n1. This paper closely resembles fDBD. Fundamentally, both papers rely on the same core insight that \"ID data are mapped further from the decision boundary.\" The primary difference is that this paper explains the same phenomenon from a geometric perspective.\n\n2. The empirical results do not demonstrate significant improvements.\n\nIn conclusion, although this paper presents some noteworthy insights, it does not meet the standards required for NeurIPS.\n\nQUESTIONS:\n1. In the conclusion, three key advantages of ORA are: (i) hyperparameter-free, (ii) model-agnostic, and (iii) scale-invariant. It would be useful to clarify whether fDBD shares these properties. If fDBD does not exhibit these attributes, please specify explicitly what distinguishes ORA from fDBD regarding each of these aspects.\n\n2. The original fDBD paper emphasized the importance of the regularization term through an ablation study. However, in this submission, this regularization term is geometrically reinterpreted as $\\sin \\alpha$, and Figure 2 suggests that its contribution may be insignificant. Clarification on how this apparent contradiction can be reconciled or further contextualized would enhance the consistency and coherence of the interpretation presented.\n\n3. Both this study and the original fDBD approach rely on the observation that \"ID data are mapped further from the decision boundary.\" Although the fDBD paper supports this claim with limited experimental results provided in Appendix J, additional insights or theoretical justifications would significantly strengthen the argument. It would be valuable to discuss whether this observation consistently holds for simpler datasets, such as MNIST, or simpler network architectures, such as LeNet, and provide reasoning or evidence explaining why this might be the case.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-27"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes ORA, a novel angle-based metric for OOD detection that leverages that exploits\nthe relationship between feature representations and classifier decision boundaries, viewed from the mean of in-distribution data. The authors demonstrate ORA's effectiveness across nine ImageNet-pretrained models, achieving top or near-top false positive rates in most cases.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n* The paper presents a novel post-hoc OOD detection method that leverages relative angles in feature space to relate feature representations to decision boundaries. These angles are computed with reference to the mean of in-distribution samples. \n\n* The paper provides strong empirical validation of the proposed method across established benchmarks. This includes strong performance in OOD detection on the ImageNet benchmark and with CLIP. Furthermore, the method demonstrates benefits when used in model ensembles or as a plug-in module with existing activation shaping algorithms.\n\nWeaknesses: \n\n* ORA and the role of ID classes: Since the method uses the mean of ID samples as a reference, it is unclear how ORA performs on the best- or worst-performing classes. Additionally, it's worth questioning whether using the ID mean remains valid for minority classes. Given that the score function is dependent on the predicted class, the paper also lacks analysis comparing correctly versus incorrectly predicted samples and their effect on ORA. \n\n* The paper refers to ORA as a “confidence measure,” but this aspect is not clearly explained and feels somewhat hand-wavy.\n \n* It is not clear how the analysis presented in Fig. 2 supports ORA. It seems this analysis may be included because the method is similar to fDBD. Clarifying this connection would be helpful.\n\nQUESTIONS:\nPlease respond to the points raised  in weakness section.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-06-30"}

comments: SUMMARY:
The problem of out-of-distribution detection for deep learning models is considered. This work introduces OOD Detection with Relative Angles (ORA), a novel approach that uses an angle-based metric calculated relative to the in-distribution structure, demonstrating that angles between feature representations and decision boundaries, when viewed from the mean of in-distribution features, effectively distinguish between ID and OOD data. ORA achieves SOTA performance on different OOD benchmarks.

STRENGTHS AND WEAKNESSES:
Strenghs  
1.ORA achieves SOTA performance on different OOD benchmarks.   
2. ORA's scale-invariant nature allows for an ensemble strategy by simply summing scores from multiple models, further enhancing OOD detection performance  

Weaknesses  
	1. Lack of theoretical justification  
	2. More recent SOTA OOD detection algorithms (e.g. NECO [T1], Mahalanobis++ [T2], NCI [T3]) are not compared to.     

[T1] NECO: NEural collapse based out-of-distribution detection. ICLR'24.   
[T2] Mahalanobis++: Improving OOD Detection via Feature Normalization. ICLR'25.   
[T3] Detecting Out-of-distribution through the Lens of Neural Collapse.

QUESTIONS:
Comments  
1. The title isn't really long and there is no need to use acronym OOD instead of Out-of-distribution.
2. Year for [Galil et al.] is missing.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper provides a new distance based out-of-distribution (OOD) detection method that extends the prior work by Liu and Qin 2024 called fDBD which utilizes the distance to the decision boundary as the OOD detection score. In particular, the proposed method centers the penultimate layer features then calculates the angle between the current sample’s feature and its projection onto the decision boundary. The OOD detection score named ORA is constructed to be the maximum of these angles over classes. The paper claims ORA’s scale invariance makes it a suitable post-hoc OOD score for a wide array of feature extractors. An exhaustive set of experiments is provided to support this claim across ensembles, CLIP models, transformer architectures, and contrastive training losses. Ablation experiments are also provided that show the impact of choice of center and OOD scoring method.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThe paper provides an effective yet simple extension to fDBD based on an intuitive geometric argument centered around providing scale invariance. The extensive set of experiments in both the main text and the supplement provide support for their claim that ORA is more effective across different feature extraction methods. \n\nWeaknesses:\n\nWhile the extensive experiments show the ability of the proposed method to adapt to a wide range of feature sets, a discussion of the findings and takeaways from these experiments would improve the impact of this paper on future development of OOD detection methods. \n\nAlso, the main text does not discuss the near-OOD performance. Several works have shown that the near-OOD scenario is more challenging and potentially more realistic [1-4]. The supplement provides results on SSB-Hard  [3] and NINCO [4] in Table 20. However, the performance of ORA on near-OOD datasets (average **78.53**% AUROC) is on par with or slightly below state-of-the-art OOD detection methods which can be found in the associated public leaderboard to [2] (see link [8]) such as [6] and [7] ~~such as ASH [5] which attains 78.17% AUROC on this task with a ResNet-50 feature set~~. It would be helpful for the paper to comment on the near-OOD performance of the method in the main text due to the importance and difficulty of near-OOD scenarios. \n\n[1] Yang, J. et al. “OpenOOD: Benchmarking Generalized Out-of-Distribution Detection.” NeurIPS Datasets and Benchmarks 2022. \n\n[2] Zhang, J., et al. \"Openood v1. 5: Enhanced benchmark for out-of-distribution detection.\" arXiv preprint arXiv:2306.09301 (2023).\n\n[3] Vaze, S. et al. “Open-Set Recognition: A Good Closed-Set Classifier is All You Need.” ICLR, 2022.\n\n[4] Bitterwolf, J. et al. “In or Out? Fixing ImageNet Out-of-Distribution Detection Evaluation.” ICML 2023.\n\n[5] Djurisic, A. et al. “Extremely simple activation shaping for out-of-distribution detection.” ICLR, 2023.\n\n[6] Mueller M. and Hein M. \"Mahalanobis++: Improving OOD Detection via Feature Normalization.\" ICML, 2025.\n\n[7] Xu K. et al. \"Scaling for Training Time and Post-hoc Out-of-distribution Detection Enhancement.\" ICLR, 2024.\n\n[8] https://zjysteven.github.io/OpenOOD/#div_imagenet1k_heading\n\nQUESTIONS:\nPlease see the strengths and weaknesses section.\n\nLIMITATIONS:\nThe authors briefly address a limitation and future work for this method in the conclusion. A discussion on future works based on the experimental findings of this paper would improve the impact and reach of this paper.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}