Deep learning models are increasingly deployed in safety-critical applications, where reliable out-of-distribution (OOD) detection is essential to ensure robustness. Existing methods predominantly rely on the penultimate-layer activations of neural networks, assuming they encapsulate the most informative in-distribution (ID) representations. In this work, we revisit this assumption to show that intermediate layers encode equally rich and discriminative information for OOD detection. Based on this observation, we propose a simple yet effective model-agnostic approach that leverages internal representations across multiple layers. Our scheme aggregates features from successive convolutional blocks, computes class-wise mean embeddings, and applies L_2 normalization to form compact ID prototypes capturing class semantics. During inference, cosine similarity between test features and these prototypes serves as an OOD score--ID samples exhibit strong affinity to at least one prototype, whereas OOD samples remain uniformly distant. Extensive experiments on state-of-the-art OOD benchmarks across diverse architectures demonstrate that our approach delivers robust, architecture-agnostic performance and strong generalization for image classification. Notably, it improves AUROC by up to 4.41% and reduces FPR by 13.58%, highlighting multi-layer feature aggregation as a powerful yet underexplored signal for OOD detection, challenging the dominance of penultimate-layer-based methods. Our code is available at: https://github.com/sgchr273/cosine-layers.git.
Figures & tables
Figure 1: Overview of the proposed training-free OOD detector. A pretrained CNN is tapped at layers ℓ1 – ℓ3 . ID calibration images are passed through the network, and per-layer features are global-average-pooled and L2 -normalized to form K class prototypes (green regions). For a test image (ID or OOD), we compute cosine similarity between its features and each layer’s prototypes (green arrows for ID, red arrows for OOD). At each layer, we retain the maximum class-wise similarity, and these per-layer maxima are averaged to produce an ID affinity score, with OODScore=1−affinity . The heatmaps on the right show that ID samples yield strong, consistent similarities across layers and classes, whereas OOD samples produce weaker and less coherent similarity patterns.
Model
Method
iSUN
LSUN
Places
iNat
Textures
Average
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
ResNet-18
MSP
89.79
47.44
94.68
15.26
89.66
48.32
89.59
44.33
87.18
63.96
90.75
39.75
MaxLogit
90.08
52.84
94.63
25.82
89.65
55.06
89.37
51.19
86.35
73.86
90.74
46.60
Energy
88.42
63.00
92.34
51.48
87.97
62.87
87.46
59.14
84.24
79.10
89.02
57.46
Mahalanobis
86.86
51.32
80.99
53.84
84.80
49.93
80.25
58.48
92.64
34.99
86.61
46.26
GradNorm
83.44
70.92
91.86
37.20
79.30
74.98
90.81
44.29
81.20
82.75
86.56
57.97
Table 1: OOD detection results on the CIFAR-10 dataset. ↑ / ↓ denote that higher/lower values are better. The first , second , and third best results are highlighted in green, orange, and blue, respectively (values in %).
Figure 2: Effect of calibration set size on AUROC (top row) and false positive rate (bottom row) for CIFAR-10, CIFAR-100, and ImageNet-1k.
ID = CIFAR-10
ID = CIFAR-100
Model
Method
CIFAR-100
SVHN
Average
CIFAR-10
SVHN
Average
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
ResNet-18
MSP
88.76
46.29
93.60
19.17
91.18
32.73
75.62
77.26
72.92
83.01
74.27
80.14
MaxLogit
88.09
53.99
94.36
20.86
91.22
37.42
72.75
84.39
67.27
90.25
70.01
87.32
Energy
85.04
64.90
93.69
29.20
89.37
47.05
66.38
86.81
58.26
91.68
62.32
89.25
Mahalanobis
82.11
59.59
94.12
29.00
88.12
44.30
70.44
78.46
77.92
61.76
74.18
70.11
Table 2: OOD detection results where CIFAR-10 is ID and OOD = CIFAR-100, SVHN) and ID = CIFAR-100 (OOD = CIFAR-10, SVHN). ↑ / ↓ denote that higher/lower is better. The first , second , and third best results are highlighted in green, orange, and blue respectively (values in %).
Model
Method
SUN
Places
iNat
Textures
Average
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
AUROC ↑
FPR ↓
ResNet-50
MSP
79.25
79.48
77.48
78.59
84.65
62.69
74.78
87.76
79.04
77.13
MaxLogit
74.78
85.81
72.64
85.90
80.25
76.47
69.25
91.74
74.23
84.98
Energy
50.82
89.72
50.55
90.23
51.27
87.51
48.57
94.28
50.30
90.44
Mahalanobis
79.60
54.97
77.26
65.66
90.48
29.89
87.13
53.09
83.62
50.90
GradNorm
30.01
94.09
29.56
95.31
30.72
90.89
39.25
91.06
32.38
92.84
Table 3: OOD detection results on the ImageNet-1k dataset. ↑ / ↓ denote that higher/lower values are better. The first , second , and third best results are highlighted in green, orange, and blue, respectively (values in %).
Figure 3: AUROC and FPR using the penultimate layer vs. the last three layers across three ID datasets: CIFAR-10 (Exp1), CIFAR-100 (Exp2), and ImageNet-1K (Exp3).
Figure 4: Impact of weighting schemes across layers on overall detection performance.
Figure 5: Per-layer cosine similarity scores for the last three layers of ResNet-18 on ID data (CIFAR-10)and four OOD datasets (SVHN, Textures, LSUN, Places).
Recent studies show that using potential out-of-distribution (OOD) labels from large corpora as auxiliary information can improve OOD detection in vision-language models (VLMs). However, these methods often fail when real-world OOD samples fall outside the predefined OOD label set. To address this limitation, we propose DynProto, a novel approach that learns OOD prototypes dynamically during testing using only in-distribution (ID) information. DynProto is inspired by a key observation: OOD samples predicted as the same ID class tend to cluster in the feature space. With this insight, we leverage easy-to-detect OOD samples as ``anchors'' to find their harder-to-detect, similar counterparts. To this end, DynProto introduces two modules: Coarse OOD Pattern Capturing Module caches OOD patterns that are easily confused with each ID class during testing, and Fine-grained OOD Pattern Refinement Module subsequently clusters these patterns within each cache and aggregates them into representative OOD prototypes. By measuring similarity to ID and dynamic OOD prototypes, DynProto enables accurate OOD detection. DynProto significantly outperforms prior methods across multiple benchmarks. On ImageNet OOD benchmark, DynProto reduces FPR95 by 11.60% and improves AUROC by 4.70%. Moreover, the framework is architecture-agnostic and can be integrated into various backbones.
Yanqi Wu, Xinhua Lu, Runhe Lai +4
School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510275, China · Peng Cheng Laboratory, Shenzhen 518066, China · Key Laboratory of Machine Intelligence and Advanced Computing, MOE, Guangzhou 510275, China +2
We introduce MM++ (Multilayer Mahalanobis++), a strictly post-hoc, and scale-invariant framework for Out-of-Distribution (OOD) detection. To address the trade-off between scale invariance and hierarchical expressivity, MM++ constructs a principled joint feature space. It first identifies discriminative intermediate layers by measuring entropy density drops, which mark the boundaries of sharp semantic compression. By fusing these selected layers with the terminal representation, the framework captures latent cross-layer correlations while mitigating early-layer noise. Crucially, a Ledoit-Wolf regularized tied covariance matrix stabilizes this unified space, enabling reliable distance estimation. Requiring no auxiliary OOD data, classifier fine-tuning, or architectural modifications, MM++ delivers robust performance across distinct architectures for both near- and far-OOD detection.
Rahim Hossain, Md Tawheedul Islam Bhuian, Md Farhan Shadiq +1
School of Computing State University of New York at Binghamton
Out-of-Distribution (OOD) detection remains a fundamental challenge for neural networks, whose predictions can be overconfident on inputs that deviate from the training distribution. Most post-hoc OOD detection methods derive scores from a single representation level (eg., logits or penultimate features) or combine multiple layers via depth selection or OOD-calibrated weighting. However, because OOD shifts are diverse, the most informative representation level can vary strongly across OOD types and domains, making fixed-layer choices and OOD-calibrated aggregation brittle. In this paper, we propose PRISM (Projected Representation with Intermediate-layer Subspace Modeling), a model-agnostic post-hoc OOD detection method that models a unified multi-layer feature representation rather than aggregating independently scored layers. PRISM fuses intermediate and deep features into a single hierarchical embedding, estimates an in-distribution (ID) principal subspace, and then combines two complementary signals: (i) a class-conditional Mahalanobis distance in the projected subspace and (ii) the residual energy orthogonal to the learned manifold. This simple design avoids OOD-tuned layer weighting while capturing both in-subspace semantic deviations and off-subspace anomalies. Across diverse benchmarks spanning natural images, medical imaging, and industrial visual inspection, PRISM achieves consistent state-of-the-art cross-domain OOD detection performance with a single default configuration across all evaluated domains and architectures. We further show that PRISM incurs minimal inference overhead, making it practical for real-world deployment.
Gerhard Krumpl, Henning Avenhaus, Horst Possegger
Institute of Visual Computing, Graz University of Technology, Austria · KESTRELEYE GmbH, Austria