Organizations: AXA AI Research · EPFL, Lausanne, Switzerland · TRAIL, Sorbonne Université, Paris, France · Polish Academy of Science, IBS PAN, Warsaw, Poland
Deep neural networks for image classification often exhibit overconfidence on out-of-distribution (OOD) samples. To address this, we introduce Geometrically Constrained Outlier Synthesis (GCOS), a training-time regularization framework aimed at improving OOD robustness during inference. GCOS addresses a limitation of prior synthesis methods by generating virtual outliers in the hidden feature space that respect the learned manifold structure of in-distribution (ID) data. The synthesis proceeds in two stages: (i) a dominant-variance subspace extracted from the training features identifies geometrically informed, off-manifold directions; (ii) a conformally-inspired shell, defined by the empirical quantiles of a nonconformity score from a calibration set, adaptively controls the synthesis magnitude to produce boundary samples. The shell ensures that generated outliers are neither trivially detectable nor indistinguishable from in-distribution data, facilitating smoother learning of robust features. This is combined with a contrastive regularization objective that promotes separability of ID and OOD samples in a chosen score space, such as Mahalanobis or energy-based. Experiments demonstrate that GCOS outperforms state-of-the-art methods using standard energy-based inference on near-OOD benchmarks, defined as tasks where outliers share the same semantic domain as in-distribution data. As an exploratory extension, the framework naturally transitions to conformal OOD inference, which translates uncertainty scores into statistically valid p-values and enables thresholds with formal error guarantees, providing a pathway toward more predictable and reliable OOD detection.
Figures & tables
Figure 1: GCOS Training Procedure Schematic. Illustration of the data flow in our online synthesis and regularization method. Epoch-level calibration on Dcalib produces class-conditional subspace models Mcalib and Mahalanobis quantiles q . During batch-level training, features are used to update a queue that generates proposer subspace models Mtrain and identifies off-manifold directions v . Outliers zood are synthesized to match the target quantiles q , as evaluated by Mcalib . The final regularization loss, Lreg , is a contrastive objective computed on the energy scores of in-distribution batch features and the synthesized outliers zood and added to cross-entropy loss, LCE , from the main classification task.
C-MNIST
Dogs
MVTec
Retino
Method
AUROC
AUPR
FPR95
AUROC
AUPR
FPR95
AUROC
AUPR
FPR95
AUROC
AUPR
FPR95
Avg. AUC
No Reg.
85.60
99.47
32.50
88.35
97.72
80.00
94.86
98.91
27.69
69.74
98.43
81.50
84.64
VOS ( Du et al., 2022 )
94.71
99.87
18.50
99.25
99.85
5.00
80.37
95.83
70.77
70.52
98.56
80.00
86.21
MSP ( Hendrycks and Gimpel, 2017 )
92.10
89.88
21.12
56.15
13.81
96.96
56.58
34.72
82.20
67.02
94.09
90.52
67.96
MaxLogit ( Hendrycks et al., 2022 )
88.88
85.68
27.59
58.42
14.27
93.69
55.30
39.20
90.24
77.21
96.41
81.39
69.95
ReAct ( Sun et al., 2021 )
89.41
86.60
24.69
57.77
14.08
94.04
57.31
36.74
87.09
77.37
96.43
75.84
70.47
Table 1: OOD detection performance across four datasets. Best values per column shown in bold.
Figure 2: UMAP Projection of Learned Features. Top: the overall feature space, showing that classes form varying shapes and are largely well separated. Bottom: a zoomed-in view highlighting the distribution of GCOS outliers in off-manifold regions and VOS outliers near cluster edges for two clusters. The panels illustrate how GCOS generates points in challenging regions beyond the main clusters, while VOS outliers remain close to class boundaries.
Appendix figures & tables13 assets
Supplementary material from the paper’s appendix.
Appendix
MVTec
Colored MNIST
Stanford Dogs
Retinopathy
AUROC
AUPR
FPR95
AUROC
AUPR
FPR95
AUROC
AUPR
FPR95
AUROC
AUPR
FPR95
GCOS + Luncertainty
50.92
83.68
100.00
98.75
99.97
2.00
50.00
83.33
100.00
67.60
98.37
77.00
GCOS + Lreg (Mahalanobis)
63.67
88.07
100.00
98.93
99.98
1.50
50.00
83.33
100.00
37.58
96.27
97.00
GCOS + Lreg (Energy)
70.62
88.50
72.31
76.00
97.85
34.00
2.40
65.43
100.00
31.11
95.30
98.00
Appendix
Table 2: Results using formal hypothesis testing ( 7 ) as OOD classification head.
Dataset
ID train
ID test
OOD
Total
Colored MNIST
60,000
10,000
10,000
80,000
MVTec
1,319
326
635
2,280
Stanford Dogs
1,394
100
856
2,350
Retinopathy
28,086
7,022
865
35,973
Appendix
Table 3: Number of ID and OOD images in each dataset.
Figure 4: Example images from four datasets. First row in each box: in-distribution; second row: outliers.
CIFAR-100
LSUN-C
Places
Textures
Mean
AUPR
AUROC
FPR95
AUPR
AUROC
FPR95
AUPR
AUROC
FPR95
AUPR
AUROC
FPR95
AUPR
AUROC
FPR95
Gaussian OOD
+ Luncertainty
99.61
87.08
49.0
99.97
98.56
6.5
99.66
89.1
39.5
99.68
88.34
49.0
99.73
90.77
36.0
GCOS OOD
+ Luncertainty
99.48
83.63
56.5
99.97
98.74
7.0
99.6
88.36
42.5
99.48
82.39
60.5
99.64
88.28
41.63
GCOS OOD
+ Lreg
99.54
82.48
72.5
99.96
98.12
8.5
99.82
92.3
41.5
99.76
90.19
50.5
99.77
90.77
43.25
Appendix
Table 4: Comparison of out-of-distribution detection performance trained on CIFAR-10.
CIFAR-10
LSUN-C
Places
Textures
Mean
AUPR
AUROC
FPR95
AUPR
AUROC
FPR95
AUPR
AUROC
FPR95
AUPR
AUROC
FPR95
AUPR
AUROC
FPR95
Gaussian OOD
+ Luncertainty
99.35
76.47
80.0
99.92
96.54
21.5
99.32
75.51
84.0
99.3
74.53
84.5
99.47
80.76
67.5
GCOS OOD
+ Luncertainty
99.33
76.13
83.5
99.94
97.1
17.0
99.37
77.18
81.0
99.23
72.96
87.5
99.47
80.84
67.25
GCOS OOD
+ Lreg
99.16
72.53
89.5
99.79
91.63
38.0
99.16
72.95
84.5
99.3
76.79
78.0
99.35
78.47
72.5
Appendix
Table 5: Comparison of out-of-distribution detection performance trained on CIFAR-100.
Textures
Places365
AUROC
FPR95
AUROC
FPR95
Free Energy ( Liu et al., 2020 )
85.35
52.46
90.02
40.11
ASH ( Djurisic et al., 2023 )
86.07
50.90
89.79
40.89
VOS ( Du et al., 2022 )
88.34
49.00
89.10
39.50
GCOS + Lreg
90.19
50.50
92.3
41.50
Appendix
Table 6: Results on CIFAR-10.
Textures
Places365
AUROC
FPR95
AUROC
FPR95
Free Energy ( Liu et al., 2020 )
76.35
79.63
75.65
80.18
ASH ( Djurisic et al., 2023 )
83.59
63.69
74.87
79.70
VOS ( Du et al., 2022 )
74.53
84.50
75.51
84.00
GCOS + Lreg
76.79
78.00
72.95
84.50
Appendix
Table 7: Results on CIFAR-100.
Dataset
Mean AUROC
Mean AUPR
Mean FPR95
Std(AUROC)
Std(AUPR)
Colored MNIST
92.90%
99.81%
23.50%
± 3.01%
± 0.10%
Stanford Dogs
97.39%
99.51%
24.00%
± 2.11%
± 0.39%
Retinopathy
76.60%
99.05%
80.00%
± 0.55%
± 0.02%
MVTec
98.71%
99.66%
3.08%
± 0.29%
± 0.12%
Appendix
Table 8: Multi-Seed Validation.
Method
FPR95 ↓
AUROC ↑
mAP (ID) ↑
OOD: MS-COCO / OpenImages
MSP ( Hendrycks and Gimpel, 2017 )
70.99 / 73.13
83.45 / 81.91
48.7
ODIN ( Liang et al., 2018 )
59.82 / 63.14
82.20 / 82.59
48.7
Mahalanobis ( Lee et al., 2018b )
96.46 / 96.27
59.25 / 57.42
48.7
Energy score ( Liu et al., 2020 )
56.89 / 58.69
83.69 / 82.98
48.7
Gram matrices ( Sastry and Oore, 2020 )
62.75 / 67.42
79.88 / 77.62
48.7
Appendix
Table 9: OOD detection comparison on PASCAL-VOC (In-Distribution) with MS-COCO and OpenImages as OOD datasets.
K
PCA (ms)
Shell Calib (ms)
Synthesis (ms)
Total (ms)
10
16.7
2.3
35.8
54.8
20
33.6
4.4
71.3
109.3
50
83.7
11.4
183.8
278.9
100
165.4
23.1
379.9
568.3
200
332.1
46.3
764.8
1143.3
1000
1663.7
239.6
3845.3
5748.6
Appendix
Table 10: Per-batch GCOS overhead by number of classes K . NVIDIA RTX 6000 Ada Generation; 100-iteration average.
OOD Dataset
GCOS AUROC
VOS AUROC
GCOS FPR@95
VOS FPR@95
iNaturalist
91.6
90.8
41.5
46.0
SUN
94.7
94.6
24.0
28.5
Places
95.0
94.7
22.5
22.5
Textures
95.9
96.4
22.5
16.5
Mean
94.3
94.1
27.6
28.4
Appendix
Table 11: OOD detection on ImageNet-100.
MVTec
Colored MNIST
Stanford Dogs
Retinopathy
AUROC
AUPR
FPR95
AUROC
AUPR
FPR95
AUROC
AUPR
FPR95
AUROC
AUPR
FPR95
GCOS + Luncertainty
93.07
98.56
33.85
93.21
99.82
25.50
99.42
99.89
0.86
80.05
99.23
71.00
GCOS + Lreg (Mahalanobis)
97.56
99.51
20.00
95.65
99.91
25.00
97.90
99.61
20.00
77.89
99.17
79.00
Appendix
Table 12: Ablation study of proposed contributions . OOD detection results on MVTec, Colored MNIST, Stanford Dogs and Retinopathy datasets. First row: GCOS outliers combined with the standard energy-based separation loss Luncertainty in ( 2 ). Second row: GCOS outliers combined with the geometric loss Lreg in ( 5 ) using the Mahalanobis score function SL=SMahal .
Detecting out-of-distribution (OOD) graphs is crucial for ensuring the safety and reliability of Graph Neural Networks. In unsupervised graph-level OOD detection, models are typically trained using only in-distribution (ID) data, resulting in incomplete feature space characterization and weak decision boundaries. Although synthesizing outliers offers a promising solution, existing approaches rely on fixed, non-adaptive sampling heuristics (e.g., distance- or density-based), limiting their ability to explore informative OOD regions. We propose a Policy-Guided Outlier Synthesis (PGOS) framework that replaces static heuristics with a learned exploration strategy. Specifically, PGOS trains a reinforcement learning agent to navigate low-density regions in a structured latent space and sample representations that most effectively refine the OOD decision boundary. These representations are then decoded into high-quality pseudo-OOD graphs to improve detector robustness. Extensive experiments demonstrate that PGOS achieves state-of-the-art performance on multiple graph OOD and anomaly detection benchmarks.
Li Sun, Lanxu Yang, Jiayu Tian +6
North China Electric Power University · Beijing University of Posts and Telecommunications · Tsinghua University +4
Deep neural networks (DNNs) experience significant performance degradation when processing noisy labels, primarily due to overfitting on mislabeled data. Current mainstream approaches attempt to mitigate this issue by passively filtering clean samples during training. However, simple sample filtering within feature spaces degraded by noise struggles to distinguish between challenging samples and noisy samples, creating a bottleneck for model performance. We highlight for the first time the fundamental importance of actively reshaping feature space geometry for learning from noisy data. We propose a novel Geometry-aware Manifold Regularization Paradigm whose core idea is to explicitly construct energy barriers between data manifolds by actively synthesizing virtual outlier samples. By imposing geometric constraints that promote intra-class compactness and inter-class separation, this approach enhances the discriminability between hard and noisy samples, leading to the learning of more robust representations. Our regularization mechanism exhibits high universality, with effectiveness independent of any prior assumptions about noise patterns. It can be integrated as a standalone mechanism into existing sample selection frameworks, providing stronger robustness against diverse noisy environments. Experiments demonstrate that our paradigm achieves performance surpassing current state-of-the-art (SOTA) methods on multiple benchmarks, including CIFAR-10, with particularly pronounced advantages under more challenging asymmetric noise conditions. Furthermore, this paradigm significantly enhances the model's capability in Out-of-Distribution (OOD) detection, ensuring superior reliability and safety for deployment in open-world scenarios.
Ningkang Peng, Jingyang Mao, Xiaoqian Peng +4
Nanjing Normal University Nanjing, China · Nanjing University of Chinese Medicine Nanjing, China
Out-of-distribution (OOD) objects are often silently overlooked by object detectors, which produce no detection for them, leaving downstream modules with nothing to act on and no indication that anything was missed. A reliable object detector must detect OOD objects by localizing and correctly classifying them as OOD. Existing approaches primarily focus on OOD detection for image classification or rely on auxiliary branches, and typically do not treat in-distribution (ID) and OOD objects in a unified manner. We present SynOE-OD, a Synthetic Outlier-Exposure-based Object Detection method, which uses text-guided inpainting and an open-vocabulary object detector to generate and verify synthetic outliers offline. These are then used to fine-tune an object detector of choice with an added OOD class, which requires no auxiliary branch at inference time. On the OoDIS benchmark, SynOE-OD outperforms the strongest open-vocabulary baseline, reaching AP_50:95 of 57.6%, 29.4% and 39.2% on RoadObstacle, RoadAnomaly and Fishyscapes, against 48.5%, 22.7% and 22.7%. This state-of-the-art performance holds for both fine-tuned closed-set and open-vocabulary detectors while maintaining competitive ID performance in street scenes.
Sadia Ilyas, Annika Mütze, Klaus Friedrichs +2
University of Wuppertal · Aptiv Services Deutschland GmbH · University of Osnabrück, Germany