A Systematic Comparison of Training Objectives for Out-of-Distribution Detection in Image Classification

Furkan Genç; Onat Özdemir; Emre Akbaş

cs.CVMar 8, 2026

A Systematic Comparison of Training Objectives for Out-of-Distribution Detection in Image Classification

Authors: Furkan Genç, Onat Özdemir, Emre Akbaş

Organizations: Dept. of Electrical and Electronics Engineering, Bilkent University · Dept. of Computer Engineering, Middle East Technical University

Abstract

Out-of-distribution (OOD) detection is critical in safety-sensitive applications. While this challenge has been addressed from various perspectives, the influence of training objectives on OOD behavior remains comparatively underexplored. In this paper, we present a systematic comparison of four widely used training objectives: Cross-Entropy Loss, Prototype Loss, Triplet Loss, and Average Precision (AP) Loss, spanning probabilistic, prototype-based, metric-learning, and ranking-based supervision, for OOD detection in image classification under standardized OpenOOD protocols. Within the evaluated ResNet-18/OpenOOD setting and objective-specific OOD scoring rules, Cross-Entropy Loss, Prototype Loss, and AP Loss achieve comparable in-distribution accuracy, while Cross-Entropy Loss provides the most consistent near- and far-OOD AUROC overall; the other objectives can be competitive in specific settings.

Figures & tables

Panel of Figure 1 — Figure 1: Results for CIFAR-10 : (a) ID Accuracy, (b) near-OOD AUROC, and (c) far-OOD AUROC. ** denotes statistically significant difference.

Panel of Figure 2 — Figure 2: Results for CIFAR-100 : (a) ID Accuracy, (b) near-OOD AUROC, and (c) far-OOD AUROC. ** denotes statistically significant difference.

Panel of Figure 3 — Figure 3: Results for ImageNet-200 : (a) ID Accuracy, (b) near-OOD AUROC, and (c) far-OOD AUROC. ** denotes statistically significant difference.

Panel of Figure 4 — Figure 4: t-SNE visualizations for ID vs near-OOD and far-OOD samples.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Objective	LR	ED	$\boldsymbol{\lambda}$ / $\boldsymbol{\tau}$	Triplet Mining	OOD score
AP Loss	0.08	–	– / –	–	Entropy
Cross-Entropy Loss	0.10	–	– / –	–	Entropy
Prototype Loss	0.10	64	0.01 / 0.1	–	Entropy
Triplet Loss	0.005	32	– / –	Random	1-NN distance

Appendix

Table 1: Selected hyperparameters and OOD post-processing for CIFAR-10.

Objective	LR	ED	$\boldsymbol{\lambda}$ / $\boldsymbol{\tau}$	Triplet Mining	OOD score
AP Loss	0.08	–	– / –	–	Entropy
Cross-Entropy Loss	0.08	–	– / –	–	Entropy
Prototype Loss	0.10	128	0.001 / 0.1	–	MSP
Triplet Loss	0.0004	256	– / –	Semi-Hard	1-NN distance

Appendix

Table 2: Selected hyperparameters and OOD post-processing for CIFAR-100.

Objective	LR	ED	$\boldsymbol{\lambda}$ / $\boldsymbol{\tau}$	Triplet Mining	OOD score
AP Loss	0.10	–	– / –	–	Entropy
Cross-Entropy Loss	0.08	–	– / –	–	Entropy
Prototype Loss	0.10	128	0.001 / 0.1	–	MSP
Triplet Loss	0.0009	512	– / –	Semi-Hard	1-NN distance

Appendix

Table 3: Selected hyperparameters and OOD post-processing for ImageNet-200.

Loss Function	ID Accuracy (%)	Near-OOD AUROC (%)	Far-OOD AUROC (%)
AP Loss	94.93 $\pm$ 0.20	88.80 $\pm$ 0.19	92.34 $\pm$ 0.53
Cross-Entropy Loss	94.95 $\pm$ 0.25	88.23 $\pm$ 0.42	90.98 $\pm$ 0.47
Prototype Loss	95.06 $\pm$ 0.14	87.87 $\pm$ 0.37	91.28 $\pm$ 0.51
Triplet Loss	93.56 $\pm$ 0.18	88.85 $\pm$ 0.20	92.25 $\pm$ 0.58

Appendix

Table 4: Extended performance comparison on CIFAR-10 OpenOOD benchmark.

Loss Function	ID Accuracy (%)	Near-OOD AUROC (%)	Far-OOD AUROC (%)
AP Loss	77.21 $\pm$ 0.46	79.32 $\pm$ 0.27	77.68 $\pm$ 1.15
Cross-Entropy Loss	77.10 $\pm$ 0.28	80.94 $\pm$ 0.24	80.46 $\pm$ 0.75
Prototype Loss	78.18 $\pm$ 0.54	79.95 $\pm$ 0.33	79.85 $\pm$ 1.42
Triplet Loss	69.00 $\pm$ 0.30	76.95 $\pm$ 0.27	80.50 $\pm$ 1.05

Appendix

Table 5: Extended performance comparison on CIFAR-100 OpenOOD benchmark.

Loss Function	ID Accuracy (%)	Near-OOD AUROC (%)	Far-OOD AUROC (%)
AP Loss	86.71 $\pm$ 0.30	82.47 $\pm$ 0.20	90.54 $\pm$ 0.28
Cross-Entropy Loss	86.66 $\pm$ 0.22	83.54 $\pm$ 0.19	91.16 $\pm$ 0.25
Prototype Loss	86.07 $\pm$ 0.34	80.78 $\pm$ 0.17	89.73 $\pm$ 0.23
Triplet Loss	68.12 $\pm$ 0.22	74.44 $\pm$ 0.14	84.70 $\pm$ 0.23

Appendix

Table 6: Extended performance comparison on ImageNet-200 OpenOOD benchmark.

Panel of Figure 5 — Figure 5: t-SNE visualizations for ID vs OOD comparison.

Panel of Figure 6 — Figure 6: UMAP visualizations for ID vs OOD comparison.

Panel of Figure 7 — Figure 7: UMAP visualizations for ID vs near-OOD and far-OOD comparison.

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Prototype Fusion: A Training-Free Multi-Layer Approach to OOD Detection

Shreen Gul, Mohamed Elmahallawy, Ardhendu Tripathy, Sanjay Madria

Missouri University of Science and Technology, Rolla, MO 65401, USA · Washington State University, Richland, WA 99354, USA

OOD Detection

Open paper AskPDF arXiv

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.

Abstract

OOD Detection

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