Papers › Single Layer Predictive Normalized Maximum Likelihood for Out-of-Distribution Detection
Single Layer Predictive Normalized Maximum Likelihood for Out-of-Distribution Detection
Koby Bibas, Meir Feder, Tal Hassner
Detecting out-of-distribution (OOD) samples is vital for developing machine learning based models for critical safety systems. Common approaches for OOD detection assume access to some OOD samples during training which may not be available in a real-life scenario. Instead, we utilize the {\em predictive normalized maximum likelihood} (pNML) learner, in which no assumptions are made on the tested input. We derive an explicit expression of the pNML and its generalization error, denoted as the {\em regret}, for a single layer neural network (NN). We show that this learner generalizes well when (i) the test vector resides in a subspace spanned by the eigenvectors associated with the large eigenvalues of the empirical correlation matrix of the training data, or (ii) the test sample is far from the decision boundary. Furthermore, we describe how to efficiently apply the derived pNML regret to any pretrained deep NN, by employing the explicit pNML for the last layer, followed by the softmax function. Applying the derived regret to deep NN requires neither additional tunable parameters nor extra data. We extensively evaluate our approach on 74 OOD detection benchmarks using DenseNet-100, ResNet-34, and WideResNet-40 models trained with CIFAR-100, CIFAR-10, SVHN, and ImageNet-30 showing a significant improvement of up to 15.6\% over recent leading methods.
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Code
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Out-of-Distribution Detection | CIFAR-10 vs Gaussian | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs Gaussian | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs ImageNet (C) | DenseNet-BC-100 | AUROC | 99.9 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs ImageNet (C) | ResNet-34 | AUROC | 99.8 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs ImageNet (R) | DenseNet-BC-100 | AUROC | 99.9 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs ImageNet (R) | ResNet-34 | AUROC | 99.9 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs LSUN (C) | DenseNet-BC-100 | AUROC | 99.9 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs LSUN (C) | ResNet-34 | AUROC | 99.5 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs LSUN (R) | ResNet-34 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs LSUN (R) | DenseNet-BC-100 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs SVHN | DenseNet-BC-100 | AUROC | 100 | #1 of 3 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs SVHN | ResNet-34 | AUROC | 99.8 | #3 of 3 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs Uniform | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs Uniform | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs iSUN | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-10 vs iSUN | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs Gaussian | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs Gaussian | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs ImageNet (C) | DenseNet-BC-100 | AUROC | 99.0 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs ImageNet (C) | ResNet-34 | AUROC | 98.4 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs ImageNet (R) | DenseNet-BC-100 | AUROC | 99.5 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs ImageNet (R) | ResNet-34 | AUROC | 99.2 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs LSUN (C) | ResNet-34 | AUROC | 97.8 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs LSUN (C) | DenseNet-BC-100 | AUROC | 96.1 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs LSUN (R) | DenseNet-BC-100 | AUROC | 99.7 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs LSUN (R) | ResNet-34 | AUROC | 99.6 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs SVHN | DenseNet-BC-100 | AUROC | 98.4 | #2 of 5 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs SVHN | ResNet-34 | AUROC | 97.9 | #3 of 5 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs Uniform | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs Uniform | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs iSUN | DenseNet-BC-100 | AUROC | 99.5 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | CIFAR-100 vs iSUN | ResNet-34 | AUROC | 99.3 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs CIFAR-10 | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs CIFAR-10 | ResNet-34 | AUROC | 99.8 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs CIFAR-100 | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs CIFAR-100 | ResNet-34 | AUROC | 99.8 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs Gaussian | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs Gaussian | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs ImageNet (C) | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs ImageNet (C) | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs ImageNet (R) | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs ImageNet (R) | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs LSUN (C) | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs LSUN (C) | ResNet-34 | AUROC | 99.9 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs LSUN (R) | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs LSUN (R) | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs Uniform | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs Uniform | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs iSUN | DenseNet-BC-100 | AUROC | 100 | #1 of 2 | Archive leaderboard | report |
| Out-of-Distribution Detection | SVHN vs iSUN | ResNet-34 | AUROC | 100 | #2 of 2 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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