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Improving Out-of-Distribution Detection with Markov Logic Networks
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Augments existing OOD detectors with Markov logic network scores over human-interpretable concepts, plus a greedy algorithm that learns logical constraints from data.
Problem
Existing OOD detectors rely on statistical patterns in latent representations, lack explainability, and cannot easily integrate prior semantic knowledge about the training distribution.
Approach
Combine a Markov logic network defined over DNN-predicted semantic concepts (predicates/functions) with existing OOD detectors by multiplying the MLN outlier score (negative weighted sum of satisfied constraints) with a GED-based survival-function normalized detector score; also learn constraints via greedy AUROC-driven search.
Key results
- On GTSRB, MLN+Ensemble reaches 99.89 AUROC and 0.54 FPR95 versus 99.80 AUROC and 0.86 FPR95 for Ensemble.
- On CelebA, MLN+Mahalanobis reaches 96.01 AUROC versus 95.12 for Mahalanobis alone, and reduces FPR95 from 17.77 to 14.17.
- With auxiliary outliers, MLN+Ensemble+ reaches 99.95 AUROC on GTSRB.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add MLN score to existing detectors (score combination) | MSP, EBO, Ensemble, SHE, Mahalanobis, ViM, DICE, ReAct on GTSRB · GTSRB | AUROC: e.g. MSP +0.64, SHE +10.91, Ensemble +0.08 | Helped |
| add MLN score to existing detectors (score combination) | MSP, EBO, Ensemble, SHE, Mahalanobis, ReAct, DICE on CelebA · CelebA | AUROC: e.g. MSP +12.04, EBO +28.65, Mahalanobis +0.89 | Helped |
| add auxiliary-outlier supervised ID predicate constraint | MLN+detectors · GTSRB and CelebA | AUROC: e.g. MLN+Ensemble+ 99.95 vs MLN+Ensemble 99.89 on GTSRB | Helped |
| apply GED survival-function score normalization vs no normalization (ablation) | MLN+Ensemble · GTSRB | AUROC: 99.88 vs 86.16 | Helped |
| share parameters across predicate DNNs (ablation) | MLN and Logic-based methods · GTSRB | AUROC: MLN -32.55, Logic -38.47 AUROC | Hurt |
| share parameters across predicate DNNs (ablation) | MLN+Ensemble · GTSRB | AUROC: -1.01 AUROC | Hurt |
| use a stronger encoder (ViT vs WideResNet-40/ResNet-18) for MLN (ablation) | MLN standalone · GTSRB | AUROC: ViT 90.3, WRN-40 86.2, ResNet-18 81.9, ConvNext 84.4 | Mixed |
Surprising findings
- Standalone MLN on CelebA outperforms several pattern-based detectors such as EBO, SHE, and ReAct.
- Sharing parameters between the concept DNNs sharply degrades MLN and Logic methods (MLN AUROC drops from about 86 to 53.6 on GTSRB).
Limitations
- Standalone MLN performs poorly on GTSRB with ResNet-18 and ViT encoders relative to ensembles, and degrades under parameter sharing.
- Learned constraints are sensitive to the OOD dataset used during search, and Gaussian Noise as search OOD data hurt performance.
- Learned constraints may encode biases, as acknowledged in the impact statement.
Experimental setup
Datasets: GTSRB CelebA LSUN TinyImageNet Places365 iNaturalist Textures 80 Million Tiny Images ImageNet
Benchmarks: GTSRB CelebA
Metrics: AUROC AUPR-ID AUPR-OOD FPR95
Baselines: MSP EBO Ensemble SHE Mahalanobis ViM DICE ReAct Logic Logic+Ensemble
Builds on: Markov logic networks LogicOOD Mahalanobis ViM ReAct
Closest papers by meaning
- Fast Decision Boundary based Out-of-Distribution Detector (ICML 2024 · similarity 0.87)
- Strengthen Out-of-Distribution Detection Capability with Progressive Self-Knowledge Distillation (ICML 2025 · similarity 0.86)
- ProHOC: Probabilistic Hierarchical Out-of-Distribution Classification via Multi-Depth Networks (CVPR 2025 · similarity 0.85)
- Expecting The Unexpected: Towards Broad Out-Of-Distribution Detection (NeurIPS 2024 · similarity 0.85)
- Can We Ignore Labels in Out of Distribution Detection? (ICLR 2025 · similarity 0.85)
- Leveraging Perturbation Robustness to Enhance Out-of-Distribution Detection (CVPR 2025 · similarity 0.85)
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