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Outlier Synthesis via Hamiltonian Monte Carlo for Out-of-Distribution Detection
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Proposes HamOS, which synthesizes diverse virtual outliers in hyperspherical feature space by running Hamiltonian Monte Carlo chains over an OOD-ness density built only from ID embeddings, and trains with CE, ID contrastive (CIDER), and OOD discernment losses.
Problem
Outlier synthesis for OOD detection without natural auxiliary outliers often yields low-quality or non-diverse virtual outliers, and generative-model approaches are costly; the paper asks how to efficiently synthesize diverse, representative outliers using only ID data.
Approach
Treat outlier synthesis as sampling from Markov chains: use Spherical Hamiltonian Monte Carlo with a potential energy equal to the negative log of a kNN-based OOD-ness density between pairs of ID class clusters, started from cluster midpoints and constrained by a vMF-KDE ID-probability hard margin.
Key results
- On CIFAR-10, HamOS achieves 10.48% FPR95 and 97.11% AUROC, versus 14.39% FPR95 for NPOS (the best baseline by FPR95 in that table).
- On CIFAR-100, HamOS reaches 46.68% FPR95 and 83.64% AUROC, improving FPR95 over CIDER (49.64%).
- On ImageNet-1K, HamOS averages 44.59% FPR95 and 88.59% AUROC, improving FPR95 by 2.98 points over VOS (47.57% implied).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HamOS instead of NPOS | CIFAR-10 OOD detection · CIFAR-10, five OOD test datasets | FPR95: 14.39_{\pm 0.87} -> 10.48_{\pm 0.76} | Helped |
| Use HamOS instead of NPOS | CIFAR-10 OOD detection · CIFAR-10, five OOD test datasets | AUROC: 96.61_{\pm 0.26} -> 97.11_{\pm 0.26} | Helped |
| Use HamOS instead of CIDER | CIFAR-100 OOD detection · CIFAR-100, five OOD test datasets | FPR95: 49.64_{\pm 1.80} -> 46.68_{\pm 1.44} | Helped |
| Use HamOS instead of CIDER | CIFAR-100 OOD detection · CIFAR-100, five OOD test datasets | AUROC: 81.77_{\pm 0.95} -> 83.64_{\pm 0.64} | Helped |
| Use HamOS instead of PALM | ImageNet-1K OOD detection · ImageNet-1K, averaged OOD datasets | FPR95: 45.62 -> 44.59 | Helped |
| Use HamOS instead of VOS | ImageNet-1K OOD detection · ImageNet-1K, averaged OOD datasets | AUROC: 87.92 -> 88.59 | Helped |
| Use HamOS instead of NPOS | CIFAR-10 outlier synthesis and detection · CIFAR-10, ID-OOD separation averaged across OOD datasets | ID-OOD separation: 70.51_{\pm 0.94} -> 78.70_{\pm 0.56} | Helped |
Surprising findings
- Authors note HMC's acceptance rate should theoretically be 1 but is occasionally below 1 due to discretization error; they report the sampler is still efficient, with time cost comparable to VOS and NPOS and lower than NPOS on ImageNet-1K.
Limitations
- Relies on a pretrained ID model and fine-tuning; experiments assume ID training data remains available.
- Many hyperparameters (k, hard margin, step size, Leapfrog steps, adjacent clusters) are tuned, and the ID buffer must be maintained during training.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 ImageNet-1K
Benchmarks: MNIST SVHN Textures Places365 LSUN iNaturalist SUN
Metrics: FPR95 AUROC AUPR ID-ACC
Baselines: MSP ODIN EBO KNN ASH Scale Relation CSI SSD+ KNN+ VOS CIDER
Builds on: CIDER VOS NPOS KNN Spherical HMC
Closest papers by meaning
- DOS: Diverse Outlier Sampling for Out-of-Distribution Detection (ICLR 2024 · similarity 0.88)
- Expecting The Unexpected: Towards Broad Out-Of-Distribution Detection (NeurIPS 2024 · similarity 0.88)
- Out-of-Distribution Detection with Prototypical Outlier Proxy (AAAI 2025 · similarity 0.87)
- Quantile-Based Maximum Likelihood Training for Outlier Detection (AAAI 2024 · similarity 0.87)
- ALTBI: Constructing Improved Outlier Detection Models via Optimization of Inlier-Memorization Effect (AAAI 2025 · similarity 0.86)
- The Best of Both Worlds: On the Dilemma of Out-of-distribution Detection (NeurIPS 2024 · similarity 0.86)
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