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Beyond Empirical Support: Structured Outlier Generation via Sinkhorn Optimal Transport

NeurIPS 2026 · Learning theory and algorithms › Optimal transport · approach: Neural optimal transport · 0 citations (OpenAlex)

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Proposes SBOG, a latent-space outlier generator that selects high Sinkhorn outlier energy (SOE) boundary anchors and semantically filtered candidates, then decodes them to inputs for time-series anomaly and image OOD benchmarks.

Problem

Generating informative, semantically controlled outliers for robustness evaluation and detector training, since existing synthesis methods rely on heuristic sparsity, low-likelihood, or boundary-crossing criteria that are unstable and modality-specific.

Approach

Defines Sinkhorn Outlier Energy (negative log entropic kernel support of a latent point under the in-distribution reference measure) as a transport-based boundary score; selects top-energy anchors and the most energetic semantically feasible candidate, and links SOE to the Gibbs normalizer in the Sinkhorn-DRO dual.

Key results

• On the five time-series benchmarks, CARLA-SBOG reaches average AU-PR 0.312 and F1 0.432, the best among CARLA variants and all baselines.
• On CIFAR-100, SBOG achieves average FPR95 12.44 and AUROC 97.23, the best average among listed methods.
• On ImageNet-100, SBOG (robust) reaches average FPR95 14.75 and AUROC 96.97, the best average, with SBOG at 15.33 / 96.90 close behind GOOD at 17.68 / 96.30.

Surprising findings

• Under the empirical Euclidean case, SOE reduces to a monotone transform of an unnormalized RBF-KDE score, so SOE is not fundamentally different from KDE in that setting.
• The robust alignment variant gives only small, consistent gains over base SBOG on ImageNet-100 and CIFAR-100.

Limitations

• Performance depends on representation quality, transport-cost design, semantic anchoring, and decoder expressiveness.
• The Sinkhorn-DRO interpretation justifies the acquisition rule but does not solve a task-specific DRO problem; the task-aware variant is left as future work.
• Stability guarantees depend on normalizer and margin conditions that can make bounds loose when epsilon is small or candidates lie in weakly supported regions.

Experimental setup

Datasets: SMD MSL SMAP SWaT WADI CIFAR-100 ImageNet-100 iNaturalist SUN Places Textures SVHN

Benchmarks: SMD MSL SMAP SWaT WADI CIFAR-100 OOD ImageNet-100 OOD

Metrics: AU-PR F1 FPR95 AUROC MMD^2 purity token cosine class margin

Baselines: CARLA CARLA-RandomNeg CARLA-kNNNeg CARLA-KDENeg AnomalyTransformer DCdetector TranAD COUTA TS2Vec ScatterAD THOC Sub-Adjacent Transformer

Builds on: CARLA Sinkhorn DRO VOS Dream-OOD NPOS

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