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OOD Score Instability Revealed by Reference Resampling

Donghoon Lee, Shinjin Kang· September 2, 2026 View original

Key takeaways

  • OOD scores are estimates whose stability depends on the reference set.
  • "Verdict instability" quantifies this variability through reference resampling.
  • Distance-based scores often assign high values to reproducible verdicts.
  • Only local dispersion estimators align with practitioner expectations for OOD detection.

Who benefits

Autonomous VehiclesHealthcareCybersecurityFinancial ServicesManufacturing

Summary

Researchers introduce "verdict instability," a metric that quantifies the variability of out-of-distribution (OOD) scores when the reference set is resampled. They show that while distance-based scores assign high values to reproducible verdicts, only local dispersion estimators align with practitioner expectations regarding OOD detection.

Out-of-distribution (OOD) detectors are crucial for identifying data points that fall outside a model's training distribution, enhancing reliability and safety. These detectors are typically fitted using a finite reference set, meaning every OOD score generated is an estimate. The stability of these scores, or "verdicts," can vary if a different reference set were chosen. This research introduces "verdict instability" to quantify this movement, measuring it as the bootstrap standard deviation of the score after resampling the reference set. The study found that verdict instability can be expressed in a closed form, revealing that it grows with local dispersion and is identifiable under class imbalance. Interestingly, distance-based OOD scores tend to assign their highest values to verdicts that are most reproducible (i.e., have low instability). However, only estimators of local dispersion produce a sign that aligns with a practitioner's intuitive expectation of OOD. The research also provides a rule to predict this sign and demonstrates that abstention based on wrong-signed scores can be worse than random abstention.

Why it matters

Understanding and quantifying OOD score instability is vital for building trustworthy AI systems, especially in high-stakes applications where reliable detection of novel or anomalous inputs is paramount.

How to implement this in your domain

  1. 1Incorporate "verdict instability" as a new metric when evaluating and deploying out-of-distribution detection systems.
  2. 2Analyze the reference sets used for OOD detectors to understand their impact on score stability and potential class imbalance issues.
  3. 3Prioritize OOD detection methods that rely on local dispersion estimators for more intuitively aligned OOD verdicts.
  4. 4Develop strategies for abstention or human-in-the-loop intervention based on OOD scores, considering their measured instability.

Original post by Donghoon Lee, Shinjin Kang

"arXiv:2609.00691v1 Announce Type: new Abstract: Post-hoc out-of-distribution detectors are fitted on a finite reference set, so every score they produce is an estimate. If we had chosen a different set, some verdicts would have moved. We measure that movement by resampling the re…"

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Originally posted by Donghoon Lee, Shinjin Kang on X · view source

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