Safety Certification is Classification

• URL: http://arxiv.org/abs/2605.06087v1
• Date: Thu, 07 May 2026 12:10:07 GMT
• Title: Safety Certification is Classification
• Abstract summary: We propose a kernel embedding framework that treats safety certification as a classification problem on trajectory data.<n>We show that the framework subsumes well-established approaches from the literature (e.g., barrier certificates, robust Markov models) as special cases.<n>We demonstrate that direct estimators remain stable independent of the certification horizon and in the non-Markovian setting.
• Score: 1.6945967751903934
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The goal of this paper is certifying safety of dynamical systems subject to uncertainty. Existing approaches use trajectory data to estimate transition probabilities, and compute safety probabilities recursively via dynamic programming (DP). This recursion may lead to compounding errors in the certified safety probability, thus collapsing to a vacuous lower bound for growing horizons $T$. We propose a kernel embedding framework that treats safety certification as a classification problem on trajectory data, directly estimating the $T$-step safety probability without recursion. We show that the framework subsumes well-established approaches from the literature (e.g., barrier certificates, robust Markov models) as special cases, and allows us to go beyond their limitations. As the main consequence, it bypasses compounding error across the horizon and enables certification for systems with non-Markovian dynamics. We demonstrate that direct estimators remain stable independent of the certification horizon and in the non-Markovian setting, whilst DP-based certificates silently go unsound -- confirmed in simulation on a neural-controlled quadrotor.

Related papers

• Conformal Changepoint Localization and Root Cause Analysis with Corrupted Observations [55.76952683833966]
  This paper proposes weighted CONCH (W-CONCH) and weighted CROC (W-CROC) to reduce confidence set size when data may be corrupted.<n>Experiments on image-based and real-world changepoint and root-cause benchmarks show that uncertainty-based weighting substantially reduces confidence set size.
  arXiv  Detail & Related papers  (2026-07-29T05:16:59Z)
• BarrierSteer: LLM Safety via Learning Barrier Steering [83.12893815611052]
  BarrierSteer is a novel framework that formalizes safety by embedding learned non-linear safety constraints directly into the model's latent representation space.<n>We show that BarrierSteer substantially reduces adversarial success rates, decreases unsafe generations, and outperforms existing methods.
  arXiv  Detail & Related papers  (2026-02-23T18:19:46Z)
• Kernel-Based Learning of Safety Barriers [0.9367224590861915]
  Rapid integration of AI algorithms in safety-critical applications is raising concerns about the ability to meet stringent safety standards.<n>Traditional tools for formal safety verification struggle with the black-box nature of AI-driven systems.<n>We present a data-driven approach for safety verification and synthesis of black-box systems with discrete-time dynamics.
  arXiv  Detail & Related papers  (2026-01-17T10:42:35Z)
• TrustLoRA: Low-Rank Adaptation for Failure Detection under Out-of-distribution Data [62.22804234013273]
  We propose a simple failure detection framework to unify and facilitate classification with rejection under both covariate and semantic shifts.<n>Our key insight is that by separating and consolidating failure-specific reliability knowledge with low-rank adapters, we can enhance the failure detection ability effectively and flexibly.
  arXiv  Detail & Related papers  (2025-04-20T09:20:55Z)
• Barrier Certificates for Unknown Systems with Latent States and Polynomial Dynamics using Bayesian Inference [4.521450956414864]
  This paper proposes a novel approach for synthesizing barrier certificates for unknown systems.<n>A prior in state-space representation is updated using output data via a targeted marginal Metropolis-Hastings sampler.<n>Probabilistic guarantees for its validity are obtained by testing on an additional set of posterior samples.
  arXiv  Detail & Related papers  (2025-04-02T15:12:34Z)
• Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes [1.6078581568133972]
  We propose a data-driven safety verification framework to verify system safety directly from noisy data.<n>Instead of trusting a single unreliable model, we construct a set of models that align with the observed data.<n>This model set is compactly represented using matrix zonotopes, enabling efficient computation and propagation of uncertainty.
  arXiv  Detail & Related papers  (2025-04-01T17:46:42Z)
• Certified Human Trajectory Prediction [66.1736456453465]
  We propose a certification approach tailored for trajectory prediction that provides guaranteed robustness.<n>To mitigate the inherent performance drop through certification, we propose a diffusion-based trajectory denoiser and integrate it into our method.<n>We demonstrate the accuracy and robustness of the certified predictors and highlight their advantages over the non-certified ones.
  arXiv  Detail & Related papers  (2024-03-20T17:41:35Z)
• Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings [0.24578723416255752]
  We develop scalable formal verification algorithms without shifting the problem to unrealistic assumptions. In a pursuit of developing scalable formal verification algorithms without shifting the problem to unrealistic assumptions, we employ the concept of barrier certificates. We show how to solve the resulting program efficiently using sum-of-squares optimization and a Gaussian process envelope.
  arXiv  Detail & Related papers  (2024-03-15T17:32:02Z)
• Safe Online Dynamics Learning with Initially Unknown Models and Infeasible Safety Certificates [45.72598064481916]
  This paper considers a learning-based setting with a robust safety certificate based on a control barrier function (CBF) second-order cone program. If the control barrier function certificate is feasible, our approach leverages it to guarantee safety. Otherwise, our method explores the system dynamics to collect data and recover the feasibility of the control barrier function constraint.
  arXiv  Detail & Related papers  (2023-11-03T14:23:57Z)
• Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions [60.26921219698514]
  We introduce a model-uncertainty-aware reformulation of CBF-based safety-critical controllers. We then present the pointwise feasibility conditions of the resulting safety controller. We use these conditions to devise an event-triggered online data collection strategy.
  arXiv  Detail & Related papers  (2022-08-23T05:02:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.