# Safety Certification is Classification

arXiv: https://arxiv.org/abs/2605.06087 · HTML: https://mlsanity.com/paper/2605.06087/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 59 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 30 of 36)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Generating Useful Accident-Prone Driving Scenarios via a Learned Traffic Prior](https://mlsanity.com/paper/2112.05077/) (2021)
- [On Adversarial Robustness of Trajectory Prediction for Autonomous Vehicles](https://mlsanity.com/paper/2201.05057/) (2022)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Distribution-free binary classification: prediction sets, confidence intervals and calibration](https://mlsanity.com/paper/2006.10564/) (2020)
- [Signature moments to characterize laws of stochastic processes](https://mlsanity.com/paper/1810.10971/) (2018)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem](https://mlsanity.com/paper/2211.08875/) (2022)
- [Automated Verification and Synthesis of Stochastic Hybrid Systems: A Survey](https://mlsanity.com/paper/2101.07491/) (2021)
- [Robust Markov Decision Processes: A Place Where AI and Formal Methods Meet](https://mlsanity.com/paper/2411.11451/) (2024)
- [A Learning-based Quadcopter Controller with Extreme Adaptation](https://mlsanity.com/paper/2409.12949/) (2024)
- [Robust Anytime Learning of Markov Decision Processes](https://mlsanity.com/paper/2205.15827/) (2022)
- [Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise](https://mlsanity.com/paper/2110.12662/) (2021)
- [Data-driven verification and synthesis of stochastic systems via barrier certificates](https://mlsanity.com/paper/2111.10330/) (2021)
- [Formal Synthesis of Controllers for Safety-Critical Autonomous Systems: Developments and Challenges](https://mlsanity.com/paper/2402.13075/) (2024)
- [Neural Abstractions](https://mlsanity.com/paper/2301.11683/) (2023)
- [A safe exploration approach to constrained Markov decision processes](https://mlsanity.com/paper/2312.00561/) (2023)
- [Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings](https://mlsanity.com/paper/2403.10497/) (2024)
- [Distributionally Robust Optimal and Safe Control of Stochastic Systems via Kernel Conditional Mean Embedding](https://mlsanity.com/paper/2304.00644/) (2023)
- [Verification of general Markov decision processes by approximate similarity relations and policy refinement](https://mlsanity.com/paper/1605.09557/) (2016)
- [Bayesian Formal Synthesis of Unknown Systems via Robust Simulation Relations](https://mlsanity.com/paper/2304.07428/) (2023)
- [On the Consistency of Kernel Methods with Dependent Observations](https://mlsanity.com/paper/2406.06101/) (2024)
- [A data-driven approach for safety quantification of non-linear stochastic systems with unknown additive noise distribution](https://mlsanity.com/paper/2410.06662/) (2024)
- [IMPaCT: Interval MDP Parallel Construction for Controller Synthesis of Large-Scale Stochastic Systems](https://mlsanity.com/paper/2401.03555/) (2024)
- [Data-Driven Abstractions via Binary-Tree Gaussian Processes for Formal Verification](https://mlsanity.com/paper/2407.21029/) (2024)

## Abstract (arXiv)

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.