mlsanityData to 14 Oct 2026

Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networks

arXiv 2506.15693 ↗First posted 27 May 2025cs.LGcited by 5

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Abstract (arXiv)

Recent learning-based safety filters have outperformed conventional methods, such as hand-crafted Control Barrier Functions (CBFs), by effectively adapting to complex constraints. However, these learning-based approaches lack formal safety guarantees. In this work, we introduce a verifiable model-free safety filter based on Hamilton-Jacobi reachability analysis. Our primary contributions include: 1) extending verifiable self-consistency properties for Q value functions, 2) proposing a multiplicative Q-network structure to mitigate zero-sublevel-set shrinkage issues, and 3) developing a verification pipeline capable of soundly verifying these self-consistency properties. Our proposed approach successfully synthesizes formally verified, model-free safety certificates across four standard safe-control benchmarks.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 19 of its 29 references that are in the map. First posted on arXiv 27 May 2025.

Builds on

19 of 29 references.

References · 19

  1. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 445
  2. 2019Control Barrier Functions: Theory and Applicationscited by 372
  3. 2019Algorithms for Verifying Deep Neural Networkscited by 221
  4. 2022Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methodscited by 151
  5. 2020Learning to be Safe: Deep RL with a Safety Criticcited by 116
  6. 2021Robust Control Barrier-Value Functions for Safety-Critical Controlcited by 51
  7. 2014Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraintscited by 44
  8. 2019Safe Control Algorithms Using Energy Functions: A Unified Framework, Benchmark, and New Directionscited by 17
  9. 2024Hamilton-Jacobi Reachability in Reinforcement Learning: A Surveycited by 16
  10. 2022Refining Control Barrier Functions through Hamilton-Jacobi Reachabilitycited by 15
  11. 2016Factorized Bilinear Models for Image Recognitioncited by 13
  12. 2022Safety Index Synthesis via Sum-of-Squares Programmingcited by 12
7 more
  1. 2024Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagationcited by 12
  2. 2018A Minimum Discounted Reward Hamilton-Jacobi Formulation for Computing Reachable Setscited by 11
  3. 2018A Classification-based Approach for Approximate Reachabilitycited by 10
  4. 2024Scalable Synthesis of Formally Verified Neural Value Function for Hamilton-Jacobi Reachability Analysiscited by 7
  5. 2024Real-Time Safe Control of Neural Network Dynamic Models with Sound Approximationcited by 5
  6. 2024Learning safety critics via a non-contractive binary bellman operatorcited by 3
  7. 2024Q-learning-based Model-free Safety Filtercited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorialcited by 1
  2. 2026VLESA: Vision-Language Embodied Safety Agent for Human Activity Monitoringcited by 0
  3. 2026ShardNet: Training Neural Controllers with Hard, Non-Convex Constraintscited by 0
  4. 2026ResSafe: Learning Safety Filtering with Residual Reinforcement Learning for Humanoidscited by 0
  5. 2026Reachability-Aware Diffusion Policy Optimizationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Statistically Assuring Safety of Control Systems using Ensembles of Safety Filters and Conformal Prediction
  2. 2026Verifiable Model-Free Safety Filters via Reinforcement Learning
  3. 2024Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanes
  4. 2024Practical Considerations for Discrete-Time Implementations of Continuous-Time Control Barrier Function-Based Safety Filters
  5. 2026Safe Flow Q-Learning: Offline Safe Reinforcement Learning with Reachability-Based Flow Policies
  6. 2024Unifying Qualitative and Quantitative Safety Verification of DNN-Controlled Systems
  7. 2025Explicit Control Barrier Function-based Safety Filters and their Resource-Aware Computation
  8. 2026Winning a Won Game: Strict Reach-Avoid-Stay Control Barrier Functions for High-Dimensional Black-Box Systems ↗