mlsanityData to 7 Oct 2026

BarrierNet: A Safety-Guaranteed Layer for Neural Networks

arXiv 2111.11277 ↗First posted 22 Nov 2021cs.LG cs.RO cs.SYcited by 11

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Abstract (arXiv)

This paper introduces differentiable higher-order control barrier functions (CBF) that are end-to-end trainable together with learning systems. CBFs are usually overly conservative, while guaranteeing safety. Here, we address their conservativeness by softening their definitions using environmental dependencies without loosing safety guarantees, and embed them into differentiable quadratic programs. These novel safety layers, termed a BarrierNet, can be used in conjunction with any neural network-based controller, and can be trained by gradient descent. BarrierNet allows the safety constraints of a neural controller be adaptable to changing environments. We evaluate them on a series of control problems such as traffic merging and robot navigations in 2D and 3D space, and demonstrate their effectiveness compared to state-of-the-art approaches.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 32 of its 46 references that are in the map. First posted on arXiv 22 Nov 2021.

Builds on

32 of 46 references.

References · 32

  1. 2017Attention Is All You Needcited by 59,932
  2. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
  5. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 261
  6. 2020Liquid Time-constant Networkscited by 160
  7. 2020Learning Control Barrier Functions from Expert Demonstrationscited by 88
  8. 2020Learning Long-Term Dependencies in Irregularly-Sampled Time Seriescited by 82
  9. 2019Learning for Safety-Critical Control with Control Barrier Functionscited by 66
  10. 2020Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functionscited by 61
  11. 2020Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approachcited by 35
  12. 2020Neural Certificates for Safe Control Policiescited by 35
20 more
  1. 2017Safe Learning of Quadrotor Dynamics Using Barrier Certificatescited by 32
  2. 2016Robustness of Control Barrier Functions for Safety Critical Controlcited by 29
  3. 2019Adaptive Safety with Control Barrier Functionscited by 25
  4. 2020On The Verification of Neural ODEs with Stochastic Guaranteescited by 24
  5. 2021Causal Navigation by Continuous-time Neural Networkscited by 23
  6. 2020Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEscited by 22
  7. 2021Adversarial Training is Not Ready for Robot Learningcited by 20
  8. 2020ShieldNN: A Provably Safe NN Filter for Unsafe NN Controllerscited by 17
  9. 2020Learning Safe Neural Network Controllers with Barrier Certificatescited by 16
  10. 2021GoTube: Scalable Stochastic Verification of Continuous-Depth Modelscited by 12
  11. 2020Lagrangian Reachtubes: The Next Generationcited by 10
  12. 2020Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbancescited by 9
  13. 2020A Control Barrier Perspective on Episodic Learning via Projection-to-State Safetycited by 7
  14. 2020Bridging the Gap between Optimal Trajectory Planning and Safety-Critical Control with Applications to Autonomous Vehiclescited by 6
  15. 2019Self-triggered Control for Safety Critical Systems using Control Barrier Functionscited by 5
  16. 2021Comparison between safety methods control barrier function vs. reachability analysiscited by 5
  17. 2021Episodic Learning for Safe Bipedal Locomotion with Control Barrier Functions and Projection-to-State Safetycited by 4
  18. 2018Decentralized Optimal Merging Control for Connected and Automated Vehiclescited by 3
  19. 2021On exploration requirements for learning safety constraintscited by 3
  20. 2021Event-Triggered Safety-Critical Control for Systems with Unknown Dynamicscited by 2

Built on by

Cited by year

Citing papers per year: 2022: 6; 2023: 0; 2024: 2; 2025: 3.

11 papers.

  1. 2022Safe Control Under Input Limits with Neural Control Barrier Functionscited by 27
  2. 2022Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Drivingcited by 10
  3. 2022On the Forward Invariance of Neural ODEscited by 10
  4. 2022Differentiable Safe Controller Design through Control Barrier Functionscited by 8
  5. 2022Are All Vision Models Created Equal? A Study of the Open-Loop to Closed-Loop Causality Gapcited by 5
  6. 2024LeTO: Learning Constrained Visuomotor Policy with Differentiable Trajectory Optimizationcited by 5
  7. 2025Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functionscited by 3
  8. 2022Interpreting Neural Policies with Disentangled Tree Representationscited by 1
  9. 2025T-CBF: Traversability-based Control Barrier Function to Navigate Vertically Challenging Terraincited by 1
  10. 2025GradSTL: Comprehensive Signal Temporal Logic for Neurosymbolic Reasoning and Learningcited by 1
  11. 2024Fault Tolerant Neural Control Barrier Functions for Robotic Systems under Sensor Faults and Attackscited by 0