mlsanityData to 7 Oct 2026

Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopes

arXiv 2207.02715 ↗First posted 6 Jul 2022cs.CV cs.AI cs.LOcited by 24

Not on the map. Why?

Abstract (arXiv)

We present a novel approach to efficiently compute tight non-convex enclosures of the image through neural networks with ReLU, sigmoid, or hyperbolic tangent activation functions. In particular, we abstract the input-output relation of each neuron by a polynomial approximation, which is evaluated in a set-based manner using polynomial zonotopes. While our approach can also can be beneficial for open-loop neural network verification, our main application is reachability analysis of neural network controlled systems, where polynomial zonotopes are able to capture the non-convexity caused by the neural network as well as the system dynamics. This results in a superior performance compared to other methods, as we demonstrate on various benchmarks.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 21 of its 49 references that are in the map. First posted on arXiv 6 Jul 2022.

Builds on

21 of 49 references.

References · 21

  1. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  2. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  3. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
  4. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
  5. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 224
  6. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  7. 2020Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifierscited by 183
  8. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 178
  9. 2019Branch and Bound for Piecewise Linear Neural Network Verificationcited by 138
  10. 2020NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systemscited by 128
  11. 2017Maximum Resilience of Artificial Neural Networkscited by 97
  12. 2018Verisig: verifying safety properties of hybrid systems with neural network controllerscited by 83
9 more
  1. 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
  2. 2021POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systemscited by 38
  3. 2020Reachable Polyhedral Marching (RPM): A Safety Verification Algorithm for Robotic Systems with Deep Neural Network Componentscited by 36
  4. 2019JuliaReach: a Toolbox for Set-Based Reachabilitycited by 28
  5. 2021Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopescited by 26
  6. 2018Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllerscited by 15
  7. 2019Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysiscited by 14
  8. 2017DeepChess: End-to-End Deep Neural Network for Automatic Learning in Chesscited by 12
  9. 2020Safety Verification of Neural Network Controlled Systemscited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 4; 2024: 8; 2025: 4; 2026: 6.

24 papers.

Sort:

By area:

  1. 2024Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programscited by 14
  2. 2025Neural Network Verification is a Programming Language Challengecited by 12
  3. 2024Formal Verification of Graph Convolutional Networks with Uncertain Node Features and Uncertain Graph Structurecited by 8
  4. 2022Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systemscited by 6
  5. 2023Fully Automatic Neural Network Reduction for Formal Verificationcited by 6
  6. 2024Set-Based Training for Neural Network Verificationcited by 6
  7. 2025Out of the Shadows: Exploring a Latent Space for Neural Network Verificationcited by 6
  8. 2025Abstraction-Based Proof Production in Formal Verification of Neural Networkscited by 5
  9. 2023Contraction-Guided Adaptive Partitioning for Reachability Analysis of Neural Network Controlled Systemscited by 3
  10. 2024Certified Robust Invariant Polytope Training in Neural Controlled ODEscited by 3
  11. 2024Certified Training with Branch-and-Bound for Lyapunov-stable Neural Controlcited by 3
  12. 2022Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopescited by 2
12 more
  1. 2023Verifying Safety of Neural Networks from Topological Perspectivescited by 1
  2. 2026The FABRIC Strategy for Verifying Neural Feedback Systemscited by 1
  3. 2023The inverse problem for neural networkscited by 0
  4. 2024UR4NNV: Neural Network Verification, Under-approximation Reachability Works!cited by 0
  5. 2024Efficient model predictive control for nonlinear systems modelled by deep neural networkscited by 0
  6. 2024Safe and High-Performance Learning of Model Predicitve Control using Kernel-Based Interpolationcited by 0
  7. 2025Language Models That Walk the Talk: A Framework for Formal Fairness Certificatescited by 0
  8. 2026Perception with Guarantees: Certified Pose Estimation via Reachability Analysiscited by 0
  9. 2026Lipschitz-Based Robustness Certification Under Floating-Point Executioncited by 0
  10. 2026Safety Screening for Voltage Control in Active Distribution Grids via Distributionally Robust Conformal Screeningcited by 0
  11. 2026Certified Mechanistic Interpretability: Lifting Single-Input Findings to Bounded Neighbourhoodscited by 0
  12. 2026Stochastic World Models for Verifying Vision-Based Neural Feedback Systemscited by 0