Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 82 tok/s
Gemini 2.5 Pro 47 tok/s Pro
GPT-5 Medium 14 tok/s Pro
GPT-5 High 16 tok/s Pro
GPT-4o 117 tok/s Pro
Kimi K2 200 tok/s Pro
GPT OSS 120B 469 tok/s Pro
Claude Sonnet 4 36 tok/s Pro
2000 character limit reached

Contraction-Guided Adaptive Partitioning for Reachability Analysis of Neural Network Controlled Systems (2304.03671v2)

Published 7 Apr 2023 in eess.SY, cs.LG, cs.SY, and math.OC

Abstract: In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate of the contraction rate of over-approximated intervals, the algorithm chooses when and where to partition. Then, by leveraging a decoupling of the neural network verification step and reachability partitioning layers, the algorithm can provide accuracy improvements for little computational cost. This approach is applicable with any sufficiently accurate open-loop interval-valued reachability estimation technique and any method for bounding the input-output behavior of a neural network. Using contraction-based robustness analysis, we provide guarantees of the algorithm's performance with mixed monotone reachability. Finally, we demonstrate the algorithm's performance through several numerical simulations and compare it with existing methods in the literature. In particular, we report a sizable improvement in the accuracy of reachable set estimation in a fraction of the runtime as compared to state-of-the-art methods.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (26)
  1. C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus, “Intriguing properties of neural networks,” in International Conference on Learning Representations, 2014.
  2. S. Dutta, X. Chen, and S. Sankaranarayanan, “Reachability analysis for neural feedback systems using regressive polynomial rule inference,” in Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control, p. 157–168, 2019.
  3. S. Gowal, K. Dvijotham, R. Stanforth, R. Bunel, C. Qin, J. Uesato, R. Arandjelovic, T. A. Mann, and P. Kohli, “Scalable verified training for provably robust image classification,” in IEEE/CVF International Conference on Computer Vision (ICCV), pp. 4841–4850, 2019.
  4. H. Zhang, T.-W. Weng, P.-Y. Chen, C.-J. Hsieh, and L. Daniel, “Efficient neural network robustness certification with general activation functions,” in Advances in Neural Information Processing Systems, vol. 31, p. 4944–4953, 2018.
  5. M. Fazlyab, M. Morari, and G. J. Pappas, “Safety verification and robustness analysis of neural networks via quadratic constraints and semidefinite programming,” IEEE Transactions on Automatic Control, vol. 67, no. 1, pp. 1–15, 2022.
  6. H.-D. Tran, X. Yang, D. Manzanas Lopez, P. Musau, L. V. Nguyen, W. Xiang, S. Bak, and T. T. Johnson, “NNV: The neural network verification tool for deep neural networks and learning-enabled cyber-physical systems,” in Computer Aided Verification, pp. 3–17, Springer International Publishing, 2020.
  7. M. Everett, G. Habibi, C. Sun, and J. P. How, “Reachability analysis of neural feedback loops,” IEEE Access, vol. 9, pp. 163938–163953, 2021.
  8. H. Hu, M. Fazlyab, M. Morari, and G. J. Pappas, “Reach-SDP: Reachability analysis of closed-loop systems with neural network controllers via semidefinite programming,” in 59th IEEE Conference on Decision and Control, pp. 5929–5934, 2020.
  9. C. Schilling, M. Forets, and S. Guadalupe, “Verification of neural-network control systems by integrating Taylor models and zonotopes,” in Proceedings of the AAAI Conference on Artificial Intelligence, pp. 8169–8177, 2022.
  10. N. Kochdumper, C. Schilling, M. Althoff, and S. Bak, “Open- and closed-loop neural network verification using polynomial zonotopes,” in NASA Formal Methods (K. Y. Rozier and S. Chaudhuri, eds.), (Cham), pp. 16–36, Springer Nature Switzerland, 2023.
  11. C. Huang, J. Fan, X. Chen, W. Li, and Q. Zhu, “POLAR: A polynomial arithmetic framework for verifying neural-network controlled systems,” in Automated Technology for Verification and Analysis: 20th International Symposium (ATVA), pp. 414–430, Springer, 2022.
  12. C. Sidrane, A. Maleki, A. Irfan, and M. J. Kochenderfer, “OVERT: An algorithm for safety verification of neural network control policies for nonlinear systems,” Journal of Machine Learning Research, vol. 23, no. 117, pp. 1–45, 2022.
  13. Y. Zhang and X. Xu, “Safety verification of neural feedback systems based on constrained zonotopes,” in 2022 IEEE 61st Conference on Decision and Control (CDC), pp. 2737–2744, 2022.
  14. S. Jafarpour, A. Harapanahalli, and S. Coogan, “Interval reachability of nonlinear dynamical systems with neural network controllers,” in Learning for Dynamics and Control Conference, pp. 12–25, PMLR, 2023.
  15. V. Rubies-Royo, R. Calandra, D. M. Stipanovic, and C. Tomlin, “Fast neural network verification via shadow prices,” arXiv preprint arXiv:1902.07247, 2019.
  16. M. Everett, G. Habibi, and J. P. How, “Robustness analysis of neural networks via efficient partitioning with applications in control systems,” IEEE Control Systems Letters, vol. 5, no. 6, pp. 2114–2119, 2021.
  17. W. Xiang, H.-D. Tran, X. Yang, and T. T. Johnson, “Reachable set estimation for neural network control systems: A simulation-guided approach,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 5, pp. 1821–1830, 2021.
  18. T. Entesari, S. Sharifi, and M. Fazlyab, “ReachLipBnB: A branch-and-bound method for reachability analysis of neural autonomous systems using lipschitz bounds,” in IEEE International Conference on Robotics and Automation (ICRA), pp. 1003–1010, 2023.
  19. A. Davydov, S. Jafarpour, and F. Bullo, “Non-Euclidean contraction theory for robust nonlinear stability,” IEEE Transactions on Automatic Control, vol. 67, no. 12, pp. 6667–6681, 2022.
  20. X. Chen, E. Ábrahám, and S. Sankaranarayanan, “Flow*: An analyzer for non-linear hybrid systems,” in Computer Aided Verification: 25th International Conference (CAV), pp. 258–263, Springer, 2013.
  21. S. Bansal, M. Chen, S. Herbert, and C. J. Tomlin, “Hamilton-Jacobi reachability: A brief overview and recent advances,” in 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pp. 2242–2253, 2017.
  22. M. Althoff, “An introduction to CORA 2015,” in Proceedings of the Workshop on Applied Verification for Continuous and Hybrid Systems, p. 120–151, 2015.
  23. S. Coogan, “Mixed monotonicity for reachability and safety in dynamical systems,” in 2020 59th IEEE Conference on Decision and Control (CDC), pp. 5074–5085, 2020.
  24. F. Bullo, Contraction Theory for Dynamical Systems. Kindle Direct Publishing, 1.0 ed., 2022.
  25. P. Polack, F. Altché, B. d’Andréa Novel, and A. de La Fortelle, “The kinematic bicycle model: A consistent model for planning feasible trajectories for autonomous vehicles?,” in 2017 IEEE Intelligent Vehicles Symposium (IV), pp. 812–818, 2017.
  26. K. Xu, Z. Shi, H. Zhang, Y. Wang, K.-W. Chang, M. Huang, B. Kailkhura, X. Lin, and C.-J. Hsieh, “Automatic perturbation analysis for scalable certified robustness and beyond,” Advances in Neural Information Processing Systems, vol. 33, pp. 1129–1141, 2020.
Citations (5)
View on Semantic Scholar
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Dice Question Streamline Icon: https://streamlinehq.com

Follow-Up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now