mlsanityData to 7 Oct 2026

Hybrid Zonotopes Exactly Represent ReLU Neural Networks

arXiv 2304.02755 ↗First posted 5 Apr 2023cs.LG cs.SY eess.SYcited by 4

Not on the map. Why?

Abstract (arXiv)

We show that hybrid zonotopes offer an equivalent representation of feed-forward fully connected neural networks with ReLU activation functions. Our approach demonstrates that the complexity of binary variables is equal to the total number of neurons in the network and hence grows linearly in the size of the network. We demonstrate the utility of the hybrid zonotope formulation through three case studies including nonlinear function approximation, MPC closed-loop reachability and verification, and robustness of classification on the MNIST dataset.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 14 of its 22 references that are in the map. First posted on arXiv 5 Apr 2023.

Builds on

14 of 22 references.

References · 14

  1. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  2. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  3. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
  4. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
  5. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
  6. 2020Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programmingcited by 43
  7. 2021Reachability Analysis of Neural Feedback Loopscited by 41
  8. 2020Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimizationcited by 17
  9. 2018Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllerscited by 15
  10. 2022Safety Verification of Neural Feedback Systems Based on Constrained Zonotopescited by 7
  11. 2021Hybrid zonotopes: a new set representation for reachability analysis of mixed logical dynamical systemscited by 6
  12. 2021Constrained Feedforward Neural Network Training via Reachability Analysiscited by 5
2 more
  1. 2022Reachability Analysis and Safety Verification of Neural Feedback Systems via Hybrid Zonotopescited by 5
  2. 2019Utilizing Dependencies to Obtain Subsets of Reachable Setscited by 3

Built on by

Cited by year

Citing papers per year: 2024: 1; 2025: 3.

4 papers.

  1. 2024Neural Network Verification with PyRATcited by 9
  2. 2025Out of the Shadows: Exploring a Latent Space for Neural Network Verificationcited by 6
  3. 2025Provably-Safe Neural Network Training Using Hybrid Zonotope Reachability Analysiscited by 3
  4. 2025Language Models That Walk the Talk: A Framework for Formal Fairness Certificatescited by 0