mlsanityData to 14 Oct 2026

Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations

arXiv 1712.08163 ↗First posted 21 Dec 2017cs.LG cs.AIcited by 22

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Abstract (arXiv)

Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for their applications in safety-critical systems.In this paper, the output reachable set computation and safety verification problems for a class of neural networks consisting of Rectified Linear Unit (ReLU) activation functions are addressed. A layer-by-layer approach is developed to compute output reachable set. The computation is formulated in the form of a set of manipulations for a union of polyhedra, which can be efficiently applied with the aid of polyhedron computation tools. Based on the output reachable set computation results, the safety verification for a ReLU neural network can be performed by checking the intersections of unsafe regions and output reachable set described by a union of polyhedra. A numerical example of a randomly generated ReLU neural network is provided to show the effectiveness of the approach developed in this paper.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 Dec 2017.

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Citing papers per year: 2021: 7; 2022: 6; 2023: 5; 2024: 2; 2025: 1; 2026: 1.

22 papers.

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  1. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 42
  2. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  3. 2021Neural Network Repair with Reachability Analysiscited by 19
  4. 2022CertiFair: A Framework for Certified Global Fairness of Neural Networkscited by 17
  5. 2021Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verificationcited by 13
  6. 2023Towards Verifying the Geometric Robustness of Large-scale Neural Networkscited by 11
  7. 2021SyReNN: A Tool for Analyzing Deep Neural Networkscited by 10
  8. 2021Benchmarking Safe Deep Reinforcement Learning in Aquatic Navigationcited by 10
  9. 2021Fast BATLLNN: Fast Box Analysis of Two-Level Lattice Neural Networkscited by 8
  10. 2024ModelVerification.jl: a Comprehensive Toolbox for Formally Verifying Deep Neural Networkscited by 7
  11. 2022Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systemscited by 6
  12. 2022Safety Verification for Neural Networks Based on Set-boundary Analysiscited by 5
10 more
  1. 2022BERN-NN: Tight Bound Propagation For Neural Networks Using Bernstein Polynomial Interval Arithmeticcited by 5
  2. 2021Reachability Analysis of Convolutional Neural Networkscited by 4
  3. 2023Safety Verification of Neural Network Control Systems Using Guaranteed Neural Network Model Reductioncited by 2
  4. 2021Robust Optimization Framework for Training Shallow Neural Networks Using Reachability Methodcited by 1
  5. 2023Vertex-based reachability analysis for verifying ReLU deep neural networkscited by 1
  6. 2023Verifying Safety of Neural Networks from Topological Perspectivescited by 1
  7. 2022Work In Progress: Safety and Robustness Verification of Autoencoder-Based Regression Models using the NNV Toolcited by 0
  8. 2024UR4NNV: Neural Network Verification, Under-approximation Reachability Works!cited by 0
  9. 2025Lipschitz-Based Robustness Certification for Recurrent Neural Networks via Convex Relaxationcited by 0
  10. 2026Exact and Asymptotically Complete Robust Verifications of Neural Networks via Ising Solverscited by 0