Data to 7 Oct 2026

Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks

arXiv 1708.03322 ↗First posted 9 Aug 2017cs.LGcited by 79

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Abstract (arXiv)

In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer perceptrons whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of proposed approaches.

Key facts. Cited by 79 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Aug 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 24; 2022: 22; 2023: 16; 2024: 11; 2025: 4; 2026: 2.

79 papers.

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2021PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximationscited by 77
2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
2023First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)cited by 58
2021Reachability Analysis of Neural Feedback Loopscited by 41
2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 41
2021Robust Machine Learning Systems: Challenges, Current Trends, Perspectives, and the Road Aheadcited by 40
2021OVERT: An Algorithm for Safety Verification of Neural Network Control Policies for Nonlinear Systemscited by 37
2021A Review of Formal Methods applied to Machine Learningcited by 33
2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
2021DNNV: A Framework for Deep Neural Network Verificationcited by 23
2021Neural Network Repair with Reachability Analysiscited by 19
2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbationscited by 19

38 more

2023Convex Bounds on the Softmax Function with Applications to Robustness Verificationcited by 19
2022Verification-Aided Deep Ensemble Selectioncited by 18
2022Scalable Verification of GNN-based Job Schedulerscited by 18
2021BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networkscited by 17
2022CertiFair: A Framework for Certified Global Fairness of Neural Networkscited by 17
2022Toward Certified Robustness Against Real-World Distribution Shiftscited by 16
2021Neural Network Verification in Controlcited by 14
2021On Recurrent Neural Networks for learning-based control: recent results and ideas for future developmentscited by 14
2023Exact Verification of ReLU Neural Control Barrier Functionscited by 14
2025Neural Network Verification is a Programming Language Challengecited by 12
2021Learning Density Distribution of Reachable States for Autonomous Systemscited by 11
2023Verifying Generalization in Deep Learningcited by 11
2021Efficient Reachability Analysis of Closed-Loop Systems with Neural Network Controllerscited by 10
2021Benchmarking Safe Deep Reinforcement Learning in Aquatic Navigationcited by 10
2024A Survey on Verification and Validation, Testing and Evaluations of Neurosymbolic Artificial Intelligencecited by 10
2024ProTIP: Probabilistic Robustness Verification on Text-to-Image Diffusion Models against Stochastic Perturbationcited by 10
2021Fast BATLLNN: Fast Box Analysis of Two-Level Lattice Neural Networkscited by 8
2022Provably Tightest Linear Approximation for Robustness Verification of Sigmoid-like Neural Networkscited by 8
2022Tighter Abstract Queries in Neural Network Verificationcited by 8
2024Formal Verification of Graph Convolutional Networks with Uncertain Node Features and Uncertain Graph Structurecited by 8
2021Verifying Quantized Neural Networks using SMT-Based Model Checkingcited by 6
2021Bisimulations for Neural Network Reductioncited by 6
2022A Hybrid Partitioning Strategy for Backward Reachability of Neural Feedback Loopscited by 6
2022Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systemscited by 6
2023Fully Automatic Neural Network Reduction for Formal Verificationcited by 6
2021Adversarial Robustness of Deep Learning: Theory, Algorithms, and Applicationscited by 5
2022Vehicle: Interfacing Neural Network Verifiers with Interactive Theorem Proverscited by 5
2022Safety Verification for Neural Networks Based on Set-boundary Analysiscited by 5
2022Discovering Closed-Loop Failures of Vision-Based Controllers via Reachability Analysiscited by 5
2022BERN-NN: Tight Bound Propagation For Neural Networks Using Bernstein Polynomial Interval Arithmeticcited by 5
2021Reachability Analysis of Convolutional Neural Networkscited by 4
2021QNNVerifier: A Tool for Verifying Neural Networks using SMT-Based Model Checkingcited by 4
2022Chordal Sparsity for SDP-based Neural Network Verificationcited by 4
2022Optimized Symbolic Interval Propagation for Neural Network Verificationcited by 4
2024Certifying Robustness of Learning-Based Keypoint Detection and Pose Estimation Methodscited by 4
2022Approximate Bisimulation Relations for Neural Networks and Application to Assured Neural Network Compressioncited by 3
2022Quantization-aware Interval Bound Propagation for Training Certifiably Robust Quantized Neural Networkscited by 3
2023A Neurosymbolic Approach to the Verification of Temporal Logic Properties of Learning enabled Control Systemscited by 3

50 most cited of 79 All 79 (JSON)