# Neural Network Verification in Control

arXiv: https://arxiv.org/abs/2110.01388 · HTML: https://mlsanity.com/paper/2110.01388/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 106 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 30 of 55)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [In-Datacenter Performance Analysis of a Tensor Processing Unit](https://mlsanity.com/paper/1704.04760/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Adversarial Attacks on Neural Network Policies](https://mlsanity.com/paper/1702.02284/) (2017)
- [Sim-to-Real: Learning Agile Locomotion For Quadruped Robots](https://mlsanity.com/paper/1804.10332/) (2018)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Caffe: Convolutional Architecture for Fast Feature Embedding](https://mlsanity.com/paper/1408.5093/) (2014)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Adversarial Policies: Attacking Deep Reinforcement Learning](https://mlsanity.com/paper/1905.10615/) (2019)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Towards Stable and Efficient Training of Verifiably Robust Neural Networks](https://mlsanity.com/paper/1906.06316/) (2019)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Soft Actor-Critic for Discrete Action Settings](https://mlsanity.com/paper/1910.07207/) (2019)
- [EPOpt: Learning Robust Neural Network Policies Using Model Ensembles](https://mlsanity.com/paper/1610.01283/) (2016)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)

## Built on by (most cited first, 14 of 14)

- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [Learning Minimally-Violating Continuous Control for Infeasible Linear Temporal Logic Specifications](https://mlsanity.com/paper/2210.01162/) (2022)
- [Chordal Sparsity for SDP-based Neural Network Verification](https://mlsanity.com/paper/2206.03482/) (2022)
- [Certifying Robustness of Learning-Based Keypoint Detection and Pose Estimation Methods](https://mlsanity.com/paper/2408.00117/) (2024)
- [Toward Evaluating Robustness of Reinforcement Learning with Adversarial Policy](https://mlsanity.com/paper/2305.02605/) (2023)
- [Achieving the Tightest Relaxation of Sigmoids for Formal Verification](https://mlsanity.com/paper/2408.10491/) (2024)
- [Deterministic World Models for Closed-loop Reachability Analysis of End-to-End Vision-based Control](https://mlsanity.com/paper/2512.08991/) (2025)
- [Certifiable Artificial Intelligence Through Data Fusion](https://mlsanity.com/paper/2111.02001/) (2021)
- [Rational Neural Network Controllers](https://mlsanity.com/paper/2307.06287/) (2023)
- [Learning a Stable, Safe, Distributed Feedback Controller for a Heterogeneous Platoon of Autonomous Vehicles](https://mlsanity.com/paper/2404.12474/) (2024)
- [Robust Verification of Controllers under State Uncertainty via Hamilton-Jacobi Reachability Analysis](https://mlsanity.com/paper/2511.14755/) (2025)
- [From Decoupled to Coupled: Robustness Verification for Learning-based Keypoint Detection with Joint Specifications](https://mlsanity.com/paper/2603.05604/) (2026)
- [(DNN)2: Doubly Non-Negative Relaxations for Deep Neural Networks](https://mlsanity.com/paper/2608.24743/) (2026)
- [Safety Screening for Voltage Control in Active Distribution Grids via Distributionally Robust Conformal Screening](https://mlsanity.com/paper/2608.30889/) (2026)

## Abstract (arXiv)

Learning-based methods could provide solutions to many of the long-standing challenges in control. However, the neural networks (NNs) commonly used in modern learning approaches present substantial challenges for analyzing the resulting control systems' safety properties. Fortunately, a new body of literature could provide tractable methods for analysis and verification of these high dimensional, highly nonlinear representations. This tutorial first introduces and unifies recent techniques (many of which originated in the computer vision and machine learning communities) for verifying robustness properties of NNs. The techniques are then extended to provide formal guarantees of neural feedback loops (e.g., closed-loop system with NN control policy). The provided tools are shown to enable closed-loop reachability analysis and robust deep reinforcement learning.