# NExG: Provable and Guided State Space Exploration of Neural Network Control Systems using Sensitivity Approximation

arXiv: https://arxiv.org/abs/2207.03884 · HTML: https://mlsanity.com/paper/2207.03884/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 8 Jul 2022.

## Builds on (most cited first, 14 of 14)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Learning Hand-Eye Coordination for Robotic Grasping with Deep Learning and Large-Scale Data Collection](https://mlsanity.com/paper/1603.02199/) (2016)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Formal Verification of Neural Network Controlled Autonomous Systems](https://mlsanity.com/paper/1810.13072/) (2018)
- [Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach](https://mlsanity.com/paper/2004.12273/) (2020)
- [Expressivity of Deep Neural Networks](https://mlsanity.com/paper/2007.04759/) (2020)
- [DRYVR:Data-driven verification and compositional reasoning for automotive systems](https://mlsanity.com/paper/1702.06902/) (2017)
- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [Neural State Classification for Hybrid Systems](https://mlsanity.com/paper/1807.09901/) (2018)
- [Bounded Verification with On-the-Fly Discrepancy Computation](https://mlsanity.com/paper/1502.01801/) (2015)
- [Diagnosis and Repair for Synthesis from Signal Temporal Logic Specifications](https://mlsanity.com/paper/1602.01883/) (2016)
- [NeuralExplorer: State Space Exploration of Closed Loop Control Systems Using Neural Networks](https://mlsanity.com/paper/2007.05685/) (2020)

## Abstract (arXiv)

We propose a new technique for performing state space exploration of closed loop control systems with neural network feedback controllers. Our approach involves approximating the sensitivity of the trajectories of the closed loop dynamics. Using such an approximator and the system simulator, we present a guided state space exploration method that can generate trajectories visiting the neighborhood of a target state at a specified time. We present a theoretical framework which establishes that our method will produce a sequence of trajectories that will reach a suitable neighborhood of the target state. We provide thorough evaluation of our approach on various systems with neural network feedback controllers of different configurations. We outperform earlier state space exploration techniques and achieve significant improvement in both the quality (explainability) and performance (convergence rate). Finally, we adopt our algorithm for the falsification of a class of temporal logic specification, assess its performance against a state-of-the-art falsification tool, and show its potential in supplementing existing falsification algorithms.