# Neural Abstraction-Based Controller Synthesis and Deployment

arXiv: https://arxiv.org/abs/2307.03783 · HTML: https://mlsanity.com/paper/2307.03783/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 7 Jul 2023.

## Builds on (most cited first, 15 of 15)

- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [Deep Neural Network Compression for Aircraft Collision Avoidance Systems](https://mlsanity.com/paper/1810.04240/) (2018)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systems](https://mlsanity.com/paper/2106.13867/) (2021)
- [ReachNN: Reachability Analysis of Neural-Network Controlled Systems](https://mlsanity.com/paper/1906.10654/) (2019)
- [Robust Tracking with Model Mismatch for Fast and Safe Planning: an SOS Optimization Approach](https://mlsanity.com/paper/1808.00649/) (2018)
- [AMYTISS: Parallelized Automated Controller Synthesis for Large-Scale Stochastic Systems](https://mlsanity.com/paper/2005.06191/) (2020)
- [Data-Driven Abstraction-Based Control Synthesis](https://mlsanity.com/paper/2206.08069/) (2022)
- [Feedback Refinement Relations for the Synthesis of Symbolic Controllers](https://mlsanity.com/paper/1503.03715/) (2015)
- [Symbolic Abstractions From Data: A PAC Learning Approach](https://mlsanity.com/paper/2104.13901/) (2021)
- [Optimal Symbolic Controllers Determinization for BDD storage](https://mlsanity.com/paper/1803.07369/) (2018)
- [On Abstraction-Based Controller Design With Output Feedback](https://mlsanity.com/paper/2002.02687/) (2020)
- [Resilient Abstraction-Based Controller Design](https://mlsanity.com/paper/2008.06315/) (2020)

## Built on by (most cited first, 2 of 2)

- [Data-Driven Probabilistic Evaluation of Logic Properties with PAC-Confidence on Mealy Machines](https://mlsanity.com/paper/2508.14710/) (2025)
- [Kernel-Based Learning of Safety Barriers](https://mlsanity.com/paper/2601.12002/) (2026)

## Abstract (arXiv)

Abstraction-based techniques are an attractive approach for synthesizing correct-by-construction controllers to satisfy high-level temporal requirements. A main bottleneck for successful application of these techniques is the memory requirement, both during controller synthesis and in controller deployment. We propose memory-efficient methods for mitigating the high memory demands of the abstraction-based techniques using neural network representations. To perform synthesis for reach-avoid specifications, we propose an on-the-fly algorithm that relies on compressed neural network representations of the forward and backward dynamics of the system. In contrast to usual applications of neural representations, our technique maintains soundness of the end-to-end process. To ensure this, we correct the output of the trained neural network such that the corrected output representations are sound with respect to the finite abstraction. For deployment, we provide a novel training algorithm to find a neural network representation of the synthesized controller and experimentally show that the controller can be correctly represented as a combination of a neural network and a look-up table that requires a substantially smaller memory. We demonstrate experimentally that our approach significantly reduces the memory requirements of abstraction-based methods. For the selected benchmarks, our approach reduces the memory requirements respectively for the synthesis and deployment by a factor of 1.31× 105 and 7.13× 103 on average, and up to 7.54× 105 and 3.18× 104. Although this reduction is at the cost of increased off-line computations to train the neural networks, all the steps of our approach are parallelizable and can be implemented on machines with higher number of processing units to reduce the required computational time.