# Verifying Aircraft Collision Avoidance Neural Networks Through Linear Approximations of Safe Regions

**Authors:** Kyle D. Julian, Shivam Sharma, Jean-Baptiste Jeannin, Mykel J. Kochenderfer  
**arXiv:** [1903.00762](https://arxiv.org/abs/1903.00762)  
**Date:** 2019-03-02  
**Summary page:** https://www.summarizepaper.com/en/paper/1903.00762v1/

## Key points

- Authors Kyle D. Julian, Shivam Sharma, Jean-Baptiste Jeannin, and Mykel J. Kochenderfer focus on enhancing the reliability of aircraft collision avoidance systems.
- Systems approach the problem as a Markov decision process and utilize dynamic programming to optimize alerting logic.
- Utilization of deep neural networks in compressing lookup tables for efficient operation on limited hardware.
- Key challenge: Ensuring reliable issuance of safe advisories for certification purposes.
- Methodology involves defining safe regions where advisories can be safely provided and using Reluplex for verification.
- Notional collision avoidance policy used as basis for training neural network representation.
- Thorough analysis using Reluplex identifies thousands of unsafe counterexamples, emphasizing the importance of this work in enhancing safety and reliability.

## Summary

In their paper titled "Verifying Aircraft Collision Avoidance Neural Networks Through Linear Approximations of Safe Regions," authors Kyle D. Julian, Shivam Sharma, Jean-Baptiste Jeannin, and Mykel J. Kochenderfer delve into the next generation of aircraft collision avoidance systems. These systems approach the problem as a Markov decision process and utilize dynamic programming to optimize alerting logic. A key component of these systems is a large lookup table that determines advisories given to pilots; however, the size of these tables can become unwieldy. To address this issue and enable operation on limited hardware, previous research explored compressing the table using deep neural networks. is a crucial aspect in ensuring flight safety. As technology advances,  are being utilized in  of safe regions for more efficient . In their study, Julian et al. focus on enhancing the reliability of aircraft collision avoidance systems by leveraging deep neural networks and rigorous verification techniques to ensure that safe advisories are consistently issued to pilots in critical situations. One key challenge in implementing neural networks for collision avoidance is ensuring that they reliably issue safe advisories for certification purposes. To tackle this challenge, the authors define  where each advisory can be safely provided. This approach allows them to leverage Reluplex, a neural network verification tool, to check if any unsafe advisories are ever issued. To validate their methodology, the researchers generate a notional collision avoidance policy which serves as the basis for training a neural network representation. Subsequently, are rigorously examined for unsafe advisories through thorough analysis using Reluplex. The results identify thousands of unsafe counterexamples, highlighting the importance of this work in enhancing the safety and reliability of aircraft collision avoidance systems.