# On the Applicability of Safety Nets: A Safety-By-Design Solution for Certifying Neural Networks

arXiv: https://arxiv.org/abs/2608.20053 · HTML: https://mlsanity.com/paper/2608.20053/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 61 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Builds on (most cited first, 19 of 19)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Deep Neural Network Compression for Aircraft Collision Avoidance Systems](https://mlsanity.com/paper/1810.04240/) (2018)
- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [Deep Network Approximation: Beyond ReLU to Diverse Activation Functions](https://mlsanity.com/paper/2307.06555/) (2023)
- [Guaranteeing Safety for Neural Network-Based Aircraft Collision Avoidance Systems](https://mlsanity.com/paper/1912.07084/) (2019)
- [Toward Certification of Machine-Learning Systems for Low Criticality Airborne Applications](https://mlsanity.com/paper/2209.13975/) (2022)
- [How to design a dataset compliant with an ML-based system ODD?](https://mlsanity.com/paper/2406.14027/) (2024)
- [LARD 2.0: Enhanced Datasets and Benchmarking for Autonomous Landing Systems](https://mlsanity.com/paper/2603.26748/) (2026)
- [Runway Sign Classifier: A DAL C Certifiable Machine Learning System](https://mlsanity.com/paper/2310.06506/) (2023)
- [Approach Towards Semi-Automated Certification for Low Criticality ML-Enabled Airborne Applications](https://mlsanity.com/paper/2501.17028/) (2025)
- [Defining Operational Conditions for Safety-Critical AI-Based Systems from Data](https://mlsanity.com/paper/2601.22118/) (2026)

## Abstract (arXiv)

The integration of Artificial Intelligence (AI) in safety-critical aviation systems presents significant challenges for certification and deployment. Aviation, often regarded as the safest form of transportation, relies on numerous safety-critical systems. For future safety-critical AI-based systems, EASA requires a Safety-by-Design approach, which can be achieved by using Safety Nets that combine neural network compression with lookup tables to ensure 100 % correct runtime behavior across the discretized operational design domain. Although Safety Nets have been studied, no comprehensive study of their performance characteristics and system design trade-offs has been conducted. This work presents the first systematic analysis of the trade-off between neural network and lookup table size in Safety Nets. By systematically comparing neural networks with diverse architectures, this study identifies optimal design parameters that minimize overall storage and memory requirements while maintaining certification compliance. Results demonstrate that architectures with 3 to 5 hidden layers, each with approximately 50 to 100 nodes, combined with one-hot encoding, achieve the best balance. In these configurations, neural networks accurately represent at least 97 % of the data, while compact lookup tables handle the remaining errors. The resulting Safety Nets reduce the system size by almost three orders of magnitude, fitting within the memory budget of current avionics hardware while guaranteeing 100 % correct outputs across the entire discretized input space, as required by EASA guidelines. This work provides the first-ever open-source implementation of Safety Nets for HCAS and VCAS with replicable results, demonstrating a practical pathway toward certifiable AI-based systems in aviation and establishing Safety Nets as a viable Safety-by-Design solution for safety-critical applications.