🤖 AI

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

This paper presents a systematic analysis and open-source implementation of Safety Nets, a Safety-by-Design solution that combines optimized neural networks with compact lookup tables to achieve 100% runtime correctness and drastically reduced memory footprints, thereby enabling the certification of AI-based systems for safety-critical aviation applications.

Original authors: Johann Maximilian Christensen, Thomas Stefani, Elena Hoemann, Frank Köster, Sven Hallerbach

Published 2026-08-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Johann Maximilian Christensen, Thomas Stefani, Elena Hoemann, Frank Köster, Sven Hallerbach

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Aviation has long been the gold standard for safety, a realm where human error is minimized by rigorous engineering and strict rules. Yet, as the skies fill with more aircraft and the number of available pilots shrinks, the industry is turning to artificial intelligence to help manage the workload. The challenge is that these new computer systems must be as reliable as the mechanical ones they replace, a requirement that is difficult to meet when the software learns from data rather than following a fixed set of instructions. In the specific case of preventing mid-air collisions, the traditional method relies on massive lookup tables—essentially giant instruction manuals that tell the computer exactly what to do in every possible situation. These tables are so large that they would overwhelm the memory of current aircraft computers, making them impossible to install. To solve this, engineers have tried to compress these instructions into smaller, smarter programs using neural networks, which are computer systems designed to mimic the way the human brain recognizes patterns. However, because these neural networks can make mistakes, regulators require a way to guarantee they will never fail in a critical moment.

Researchers at the German Aerospace Center have developed a solution called a "safety net" to bridge this gap, and they have now systematically tested how to make these nets as small and efficient as possible. Their work focuses on two specific collision-avoidance systems: one that tells a pilot when to turn left or right, and another that advises when to climb or descend. The core idea is simple but powerful: use a neural network to handle the vast majority of situations, but keep a small, perfect backup list for the rare cases where the network might get confused. The researchers treated the size of the neural network and the size of this backup list as a balancing act. They wanted to find the exact shape and size of the neural network that would make the backup list as tiny as possible without making the network itself too big to fit on the plane.

To find this sweet spot, the team ran thousands of experiments, tweaking the internal structure of the neural networks like a mechanic adjusting an engine. They tested different types of mathematical functions that help the network learn, varying the number of layers within the network, and changing how many processing units were in each layer. They also experimented with different ways of teaching the network, such as asking it to predict a specific value versus simply asking it to choose the single best option from a list. The results were surprisingly specific. The team discovered that the most efficient designs were not the most complex ones. Instead, networks with three to five layers, each containing roughly fifty to one hundred processing units, struck the perfect balance. Furthermore, they found that a standard mathematical function known as ReLU worked better than more advanced alternatives, and that teaching the network to simply pick the best choice worked far better than asking it to calculate complex numbers.

When these optimal settings were applied, the results were dramatic. For the system that handles horizontal turns, the combined size of the neural network and the backup list shrank to just 4.76 megabytes. For the vertical system, which deals with climbing and descending, the total size was 222.83 megabytes. These numbers represent a massive reduction from the original instruction manuals, which would have required four gigabytes of memory—roughly a thousand times more space than the new system for the turning scenario. This reduction means the system can now fit comfortably on the computers currently used in aircraft, a feat that was previously impossible. The researchers also confirmed that the system is incredibly fast, making decisions in microseconds, which is far quicker than the one-second update cycle required for flight safety.

Perhaps most importantly, the study proved that this approach meets the strictest safety standards. Because the backup list contains the correct answer for every single situation the neural network might get wrong, the combined system is guaranteed to be 100 percent correct across the entire range of possible flight scenarios. This means the system does not rely on probability or hope; it is mathematically certain to provide the right advice. The researchers released all their code and data to the public, allowing other engineers to verify their findings and build upon them. By demonstrating that a neural network can be paired with a small, perfect backup to create a system that is both compact and infallible, this work provides a clear, practical path toward certifying artificial intelligence for use in the most safety-critical parts of aviation. The study shows that with the right design, we can have the adaptability of machine learning without sacrificing the absolute reliability that keeps passengers safe in the sky.

Technical Summary: Applicability of Safety Nets for Certifying Neural Networks in Aviation

Problem Statement
The integration of Artificial Intelligence (AI) into safety-critical aviation systems, specifically Airborne Collision Avoidance Systems (ACAS X), faces a critical barrier: the memory requirements of the underlying Markov Decision Process (MDP) lookup tables far exceed the capacity of current avionics hardware. For instance, the raw dynamic-programming output for ACAS X requires hundreds of gigabytes, while even downsampled logic tables exceed 2 GB. In contrast, modern flight management computers typically offer only hundreds of megabytes (e.g., 512 MB). While neural networks have been proposed to compress these tables, their deployment in safety-critical contexts requires a "Safety-by-Design" approach to ensure 100% correctness across the entire Operational Design Domain (ODD), a requirement that statistical testing alone cannot satisfy. Previous studies on "Safety Nets"—hybrid systems combining neural networks with lookup tables—lacked a comprehensive analysis of architectural trade-offs and did not provide reproducible implementations.

Methodology
This work presents a systematic analysis of Safety Nets applied to the open-source Horizontal Collision Avoidance System (HCAS) and Vertical Collision Avoidance System (VCAS), which serve as proof-of-concept approximations for ACAS Xa and ACAS Xu. The methodology follows an extended W-shaped development process compliant with EASA guidelines, focusing on the following steps:

System Decomposition: Both HCAS and VCAS are treated as ensembles of smaller neural networks (40 subsystems for HCAS, 9 for VCAS), each handling specific combinations of previous advisories and time-to-closest-point-of-approach ( $\tau$ ).
Hyperparameter Sweep: A rigorous study was conducted to identify optimal neural network architectures. The study varied:
- Activation Functions: ReLU, LeakyReLU, and GELU.
- Architecture Depth: 2, 3, 5, and 7 hidden layers.
- Architecture Width: 25, 50, 100, 150, and 200 nodes per layer.
- Output Encoding: Target encoding (regression of full Q-values) vs. One-hot encoding (classification of the optimal advisory).
Training Protocol: Unlike generalization tasks, the entire discrete input space served as the training, validation, and testing set to ensure exact memorization of the known MDP policy. Training utilized Mean Squared Error for target encoding and Cross Entropy for one-hot encoding, with early stopping to prevent wasted computation.
Safety Net Construction: For each configuration, the neural network was evaluated against the ground-truth lookup table. Input vectors where the network produced incorrect outputs were stored in a lookup table (LUT). The total system size is the sum of the neural network parameters and the LUT entries.
Verification: The resulting Safety Nets guarantee 100% correctness across the discretized input space by construction, as any error is corrected by the LUT.

Key Results
The study identified specific design parameters that minimize total system size while maintaining certification compliance:

Optimal Architecture: Networks with 3 to 5 hidden layers and 50 to 100 nodes per layer achieved the best balance. Increasing depth beyond 5 layers or width beyond 100 nodes yielded diminishing returns in retrieval rates while increasing variance and memory footprint.
Activation Function: Contrary to trends in general classification literature, ReLU outperformed LeakyReLU and GELU. The authors attribute this to the discrete, bounded, and piecewise-constant nature of the MDP policy, where ReLU's sparse activation patterns align better with the step-like decision boundaries.
Encoding Strategy: One-hot encoding consistently outperformed target encoding by at least one order of magnitude in terms of the percentage of data stored in the LUT, particularly for smaller architectures.
System Performance:
- HCAS: Achieved 99.65% neural network coverage. The combined system size was 4.76 MiB (3.22 MiB network + 1.54 MiB LUT), a reduction of nearly three orders of magnitude compared to the monolithic MDP table.
- VCAS: Achieved 97.77% coverage. The combined system size was 222.83 MiB (1.44 MiB network + 221.40 MiB LUT), a reduction of slightly more than one order of magnitude. The LUT dominates the VCAS size due to the larger input space and policy complexity.
- Runtime: Inference times were sub-millisecond (approx. 20–57 $\mu$ s), well within the 1-second update budget of ACAS X.

Significance and Claims
The paper claims to provide the first systematic analysis of the trade-offs between neural network architecture and lookup table size in Safety Nets for aviation collision avoidance. Its primary contributions are:

Design Guidelines: It establishes that for MDP-based policy compression, ReLU and moderate network widths (50–100 nodes) are superior to alternatives, challenging assumptions derived from general machine learning benchmarks.
Certification Pathway: The work demonstrates that Safety Nets satisfy EASA's learning assurance and implementation objectives (specifically LM-04, LM-10, and IMP-11) by construction. By exhaustively verifying the network against the ground truth and storing deviations, the system achieves a deterministic, zero-error bound over the discretized ODD, eliminating the need for statistical generalization arguments.
Reproducibility: The authors release the first open-source implementation of Safety Nets for HCAS and VCAS, including training scripts and manifest files, addressing a gap in prior work where implementation details were undisclosed.
Feasibility: The results show that Safety Nets can compress safety-critical AI systems to fit within the memory constraints of current avionics hardware, providing a practical pathway toward certifiable AI-based systems.

The authors note that the reported sizes are based on proof-of-concept implementations (HCAS/VCAS) which represent reduced subsets of the full ACAS Xa/Xu operational envelopes. Consequently, while the methodology is validated, the absolute size figures for a full production-scale system would be larger, though the order-of-magnitude reductions and the "correct-by-design" certification argument remain applicable.

Technical Summary: Applicability of Safety Nets for Certifying Neural Networks in Aviation

More like this