On the Applicability of Safety Nets: A Safety-By-Design Solution for Certifying Neural Networks
Authors: Johann Maximilian Christensen, Thomas Stefani, Elena Hoemann, Frank Köster, Sven Hallerbach
Organizations: Institute for AI Safety and Security, German Aerospace Center (DLR), Sankt Augustin, Germany · Institute for AI Safety and Security, German Aerospace Center (DLR), Ulm, Germany
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.
Learning neural-network models of dynamical systems with safety guarantees is a fundamental requirement for their deployment in safety-critical settings. Safety is commonly established by proving the invariance of a desired subset in state-space, ensuring that every trajectory initialized in this subset remains confined to it for all time under admissible inputs. Existing frameworks, however, either rely on computationally expensive post-hoc verification or employ safety-enforcing mechanisms without formal correctness guarantees. In this paper, we introduce a novel neural architecture grounded in energy-based modern Hopfield networks to guarantee safety-by-design while retaining sufficient expressiveness to model complex nonlinear dynamics. Specifically, we integrate modern Hopfield networks with a port-Hamiltonian neural ODE, enabling by design the construction of barrier functions yielding explicit admissible-input sets and quantitative robustness radii. Across several benchmarks, including an 12-dimensional nanodrone model, our framework achieves state-of-the-art performance while producing certified invariant sets that are more robust to external solicitations than comparable existing approaches.
Simone Betteti, Morteza Lahijanian, Luca Laurenti
RIAS Lab The Italian Institute of Artificial Intelligence for Industry Torino, 10129, ITA · RECUV University of Colorado Boulder Boulder, CO 80303, USA · Delft Center for Systems and Control, TU Delft, Delft, 2600 AA, The Netherlands
A primary challenge in AI safety is the existence of adversarial examples -- slightly distorted inputs that cause a neural network (NN) to misclassify. To mitigate this problem, recent research focuses on the computation of robustness certifications, which, for a given input, determine the largest distortion the input may receive without breaking the network's prediction. Robustness certifications can be interpreted as an axis-aligned hyper-rectangle (multi-dimensional intervals). Most existing approaches focus on maximizing the certification's volume, but recent intractability results prohibit the computation of volume-optimal certifications in reasonable time. We introduce the apothem measure and show how to compute apothem-optimal certifications in a linear number of calls to a NN verifier (oracle) w.r.t. the input domain's diameter. Moreover, we prove that we cannot have a volume-optimal, oracle-based algorithm, even if we discard the oracle costs. Also, we introduce dual certifications -- an interval including all instances of a class -- thus providing apothem-minimum upper bounds to a robustness certification. Further, we present the ParallelepipedoNN system, which we evaluate on the standard MNIST and Fashion MNIST benchmarks. A preliminary comparison with existing work on the same datasets reveals at least two-fold improvement w.r.t. the minimum edge length.
Foundation for Reasearch and Technology - Hellas, Heraklion, Greece · University of Crete, Heraklion, Greece · Catalan Institution for Research and Advanced Studies, Barcelona, Spain +1
Deploying Deep Neural Networks (DNNs) on resource-constrained embedded systems requires aggressive model compression techniques like quantization and pruning. However, ensuring that the compressed model preserves the behavioral fidelity of the original design is a critical challenge in the safety-critical system design flow. Existing verification methods often lack scalability or fail to handle the architectural heterogeneity introduced by pruning. In this work, we propose SimCert, a probabilistic certification framework for verifying the behavioral similarity of compressed neural networks. Unlike worst-case analysis, SimCert provides quantitative safety guarantees with adjustable confidence levels. Our framework features: (1) A dual-network symbolic propagation method supporting both quantization and pruning; (2) A variance-aware bounding technique using Bernstein's inequality to tighten safety certificates; and (3) An automated verification toolchain. Experimental results on ACAS Xu and computer vision benchmarks demonstrate that SimCert outperforms state-of-the-art baselines.
Jingyang Li, Fu Song, Guoqiang Li
Shanghai Jiao Tong University, Shanghai 200240, China · Institute of Software, Chinese Academy of Sciences, Beijing 100190, China