An arXiv preprint dated 20 Aug 2026 reports a way to reduce the memory footprint of two proof-of-concept collision-avoidance implementations while preserving exact agreement with a reference policy on the tested input grids. The combined Safety Net measured 4.76 MiB for HCAS and 222.83 MiB for VCAS, compared with at least 4 GiB for the monolithic lookup-table reference; by construction, agreement with lookup-table ground truth reached 100% across the complete discretized input space.
Called a Safety Net in the study, the design pairs a neural network with a lookup table—a stored set of answers for points on the finite grid—that corrects mismatches with the discrete policy. The central question was which network architecture and output encoding could minimize the combined storage burden while preserving that policy.
The engineering trade-off
The evaluation covered all 40 HCAS and 9 VCAS subsystems, varying activation function, hidden-layer count, layer width and output encoding. Each configuration was trained five times, for up to 10,000 epochs, with early stopping after 1,000 consecutive epochs without improvement. The entire finite data set was used for training, validation and testing.
ReLU produced a lower median lookup-table percentage than LeakyReLU or GELU. One-hot encoding outperformed target encoding by at least one order of magnitude on median lookup-table percentage, particularly for smaller networks.
The most favorable depth was between 3 and 5 hidden layers; deeper networks had a deteriorating median. Beyond roughly 50 to 100 nodes per hidden layer, wider networks delivered diminishing median gains and substantially more variation from one training run to the next.
The selected final configurations used 3 hidden layers and 100 nodes per layer for HCAS, and 5 hidden layers and 100 nodes per layer for VCAS.
What the combined system covered
The neural-network component covered 99.65% of the HCAS input space and 97.77% of the VCAS input space on average. Lookup-table correction handled the deviations, and the combined Safety Net guaranteed 100% agreement with ground truth across the complete discretized input space.
On the study workstation, mean inference times per sample, averaged over 5,000 samples per subsystem, were 33.2 ± 1.5 microseconds for HCAS and 57.3 ± 12.7 microseconds for VCAS on a GPU. On a CPU, the corresponding means were 20.2 ± 4.3 and 46.4 ± 13.0 microseconds. The paper does not specify what the plus-or-minus values represent.
The boundary of the result
The 100% figure has a narrow meaning. Continuous states are mapped to the closest grid point, so the guarantee applies only to the discretized operational design domain; behavior between grid points was not guaranteed.
The memory comparison is similarly bounded. HCAS and VCAS are proof-of-concept approximations, not full operational specifications, so their reported sizes should not be read as estimates for production deployment or as evidence of aviation certification.
Uncertainty in the architecture comparisons came mainly from run-to-run spread: results were summarized by medians across five training runs, with the full range shown in the parameter-study plots. No inferential hypothesis tests or confidence intervals were reported.
The trained networks, lookup tables, manifest files and training scripts were released alongside the preprint.
Paper data and sources
Original title: On the Applicability of Safety Nets: A Safety-By-Design Solution for Certifying Neural Networks
Authors: Johann Maximilian Christensen, Thomas Stefani, Elena Hoemann et al.
Journal/Repository: 35th Congress of the International Councilof the Aeronautical Sciences (ICAS) 2026
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: 10.71945/icas2026_0210
Original paper · Full text