Continuous-domain extension of the Safety Net guarantee

Extend the point-wise correctness guarantee of the HCAS and VCAS Safety Nets from the discretized input grids to interval-based coverage of the continuous operational input spaces.

Background

The reported Safety Nets guarantee 100% agreement with the lookup-table ground truth only at the discrete input vectors enumerated in the manifests. Continuous runtime states are quantized to the nearest available grid point before the Safety Net is queried, so the behavior between grid points is not covered by the same correctness guarantee.

Earlier box-based Safety Net studies certified agreement over continuous regions, whereas the present work uses an exhaustive point-wise sweep over a discretized grid. The authors explicitly leave open the task of extending the current guarantee to interval-based coverage, which would provide stronger assurance for continuous runtime states and reduce dependence on quantization behavior.

References

The \qty{100}{\percent} correctness guarantee therefore applies to the discretized ODD, while this quantization determines the behavior between grid points. This constitutes a deliberate deviation from the original table-based implementations, which interpolate the Q-values between grid vertices, and from the box-based verification, which proves agreement over continuous regions; extending the point-wise guarantee to interval-based coverage of the continuous input space is left to future work.

— On the Applicability of Safety Nets: A Safety-By-Design Solution for Certifying Neural Networks  (2608.20053 - Christensen et al., 20 Aug 2026) in Section 5, Safety Net