Rigorous sampled-data safety certificate

Derive a rigorous sampled-data safety certificate for the BLF-filtered continuous-time transformer model and determine the corresponding sampling-step selection needed to account for inter-sample constraint violations.

Background

The theoretical guarantees are established for a continuously updated controller, whereas the presented algorithm evaluates the quadratic-program filter at sampling instants and holds the control between samples. The authors explain that this introduces an inter-sample error that is of order proportional to the sampling interval on compact regions.

Although the error may potentially be handled by tightening the constraint, the constants and a rigorous certificate for the sampled implementation are not derived. The unresolved issue is particularly relevant because strict-margin violations appear in the sampled simulations.

References

We do not derive the constants here: a rigorous sampled-data certificate, and the corresponding selection of $\Delta t$, are left to future work.

— Enforcing a Strict Safety Margin in LLM Text Generation via Barrier Lyapunov Control  (2610.17929 - Singh et al., 13 Oct 2026) in Section 3.3, subsection “BLF-Based Safety Filter,” discussion of continuous-time guarantees versus discrete-time implementation

Confirming this by refining $\Delta t$ is left to future work.

— Enforcing a Strict Safety Margin in LLM Text Generation via Barrier Lyapunov Control  (2610.17929 - Singh et al., 13 Oct 2026) in Section 5, subsection “Nominal clearance and control effort,” discussion following Figure 1