Latent Safety Filters: When a Lossy Encoder Admits a Transferable Certificate
Authors: Johannes Mootz, Zahra Nili Ahmadabadi, Reza Akhavian
Organizations: Department of Civil, Construction, and Environmental Engineering, San Diego State University, San Diego, CA 92182, USA. · Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093, USA. · Department of Mechanical Engineering, San Diego State University, San Diego, CA 92182, USA.
Latent safety filters certify safety on a learned low-dimensional representation of the state, enabling constraints that resist analytic description. Because the encoder is lossy, a filter can report safe while the physical state is unsafe, with no detectable model error. Existing transfer conditions leave the effect of discarded safety information implicit. We ask when a lossy encoder admits a safety certificate that transfers to the physical system, and show the answer is governed by the detectability of the discarded safety-relevant dynamics. We construct a system whose latent model is exact and whose latent signals always report safe, while the physical state becomes arbitrarily unsafe. For this system no certificate exists and no monitor downstream of the encoder can detect the failure. When the discarded dynamics contract, a latent barrier certifies true safety up to two explicit margins, one for the latent-model error and one for the variation of safety across states the encoder cannot distinguish. In the linear case and under boundedness and non-degeneracy conditions, every calibrated barrier transfers with a finite margin when the safety-relevant subspace is detectable, and none does otherwise. On learned cartpole encoders, the model error does not indicate for which representations the estimated bound is non-vacuous, while the second margin does.
Figures & tables
Fig. 1 : The dashed line is the fiber {x1=const} over z , and the blue arrow is a trajectory that moves up the fiber while z stays fixed. ( 1(a) ) h is constant along each fiber, so the trajectory is harmless. ( 1(b) ) The same trajectory leaves the safe set. ( 1(c) ) The fall of h saturates, so a finite certificate remains possible.
Fig. 2 : Overview of the main results.
Fig. 3 : Stability sweep on one fiber of ( 1 ) with u≡0 and exact latent model: the barrier ϕ(z0) , the true worst-case h and the uniform floor of Theorem 1 .
Fig. 4 : Learned encoders over 30 matched seeds: (a) safety-readout RMSE, (b) latent-model error γ^ , (c) empirical fiber defect Dˉ^ , (d) half-width of the empirical transfer corridor at α=4 , zero when the corridor is empty, nonempty for 0 of 29 plain and 29 of 30 safety-readout encoders.