Latent Safety Filters: When a Lossy Encoder Admits a Transferable Certificate

2026-10-03

AI Summary

This study addresses the challenge that lossy encoders impede the reliable transfer of safety certificates from latent spaces to physical systems. Drawing upon linear systems theory and barrier functions, this work reveals that the detectability of discarded dynamics constitutes a necessary and sufficient condition for certificate transferability. Accordingly, an explicit dual-margin safety certification framework is constructed to effectively distinguish model errors from safety-relevant variations. The primary contribution lies in establishing the first theoretical connection between detectability and certificate transferability. Experimental validation on an inverted pendulum demonstrates that the proposed secondary margin accurately indicates non-trivial safety bounds, whereas conventional model error metrics fail in this setting.

Abstract

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.

Problem

• latent safety filters
• lossy encoder
• safety certificate
• transferability
• detectability

Innovation

• Latent Safety Filters
• Lossy Encoder
• Transferable Certificate
• Detectability
• Barrier Function