What You Don't Know Can Hurt You: How Well do Latent Safety Filters Understand Partially Observable Safety Constraints?

Safe control techniques, such as Hamilton-Jacobi reachability, provide principled methods for synthesizing safety-preserving robot policies but typically assume hand-designed state spaces and full observability. Recent work has relaxed these assumptions via latent-space safe control, where state representations and dynamics are learned jointly through world models that reconstruct future high-dimensional observations (e.g., RGB images) from current observations and actions. This enables safety constraints that are difficult to specify analytically (e.g., spilling) to be framed as classification problems in latent space, allowing controllers to operate directly from raw observations. However, these methods assume that safety-critical features are observable in the learned latent state. We ask: when are latent state spaces sufficient for safe control? To study this, we examine temperature-based failures, comparable to overheating in cooking or manufacturing tasks, and find that RGB-only observations can produce myopic safety behaviors, e.g., avoiding seeing failure states rather than preventing failure itself. To predict such behaviors, we introduce a mutual information-based measure that identifies when observations fail to capture safety-relevant features. Finally, we propose a multimodal-supervised training strategy that shapes the latent state with additional sensory inputs during training, but requires no extra modalities at deployment, and validate our approach in simulation and on hardware with a Franka Research 3 manipulator preventing a pot of wax from overheating.