# From Points to Sets: Set-Based Safety Verification in the Latent Space

arXiv: https://arxiv.org/abs/2604.05799 · HTML: https://mlsanity.com/paper/2604.05799/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2026.

## Built on by (most cited first, 1 of 1)

- [Latent Safety Filters: When a Lossy Encoder Admits a Transferable Certificate](https://mlsanity.com/paper/2610.04297/) (2026)

## Abstract (arXiv)

We extend latent representation methods for safety control design to set-valued states. Recent work has shown that barrier functions designed in a learned latent space can transfer safety guarantees back to the original system, but these methods evaluate certificates at single state points, ignoring state uncertainty. A fixed safety margin can partially address this but cannot adapt to the anisotropic and time-varying nature of the uncertainty gap across different safety constraints. We instead represent the system state as a zonotope, propagate it through the encoder to obtain a latent zonotope, and evaluate certificates over the worst case of the entire set. On a 16-dimensional quadrotor suspended-load gate passage task, set-valued evaluation achieves 5/5 collision-free passages, compared to 1/5 for point-based evaluation and 2/5 for a fixed-margin baseline. Set evaluation reports safety in 44.4% of per-head evaluations versus 48.5% for point-based, and this greater conservatism detects 4.1% blind spots where point evaluation falsely certifies safety, enabling earlier corrective control. The safety gap between point and set evaluation varies up to 12× across certificate heads, explaining why no single fixed margin suffices and confirming the need for per-head, per-timestep adaptation, which set evaluation provides by construction.