# Deterministic World Models for Closed-loop Reachability Analysis of End-to-End Vision-based Control

arXiv: https://arxiv.org/abs/2512.08991 · HTML: https://mlsanity.com/paper/2512.08991/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Embodied and robot world models, one of 11 directions in World models.
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Placed in

- World models / [Embodied and robot world models](https://mlsanity.com/wm/embodied-and-robot-world-models/)

## Builds on (most cited first, 13 of 13)

- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Toward Multimodal Image-to-Image Translation](https://mlsanity.com/paper/1711.11586/) (2017)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [Generative Data Augmentation for Commonsense Reasoning](https://mlsanity.com/paper/2004.11546/) (2020)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [NNLander-VeriF: A Neural Network Formal Verification Framework for Vision-Based Autonomous Aircraft Landing](https://mlsanity.com/paper/2203.15841/) (2022)
- [Maneuver-based Trajectory Prediction for Self-driving Cars Using Spatio-temporal Convolutional Networks](https://mlsanity.com/paper/2109.07365/) (2021)
- [Neural Network Verification in Control](https://mlsanity.com/paper/2110.01388/) (2021)
- [Robust Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1805.08657/) (2018)
- [Scalable Surrogate Verification of Image-based Neural Network Control Systems using Composition and Unrolling](https://mlsanity.com/paper/2405.18554/) (2024)
- [Bridging Dimensions: Confident Reachability for High-Dimensional Controllers](https://mlsanity.com/paper/2311.04843/) (2023)
- [State-Dependent Conformal Perception Bounds for Neuro-Symbolic Verification of Autonomous Systems](https://mlsanity.com/paper/2502.21308/) (2025)

## Built on by (most cited first, 2 of 2)

- [Certified World Models as Sensing Clocks: Drift-Aware Deadlines for Active Perception](https://mlsanity.com/paper/2607.01537/) (2026)
- [Stochastic World Models for Verifying Vision-Based Neural Feedback Systems](https://mlsanity.com/paper/2609.38120/) (2026)

## Abstract (arXiv)

End-to-end image controllers that map raw camera frames directly to control actions are increasingly deployed in safety-critical systems. However, formally verifying their closed-loop behavior remains an open challenge because cameras produce high-dimensional images whose generation cannot easily be described in a closed mathematical form. We propose a Deterministic World Model (DWM), a latent-free neural decoder that maps physical states (e.g., position and velocity) directly to synthetic camera images, enabling closed-loop reachability analysis without the overapproximation caused by stochastic latent variables. The DWM is trained with a novel dual loss combining saliency-map reconstruction and a control-consistent term that preserves behavioral consistency with the real controller. We integrate the DWM into closed-loop reachability analysis and apply conformal prediction to inflate the reachable sets by a distribution-free trajectory-tube deviation bound, transferring the surrogate guarantee to the real system with high probability. Experiments on a CARLA braking system and three Gym benchmarks (CartPole, MountainCar, Pendulum) show that the DWM produces substantially tighter reachable tubes than a cGAN and trajectory predictor baselines while meeting the target coverage after conformal inflation.