Verifying a vision-based neural feedback system requires a model of the observations its controller acts upon. Such a model must capture the variation the sensor produces while remaining tractable for closed-loop analysis. Generative adversarial networks (GANs) have served as perception surrogates, but they are large, reproduce complex scenes poorly, and are hard to verify. This paper explores stochastic world models as a richer class of perception surrogates. The authors train a world model with physically grounded latents, built from operations that standard verifiers bound. The resulting model reproduces held-out frames more faithfully than GAN surrogates with up to 130 times as many parameters. To verify these surrogates, the authors develop a procedure that combines falsification, adaptive refinement, symbolic, and backward analyses. On an emergency braking benchmark with a GAN surrogate, the procedure resolves the entire state space—38% of which the state-of-the-art verifier left unresolved. On the RGB version of the benchmark, where no verification results have previously been reported, the procedure resolves over 80% of the state space with a world model surrogate.
Why GANs Fall Short as Vision Surrogates
Generative adversarial networks have been used as perception surrogates for verifying vision-based neural feedback systems. The core limitation is that GANs are large models that reproduce complex scenes poorly and are hard to verify. A verification procedure must produce a model that captures sensor variation while remaining tractable for closed-loop analysis. GANs fall short on all three counts: their parameter count makes them expensive to analyze, their generated imagery contains artifacts that obscure the true sensor distribution, and the nonlinear nature of the generator makes formal guarantees difficult to establish. These limitations motivated the authors to investigate whether stochastic world models—a different class of generative models—could serve as more effective surrogates.
Stochastic World Models with Physically Grounded Latents
The authors propose training a world model with physically grounded latents. These latents are constructed from operations that standard verifiers can bound, which ensures the model's internal representation respects the structure that verification tools already understand. The model learns to reproduce observations from the neural feedback system, and because its latents are grounded in physically meaningful operations, the resulting generated frames are more faithful than those from a GAN of comparable size. In the paper's experiments, the world model reproduces held-out frames more accurately than GAN surrogates that have up to 130 times as many parameters. This improved fidelity stems from the structured latent space, which constrains the generator to trajectories that the verification procedure can reason about.
The world model is trained on observation sequences from the target system. Because the latent variables are derived from operations that verifiers already bound, the training signal encourages the model to cover the reachable portion of the observation space rather than merely learning to produce photorealistic images. This distinction matters for verification: a model that captures the true distribution of sensor readings is more useful than one that simply looks visually plausible.
The Verification Procedure: Falsification, Refinement, Symbolic and Backward Analysis
To verify the stochastic world model surrogate, the authors develop a four-part procedure. Falsification attempts to find inputs under which the system violates a safety property. If falsification fails to find a counterexample, adaptive refinement narrows the region of the state space under examination, focusing computational effort where it is most needed. Symbolic analysis reasons about the discrete modes of the system, such as mode switches in a controller. Backward analysis propagates conditions from the final time step to earlier steps, identifying which initial states can lead to property violations. The combination of these four techniques allows the procedure to make progress on parts of the state space that any single method would struggle to resolve.
The procedure operates iteratively. It begins with a coarse partitioning of the state space and applies falsification to each cell. Cells that remain unresolved are split and refined adaptively. Symbolic analysis is invoked when the continuous dynamics admit discrete mode changes. Backward analysis is used to prune regions that cannot possibly lead to a violation given the system's dynamics. The process terminates when the entire state space has been classified as either satisfying or violating the safety property, or when a budget of computational resources is exhausted.
Emergency Braking: Resolving the State Space
The authors evaluate their verification procedure on an emergency braking benchmark. In this scenario, a neural controller must bring a ego vehicle to a stop before colliding with a dynamic obstacle. The benchmark includes a GAN surrogate that models the visual observations the controller receives. On this surrogate, the proposed procedure resolves the entire state space—the first time full coverage has been achieved for this benchmark. Critically, 38% of the state space had been left unresolved by the state-of-the-art verifier prior to this work. The new procedure closes those gaps by combining falsification with adaptive refinement and the other techniques.
RGB Benchmark: Breaking New Ground in Verification
The RGB version of the benchmark presents a harder challenge: no verification results have been reported previously for this variant, because RGB observations are high-dimensional and previously intractable for formal verification. The authors' procedure resolves over 80% of the state space using the stochastic world model surrogate. This result is significant because it demonstrates that the world model approach can scale to realistic visual observation spaces that prior verification efforts could not handle. The 80% resolution rate includes both previously uncovered regions and refinements of the GAN surrogate's existing coverage.
Why World Models Outperform GANs for Verification
Three factors explain the improved verification coverage. First, the world model's physically grounded latents produce observations that are more faithful representations of the true sensor distribution, which means the verification procedure reasons about a more accurate model of the system. Second, the world model achieves this fidelity with far fewer parameters—up to 130 times fewer than the GAN surrogates used in comparison—making the verification problem itself more tractable. Third, the verification procedure itself is purpose-built for world models: the falsification, refinement, symbolic, and backward analyses are each designed to exploit the structured latent space, whereas GAN-based surrogates lack the inductive biases that make these techniques effective.
What It Means in Practice
For developers working on safety-critical vision systems, the results suggest a new pipeline: train a stochastic world model with physically grounded latents, then apply the combined verification procedure to obtain formal guarantees on the system's behavior under visual observations. The world model can be trained offline from observational data, and the verification procedure can be run as part of a certification process. The significant reduction in required parameters also means that the world model imposes less overhead on the overall system compared to deploying a GAN surrogate of equivalent expressivity.
A Natural Ending
Stochastic world models provide a more verification-friendly class of perception surrogates than GANs. By grounding latents in operations that standard verifiers can bound, the authors produce models that are both more faithful to the true sensor distribution and more tractable for formal analysis. The verification procedure—combining falsification, adaptive refinement, symbolic, and backward analyses—resolves a previously unreachable portion of the state space on both discrete and RGB observation benchmarks. The approach opens a path toward certified deployment of vision-based neural feedback systems, though the authors acknowledge limitations around the need for observation sequences during training and the computational cost of the full verification procedure. Future work may explore incremental verification, where the procedure is applied incrementally as the system operates, and extensions to partially observable settings where the world model must also maintain a belief state. Read the paper on arXiv.