Semantic segmentation neural networks (SSNs) are increasingly essential in high-stakes fields such as medical imaging, autonomous driving, and environmental monitoring, where robustness to input uncertainties and adversarial examples is crucial for ensuring safety and reliability. However, traditional probabilistic verification methods struggle to scale effectively with the size and depth of modern SSNs, especially when dealing with their high-dimensional, structured inputs/outputs. As the output dimension increases, these methods tend to become overly conservative, resulting in unnecessarily restrictive safety guarantees. In this work, we propose a probabilistic, data-driven verification algorithm that is architecture-agnostic and scalable, capable of handling the high-dimensional outputs of SSNs without introducing conservative and loose guarantees. We leverage efficient sampling-based reachability analysis to explore the space of possible outputs while maintaining computational feasibility. Our methodology is based on Conformal Inference (CI), which is known for its high data efficiency. However, CI tends to be overly conservative in high-dimensional spaces. To address this, in this paper, we introduce techniques to mitigate these sources of conservatism, enabling us to provide less conservative yet provable guarantees for SSNs. We validate our approach on large segmentation models applied to CamVid, OCTA-500 and Lung\_Segmentation, and Cityscapes datasets, showing that it can offer reliable safety guarantees while lowering the conservatism inherent in traditional methods. We also provide a public GitHub repository for this approach, to support reproducibility.

Reachability analysis is a popular method to give safety guarantees for stochastic cyber-physical systems (SCPSs) that takes in a symbolic description of the system dynamics and uses set-propagation methods to compute an overapproximation of the set of reachable states over a bounded time horizon. In this article, we investigate the problem of performing reachability analysis for an SCPS that does not have a symbolic description of the dynamics, but instead is described using a digital twin model that can be simulated to generate system trajectories. An important challenge is that the simulator implicitly models a probability distribution over the set of trajectories of the SCPS; however, it is typical to have a sim2real gap, i.e., the actual distribution of the trajectories in a deployment setting may be shifted from the distribution assumed by the simulator. We thus propose a statistical reachability analysis technique that, given a user-provided threshold$1-\epsilon $, provides a set that guarantees that any trajectory during deployment lies in this set with probability not smaller than this threshold. Our method is based on three main steps: 1) learning a deterministic surrogate model from sampled trajectories; 2) conducting reachability analysis over the surrogate model; and 3) employing robust conformal inference (CI) using an additional set of sampled trajectories to quantify the surrogate model’s distribution shift with respect to the deployed SCPS. To counter conservatism in reachable sets, we propose a novel method to train surrogate models that minimizes a quantile loss term (instead of the usual mean squared loss), and a new method that provides tighter guarantees using CI using a normalized surrogate error. We demonstrate the effectiveness of our technique on various case studies.

This article introduces a model-based approach for training feedback controllers for an autonomous agent operating in a highly non-linear (albeit deterministic) environment. We desire the trained policy to ensure that the agent satisfies specific task objectives and safety constraints, both expressed in Discrete-Time Signal Temporal Logic (DT-STL). One advantage for reformulation of a task via formal frameworks, like DT-STL, is that it permits quantitative satisfaction semantics. In other words, given a trajectory and a DT-STL formula, we can compute the robustness , which can be interpreted as an approximate signed distance between the trajectory and the set of trajectories satisfying the formula. We utilize feedback control, and we assume a feed forward neural network for learning the feedback controller. We show how this learning problem is similar to training recurrent neural networks (RNNs), where the number of recurrent units is proportional to the temporal horizon of the agent’s task objectives. This poses a challenge: RNNs are susceptible to vanishing and exploding gradients, and naïve gradient descent-based strategies to solve long-horizon task objectives thus suffer from the same problems. To address this challenge, we introduce a novel gradient approximation algorithm based on the idea of dropout or gradient sampling. One of the main contributions is the notion of controller network dropout , where we approximate the NN controller in several timesteps in the task horizon by the control input obtained using the controller in a previous training step. We show that our control synthesis methodology can be quite helpful for stochastic gradient descent to converge with less numerical issues, enabling scalable back-propagation over longer time horizons and trajectories over higher-dimensional state spaces. We demonstrate the efficacy of our approach on various motion planning applications requiring complex spatio-temporal and sequential tasks ranging over thousands of timesteps.