Abstract Agents in cyber-physical systems are increasingly entrusted with safety-critical tasks. Ensuring the safety of these agents often requires localizing their pose for subsequent actions. Pose estimates can, e.g., be obtained from various combinations of lidar sensors, cameras, and external services such as GPS. Crucially, in safety-critical domains, a rough estimate is insufficient to formally determine safety, i.e., to guarantee safety even in extreme scenarios, and external services may additionally be untrustworthy. We address this problem by presenting an approach for certified pose estimation in 3D solely from a camera image and a well-known target geometry. This is realized by formally bounding the pose, which is computed by leveraging recent results from reachability analysis and formal neural network verification. Our experiments demonstrate that our approach efficiently and accurately localizes agents in both synthetic and real-world experiments.

Training and running inference of large neural networks comes with excessive cost and power consumption. Thus, realizing these networks as analog circuits is an energy-and areaefficient alternative. However, analog neural networks suffer from inherent deviations within their circuits, requiring extensive testing for their correct behavior under these deviations. Unfortunately, tests based on Monte Carlo simulations are extremely time- and resource-intensive. We present an alternative approach to proving the correctness of the neural network using formal neural network verification techniques and developing a modeling methodology for these analog neural circuits. Our experimental results compare two methods based on reachability analysis showing their effectiveness by reducing the test time from days to milliseconds. Thus, they offer a faster, more scalable solution for verifying the correctness of analog neural circuits.

Despite significant advancements in post-hoc explainability techniques for neural networks, many current methods rely on heuristics and do not provide formally provable guarantees over the explanations provided. Recent work has shown that it is possible to obtain explanations with formal guarantees by identifying subsets of input features that are sufficient to determine that predictions remain unchanged using neural network verification techniques. Despite the appeal of these explanations, their computation faces significant scalability challenges. In this work, we address this gap by proposing a novel abstraction-refinement technique for efficiently computing provably sufficient explanations of neural network predictions. Our method *abstracts* the original large neural network by constructing a substantially reduced network, where a sufficient explanation of the reduced network is also *provably sufficient* for the original network, hence significantly speeding up the verification process. If the explanation is insufficient on the reduced network, we iteratively *refine* the network size by gradually increasing it until convergence. Our experiments demonstrate that our approach enhances the efficiency of obtaining provably sufficient explanations for neural network predictions while additionally providing a fine-grained interpretation of the network's predictions across different abstraction levels.

Formal verification of neural networks is a challenging problem due to the complexity and nonlinearity of neural networks. It has been shown that polynomial zonotopes can tightly enclose the output set of a neural network. Unfortunately, the tight enclosure comes with additional complexity in the set representation, thus, rendering subsequent operations expensive to compute, such as computing interval bounds and intersection checking. To address this issue, we present a novel approach to restructure a polynomial zonotope to tightly enclose the original polynomial zonotope while drastically reducing its complexity. The restructuring is achieved by relaxing the exponents of the dependent factors of polynomial zonotopes and finding an appropriate approximation error. We demonstrate the applicability of our approach on output sets of neural networks, where we obtain tighter results in various subsequent operations, such as order reduction, zonotope enclosure, and range bounding.

The formal verification of neural networks is essential for their application in safety-critical environments. However, the set-based verification of neural networks using linear approximations often obtains overly conservative results, while nonlinear approximations quickly become computationally infeasible in deep neural networks. We address this issue for the first time by automatically balancing between precision and computation time without splitting the propagated set. Our work introduces a novel automatic abstraction refinement approach using sensitivity analysis to iteratively reduce the abstraction error at the neuron level until either the specifications are met or a maximum number of iterations is reached. Our evaluation shows that we can tightly over-approximate the output sets of deep neural networks and that our approach is up to a thousand times faster than a naive approach. We further demonstrate the applicability of our approach in closed-loop settings.