In this work, we propose aframework to improvethe certified safety region for these smoothed classifiers without changing the underlying smoothing scheme.

Randomized smoothing is a recently proposed defense against adversarial attacks that has achieved state-of-the-art provable robustness against $\ell_2$ perturbations. A number of works have extended the guarantees to other metrics, such as $\ell_1$ or $\ell_\infty$, by using different smoothing measures. Although the current framework has been shown to yield near-optimal $\ell_p$ radii, the total safety region certified by the current framework can be arbitrarily small compared to the optimal. In this work, we propose a framework to improve the certified safety region for these smoothed classifiers without changing the underlying smoothing scheme. The theoretical contributions are as follows: 1) We generalize the certification for randomized smoothing by reformulating certified radius calculation as a nested optimization problem over a class of functions.

Effective, reliable, and efficient evaluation of autonomous driving safety is essential to demonstrate its trustworthiness. Criticality metrics provide an objective means of assessing safety. However, as existing metrics primarily target longitudinal conflicts, accurately quantifying the risks of lateral conflicts - prevalent in urban settings - remains challenging. This paper proposes the Modified-Emergency Index (MEI), a metric designed to quantify evasive effort in lateral conflicts. Compared to the original Emergency Index (EI), MEI refines the estimation of the time available for evasive maneuvers, enabling more precise risk quantification. We validate MEI on a public lateral conflict dataset based on Argoverse-2, from which we extract over 1,500 high-quality AV conflict cases, including more than 500 critical events. MEI is then compared with the well-established ACT and the widely used PET metrics. Results show that MEI consistently outperforms them in accurately quantifying criticality and capturing risk evolution. Overall, these findings highlight MEI as a promising metric for evaluating urban conflicts and enhancing the safety assessment framework for autonomous driving. The open-source implementation is available at https://github.com/AutoChengh/MEI.

In this work, we propose a framework to improve the certified safety region for these smoothed classifiers without changing the underlying smoothing scheme.

The recent adoption of artificial intelligence (AI) in robotics has driven the development of algorithms that enable autonomous systems to adapt to complex social environments. In particular, safe and efficient social navigation is a key challenge, requiring AI not only to avoid collisions and deadlocks but also to interact intuitively and predictably with its surroundings. To date, methods based on probabilistic models and the generation of conformal safety regions have shown promising results in defining safety regions with a controlled margin of error, primarily relying on classification approaches and explicit rules to describe collision-free navigation conditions. This work explores how topological features contribute to explainable safety regions in social navigation. Instead of using behavioral parameters, we leverage topological data analysis to classify and characterize different simulation behaviors. First, we apply global rule-based classification to distinguish between safe (collision-free) and unsafe scenarios based on topological properties. Then, we define safety regions, $S_\varepsilon$, in the topological feature space, ensuring a maximum classification error of $\varepsilon$. These regions are built with adjustable SVM classifiers and order statistics, providing robust decision boundaries. Local rules extracted from these regions enhance interpretability, keeping the decision-making process transparent. Our approach initially separates simulations with and without collisions, outperforming methods that not incorporate topological features. It offers a deeper understanding of robot interactions within a navigable space. We further refine safety regions to ensure deadlock-free simulations and integrate both aspects to define a compliant simulation space that guarantees safe and efficient navigation.

Randomized smoothing is a recently proposed defense against adversarial attacks that has achieved state-of-the-art provable robustness against \ell_2 perturbations. A number of works have extended the guarantees to other metrics, such as \ell_1 or \ell_\infty, by using different smoothing measures. Although the current framework has been shown to yield near-optimal \ell_p radii, the total safety region certified by the current framework can be arbitrarily small compared to the optimal. In this work, we propose a framework to improve the certified safety region for these smoothed classifiers without changing the underlying smoothing scheme. The theoretical contributions are as follows: 1) We generalize the certification for randomized smoothing by reformulating certified radius calculation as a nested optimization problem over a class of functions.

Safety is a fundamental requirement of many robotic systems. Control barrier function (CBF)-based approaches have been proposed to guarantee the safety of robotic systems. However, the effectiveness of these approaches highly relies on the choice of CBFs. Inspired by the universal approximation power of neural networks, there is a growing trend toward representing CBFs using neural networks, leading to the notion of neural CBFs (NCBFs). Current NCBFs, however, are trained and deployed in benign environments, making them ineffective for scenarios where robotic systems experience sensor faults and attacks. In this paper, we study safety-critical control synthesis for robotic systems under sensor faults and attacks. Our main contribution is the development and synthesis of a new class of CBFs that we term fault tolerant neural control barrier function (FT-NCBF). We derive the necessary and sufficient conditions for FT-NCBFs to guarantee safety, and develop a data-driven method to learn FT-NCBFs by minimizing a loss function constructed using the derived conditions. Using the learned FT-NCBF, we synthesize a control input and formally prove the safety guarantee provided by our approach. We demonstrate our proposed approach using two case studies: obstacle avoidance problem for an autonomous mobile robot and spacecraft rendezvous problem, with code available via https://github.com/HongchaoZhang-HZ/FTNCBF.

Supervised classification recognizes patterns in the data to separate classes of behaviours. Canonical solutions contain misclassification errors that are intrinsic to the numerical approximating nature of machine learning. The data analyst may minimize the classification error on a class at the expense of increasing the error of the other classes. The error control of such a design phase is often done in a heuristic manner. In this context, it is key to develop theoretical foundations capable of providing probabilistic certifications to the obtained classifiers. In this perspective, we introduce the concept of probabilistic safety region to describe a subset of the input space in which the number of misclassified instances is probabilistically controlled. The notion of scalable classifiers is then exploited to link the tuning of machine learning with error control. Several tests corroborate the approach. They are provided through synthetic data in order to highlight all the steps involved, as well as through a smart mobility application.

A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of the system is required to stay within a safety region for a horizon of $T$ time steps under the action of all dynamical systems that (i) belong to a given initial uncertainty set, and (ii) are consistent with the information gathered so far. For our first set of results, we consider the setting of safely learning a linear dynamical system involving $n$ states. For the case $T=1$, we present a linear programming-based algorithm that either safely recovers the true dynamics from at most $n$ trajectories, or certifies that safe learning is impossible. For $T=2$, we give a semidefinite representation of the set of safe initial conditions and show that $\lceil n/2 \rceil$ trajectories generically suffice for safe learning. Finally, for $T = \infty$, we provide semidefinite representable inner approximations of the set of safe initial conditions and show that one trajectory generically suffices for safe learning. Our second set of results concerns the problem of safely learning a general class of nonlinear dynamical systems. For the case $T=1$, we give a second-order cone programming based representation of the set of safe initial conditions. For $T=\infty$, we provide semidefinite representable inner approximations to the set of safe initial conditions. We show how one can safely collect trajectories and fit a polynomial model of the nonlinear dynamics that is consistent with the initial uncertainty set and best agrees with the observations.