Abstract--A learning task, understood as the problem of fitting a parametric model from supervised data, fundamentally requires the dataset to be large enough to be representative of the underlying distribution of the source. When data is limited, the learned models fail generalize to cases not seen during training. This paper introduces a multi-task cross-learning framework to overcome data scarcity by jointly estimating deterministic parameters across multiple, related tasks. We formulate this joint estimation as a constrained optimization problem, where the constraints dictate the resulting similarity between the parameters of the different models, allowing the estimated parameters to differ across tasks while still combining information from multiple data sources. This framework enables knowledge transfer from tasks with abundant data to those with scarce data, leading to more accurate and reliable parameter estimates, providing a solution for scenarios where parameter inference from limited data is critical. We provide theoretical guarantees in a controlled framework with Gaussian data, and show the efficiency of our cross-learning method in applications with real data including image classification and propagation of infectious diseases. The machine learning problem, in general, involves extracting information from a dataset, which is typically achieved by fitting the parameters of a model [1], whether it be a neural network or a more specific parametric function that incorporates additional knowledge about the data source. Once fitted, this parametric model can be used for classification, prediction, or estimation, serving various purposes.

Finding a control Lyapunov function (CLF) in a dynamical system with a controller is an effective way to guarantee stability, which is a crucial issue in safety-concerned applications. Recently, deep learning models representing CLFs have been applied into a learner-verifier framework to identify satisfiable candidates. However, the learner treats Lyapunov conditions as complex constraints for optimisation, which is hard to achieve global convergence. It is also too complicated to implement these Lyapunov conditions for verification. To improve this framework, we treat Lyapunov conditions as inductive biases and design a neural CLF and a CLF-based controller guided by this knowledge. This design enables a stable optimisation process with limited constraints, and allows end-to-end learning of both the CLF and the controller. Our approach achieves a higher convergence rate and larger region of attraction (ROA) in learning the CLF compared to existing methods among abundant experiment cases. We also thoroughly reveal why the success rate decreases with previous methods during learning.

Abstract-- In a companion paper, we present a modular framework for unicycle stabilization in polar coordinates that provides smooth steering laws through backstepping. Surprisingly, the same problem also allows application of integrator forwarding. In this work, we leverage this feature and construct new smooth steering laws together with control Lyapunov functions (CLFs), expanding the set of CLFs available for inverse optimal control design. In the case of constant forward velocity (Dubins car), backstepping produces finite-time (deadbeat) parking, and we show that integrator forwarding yields the very same class of solutions. This reveals a fundamental connection between backstepping and forwarding in addressing both the unicycle and, the Dubins car parking problems.

Abstract-- Since the mid-1990s, it has been known that, unlike in Cartesian form where Brockett's condition rules out static feedback stabilization, the unicycle is globally asymptotically stabilizable by smooth feedback in polar coordinates. In this note, we introduce a modular framework for designing smooth feedback laws that achieve global asymptotic stabilization in polar coordinates. These laws are bidirectional, enabling efficient parking maneuvers, and are paired with families of strict control Lyapunov functions (CLFs) constructed in a modular fashion. The resulting CLFs guarantee global asymptotic stability with explicit convergence rates and include barrier variants that yield "almost global" stabilization, excluding only zero-measure subsets of the rotation manifolds. The strictness of the CLFs is further leveraged in our companion paper, where we develop inverse-optimal redesigns with meaningful cost functions and infinite gain margins.

The imperative of user privacy protection and regulatory compliance necessitates sensitive data removal in model training, yet this process often induces distributional shifts that undermine model performance-particularly in out-of-distribution (OOD) scenarios. We propose a novel data removal approach that enhances deep predictive models through factor decorrelation and loss perturbation. Our approach introduces: (1) a discriminative-preserving factor decorrelation module employing dynamic adaptive weight adjustment and iterative representation updating to reduce feature redundancy and minimize inter-feature correlations. (2) a smoothed data removal mechanism with loss perturbation that creates information-theoretic safeguards against data leakage during removal operations. Extensive experiments on five benchmark datasets show that our approach outperforms other baselines and consistently achieves high predictive accuracy and robustness even under significant distribution shifts. The results highlight its superior efficiency and adaptability in both in-distribution and out-of-distribution scenarios.

The growing adoption of Graph Neural Networks (GNNs) in high-stakes domains like healthcare and finance demands reliable explanations of their decision-making processes. While inherently interpretable GNN architectures like Graph Multi-linear Networks (GMT) have emerged, they remain vulnerable to generating explanations based on spurious correlations, potentially undermining trust in critical applications. We present MetaGMT, a meta-learning framework that enhances explanation fidelity through a novel bi-level optimization approach. We demonstrate that MetaGMT significantly improves both explanation quality (AUC-ROC, Precision@K) and robustness to spurious patterns, across BA-2Motifs, MUTAG, and SP-Motif benchmarks. Our approach maintains competitive classification accuracy while producing more faithful explanations (with an increase up to 8% of Explanation ROC on SP-Motif 0.5) compared to baseline methods. These advancements in interpretability could enable safer deployment of GNNs in sensitive domains by (1) facilitating model debugging through more reliable explanations, (2) supporting targeted retraining when biases are identified, and (3) enabling meaningful human oversight. By addressing the critical challenge of explanation reliability, our work contributes to building more trustworthy and actionable GNN systems for real-world applications.

Designing safety-critical controllers for acceleration-controlled unicycle robots is challenging, as control inputs may not appear in the constraints of control Lyapunov functions(CLFs) and control barrier functions (CBFs), leading to invalid controllers. Existing methods often rely on state-feedback-based CLFs and high-order CBFs (HOCBFs), which are computationally expensive to construct and fail to maintain effectiveness in dynamic environments with fast-moving, nearby obstacles. To address these challenges, we propose constructing velocity obstacle-based CBFs (VOCBFs) in the velocity space to enhance dynamic collision avoidance capabilities, instead of relying on distance-based CBFs that require the introduction of HOCBFs. Additionally, by extending VOCBFs using variants of VO, we enable reactive collision avoidance between robots. We formulate a safety-critical controller for acceleration-controlled unicycle robots as a mixed-integer quadratic programming (MIQP), integrating state-feedback-based CLFs for navigation and VOCBFs for collision avoidance. To enhance the efficiency of solving the MIQP, we split the MIQP into multiple sub-optimization problems and employ a decision network to reduce computational costs. Numerical simulations demonstrate that our approach effectively guides the robot to its target while avoiding collisions. Compared to HOCBFs, VOCBFs exhibit significantly improved dynamic obstacle avoidance performance, especially when obstacles are fast-moving and close to the robot. Furthermore, we extend our method to distributed multi-robot systems.

Control Lyapunov functions are a central tool in the design and analysis of stabilizing controllers for nonlinear systems. Constructing such functions, however, remains a significant challenge. In this paper, we investigate physics-informed learning and formal verification of neural network control Lyapunov functions. These neural networks solve a transformed Hamilton-Jacobi-Bellman equation, augmented by data generated using Pontryagin's maximum principle. Similar to how Zubov's equation characterizes the domain of attraction for autonomous systems, this equation characterizes the null-controllability set of a controlled system. This principled learning of neural network control Lyapunov functions outperforms alternative approaches, such as sum-of-squares and rational control Lyapunov functions, as demonstrated by numerical examples. As an intermediate step, we also present results on the formal verification of quadratic control Lyapunov functions, which, aided by satisfiability modulo theories solvers, can perform surprisingly well compared to more sophisticated approaches and efficiently produce global certificates of null-controllability.