Structural vibrations are a source of unwanted noise in engineering systems like cars, trains or airplanes. Minimizing these vibrations is crucial for improving passenger comfort. This work presents a novel design optimization approach based on guided flow matching for reducing vibrations by placing beadings (indentations) in plate-like structures. Our method integrates a generative flow matching model and a surrogate model trained to predict structural vibrations. During the generation process, the flow matching model pushes towards manufacturability while the surrogate model pushes to low-vibration solutions. The flow matching model and its training data implicitly define the design space, enabling a broader exploration of potential solutions as no optimization of manually-defined design parameters is required. We apply our method to a range of differentiable optimization objectives, including direct optimization of specific eigenfrequencies through careful construction of the objective function. Results demonstrate that our method generates diverse and manufacturable plate designs with reduced structural vibrations compared to designs from random search, a criterion-based design heuristic and genetic optimization. The code and data are available from https://github.com/ecker-lab/Optimizing_Vibrating_Plates.

Adversarial attacks in machine learning have been extensively reviewed in areas like computer vision and NLP, but research on tabular data remains scattered. This paper provides the first systematic literature review focused on adversarial attacks targeting tabular machine learning models. We highlight key trends, categorize attack strategies and analyze how they address practical considerations for real-world applicability. Additionally, we outline current challenges and open research questions. By offering a clear and structured overview, this review aims to guide future efforts in understanding and addressing adversarial vulnerabilities in tabular machine learning.

--The computation demands from the maritime Internet of Things (MIoT) increase rapidly in recent years, and the unmanned aerial vehicles (UA Vs) and vessels based multi-access edge computing (MEC) can fulfill these MIoT requirements. In this paper, we focus on the maritime computation offloading and resource allocation through the cooperation of UA Vs and vessels, with consideration of uncertain tasks. Specifically, we propose a cooperative MEC framework for computation offloading and resource allocation, including MIoT devices, UA Vs and vessels. Then, we formulate the optimization problem to minimize the total execution time. As for the uncertain MIoT tasks, we leverage Lyapunov optimization to tackle the unpredictable task arrivals and varying computational resource availability. By converting the long-term constraints into short-term constraints, we obtain a set of small-scale optimization problems. Moreover, a heterogeneous-agent soft actor-critic is proposed to sequentially update various neural networks and effectively solve the MG problem. Finally, simulations are conducted to verify the effectiveness in addressing computational offloading and resource allocation. Then, the maritime Internet of Things (MIoT) employs sensors and wireless networks to collect, transmit, analyze data, and enhance the intelligence of maritime management. Jiahao Y ou, Chao Dong, and Qihui Wu are with the College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China (e-mail: yjiahao@nuaa.edu.cn, Ziye Jia is with the College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China, and also with the National Mobile Communications Research Laboratory, Southeast University, Nanjing, Jiangsu, 211111, China (e-mail: jiaziye@nuaa.edu.cn).

The pursuit of faster optimization algorithms remains an active and important research direction in deep learning. Recently, the Muon optimizer [JJB+24] has demonstrated promising empirical performance, but its theoretical foundation remains less understood. In this paper, we bridge this gap and provide a theoretical analysis of Muon by placing it within the Lion-$\mathcal{K}$ family of optimizers [CLLL24]. Specifically, we show that Muon corresponds to Lion-$\mathcal{K}$ when equipped with the nuclear norm, and we leverage the theoretical results of Lion-$\mathcal{K}$ to establish that Muon (with decoupled weight decay) implicitly solves an optimization problem that enforces a constraint on the spectral norm of weight matrices. This perspective not only demystifies the implicit regularization effects of Muon but also leads to natural generalizations through varying the choice of convex map $\mathcal{K}$, allowing for the exploration of a broader class of implicitly regularized and constrained optimization algorithms.

Recently, Large Language Models (LLMs) have rapidly evolved, approaching Artificial General Intelligence (AGI) while benefiting from large-scale reinforcement learning to enhance Human Alignment (HA) and Reasoning. Recent reward-based optimization algorithms, such as Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO) have achieved significant performance on reasoning tasks, whereas preference-based optimization algorithms such as Direct Preference Optimization (DPO) significantly improve the performance of LLMs on human alignment. However, despite the strong performance of reward-based optimization methods in alignment tasks , they remain vulnerable to reward hacking. Furthermore, preference-based algorithms (such as Online DPO) haven't yet matched the performance of reward-based optimization algorithms (like PPO) on reasoning tasks, making their exploration in this specific area still a worthwhile pursuit. Motivated by these challenges, we propose the Trust Region Preference Approximation (TRPA) algorithm, which integrates rule-based optimization with preference-based optimization for reasoning tasks. As a preference-based algorithm, TRPA naturally eliminates the reward hacking issue. TRPA constructs preference levels using predefined rules, forms corresponding preference pairs, and leverages a novel optimization algorithm for RL training with a theoretical monotonic improvement guarantee. Experimental results demonstrate that TRPA not only achieves competitive performance on reasoning tasks but also exhibits robust stability. The code of this paper are released and updating on https://github.com/XueruiSu/Trust-Region-Preference-Approximation.git.

--This work studies the problem of sparse signal recovery with automatic grouping of variables. T o this end, we investigate sorted nonsmooth penalties as a regularization approach for generalized linear models. These penalties are designed to promote clustering of variables due to their sorted nature, while the nonconvexity reduces the shrinkage of coefficients. Our goal is to provide efficient ways to compute their proximal operator, enabling the use of popular proximal algorithms to solve composite optimization problems with this choice of sorted penalties. We distinguish between two classes of problems: the weakly convex case where computing the proximal operator remains a convex problem, and the nonconvex case where computing the proximal operator becomes a challenging nonconvex combinatorial problem. We demonstrate the practical interest of using such penalties on several experiments. R is a data-fidelity term and the penalty Ψ is a regularization term that should embed some properties of the solution. Among them, sparsity and structure are particularly useful for a model as they improve its in-terpretability and decrease its complexity. Sparsity is most usually enforced through a penalty term favoring variable selection, i.e. solutions that use only a subset of features.

-- This paper presents a generalization of the trajectory general optimal sub-pattern assignment (GOSPA) metric for evaluating multi-object tracking algorithms that provide trajectory estimates with track-level uncertainties. This metric builds on the recently introduced probabilistic GOSPA metric to account for both the existence and state estimation uncertainties of individual object states. Similar to trajectory GOSPA (TGOSPA), it can be formulated as a multidimensional assignment problem, and its linear programming relaxation--also a valid metric--is computable in polynomial time. Additionally, this metric retains the interpretability of TGOSPA, and we show that its decomposition yields intuitive costs terms associated to expected localization error and existence probability mismatch error for properly detected objects, expected missed and false detection error, and track switch error . The effectiveness of the proposed metric is demonstrated through a simulation study.

-- Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot's geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics, collision avoidance, and manipulation planning) often treat these problems as constrained optimization, many existing solvers focus on specific problem domains or do not exploit geometric constraints effectively. We propose an efficient first-order method, Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG), which leverages geometric projections via Euclidean projections, Minkowski sums, and basis functions. We show that by using geometric constraints rather than full constraints and gradients, ALSPG significantly improves real-time performance. Compared to second-order methods like iLQR, ALSPG remains competitive in the unconstrained case. We validate our method through toy examples and extensive simulations, and demonstrate its effectiveness on a 7-axis Franka robot, a 6-axis P-Rob robot and a 1:10 scale car in real-world experiments. Source codes, experimental data and videos are available on the project webpage: https://sites.google.com/view/alspg-oc

We present a complementarity-based collision resolution algorithm for smooth, non-spherical, rigid bodies. Unlike discrete surface representation approaches, which approximate surfaces using discrete elements (e.g., tessellations or sub-spheres) with constraints between nearby faces, edges, nodes, or sub-objects, our algorithm solves a recursively generated linear complementarity problem (ReLCP) to adaptively identify potential collision locations during the collision resolution procedure. Despite adaptively and in contrast to Newton-esque schemes, we prove conditions under which the resulting solution exists and the center of mass translational and rotational dynamics are unique. Because increasing the surface resolution in discrete representation methods necessitates subdividing geometry into finer elements--leading to a super-linear increase in the number of collision constraints--these approaches scale poorly with increased surface resolution. In contrast, our adaptive ReLCP framework begins with a single constraint per pair of nearby bodies and introduces new constraints only when unconstrained motion would lead to overlap, circumventing the oversampling required by discrete methods. By requiring one to two orders of magnitude fewer collision constraints to achieve the same surface resolution, we observe 10-100x speedup in densely packed applications. We validate our ReLCP method against multisphere and single-constraint methods, comparing convergence in a two-ellipsoid collision test, scalability and performance in a compacting ellipsoid suspension and growing bacterial colony, and stability in a taut chainmail network, highlighting our ability to achieve high-fidelity surface representations without su ff ering from poor scalability or artificial surface roughness. Keywords: Rigid body dynamics, Nonsmooth dynamics, Linear complementarity problem, Collision resolution, ReLCP 1. Introduction The simulation of collision and contact dynamics in rigid and flexible body systems has a rich and extensive history in scientific computing, engineering, and computer graphics. Methods for managing frictional contact and resolving collisions can be broadly categorized into three types: piecewise-smooth, smooth (penalty-based), and nonsmooth (complementarity-based) methods. Piecewise-smooth approaches focus on identifying the precise times and locations of collision events, applying instantaneous impulses to uphold the conservation of momentum. While these methods are conceptually straightforward and lend themselves well to analytical treatment, they are rarely employed in large-scale simulations.

The classical Job Shop Scheduling Problem (JSSP) focuses on optimizing makespan under deterministic constraints. Real-world production environments introduce additional complexities that cause traditional scheduling approaches to be less effective. Reinforcement learning (RL) holds potential in addressing these challenges, as it allows agents to learn adaptive scheduling strategies. However, there is a lack of a comprehensive, general-purpose frameworks for effectively training and evaluating RL agents under real-world constraints. To address this gap, we propose a modular framework that extends classical JSSP formulations by incorporating key real-world constraints inherent to the shopfloor, including transport logistics, buffer management, machine breakdowns, setup times, and stochastic processing conditions, while also supporting multi-objective optimization. The framework is a customizable solution that offers flexibility in defining problem instances and configuring simulation parameters, enabling adaptation to diverse production scenarios. A standardized interface ensures compatibility with various RL approaches, providing a robust environment for training RL agents and facilitating the standardized comparison of different scheduling methods under dynamic and uncertain conditions. We release JobShopLab as an open-source tool for both research and industrial applications, accessible at: https://github.com/proto-lab-ro/jobshoplab