Autoregressive pre-trained models combined with decoding methods have achieved impressive performance on complex reasoning tasks. While mainstream decoding strategies such as beam search can generate plausible candidate sets, they often lack provable coverage guarantees, and struggle to effectively balance search efficiency with the need for versatile trajectories, particularly those involving long-tail sequences that are essential in certain real-world applications. To address these limitations, we propose \textsc{CoVeR}, a novel model-free decoding strategy wihtin the conformal prediction framework that simultaneously maintains a compact search space and ensures high coverage probability over desirable trajectories. Theoretically, we establish a PAC-style generalization bound, guaranteeing that \textsc{CoVeR} asymptotically achieves a coverage rate of at least $1 - α$ for any target level $α\in (0,1)$.

Digital maps play a crucial role in various applications such as navigation, fleet management, and ride-sharing, necessitating their accuracy and currency, which require timely updates. While the majority of geospatial databases (GDBs) provide high-quality information, their data is (i) limited to specific regions and/or (ii) missing some entities, even in their covered areas. Map conflation is the process of augmentation of a GDB using another GDB to conflate missing spatial features. Existing map conflation methods suffer from two main limitations: (1) They are designed for the conflation of linear objects (e.g., road networks) and cannot simply be extended to non-linear objects, thus missing information about most entities in the map. (2) They are heuristic algorithmic approaches that are based on pre-defined rules, unable to learn entities matching in a data-driven manner. To address these limitations, we design KRAFT, a learning based approach consisting of three parts: (1) Knowledge Graph Construction - where each GDB is represented by a knowledge graph, (2) Map Matching - where we use a knowledge graph alignment method as well as a geospatial feature encoder to match entities in obtained knowledge graphs, and (3) Map Merging - where we merge matched entities in the previous modules in a consistent manner, using a mixed integer linear programming formulation that fully merges the GDBs without adding any inconsistencies. Our experimental evaluation shows that not only does KRAFT achieve outstanding performance compared to state-of-the-art and baseline methods in map conflation tasks, but each of its modules (e.g., Map Matching and Map Merging) also separately outperforms traditional matching and merging methods.

Differential privacy (DP) is the standard for privacy-preserving analysis, and introduces a fundamental trade-off between privacy guarantees and model performance. Selecting the optimal balance is a critical challenge that can be framed as a multi-objective optimization (MOO) problem where one first discovers the set of optimal trade-offs (the Pareto front) and then learns a decision-maker's preference over them. While a rich body of work on interactive MOO exists, the standard approach -- modeling the objective functions with generic surrogates and learning preferences from simple pairwise feedback -- is inefficient for DP because it fails to leverage the problem's unique structure: a point on the Pareto front can be generated directly by maximizing accuracy for a fixed privacy level. Motivated by this property, we first derive the shape of the trade-off theoretically, which allows us to model the Pareto front directly and efficiently. To address inefficiency in preference learning, we replace pairwise comparisons with a more informative interaction. In particular, we present the user with hypothetical trade-off curves and ask them to pick their preferred trade-off. Our experiments on differentially private logistic regression and deep transfer learning across six real-world datasets show that our method converges to the optimal privacy-accuracy trade-off with significantly less computational cost and user interaction than baselines.

-- Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to synthesize provably safe controllers that handle multiple state constraints. This paper presents a framework for constrained control of nonlinear systems subject to box constraints on the systems' vector-valued outputs using multiple CBFs. Our results illustrate that when the output has a vector relative degree, the CBF constraints encoding these box constraints are compatible, and the resulting optimization-based controller is locally Lipschitz continuous and admits a closed-form expression. Additional results are presented to characterize the degradation of nominal tracking objectives in the presence of safety constraints. Simulations of a planar quadrotor are presented to demonstrate the efficacy of the proposed framework.

The assignment problem, a cornerstone of operations research, seeks an optimal one-to-one mapping between agents and tasks to minimize total cost. This work traces its evolution from classical formulations and algorithms to modern optimal transport (OT) theory, positioning the Quadratic Assignment Problem (QAP) and related structural matching tasks within this framework. We connect the linear assignment problem to Monge's transport problem, Kantorovich's relaxation, and Wasserstein distances, then extend to cases where source and target lie in different metric-measure spaces requiring Gromov-Wasserstein (GW) distances. GW formulations, including the fused GW variant that integrates structural and feature information, naturally address QAP-like problems by optimizing alignment based on both intra-domain distances and cross-domain attributes. Applications include graph matching, keypoint correspondence, and feature-based assignments. We present exact solvers, Genetic Algorithms (GA), and multiple GW variants, including a proposed multi-initialization strategy (GW-MultiInit) that mitigates the risk of getting stuck in local optima alongside entropic Sinkhorn-based approximations and fused GW. Computational experiments on capacitated QAP instances show that GW-MultiInit consistently achieves near-optimal solutions and scales efficiently to large problems where exact methods become impractical, while parameterized EGW and FGW variants provide flexible trade-offs between accuracy and runtime. Our findings provide theoretical foundations, computational insights, and practical guidelines for applying OT and GW methods to QAP and other real-world matching problems, such as those in machine learning and logistics.

Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs generally involves addressing a complex robust optimization problem, which can be intractable. Scenario-based methods have been proposed to simplify this computation. Then, one needs to verify if the CBF actually satisfies the robust constraints. We present an approach to perform this verification that relies on Lipschitz arguments, and forms the basis of a certification algorithm designed for sample efficiency. Through a numerical example, we validated the efficiency of the proposed procedure.

Community detection is one of the fundamental problems in data science which consists of partitioning nodes into disjoint communities. We present a game-theoretic perspective on the Constant Potts Model (CPM) for partitioning networks into disjoint communities, emphasizing its efficiency, robustness, and accuracy. Efficiency: We reinterpret CPM as a potential hedonic game by decomposing its global Hamiltonian into local utility functions, where the local utility gain of each agent matches the corresponding increase in global utility. Leveraging this equivalence, we prove that local optimization of the CPM objective via better-response dynamics converges in pseudo-polynomial time to an equilibrium partition. Robustness: We introduce and relate two stability criteria: a strict criterion based on a novel notion of robustness, requiring nodes to simultaneously maximize neighbors and minimize non-neighbors within communities, and a relaxed utility function based on a weighted sum of these objectives, controlled by a resolution parameter. Accuracy: In community tracking scenarios, where initial partitions are used to bootstrap the Leiden algorithm with partial ground-truth information, our experiments reveal that robust partitions yield higher accuracy in recovering ground-truth communities.

Department of Physics, Arizona State University, Tempe, Arizona 85287, USA (Dated: September 5, 2025) Finding the governing equations from data by sparse optimization has become a popular approach to deterministic modeling of dynamical systems. Considering the physical situations where the data can be imperfect due to disturbances and measurement errors, we show that for many chaotic systems, widely used sparse-optimization methods for discovering governing equations produce models that depend sensitively on the measurement procedure, yet all such models generate virtually identical chaotic attractors, leading to a striking limitation that challenges the conventional notion of equation-based modeling in complex dynamical systems. Calculating the Koopman spectra, we find that the different sets of equations agree in their large eigenvalues and the differences begin to appear when the eigenvalues are smaller than an equation-dependent threshold. The results suggest that finding the governing equations of the system and attempting to interpret them physically may lead to misleading conclusions. It would be more useful to work directly with the available data using, e.g., machine-learning methods. In physical science, a methodology of biblical importance is developing a quantitative model by extracting a set of governing equations from experimental data.

--Federated learning (FL) effectively promotes collaborative training among distributed clients with privacy considerations in the Internet of Things (IoT) scenarios. Despite of data heterogeneity, FL clients may also be constrained by limited energy and availability budgets. Therefore, effective selection of clients participating in training is of vital importance for the convergence of the global model and the balance of client contributions. In this paper, we discuss the performance impact of client availability with time-series data on federated learning. We set up three different scenarios that affect the availability of time-series data and propose FedDeCAB, a novel, semi-decentralized client selection method applying probabilistic rankings of available clients. When a client is disconnected from the server, FedDeCAB allows obtaining partial model parameters from the nearest neighbor clients for joint optimization, improving the performance of offline models and reducing communication overhead. Experiments based on real-world large-scale taxi and vessel trajectory datasets show that FedDeCAB is effective under highly heterogeneous data distribution, limited communication budget, and dynamic client offline or rejoining. Traditional machine learning (ML) requires the central server to gather data from various node devices for model training. However, the access to personal data from edge devices is usually subject to privacy restrictions and the large scale of local data in common edge computing environments or scenarios with a large number of Internet of Things (IoT) devices.

In the context of continuously rising global air traffic, efficient and safe Conflict Detection and Resolution (CD&R) is paramount for air traffic management. Although Deep Reinforcement Learning (DRL) offers a promising pathway for CD&R automation, existing approaches commonly suffer from a "unimodal bias" in their policies. This leads to a critical lack of decision-making flexibility when confronted with complex and dynamic constraints, often resulting in "decision deadlocks." To overcome this limitation, this paper pioneers the integration of diffusion probabilistic models into the safety-critical task of CD&R, proposing a novel autonomous conflict resolution framework named Diffusion-AC. Diverging from conventional methods that converge to a single optimal solution, our framework models its policy as a reverse denoising process guided by a value function, enabling it to generate a rich, high-quality, and multimodal action distribution. This core architecture is complemented by a Density-Progressive Safety Curriculum (DPSC), a training mechanism that ensures stable and efficient learning as the agent progresses from sparse to high-density traffic environments. Extensive simulation experiments demonstrate that the proposed method significantly outperforms a suite of state-of-the-art DRL benchmarks. Most critically, in the most challenging high-density scenarios, Diffusion-AC not only maintains a high success rate of 94.1% but also reduces the incidence of Near Mid-Air Collisions (NMACs) by approximately 59% compared to the next-best-performing baseline, significantly enhancing the system's safety margin. This performance leap stems from its unique multimodal decision-making capability, which allows the agent to flexibly switch to effective alternative maneuvers.