Multisource data has spurred the development of advanced clustering algorithms, such as multi-view clustering, which critically relies on constructing similarity matrices. Traditional algorithms typically generate these matrices from sample attributes alone. However, real-world networks often include pairwise directed topological structures critical for clustering. This paper introduces a novel multi-view clustering algorithm, AAS. It utilizes a two-step proximity approach via anchors in each view, integrating attribute and directed structural information. This approach enhances the clarity of category characteristics in the similarity matrices. The anchor structural similarity matrix leverages strongly connected components of directed graphs. The entire process-from similarity matrices construction to clustering - is consolidated into a unified optimization framework. Comparative experiments on the modified Attribute SBM dataset against eight algorithms affirm the effectiveness and superiority of AAS.

Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous mathematical framework for analyzing the behaviors of neural operators, with a focus on their stability, convergence, clustering dynamics, universality, and generalization error. By proposing a list of novel theorems, we provide stability bounds in Sobolev spaces and demonstrate clustering in function space via gradient flow interpretation, guiding neural operator design and optimization. Based on these theoretical gurantees, we aim to offer clear and unified guidance in a single setting for the future design of neural operator-based methods.

Global Trajectory Optimization Competitions (GTOC) [1] represent a biennial cornerstone event within the international aerospace community, dedicated to addressing the intricacies of interplanetary trajectory optimization. The 12th edition of this well established competition, held in June-July 2023, proposed a challenging design of a "sustainable asteroid mining" mission. The problem demanded the concurrent extraction of resources from a set A of 60,000 target asteroids, to be accomplished during a fixed 15 years wide window (from 2035-Jan-01 to 2050-Jan-01) by multiple spacecraft. The participating spacecraft, dispatched from Earth and possibly flying by Venus and Mars, had to be meticulously designed to maximize the quantity of mined material returned to our home planet. A comprehensive exposition of the mathematical intricacies underpinning the problem definition can be found in [2], while in this paper we will primarily provide essential definitions and selectively reference these mathematical foundations. For the purpose of clarity, we shall employ the term'ship' interchangeably with'spacecraft.' In the context of the multi-spacecraft asteroid mining mission presented in GTOC12, each ship possesses the capability to deploy a specified number of mining devices onto the asteroids' surface. Furthermore, these ships have the capacity to collect mined resources if a mining device is already in place on the visited asteroid. Importantly, each ship is not confined to gathering material exclusively from asteroids where it initially deposited a miner; it can collect resources from asteroids where miners were deployed by other ships.

Low-Earth orbit (LEO) satellites utilizing beam hopping (BH) technology offer extensive coverage, low latency, high bandwidth, and significant flexibility. However, the uneven geographical distribution and temporal variability of ground traffic demands, combined with the high mobility of LEO satellites, present significant challenges for efficient beam resource utilization. Traditional BH methods based on GEO satellites fail to address issues such as satellite interference, overlapping coverage, and mobility. This paper explores a Digital Twin (DT)-based collaborative resource allocation network for multiple LEO satellites with overlapping coverage areas. A two-tier optimization problem, focusing on load balancing and cell service fairness, is proposed to maximize throughput and minimize inter-cell service delay. The DT layer optimizes the allocation of overlapping coverage cells by designing BH patterns for each satellite, while the LEO layer optimizes power allocation for each selected service cell. At the DT layer, an Actor-Critic network is deployed on each agent, with a global critic network in the cloud center. The A3C algorithm is employed to optimize the DT layer. Concurrently, the LEO layer optimization is performed using a Multi-Agent Reinforcement Learning algorithm, where each beam functions as an independent agent. The simulation results show that this method reduces satellite load disparity by about 72.5% and decreases the average delay to 12ms. Additionally, our approach outperforms other benchmarks in terms of throughput, ensuring a better alignment between offered and requested data.

We consider Bayesian algorithm execution (BAX), a framework for efficiently selecting evaluation points of an expensive function to infer a property of interest encoded as the output of a base algorithm. Since the base algorithm typically requires more evaluations than are feasible, it cannot be directly applied. Instead, BAX methods sequentially select evaluation points using a probabilistic numerical approach. Current BAX methods use expected information gain to guide this selection. However, this approach is computationally intensive. Observing that, in many tasks, the property of interest corresponds to a target set of points defined by the function, we introduce PS-BAX, a simple, effective, and scalable BAX method based on posterior sampling. PS-BAX is applicable to a wide range of problems, including many optimization variants and level set estimation. Experiments across diverse tasks demonstrate that PS-BAX performs competitively with existing baselines while being significantly faster, simpler to implement, and easily parallelizable, setting a strong baseline for future research. Additionally, we establish conditions under which PS-BAX is asymptotically convergent, offering new insights into posterior sampling as an algorithm design paradigm.

We consider a class of learning problem of point estimation for modeling high-dimensional nonlinear functions, whose learning dynamics is guided by model training dataset, while the estimated parameter in due course provides an acceptable prediction accuracy on a different model validation dataset. Here, we establish an evidential connection between such a learning problem and a hierarchical optimal control problem that provides a framework how to account appropriately for both generalization and regularization at the optimization stage. In particular, we consider the following two objectives: (i) The first one is a controllability-type problem, i.e., generalization, which consists of guaranteeing the estimated parameter to reach a certain target set at some fixed final time, where such a target set is associated with model validation dataset. (ii) The second one is a regularization-type problem ensuring the estimated parameter trajectory to satisfy some regularization property over a certain finite time interval. First, we partition the control into two control strategies that are compatible with two abstract agents, namely, a leader, which is responsible for the controllability-type problem and that of a follower, which is associated with the regularization-type problem. Using the notion of Stackelberg's optimization, we provide conditions on the existence of admissible optimal controls for such a hierarchical optimal control problem under which the follower is required to respond optimally to the strategy of the leader, so as to achieve the overall objectives that ultimately leading to an optimal parameter estimate. Moreover, we provide a nested algorithm, arranged in a hierarchical structure-based on successive approximation methods, for solving the corresponding optimal control problem. Finally, we present some numerical results for a typical nonlinear regression problem.

Low-rank adaption (LoRA) is a widely used parameter-efficient finetuning method for LLM that reduces memory requirements. However, current LoRA optimizers lack transformation invariance, meaning the actual updates to the weights depends on how the two LoRA factors are scaled or rotated. This deficiency leads to inefficient learning and sub-optimal solutions in practice. This paper introduces LoRA-RITE, a novel adaptive matrix preconditioning method for LoRA optimization, which can achieve transformation invariance and remain computationally efficient. We provide theoretical analysis to demonstrate the benefit of our method and conduct experiments on various LLM tasks with different models including Gemma 2B, 7B, and mT5-XXL. The results demonstrate consistent improvements against existing optimizers. For example, replacing Adam with LoRA-RITE during LoRA fine-tuning of Gemma-2B yielded 4.6\% accuracy gain on Super-Natural Instructions and 3.5\% accuracy gain across other four LLM benchmarks (HellaSwag, ArcChallenge, GSM8K, OpenBookQA).

Abstract-- In this paper, we develop an uncertainty-aware decision-making and motion-planning method for an autonomous ego vehicle in forced merging scenarios, considering the motion uncertainty of surrounding vehicles. The forced merging scenario on the highway. Following the decision and the SVs' occupancy, the reference trajectory for the EV is calculated I. However, the motion uncertainties of dynamic obstacles The method is aware of the environmental uncertainties using introduce challenges to the safety in motion-planning online estimation of the acceleration bounds of the SVs, such problems. Among various uncertain scenarios, forced merging that it dynamically captures the uncertainties of SVs without on highways presents notable difficulties, as it demands inferring their intentions.

Distributed Machine Learning (DML) on resource-constrained edge devices holds immense potential for real-world applications. However, achieving fast convergence in DML in these heterogeneous environments remains a significant challenge. Traditional frameworks like Bulk Synchronous Parallel and Asynchronous Stochastic Parallel rely on frequent, small updates that incur substantial communication overhead and hinder convergence speed. Furthermore, these frameworks often employ static dataset sizes, neglecting the heterogeneity of edge devices and potentially leading to straggler nodes that slow down the entire training process. The straggler nodes, i.e., edge devices that take significantly longer to process their assigned data chunk, hinder the overall training speed. To address these limitations, this paper proposes Hermes, a novel probabilistic framework for efficient DML on edge devices. This framework leverages a dynamic threshold based on recent test loss behavior to identify statistically significant improvements in the model's generalization capability, hence transmitting updates only when major improvements are detected, thereby significantly reducing communication overhead. Additionally, Hermes employs dynamic dataset allocation to optimize resource utilization and prevents performance degradation caused by straggler nodes. Our evaluations on a real-world heterogeneous resource-constrained environment demonstrate that Hermes achieves faster convergence compared to state-of-the-art methods, resulting in a remarkable $13.22$x reduction in training time and a $62.1\%$ decrease in communication overhead.

Optimal path planning often suffers from getting stuck in a local optimum. This is often the case for mobile manipulators due to nonconvexities induced by obstacles and robot kinematics. This paper attempts to circumvent this issue by proposing a pipeline to obtain multiple distinct local optima. By evaluating and selecting the optimum among multiple distinct local optima, it is likely to obtain a closer approximation of the global optimum. We demonstrate this capability in optimal path planning of nonholonomic mobile manipulators in the presence of obstacles and subject to end effector path constraints. The nonholomicity, obstacles, and end effector path constraints often cause direct optimal path planning approaches to get stuck in local optima. We demonstrate that our pipeline is able to circumvent this issue and produce a final local optimum that is close to the global optimum.