Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a relationship between the observed and unobserved entries of the tensor. The low-rank tensor completion problem is typically solved using numerical optimization techniques, where the rank information is used either implicitly (in the rank minimization approach) or explicitly (in the error minimization approach). Current theories concerning these techniques often study probabilistic recovery guarantees under conditions such as random uniform observations and incoherence requirements. However, if an observation pattern exhibits some low-rank structure that can be exploited, more efficient algorithms with deterministic recovery guarantees can be designed by leveraging this structure. This work shows how to use only standard linear algebra operations to compute the tensor train decomposition of a specific type of ``fiber-wise" observed tensor, where some of the fibers of a tensor (along a single specific mode) are either fully observed or entirely missing, unlike the usual entry-wise observations. From an application viewpoint, this setting is relevant when it is easier to sample or collect a multiway data tensor along a specific mode (e.g., temporal). The proposed completion method is fast and is guaranteed to work under reasonable deterministic conditions on the observation pattern. Through numerical experiments, we showcase interesting applications and use cases that illustrate the effectiveness of the proposed approach.

Multi-agent systems (MAS) have emerged as a powerful paradigm for orchestrating large language models (LLMs) and specialized tools to collaboratively address complex tasks. However, existing MAS frameworks often require manual workflow configuration and lack native support for dynamic evolution and performance optimization. In addition, many MAS optimization algorithms are not integrated into a unified framework. In this paper, we present EvoAgentX, an open-source platform that automates the generation, execution, and evolutionary optimization of multi-agent workflows. EvoAgentX employs a modular architecture consisting of five core layers: the basic components, agent, workflow, evolving, and evaluation layers. Specifically, within the evolving layer, EvoAgentX integrates three MAS optimization algorithms, TextGrad, AFlow, and MIPRO, to iteratively refine agent prompts, tool configurations, and workflow topologies. We evaluate EvoAgentX on HotPotQA, MBPP, and MATH for multi-hop reasoning, code generation, and mathematical problem solving, respectively, and further assess it on real-world tasks using GAIA. Experimental results show that EvoAgentX consistently achieves significant performance improvements, including a 7.44% increase in HotPotQA F1, a 10.00% improvement in MBPP pass@1, a 10.00% gain in MATH solve accuracy, and an overall accuracy improvement of up to 20.00% on GAIA. The source code is available at: https://github.com/EvoAgentX/EvoAgentX

Robotic manipulation in dynamic environments often requires seamless transitions between different grasp types to maintain stability and efficiency. However, achieving smooth and adaptive grasp transitions remains a challenge, particularly when dealing with external forces and complex motion constraints. Existing grasp transition strategies often fail to account for varying external forces and do not optimize motion performance effectively. In this work, we propose an Imitation-Guided Bimanual Planning Framework that integrates efficient grasp transition strategies and motion performance optimization to enhance stability and dexterity in robotic manipulation. Our approach introduces Strategies for Sampling Stable Intersections in Grasp Manifolds for seamless transitions between uni-manual and bi-manual grasps, reducing computational costs and regrasping inefficiencies. Additionally, a Hierarchical Dual-Stage Motion Architecture combines an Imitation Learning-based Global Path Generator with a Quadratic Programming-driven Local Planner to ensure real-time motion feasibility, obstacle avoidance, and superior manipulability. The proposed method is evaluated through a series of force-intensive tasks, demonstrating significant improvements in grasp transition efficiency and motion performance. A video demonstrating our simulation results can be viewed at \href{https://youtu.be/3DhbUsv4eDo}{\textcolor{blue}{https://youtu.be/3DhbUsv4eDo}}.

Abstract--The Minimum Bisection Problem is a well-known NP-hard problem in combinatorial optimization, with practical applications in areas such as parallel computing, network design, and machine learning. In this paper, we examine the potential of using D-Wave Systems' quantum annealing solvers to solve the Minimum Bisection Problem, which we formulate as a Quadratic Unconstrained Binary Optimization model. A key challenge in this formulation lies in choosing an appropriate penalty parameter, as it plays a crucial role in ensuring both the quality of the solution and the satisfaction of the problem's constraints. T o address this, we introduce a novel machine learning-based approach for adaptive tuning of the penalty parameter . Specifically, we use a Gradient Boosting Regressor model trained to predict suitable penalty parameter values based on structural properties of the input graph, the number of nodes and the graph's density. This method enables the penalty parameter to be adjusted dynamically for each specific problem instance, improving the solver's ability to balance the competing goals of minimizing the cut size and maintaining equally sized partitions. We test our approach on a large dataset of randomly generated Erd os-R enyi graphs with up to 4000 nodes, and we compare the results with classical partitioning algorithms, Metis and Kernighan-Lin. Experimental findings demonstrate that our adaptive tuning strategy significantly improves the performance of quantum annealing hybrid solver and consistently outperforms the classical methods used, indicating its potential as an alternative for graph partitioning problem. RAPH partitioning is a fundamental problem in combinatorial optimization with applications in task scheduling for multiprocessor computers with focus on parallel computation, partitioning the circuit with applications in microchips design, social network analysis e.g. The problem involves dividing a given graph G into two or more subsets while optimizing certain objective, such as minimizing the number of inter-edges and/or assigned costs between them and producing balanced partitions. While general Graph Partitioning Problem (GPP) allow for flexible partition sizes, a significant special case is the Minimum Bisection Problem (MBP), where the graph is partitioned into two equal-sized subsets while minimizing the number of inter-edges [1].

Object shape and pose estimation is a foundational robotics problem, supporting tasks from manipulation to scene understanding and navigation. We present a fast local solver for shape and pose estimation which requires only category-level object priors and admits an efficient certificate of global optimality. Given an RGB-D image of an object, we use a learned front-end to detect sparse, category-level semantic keypoints on the target object. We represent the target object's unknown shape using a linear active shape model and pose a maximum a posteriori optimization problem to solve for position, orientation, and shape simultaneously. Expressed in unit quaternions, this problem admits first-order optimality conditions in the form of an eigenvalue problem with eigenvector nonlinearities. Our primary contribution is to solve this problem efficiently with self-consistent field iteration, which only requires computing a 4-by-4 matrix and finding its minimum eigenvalue-vector pair at each iterate. Solving a linear system for the corresponding Lagrange multipliers gives a simple global optimality certificate. One iteration of our solver runs in about 100 microseconds, enabling fast outlier rejection. We test our method on synthetic data and a variety of real-world settings, including two public datasets and a drone tracking scenario. Code is released at https://github.com/MIT-SPARK/Fast-ShapeAndPose.

Vision-Language-Action (VLA) models have emerged as promising solutions for robotic manipulation, yet their robustness to real-world physical variations remains critically underexplored. To bridge this gap, we propose Eva-VLA, the first unified framework that systematically evaluates the robustness of VLA models by transforming discrete physical variations into continuous optimization problems. However, comprehensively assessing VLA robustness presents two key challenges: (1) how to systematically characterize diverse physical variations encountered in real-world deployments while maintaining evaluation reproducibility, and (2) how to discover worst-case scenarios without prohibitive real-world data collection costs efficiently. To address the first challenge, we decompose real-world variations into three critical domains: object 3D transformations that affect spatial reasoning, illumination variations that challenge visual perception, and adversarial patches that disrupt scene understanding. For the second challenge, we introduce a continuous black-box optimization framework that transforms discrete physical variations into parameter optimization, enabling systematic exploration of worst-case scenarios. Extensive experiments on state-of-the-art OpenVLA models across multiple benchmarks reveal alarming vulnerabilities: all variation types trigger failure rates exceeding 60%, with object transformations causing up to 97.8% failure in long-horizon tasks. Our findings expose critical gaps between controlled laboratory success and unpredictable deployment readiness, while the Eva-VLA framework provides a practical pathway for hardening VLA-based robotic manipulation models against real-world deployment challenges.

The well-known graph-based clustering methods, including spectral clustering, symmetric non-negative matrix factorization, and doubly stochastic normalization, can be viewed as relaxations of the kernel $k$-means approach. However, we posit that these methods excessively relax their inherent low-rank, nonnegative, doubly stochastic, and orthonormal constraints to ensure numerical feasibility, potentially limiting their clustering efficacy. In this paper, guided by our theoretical analyses, we propose \textbf{Lo}w-\textbf{R}ank \textbf{D}oubly stochastic clustering (\textbf{LoRD}), a model that only relaxes the orthonormal constraint to derive a probabilistic clustering results. Furthermore, we theoretically establish the equivalence between orthogonality and block diagonality under the doubly stochastic constraint. By integrating \textbf{B}lock diagonal regularization into LoRD, expressed as the maximization of the Frobenius norm, we propose \textbf{B-LoRD}, which further enhances the clustering performance. To ensure numerical solvability, we transform the non-convex doubly stochastic constraint into a linear convex constraint through the introduction of a class probability parameter. We further theoretically demonstrate the gradient Lipschitz continuity of our LoRD and B-LoRD enables the proposal of a globally convergent projected gradient descent algorithm for their optimization. Extensive experiments validate the effectiveness of our approaches. The code is publicly available at https://github.com/lwl-learning/LoRD.

We study nonstationary newsvendor problems under nonparametric demand models and general distributional measures of nonstationarity, addressing the practical challenges of unknown degree of nonstationarity and demand censoring. We propose a novel distributional-detection-and-restart framework for learning in nonstationary environments, and instantiate it through two efficient algorithms for the uncensored and censored demand settings. The algorithms are fully adaptive, requiring no prior knowledge of the degree and type of nonstationarity, and offer a flexible yet powerful approach to handling both abrupt and gradual changes in nonstationary environments. We establish a comprehensive optimality theory for our algorithms by deriving matching regret upper and lower bounds under both general and refined structural conditions with nontrivial proof techniques that are of independent interest. Numerical experiments using real-world datasets, including nurse staffing data for emergency departments and COVID-19 test demand data, showcase the algorithms' superior and robust empirical performance. While motivated by the newsvendor problem, the distributional-detection-and-restart framework applies broadly to a wide class of nonstationary stochastic optimization problems. Managerially, our framework provides a practical, easy-to-deploy, and theoretically grounded solution for decision-making under nonstationarity.

Abstract--Formation maintenance with varying number of drones in narrow environments hinders the convergence of planning to the desired configurations. T o address this challenge, this paper proposes a formation planning method guided by De-formable Virtual Structures (DVS) with continuous spatiotemporal transformation. Firstly, to satisfy swarm safety distance and preserve formation shape filling integrity for irregular formation geometries, we employ Lloyd algorithm for uniform PA rtitioning and Hungarian algorithm for AS signment (PAAS) in DVS. Subsequently, a spatiotemporal trajectory involving DVS is planned using primitive-based path search and nonlinear trajectory optimization. The DVS trajectory achieves adaptive transitions with respect to a varying number of drones while ensuring adaptability to narrow environments through affine transformation. Finally, each agent conducts distributed trajectory planning guided by desired spatiotemporal positions within the DVS, while incorporating collision avoidance and dynamic feasibility requirements. Our method enables up to 15% of swarm numbers to join or leave in cluttered environments while rapidly restoring the desired formation shape in simulation. Compared to cutting-edge formation planning method, we demonstrate rapid formation recovery capacity and environmental adaptability. In recent years, formation flight becomes the foundation requirement for aerial swarms in practical applications, such as collaborative exploration [1], light show [2], search and rescue [3]. For large-scale swarms [4], [5], formation inevitably encounters agent loss in narrow environments [6]- [8].