arXiv subjects

Tianyu Wang

Publications and source records attributed to Tianyu Wang.

At least 109 records · Page 6Linked to original sources

arXiv2025

rDSM -- A robust Downhill Simplex Method software package for optimization problems in high dimensions

The Downhill Simplex Method (DSM) is a fast-converging derivative-free optimization technique for nonlinear systems. However, the optimization process is often subject to premature convergence due to degenerated simplices or noise-induced spurious minima. This study introduces a software package for the robust Downhill Simplex Method (rDSM), which incorporates two key enhancements. First, simplex degeneracy is detected and corrected by volume maximization under constraints. Second, the real objective value of noisy problems is estimated by reevaluating the long-standing points. Thus, rDSM improves the convergence of DSM, and may increase the applicability of DSM to higher dimensions, even in the presence of noise. The rDSM software package thus provides a robust and efficient solution for both analytical and experimental optimization scenarios. This methodological advancement extends the applicability of simplex-based optimization to complex experimental systems where gradient information remains inaccessible and measurement noise proves non-negligible.

math.OC↗

arXiv2025

Zeroth-order Stochastic Cubic Newton Method Revisited

This paper studies stochastic minimization of a finite-sum loss $ F (\mathbf{x}) = \frac{1}{N} \sum_{ξ=1}^N f(\mathbf{x};ξ) $. In many real-world scenarios, the Hessian matrix of such objectives exhibits a low-rank structure on a batch of data. At the same time, zeroth-order optimization has gained prominence in important applications such as fine-tuning large language models. Drawing on these observations, we propose a novel stochastic zeroth-order cubic Newton method that leverages the low-rank Hessian structure via a matrix recovery-based estimation technique. Our method circumvents restrictive incoherence assumptions, enabling accurate Hessian approximation through finite-difference queries. Theoretically, we establish that for most real-world problems in $\mathbb{R}^n$, $\mathcal{O}\left(\frac{n}{η^{\frac{7}{2}}}\right)+\widetilde{\mathcal{O}}\left(\frac{n^2 }{η^{\frac{5}{2}}}\right)$ function evaluations suffice to attain a second-order $η$-stationary point with high probability. This represents a significant improvement in dimensional dependence over existing methods. This improvement is mostly due to a new Hessian estimator that achieves superior sample complexity; This new Hessian estimation method might be of separate interest. Numerical experiments on matrix recovery and machine learning tasks validate the efficacy and scalability of our approach.

math.OC↗

arXiv2025

Super-resolution femtosecond electron diffraction reveals electronic and nuclear dynamics at conical intersections

Conical intersections play a pivotal role in excited-state quantum dynamics. Capturing transient molecular structures near conical intersections remains challenging due to the rapid timescales and subtle structural changes involved. We overcome this by combining the enhanced temporal resolution of mega-electron-volt ultrafast electron diffraction with a super-resolution real-space inversion algorithm, enabling visualization of nuclear and electronic motions at conical intersections with sub-angstrom resolution, surpassing the diffraction limit. We apply this technique to the textbook example of the ring-opening reaction of 1,3-cyclohexadiene, which proceeds through two conical intersections within 100 femtoseconds. The super-resolved transient structures near conical intersections reveal a C-C bond length difference of less than 0.4 angstrom and an approximately 30-femtosecond traversal time of the nuclear wave packet between them. These findings establish super-resolution ultrafast scattering as a transformative tool for uncovering quantum dynamics in molecules and open new avenues for studying light-matter interactions at the most fundamental level.

physics.chem-ph↗

arXiv2025

LLM Web Dynamics: Tracing Model Collapse in a Network of LLMs

The increasing use of synthetic data from the public Internet has enhanced data usage efficiency in large language model (LLM) training. However, the potential threat of model collapse remains insufficiently explored. Existing studies primarily examine model collapse in a single model setting or rely solely on statistical surrogates. In this work, we introduce LLM Web Dynamics (LWD), an efficient framework for investigating model collapse at the network level. By simulating the Internet with a retrieval-augmented generation (RAG) database, we analyze the convergence pattern of model outputs. Furthermore, we provide theoretical guarantees for this convergence by drawing an analogy to interacting Gaussian Mixture Models.

cs.LG↗

arXiv2025

Aubry-André Localization Transition for an Active Undulator

The transport of deformable self-propelling objects like bacteria, worms, snakes, and robots through heterogeneous environments is poorly understood. In this paper, we use experiment, simulation, and theory to study a snake-like robot as it undulates without sensory feedback through a narrow channel containing a linear array of boulder-like hemispherical obstacles. The profile of the boulder landscape approximates a one-dimensional potential introduced by Aubry and André (AA) to study wave function localization in aperiodic lattices. The AA model provides a deterministically disordered alternative to the better-known phenomenon of Anderson localization, which occurs in truly random disordered lattices. When the boulder landscape is strictly periodic, the robot can pass completely through the channel. But if the landscape is sufficiently aperiodic, the robot becomes trapped and fails to exit the channel. The metrics we use to quantify this transition -- including exponential distributions of robot position when localized -- agree well with earlier experimental and theoretical work on a localization transition that occurs when quantum waves interact with the AA potential. A theoretical treatment of the robot's motion using resistive force theory modified to include spatially varying drag forces reproduces the behavior we observe. Further, our results indicate that the transition is generated by large fluctuations in the driving torques required for self-propulsion. These results point to a potentially fundamental connection between classical and quantum wave mechanics and the locomotion of undulators. Our study illustrates how analogies with models from condensed matter physics and wave optics can lead to the discovery of principles of self-propulsion in non-periodic landscapes.

physics.bio-ph↗

arXiv2025

Optimizer's Information Criterion: Dissecting and Correcting Bias in Data-Driven Optimization

In data-driven optimization, the sample performance of the obtained decision typically incurs an optimistic bias against the true performance, a phenomenon commonly known as the Optimizer's Curse and intimately related to overfitting in machine learning. Common techniques to correct this bias, such as cross-validation, require repeatedly solving additional optimization problems and are therefore computationally expensive. We develop a general bias correction approach, building on what we call Optimizer's Information Criterion (OIC), that directly approximates the first-order bias and does not require solving any additional optimization problems. Our OIC generalizes the celebrated Akaike Information Criterion to evaluate the objective performance in data-driven optimization, which crucially involves not only model fitting but also its interplay with the downstream optimization. As such it can be used for decision selection instead of only model selection. We apply our approach to a range of data-driven optimization formulations comprising empirical and parametric models, their regularized counterparts, and furthermore contextual optimization. Finally, we provide numerical validation on the superior performance of our approach under synthetic and real-world datasets.

cs.LG↗

arXiv2025

DCHM: Depth-Consistent Human Modeling for Multiview Detection

Multiview pedestrian detection typically involves two stages: human modeling and pedestrian localization. Human modeling represents pedestrians in 3D space by fusing multiview information, making its quality crucial for detection accuracy. However, existing methods often introduce noise and have low precision. While some approaches reduce noise by fitting on costly multiview 3D annotations, they often struggle to generalize across diverse scenes. To eliminate reliance on human-labeled annotations and accurately model humans, we propose Depth-Consistent Human Modeling (DCHM), a framework designed for consistent depth estimation and multiview fusion in global coordinates. Specifically, our proposed pipeline with superpixel-wise Gaussian Splatting achieves multiview depth consistency in sparse-view, large-scaled, and crowded scenarios, producing precise point clouds for pedestrian localization. Extensive validations demonstrate that our method significantly reduces noise during human modeling, outperforming previous state-of-the-art baselines. Additionally, to our knowledge, DCHM is the first to reconstruct pedestrians and perform multiview segmentation in such a challenging setting. Code is available on the \href{https://jiahao-ma.github.io/DCHM/}{project page}.

cs.CV↗

arXiv2025

The Anytime Convergence of Stochastic Gradient Descent with Momentum: From a Continuous-Time Perspective

We study the stochastic optimization problem from a continuous-time perspective, with a focus on the Stochastic Gradient Descent with Momentum (SGDM) method. We show that the trajectory of SGDM, despite its \emph{stochastic} nature, converges in $L_2$-norm to a \emph{deterministic} second-order Ordinary Differential Equation (ODE) as the stepsize goes to zero. The connection between the ODE and the algorithm results in a useful development for the discrete-time convergence analysis. More specifically, we develop, through the construction of a suitable Lyapunov function, convergence results for the ODE, which are then translated to the corresponding convergence results for the discrete-time case. This approach yields a novel \emph{anytime} convergence guarantee for stochastic gradient methods. In particular, we prove that the sequence $\{ x_k \}$, governed by running SGDM on a smooth convex function $f$, satisfies \begin{align*} \mathbb{P}\left(f (x_k) - f^* \le C\left(1+\log\frac{1}β\right)\frac{\log k}{\sqrt{k}},\;\text{for all $k$}\right)\ge 1-β\quad\text{ for any $β>0$,} \end{align*} where $f^*=\min_{x\in\mathbb{R}^n} f(x)$, and $C$ is a constant. Rather than at a single step, this result captures the convergence behavior across the entire trajectory of the algorithm.

math.OC↗

arXiv2025

Breaking a Logarithmic Barrier in the Stopping Time Convergence Rate of Stochastic First-order Methods

This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches, our analysis: 1. Directly characterizes convergence in terms of stopping times adapted to the underlying stochastic process. 2. Breaks a logarithmic barrier in existing results. Key to our results is the development of a lemma to control the large deviation property of almost super-martingales. This lemma might be of broader interest.

math.OC↗

arXiv2025

An Experimental Approach for Running-Time Estimation of Multi-objective Evolutionary Algorithms in Numerical Optimization

Multi-objective evolutionary algorithms (MOEAs) have become essential tools for solving multi-objective optimization problems (MOPs), making their running time analysis crucial for assessing algorithmic efficiency and guiding practical applications. While significant theoretical advances have been achieved for combinatorial optimization, existing studies for numerical optimization primarily rely on algorithmic or problem simplifications, limiting their applicability to real-world scenarios. To address this gap, we propose an experimental approach for estimating upper bounds on the running time of MOEAs in numerical optimization without simplification assumptions. Our approach employs an average gain model that characterizes algorithmic progress through the Inverted Generational Distance metric. To handle the stochastic nature of MOEAs, we use statistical methods to estimate the probabilistic distribution of gains. Recognizing that gain distributions in numerical optimization exhibit irregular patterns with varying densities across different regions, we introduce an adaptive sampling method that dynamically adjusts sampling density to ensure accurate surface fitting for running time estimation. We conduct comprehensive experiments on five representative MOEAs (NSGA-II, MOEA/D, AR-MOEA, AGEMOEA-II, and PREA) using the ZDT and DTLZ benchmark suites. The results demonstrate the effectiveness of our approach in estimating upper bounds on the running time without requiring algorithmic or problem simplifications. Additionally, we provide a web-based implementation to facilitate broader adoption of our methodology. This work provides a practical complement to theoretical research on MOEAs in numerical optimization.

cs.NE↗

arXiv2025

Probing valence electron and hydrogen dynamics using charge-pair imaging with ultrafast electron diffraction

A key challenge in ultrafast science has been to directly track the coupled motions of electrons and nuclei in real-space and real-time. This study presents a significant step towards this goal by demonstrating the feasibility of time-resolved real-space tracking of valence electron and hydrogen dynamics during the photodissociation of ammonia (NH3) using MeV ultrafast electron diffraction. It is demonstrated that the enhanced temporal resolution, in conjunction with the analysis of the charge-pair distribution function, enables the disentanglement of the correlated motion of valence electrons and hydrogens in photoexcited ammonia molecule. The methodology employed in this study, which utilizes the charge-pair distribution function from ultrafast electron scattering to retrieve intertwined electron and nucleus dynamics, may open up new opportunities in the study of quantum dynamics for a wide range of molecules.

physics.chem-ph↗

arXiv2025

Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls

In contextual optimization, a decision-maker leverages contextual information, often referred to as covariates, to better resolve uncertainty and make informed decisions. In this paper, we examine the challenges of contextual decision-making under covariate shift, a phenomenon where the distribution of covariates differs between the training and test environments. Such shifts can lead to inaccurate upstream estimations for test covariates that lie far from the training data, ultimately resulting in suboptimal downstream decisions. To tackle these challenges, we propose a novel approach called Intersection Wasserstein-balls DRO (IW-DRO), which integrates multiple estimation methods into the distributionally robust optimization (DRO) framework. At the core of our approach is an innovative ambiguity set defined as the intersection of two Wasserstein balls, with their centers constructed using appropriate nonparametric and parametric estimators. On the computational side, we reformulate the IW-DRO problem as a tractable convex program and develop an approximate algorithm tailored for large-scale problems to enhance computational efficiency. From a theoretical perspective, we demonstrate that IW-DRO achieves superior performance compared to single Wasserstein-ball DRO models. We further establish performance guarantees by analyzing the coverage of the intersection ambiguity set and the measure concentration of both estimators under the Wasserstein distance. Notably, we derive a finite-sample concentration result for the Nadaraya-Watson kernel estimator under covariate shift. The proposed IW-DRO framework offers practical value for decision-makers operating in uncertain environments affected by covariate shifts.

math.OC↗

arXiv2025

RAG-6DPose: Retrieval-Augmented 6D Pose Estimation via Leveraging CAD as Knowledge Base

Accurate 6D pose estimation is key for robotic manipulation, enabling precise object localization for tasks like grasping. We present RAG-6DPose, a retrieval-augmented approach that leverages 3D CAD models as a knowledge base by integrating both visual and geometric cues. Our RAG-6DPose roughly contains three stages: 1) Building a Multi-Modal CAD Knowledge Base by extracting 2D visual features from multi-view CAD rendered images and also attaching 3D points; 2) Retrieving relevant CAD features from the knowledge base based on the current query image via our ReSPC module; and 3) Incorporating retrieved CAD information to refine pose predictions via retrieval-augmented decoding. Experimental results on standard benchmarks and real-world robotic tasks demonstrate the effectiveness and robustness of our approach, particularly in handling occlusions and novel viewpoints. Supplementary material is available on our project website: https://sressers.github.io/RAG-6DPose .

cs.CV↗

arXiv2025

Robust control for multi-legged elongate robots in noisy environments

Modern two and four legged robots exhibit impressive mobility on complex terrain, largely attributed to advancement in learning algorithms. However, these systems often rely on high-bandwidth sensing and onboard computation to perceive/respond to terrain uncertainties. Further, current locomotion strategies typically require extensive robot-specific training, limiting their generalizability across platforms. Building on our prior research connecting robot-environment interaction and communication theory, we develop a new paradigm to construct robust and simply controlled multi-legged elongate robots (MERs) capable of operating effectively in cluttered, unstructured environments. In this framework, each leg-ground contact is thought of as a basic active contact (bac), akin to bits in signal transmission. Reliable locomotion can be achieved in open-loop on "noisy" landscapes via sufficient redundancy in bacs. In such situations, robustness is achieved through passive mechanical responses. We term such processes as those displaying mechanical intelligence (MI) and analogize these processes to forward error correction (FEC) in signal transmission. To augment MI, we develop feedback control schemes, which we refer to as computational intelligence (CI) and such processes analogize automatic repeat request (ARQ) in signal transmission. Integration of these analogies between locomotion and communication theory allow analysis, design, and prediction of embodied intelligence control schemes (integrating MI and CI) in MERs, showing effective and reliable performance (approximately half body lengths per cycle) on complex landscapes with terrain "noise" over twice the robot's height. Our work provides a foundation for systematic development of MER control, paving the way for terrain-agnostic, agile, and resilient robotic systems capable of operating in extreme environments.

cs.RO↗

arXiv2025

You Only Estimate Once: Unified, One-stage, Real-Time Category-level Articulated Object 6D Pose Estimation for Robotic Grasping

This paper addresses the problem of category-level pose estimation for articulated objects in robotic manipulation tasks. Recent works have shown promising results in estimating part pose and size at the category level. However, these approaches primarily follow a complex multi-stage pipeline that first segments part instances in the point cloud and then estimates the Normalized Part Coordinate Space (NPCS) representation for 6D poses. These approaches suffer from high computational costs and low performance in real-time robotic tasks. To address these limitations, we propose YOEO, a single-stage method that simultaneously outputs instance segmentation and NPCS representations in an end-to-end manner. We use a unified network to generate point-wise semantic labels and centroid offsets, allowing points from the same part instance to vote for the same centroid. We further utilize a clustering algorithm to distinguish points based on their estimated centroid distances. Finally, we first separate the NPCS region of each instance. Then, we align the separated regions with the real point cloud to recover the final pose and size. Experimental results on the GAPart dataset demonstrate the pose estimation capabilities of our proposed single-shot method. We also deploy our synthetically-trained model in a real-world setting, providing real-time visual feedback at 200Hz, enabling a physical Kinova robot to interact with unseen articulated objects. This showcases the utility and effectiveness of our proposed method.

cs.CV↗

arXiv2025

Collision Induced Binding and Transport of Shape Changing Robot Pairs

We report in experiment and simulation the spontaneous formation of dynamically bound pairs of shape changing robots undergoing locally repulsive collisions. These physical `gliders' robustly emerge from an ensemble of individually undulating three-link two-motor robots and can remain bound for hundreds of undulations and travel for multiple robot dimensions. Gliders occur in two distinct binding symmetries and form over a wide range of angular oscillation extent. This parameter sets the maximal concavity which influences formation probability and translation characteristics. Analysis of dynamics in simulation reveals the mechanism of effective dynamical attraction -- a result of the emergent interplay of appropriately oriented and timed repulsive interactions. Tactile sensing stabilizes the short-lived conformation via concavity modulation.

cs.RO↗

arXiv2025

CAP-Net: A Unified Network for 6D Pose and Size Estimation of Categorical Articulated Parts from a Single RGB-D Image

This paper tackles category-level pose estimation of articulated objects in robotic manipulation tasks and introduces a new benchmark dataset. While recent methods estimate part poses and sizes at the category level, they often rely on geometric cues and complex multi-stage pipelines that first segment parts from the point cloud, followed by Normalized Part Coordinate Space (NPCS) estimation for 6D poses. These approaches overlook dense semantic cues from RGB images, leading to suboptimal accuracy, particularly for objects with small parts. To address these limitations, we propose a single-stage Network, CAP-Net, for estimating the 6D poses and sizes of Categorical Articulated Parts. This method combines RGB-D features to generate instance segmentation and NPCS representations for each part in an end-to-end manner. CAP-Net uses a unified network to simultaneously predict point-wise class labels, centroid offsets, and NPCS maps. A clustering algorithm then groups points of the same predicted class based on their estimated centroid distances to isolate each part. Finally, the NPCS region of each part is aligned with the point cloud to recover its final pose and size. To bridge the sim-to-real domain gap, we introduce the RGBD-Art dataset, the largest RGB-D articulated dataset to date, featuring photorealistic RGB images and depth noise simulated from real sensors. Experimental evaluations on the RGBD-Art dataset demonstrate that our method significantly outperforms the state-of-the-art approach. Real-world deployments of our model in robotic tasks underscore its robustness and exceptional sim-to-real transfer capabilities, confirming its substantial practical utility. Our dataset, code and pre-trained models are available on the project page.

cs.CV↗

arXiv2025

MegaAgent: A Large-Scale Autonomous LLM-based Multi-Agent System Without Predefined SOPs

LLM-based multi-agent systems (MAS) have shown promise in tackling complex tasks. However, existing solutions often suffer from limited agent coordination and heavy reliance on predefined Standard Operating Procedures (SOPs), which demand extensive human input. To address these limitations, we propose MegaAgent, a large-scale autonomous LLM-based multi-agent system. MegaAgent generates agents based on task complexity and enables dynamic task decomposition, parallel execution, efficient communication, and comprehensive system monitoring of agents. In evaluations, MegaAgent demonstrates exceptional performance, successfully developing a Gobang game within 800 seconds and scaling up to 590 agents in a national policy simulation to generate multi-domain policies. It significantly outperforms existing systems, such as MetaGPT, in both task completion efficiency and scalability. By eliminating the need for predefined SOPs, MegaAgent demonstrates exceptional scalability and autonomy, setting a foundation for advancing true autonomy in MAS. Our code is available at https://github.com/Xtra-Computing/MegaAgent .

cs.MA↗