arXiv subjects

Yang Zheng

Publications and source records attributed to Yang Zheng.

At least 37 records · Page 2Linked to original sources

arXiv2026

Image2Garment: Simulation-ready Garment Generation from a Single Image

Estimating physically accurate, simulation-ready garments from a single image is challenging due to the absence of image-to-physics datasets and the ill-posed nature of this problem. Prior methods either require multi-view capture and expensive differentiable simulation or predict only garment geometry without the material properties required for realistic simulation. We propose a feed-forward framework that sidesteps these limitations by first fine-tuning a vision-language model to infer material composition and fabric attributes from real images, and then training a lightweight predictor that maps these attributes to the corresponding physical fabric parameters using a small dataset of material-physics measurements. Our approach introduces two new datasets (FTAG and T2P) and delivers simulation-ready garments from a single image without iterative optimization. Experiments show that our estimator achieves superior accuracy in material composition estimation and fabric attribute prediction, and by passing them through our physics parameter estimator, we further achieve higher-fidelity simulations compared to state-of-the-art image-to-garment methods.

cs.CV↗

arXiv2026

Online Tracking with Predictions for Nonlinear Systems with Koopman Linear Embedding

We study the problem of online tracking in unknown nonlinear dynamical systems, where only short-horizon predictions of future target states are available. This setting arises in practical scenarios where full future information and exact system dynamics are unavailable. We focus on a class of nonlinear systems that admit a Koopman linear embedding, enabling the dynamics to evolve linearly in a lifted space. Exploiting this structure, we analyze a model-free predictive tracking algorithm based on Willems' fundamental lemma, which imposes dynamic constraints using only past data within a receding-horizon control framework. We show that, for Koopman-linearizable systems, the cumulative cost and dynamic regret of the nonlinear tracking problem coincide with those of the lifted linear counterpart. Moreover, we prove that the dynamic regret of our algorithm decays exponentially with the prediction horizon, as validated by numerical experiments.

math.OC↗

arXiv2026

Policy Optimization of Mixed H2/H-infinity Control: Benign Nonconvexity and Global Optimality

Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer limited insight into the nonconvex optimization landscape and do not readily scale to large-scale or data-driven settings. In this paper, we revisit mixed H2/H-infinity control from a modern policy optimization viewpoint, including the general two-channel and single-channel cases. One central result is that both cases enjoy a benign nonconvex structure: every stationary point is globally optimal. We characterize the H-infinity-constrained feasible set, which is open, path-connected, with boundary given exactly by policies saturating the H-infinity constraint. We also show that the mixed objective is real analytic in the interior with explicit gradient formulas. Our key analysis builds on an Extended Convex Lifting (ECL) framework that bridges nonconvex policy optimization and convex reformulations. The ECL constructions rely on non-strict Riccati inequalities that allow us to characterize global optimality. These insights reveal hidden convexity in mixed H2/H-infinity control and facilitate the design of scalable policy iteration methods in large-scale settings.

math.OC↗

arXiv2026

Regret Guarantees for Model-Free Cooperative Filtering under Asynchronous Observations

Predicting the output of a dynamical system from streaming data is fundamental to real-time feedback control and decision-making. We first derive an autoregressive representation that relates future local outputs to asynchronous past outputs. Building on this structure, we propose an online least-squares algorithm to learn this autoregressive model for real-time prediction. We then establish a regret bound of O(log^3 N) relative to the optimal model-based predictor, which holds for marginally stable systems. Moreover, we provide a sufficient condition characterized via a symplectic matrix, under which the proposed cooperative online learning method provably outperforms the optimal model-based predictor that relies solely on local observations. From a technical standpoint, our analysis exploits the orthogonality of the innovation process under asynchronous data structure and the persistent excitation of the Gram matrix despite delay-induced asymmetries. Overall, these results offer both theoretical guarantees and practical algorithms for model-free cooperative prediction with asynchronous observations, thereby enriching the theory of online learning for dynamical systems.

eess.SY↗

arXiv2026

Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems

Despite its nonconvexity, policy optimization for the Linear Quadratic Regulator (LQR) admits a favorable structural property known as gradient dominance, which facilitates linear convergence of policy gradient methods to the globally optimal gain. While gradient dominance has been extensively studied, continuous-time and discrete-time LQRs have largely been analyzed separately, relying on slightly different assumptions, proof strategies, and resulting guarantees. In this paper, we present a unified gradient dominance property for both continuous-time and discrete-time LQRs under mild stabilizability and detectability assumptions. Our analysis is based on a convex reformulation derived from a common Lyapunov inequality representation and a unified change-of-variables procedure. This convex-lifting perspective yields a single proof framework applicable to both time models. The unified treatment clarifies how differences between continuous-time and discrete-time dynamics influence theoretical guarantees and reveals a deeper structural symmetry between the two formulations. Numerical examples illustrate and support the theoretical findings.

math.OC↗

arXiv2026

On the Existence of Koopman Linear Embeddings for Controlled Nonlinear Systems

Koopman linear representations have become a popular tool for control design of nonlinear systems, yet it remains unclear when such representations are exact. In this paper, we establish sufficient and necessary conditions under which a controlled nonlinear system admits an exact finite-dimensional Koopman linear representation, which we term Koopman linear embedding. We show that such a system must be transformable into a special control-affine preserved (CAP) structure, which enforces affine dependence of the state on the control input and isolates all nonlinearities into an autonomous subsystem. We further prove that this autonomous subsystem must itself admit a finite-dimensional Koopman linear model with a sufficiently-rich Koopman invariant subspace. Finally, we introduce a symbolic procedure to determine whether a given controlled nonlinear system admits the CAP structure, thereby elucidating whether Koopman approximation errors arise from intrinsic system dynamics or from the choice of lifting functions.

math.OC↗

arXiv2026

An Overview and Comparison of Spectral Bundle Methods for Primal and Dual Semidefinite Programs

The spectral bundle method developed by Helmberg and Rendl is well-established for solving large-scale semidefinite programs (SDPs) in the dual form, especially when the SDPs admit $\textit{low-rank primal solutions}$. Under mild regularity conditions, a recent result by Ding and Grimmer has established fast linear convergence rates when the bundle method captures $\textit{the rank of primal solutions}$. In this paper, we present an overview and comparison of spectral bundle methods for solving both $\textit{primal}$ and $\textit{dual}$ SDPs. In particular, we introduce a new family of spectral bundle methods for solving SDPs in the $\textit{primal}$ form. The algorithm developments are parallel to those by Helmberg and Rendl, mirroring the elegant duality between primal and dual SDPs. The new family of spectral bundle methods also achieves linear convergence rates for primal feasibility, dual feasibility, and duality gap when the algorithm captures $\textit{the rank of the dual solutions}$. Therefore, the original spectral bundle method by Helmberg and Rendl is well-suited for SDPs with $\textit{low-rank primal solutions}$, while on the other hand, our new spectral bundle method works well for SDPs with $\textit{low-rank dual solutions}$. These theoretical findings are supported by a range of large-scale numerical experiments. Finally, we demonstrate that our new spectral bundle method achieves state-of-the-art efficiency and scalability for solving polynomial optimization compared to a set of baseline solvers $\textsf{SDPT3}$, $\textsf{MOSEK}$, $\textsf{CDCS}$, and $\textsf{SDPNAL+}$.

math.OC↗

arXiv2026

Error bounds, PL condition, and quadratic growth for weakly convex functions, and linear convergences of proximal point methods

Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among different conditions for convex and smooth functions is well-understood, it is not the case for the nonsmooth setting. In this paper, we go beyond convexity and smoothness, and clarify the connections among common regularity conditions in the class of weakly convex functions, including $\textit{strong convexity}$, $\textit{restricted secant inequality}$, $\textit{subdifferential error bound}$, $\textit{Polyak-Łojasiewicz inequality}$, and $\textit{quadratic growth}$. In addition, using these regularity conditions, we present a simple and modular proof for the linear convergence of the proximal point method (PPM) for convex and weakly convex optimization problems. The linear convergence also holds when the subproblems of PPM are solved inexactly with a proper control of inexactness.

math.OC↗

arXiv2026

On the Spectral Flattening of Quantized Embeddings

Training Large Language Models (LLMs) at ultra-low precision is critically impeded by instability rooted in the conflict between discrete quantization constraints and the intrinsic heavy-tailed spectral nature of linguistic data. By formalizing the connection between Zipfian statistics and random matrix theory, we prove that the power-law decay in the singular value spectra of embeddings is a fundamental requisite for semantic encoding. We derive theoretical bounds showing that uniform quantization introduces a noise floor that disproportionately truncates this spectral tail, which induces spectral flattening and a strictly provable increase in the stable rank of representations. Empirical validation across diverse architectures including GPT-2 and TinyLlama corroborates that this geometric degradation precipitates representational collapse. This work not only quantifies the spectral sensitivity of LLMs but also establishes spectral fidelity as a necessary condition for stable low-bit optimization.

cs.LG↗

arXiv2025

Logarithmic Regret and Polynomial Scaling in Online Multi-step-ahead Prediction

This letter studies the problem of online multi-step-ahead prediction for unknown linear stochastic systems. Using conditional distribution theory, we derive an optimal parameterization of the prediction policy as a linear function of future inputs, past inputs, and past outputs. Based on this characterization, we propose an online least-squares algorithm to learn the policy and analyze its regret relative to the optimal model-based predictor. We show that the online algorithm achieves logarithmic regret with respect to the optimal Kalman filter in the multi-step setting. Furthermore, with new proof techniques, we establish an almost-sure regret bound that does not rely on fixed failure probabilities for sufficiently large horizons $N$. Finally, our analysis also reveals that, while the regret remains logarithmic in $N$, its constant factor grows polynomially with the prediction horizon $H$, with the polynomial order set by the largest Jordan block of eigenvalue 1 in the system matrix.

cs.LG↗

arXiv2025

Introducing LongCat-Flash-Thinking: A Technical Report

We present LongCat-Flash-Thinking, an efficient 560-billion-parameter open-source Mixture-of-Experts (MoE) reasoning model. Its advanced capabilities are cultivated through a meticulously crafted training process, beginning with long Chain-of-Thought (CoT) data cold-start and culminating in large-scale Reinforcement Learning (RL). We first employ a well-designed cold-start training strategy, which significantly enhances the reasoning potential and equips the model with specialized skills in both formal and agentic reasoning. Then, a core innovation is our domain-parallel training scheme, which decouples optimization across distinct domains (e.g., STEM, Code, Agentic) and subsequently fuses the resulting expert models into a single, nearly Pareto-optimal model. This entire process is powered by our Dynamic ORchestration for Asynchronous rollout (DORA) system, a large-scale RL framework that delivers a greater than threefold training speedup over synchronous methods on tens of thousands of accelerators. As a result, LongCat-Flash-Thinking achieves state-of-the-art performance among open-source models on a suite of complex reasoning tasks. The model exhibits exceptional efficiency in agentic reasoning, reducing average token consumption by 64.5% (from 19, 653 to 6, 965) on AIME-25, without degrading task accuracy. We release LongCat-Flash-Thinking to promote further advances in reasoning systems and agentic AI research.

cs.AI↗

arXiv2025

On the Exponential Stability of Koopman Model Predictive Control

Koopman Model Predictive Control (MPC) uses a lifted linear predictor to efficiently handle constrained nonlinear systems. While constraint satisfaction and (practical) asymptotic stability have been studied, explicit guarantees of local exponential stability seem to be missing. This paper revisits the exponential stability for Koopman MPC. We first analyze a Koopman LQR problem and show that 1) with zero modeling error, the lifted LQR policy is globally optimal and globally asymptotically stabilizes the nonlinear plant, and 2) with the lifting function and one-step prediction error both Lipschitz at the origin, the closed-loop system is locally exponentially stable. These results facilitate terminal cost/set design in the lifted Koopman space. Leveraging linear-MPC properties (boundedness, value decrease, recursive feasibility), we then prove local exponential stability for a stabilizing Koopman MPC under the same conditions as Koopman LQR. Experiments on an inverted pendulum show better convergence performance and lower accumulated cost than the traditional Taylor-linearized MPC approaches.

math.OC↗

arXiv2025

Neutral Agent-based Adversarial Policy Learning against Deep Reinforcement Learning in Multi-party Open Systems

Reinforcement learning (RL) has been an important machine learning paradigm for solving long-horizon sequential decision-making problems under uncertainty. By integrating deep neural networks (DNNs) into the RL framework, deep reinforcement learning (DRL) has emerged, which achieved significant success in various domains. However, the integration of DNNs also makes it vulnerable to adversarial attacks. Existing adversarial attack techniques mainly focus on either directly manipulating the environment with which a victim agent interacts or deploying an adversarial agent that interacts with the victim agent to induce abnormal behaviors. While these techniques achieve promising results, their adoption in multi-party open systems remains limited due to two major reasons: impractical assumption of full control over the environment and dependent on interactions with victim agents. To enable adversarial attacks in multi-party open systems, in this paper, we redesigned an adversarial policy learning approach that can mislead well-trained victim agents without requiring direct interactions with these agents or full control over their environments. Particularly, we propose a neutral agent-based approach across various task scenarios in multi-party open systems. While the neutral agents seemingly are detached from the victim agents, indirectly influence them through the shared environment. We evaluate our proposed method on the SMAC platform based on Starcraft II and the autonomous driving simulation platform Highway-env. The experimental results demonstrate that our method can launch general and effective adversarial attacks in multi-party open systems.

cs.LG↗

arXiv2025

ElasWave: An Elastic-Native System for Scalable Hybrid-Parallel Training

Large-scale LLM pretraining now runs across $10^5$--$10^6$ accelerators, making failures routine and elasticity mandatory. We posit that an elastic-native training system must jointly deliver (i) parameter consistency, (ii) low mean time to recovery (MTTR), (iii) high post-change throughput, and (iv) computation consistency. No prior system achieves all four simultaneously. To achieve these goals, we present ElasWave, which delivers per-step fault tolerance via multi-dimensional scheduling across graph, dataflow, DVFS, and RNG. ElasWave reshapes and reshards micro-batches while preserving the global batch size and gradient scale. It performs online pipeline resharding with asynchronous parameter migration and interleaves ZeRO partitions, reducing parameter recovery processes to disjoint rank-to-rank transfers. It further leverages DVFS to absorb pipeline bubbles and reshards RNG to keep computation consistency. Together, a dynamic communicator enables in-place communication group edits, while per-step in-memory snapshots support online verification and redistribution. We evaluate ElasWave on 96 NPUs and benchmark it against state-of-the-art baselines: throughput improves by $1.35\times$ over ReCycle and $1.60\times$ over TorchFT; communicator recovery completes within one second (up to $82\times/3.6\times$ faster than full/partial rebuilds); migration MTTR drops by as much as $51\%$; and convergence deviation is reduced by approximately $78\%$.

cs.DC↗

arXiv2025

Policy Optimization in Robust Control: Weak Convexity and Subgradient Methods

Robust control seeks stabilizing policies that perform reliably under adversarial disturbances, with $\mathcal{H}_\infty$ control as a classical formulation. It is known that policy optimization of robust $\mathcal{H}_\infty$ control naturally lead to nonsmooth and nonconvex problems. This paper builds on recent advances in nonsmooth optimization to analyze discrete-time static output-feedback $\mathcal{H}_\infty$ control. We show that the $\mathcal{H}_\infty$ cost is weakly convex over any convex subset of a sublevel set. This structural property allows us to establish the first non-asymptotic deterministic convergence rate for the subgradient method under suitable assumptions. In addition, we prove a weak Polyak-Łojasiewicz (PL) inequality in the state-feedback case, implying that all stationary points are globally optimal. We finally present a few numerical examples to validate the theoretical results.

math.OC↗

arXiv2025

Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models

Inverse problems (IPs) involve reconstructing signals from noisy observations. Recently, diffusion models (DMs) have emerged as a powerful framework for solving IPs, achieving remarkable reconstruction performance. However, existing DM-based methods frequently encounter issues such as heavy computational demands and suboptimal convergence. In this work, building upon the idea of the recent work DMPlug, we propose two novel methods, DMILO and DMILO-PGD, to address these challenges. Our first method, DMILO, employs intermediate layer optimization (ILO) to alleviate the memory burden inherent in DMPlug. Additionally, by introducing sparse deviations, we expand the range of DMs, enabling the exploration of underlying signals that may lie outside the range of the diffusion model. We further propose DMILO-PGD, which integrates ILO with projected gradient descent (PGD), thereby reducing the risk of suboptimal convergence. We provide an intuitive theoretical analysis of our approaches under appropriate conditions and validate their superiority through extensive experiments on diverse image datasets, encompassing both linear and nonlinear IPs. Our results demonstrate significant performance gains over state-of-the-art methods, highlighting the effectiveness of DMILO and DMILO-PGD in addressing common challenges in DM-based IP solvers.

cs.CV↗

arXiv2025

A Proximal Descent Method for Minimizing Weakly Convex Optimization

We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a $\textit{proximal descent method}$, a simple and efficient first-order algorithm that combines the inexact proximal point method with classical convex bundle techniques. Our analysis establishes explicit non-asymptotic convergence rates in terms of $(η,ε)$-inexact stationarity. In particular, the method finds an $(η,ε)$-inexact stationary point using at most $\mathcal{O}\!\left( \Big(\tfrac{1}{η^2} + \tfrac{1}ε\Big) \max\!\left\{\tfrac{1}{η^2}, \tfrac{1}ε\right\} \right)$ function value and subgradient evaluations. Consequently, the algorithm also achieves the best-known complexity of $\mathcal{O}(1/δ^4)$ for finding an approximate Moreau stationary point with $\|\nabla f_{2m}(x)\|\leq δ$. A distinctive feature of our method is its \emph{automatic adaptivity}: with no parameter tuning or algorithmic modification, it accelerates to $\mathcal{O}(1/δ^2)$ complexity under smoothness and further achieves linear convergence under quadratic growth. Overall, this work bridges convex bundle methods and weakly convex optimization, while providing accelerated guarantees under structural assumptions.

math.OC↗

arXiv2025

AllTracker: Efficient Dense Point Tracking at High Resolution

We introduce AllTracker: a model that estimates long-range point tracks by way of estimating the flow field between a query frame and every other frame of a video. Unlike existing point tracking methods, our approach delivers high-resolution and dense (all-pixel) correspondence fields, which can be visualized as flow maps. Unlike existing optical flow methods, our approach corresponds one frame to hundreds of subsequent frames, rather than just the next frame. We develop a new architecture for this task, blending techniques from existing work in optical flow and point tracking: the model performs iterative inference on low-resolution grids of correspondence estimates, propagating information spatially via 2D convolution layers, and propagating information temporally via pixel-aligned attention layers. The model is fast and parameter-efficient (16 million parameters), and delivers state-of-the-art point tracking accuracy at high resolution (i.e., tracking 768x1024 pixels, on a 40G GPU). A benefit of our design is that we can train jointly on optical flow datasets and point tracking datasets, and we find that doing so is crucial for top performance. We provide an extensive ablation study on our architecture details and training recipe, making it clear which details matter most. Our code and model weights are available at https://alltracker.github.io

cs.CV↗