arXiv subjects

Chen Ouyang

Publications and source records attributed to Chen Ouyang.

11 recordsLinked to original sources

arXiv2026

Adaptive Polyak Stepsize with Level-value Adjustment for Distributed Optimization

Stepsize selection remains a critical challenge in the practical implementation of distributed optimization. Existing distributed algorithms often rely on restrictive prior knowledge of global objective functions, such as Lipschitz constants. While centralized Polyak stepsizes have recently gained attention for their parameter-free adaptability and fast convergence. However, their extension to distributed settings is hindered by the requirement for local function values at the global optimum, which are typically unavailable to individual agents. To bridge this gap, we design a novel distributed adaptive Polyak stepsize algorithm with level-value adjustment (DPS-LA), where each agent only needs to solve a computationally efficient linear feasibility problem, thereby eliminating the dependency on global optimal values. Theoretical analysis proves that DPS-LA guarantees network consensus and achieves a linear speedup convergence rate of $\mathcal{O}(1/\sqrt{nT})$. Numerical results confirm the efficiency of the proposed algorithm.

math.OC↗

arXiv2026

Loopless Proximal Riemannian Gradient EXTRA for Distributed Optimization on Compact Manifolds

Distributed optimization has gained substantial interest in recent years due to its wide applications in machine learning. However, most of existing algorithms are designed for Euclidean spaces, leaving composite optimization on Riemannian manifolds largely unexplored. To bridge this gap, we propose the proximal Riemannian gradient EXTRA algorithm (PR-EXTRA) to solve distributed composite optimization problem with nonsmooth regularizer over compact manifolds. In each iteration, PR-EXTRA requires only a single round communication, coupled with local gradient evaluations and proximal mappings. Furthermore, a manifold projection operator is integrated to ensure the feasibility of all iterates throughout the optimization process. Theoretical analysis shows that with a constant stepsize, PR-EXTRA achieves a sublinear convergence rate of $\mathcal{O}(1/K)$ to a stationary point, matching the proximal gradient EXTRA algorithm in Euclidean spaces. Numerical experiments show the effectiveness of the proposed algorithm.

math.OC↗

arXiv2026

Compressed Proximal Federated Learning for Non-Convex Composite Optimization on Heterogeneous Data

Federated Composite Optimization (FCO) has emerged as a promising framework for training models with structural constraints (e.g., sparsity) in distributed edge networks. However, simultaneously achieving communication efficiency and convergence robustness remains a significant challenge, particularly when dealing with non-smooth regularizers, statistical heterogeneity, and the restrictions of biased compression. To address these issues, we propose FedCEF (Federated Composite Error Feedback), a novel algorithm tailored for non-convex FCO. FedCEF introduces a decoupled proximal update scheme that separates the proximal operator from communication, enabling clients to handle non-smooth terms locally while transmitting compressed information. To mitigate the noise from aggressive quantization and the bias from non-IID data, FedCEF integrates a rigorous error feedback mechanism with control variates. Furthermore, we design a communication-efficient pre-proximal downlink strategy that allows clients to exactly reconstruct global control variables without explicit transmission. We theoretically establish that FedCEF achieves sublinear convergence to a bounded residual error under general non-convexity, which is controllable via the step size and batch size. Extensive experiments on real datasets validate FedCEF maintains competitive model accuracy even under extreme compression ratios (e.g., 1%), significantly reducing the total communication volume compared to uncompressed baselines.

math.OC↗

arXiv2025

Enabling Ultra-Fast Cardiovascular Imaging Across Heterogeneous Clinical Environments with A Generalist Foundation Model and Multimodal Database

Multimodal cardiovascular magnetic resonance (CMR) imaging provides comprehensive and non-invasive insights into cardiovascular disease (CVD) diagnosis and underlying mechanisms. Despite decades of advancements, its widespread clinical adoption remains constrained by prolonged scan times, inconsistent image quality, and heterogeneity across medical environments. This underscores the urgent need for a generalist reconstruction foundation model for ultra-fast CMR imaging, one formulated for physics-constrained inverse problems in the sensor (k-space) domain, capable of adapting across diverse imaging scenarios and serving as the essential substrate for all downstream analyses. To enable this goal, we curate MMCMR-427K, the largest and most comprehensive multimodal CMR k-space database to date, comprising 427,465 multi-coil k-space data paired with structured metadata across 13 international centers, 12 CMR modalities, 15 scanners spanning four field strengths, and 17 CVD categories in populations across three continents. Building on this unprecedented resource, we introduce CardioMM, a generalist reconstruction foundation model capable of dynamically adapting to heterogeneous fast CMR imaging scenarios. CardioMM unifies semantic contextual understanding with physics-informed data consistency to deliver robust reconstructions across varied scanners, protocols, and patient presentations. Comprehensive evaluations demonstrate that CardioMM achieves state-of-the-art performance across internal centers and exhibits strong zero-shot generalization to unseen external settings. Importantly, CardioMM supports acceleration up to 24x, providing the first evidence that such extreme acquisition speed can preserve key cardiac phenotypes, quantitative myocardial biomarkers, and diagnostic image quality without compromising clinical integrity.

eess.IV↗

arXiv2024

Unit Dual Quaternion Directed Graphs, Formation Control and General Weighted Directed Graphs

We study the multi-agent formation control problem in a directed graph. The relative configurations are expressed by unit dual quaternions (UDQs). We call such a weighted directed graph a unit dual quaternion directed graph (UDQDG). We show that a desired relative configuration scheme is reasonable or balanced in a UDQDG if and only if the dual quaternion Laplacian is similar to the unweighted Laplacian of the underlying directed graph. A direct method and a unit gain graph method are proposed to solve the balance problem of general unit weighted directed graphs. We then study the balance problem of general non-unit weighted directed graphs. Numerical experiments for UDQDG are reported.

math.RA↗

arXiv2021

An Orthogonal Equivalence Theorem for Third Order Tensors

In 2011, Kilmer and Martin proposed tensor singular value decomposition (T-SVD) for third order tensors. Since then, T-SVD has applications in low rank tensor approximation, tensor recovery, multi-view clustering, multi-view feature extraction, tensor sketching, etc. By going through the Discrete Fourier Transform (DFT), matrix SVD and inverse DFT, a third order tensor is mapped to an f-diagonal third order tensor. We call this a Kilmer-Martin mapping. We show that the Kilmer-Martin mapping of a third order tensor is invariant if that third order tensor is taking T-product with some orthogonal tensors. We define singular values and T-rank of that third order tensor based upon its Kilmer-Martin mapping. Thus, tensor tubal rank, T-rank, singular values and T-singular values of a third order tensor are invariant when it is taking T-product with some orthogonal tensors. Some properties of singular values, T-rank and best T-rank one approximation are discussed.

math.NA↗

arXiv2021

ST-SVD Factorization and s-Diagonal Tensors

A third order real tensor is mapped to a special f-diagonal tensor by going through Discrete Fourier Transform (DFT), standard matrix SVD and inverse DFT. We call such an f-diagonal tensor an s-diagonal tensor. An f-diagonal tensor is an s-diagonal tensor if and only if it is mapped to itself in the above process. The third order tensor space is partitioned to orthogonal equivalence classes. Each orthogonal equivalence class has a unique s-diagonal tensor. Two s-diagonal tensors are equal if they are orthogonally equivalent. Third order tensors in an orthogonal equivalence class have the same tensor tubal rank and T-singular values. Four meaningful necessary conditions for s-diagonal tensors are presented. Then we present a set of sufficient and necessary conditions for s-diagonal tensors. Such conditions involve a special complex number. In the cases that the dimension of the third mode of the considered tensor is $2, 3$ and $4$, we present direct sufficient and necessary conditions which do not involve such a complex number.

math.NA↗

arXiv2020

Generation and manipulation of chiral terahertz waves emitted from the three-dimensional topological insulator Bi2Te3

Arbitrary manipulation of broadband terahertz waves with flexible polarization shaping at the source has great potential in expanding real applications such as imaging, information encryption, and all-optically coherent control of terahertz nonlinear phenomena. Topological insulators featuring unique spin-momentum locked surface state have already exhibited very promising prospects in terahertz emission, detection and modulation, which may lay a foundation for future on-chip topological insulator-based terahertz systems. However, polarization shaped terahertz emission with prescribed manners of arbitrarily manipulated temporal evolution of the amplitude and electric-field vector direction based on topological insulators have not yet been explored. Here we systematically investigated the terahertz radiation from topological insulator Bi2Te3 nanofilms driven by femtosecond laser pulses, and successfully realized the generation of efficient chiral terahertz waves with controllable chirality, ellipticity, and principle axis. The convenient engineering of the chiral terahertz waves was interpreted by photogalvanic effect induced photocurrent, while the linearly polarized terahertz waves originated from linear photogalvanic effect induced shift currents. We believe our works not only help further understanding femtosecond coherent control of ultrafast spin currents in light-matter interaction but also provide an effective way to generate spin-polarized terahertz waves and accelerate the proliferation of twisting the terahertz waves at the source.

physics.optics↗

arXiv2020

Terahertz Strong-Field Physics in Light-Emitting Diodes for Terahertz Detection and Imaging

Intense terahertz (THz) electromagnetic fields have been utilized to reveal a variety of extremely nonlinear optical effects in many materials through nonperturbative driving of elementary and collective excitations. However, such nonlinear photoresponses have not yet been discovered in light-emitting diodes (LEDs), letting alone employing them as fast, cost effective,compact, and room-temperature-operating THz detectors and cameras. Here we report ubiquitously available LEDs exhibited gigantic and fast photovoltaic signals with excellent signal-to-noise ratios when being illuminated by THz field strengths >50 kV/cm. We also successfully demonstrated THz-LED detectors and camera prototypes. These unorthodox THz detectors exhibited high responsivities (>1 kV/W) with response time shorter than those of pyroelectric detectors by four orders of magnitude. The detection mechanism was attributed to THz-field-induced nonlinear impact ionization and Schottky contact. These findings not only help deepen our understanding of strong THz field-matter interactions but also greatly contribute to the applications of strong-field THz diagnosis.

physics.optics↗

arXiv2016

Some properties and applications of odd-colorable $r$-hypergraphs

Let $r\geq2$ and $r$ be even. An $r$-hypergraph $G$ on $n$ vertices is called odd-colorable if there exists a map $φ:[n]\rightarrow\lbrack r]$ such that for any edge $\{j_{1},j_{2},\cdots,j_{r}\}$ of $G$, we have $φ(j_{1})+φ(j_{2})+\cdot\cdot\cdot+φ(j_{r})\equiv r/2(\operatorname{mod}r).$ In this paper, we first determine that, if $r=2^{q}(2t+1)$ and $n\ge 2^{q}(2^{q}-1)r$, then the maximum chromatic number in the class of the odd-colorable $r$-hypergraphs on $n$ vertices is $2^q$, which answers a question raised by V. Nikiforov recently in [V. Nikiforov, Hypergraphs and hypermatrices with symmetric spectrum. Prinprint available in arXiv:1605.00709v2, 10 May, 2016]. We also study some applications of the symmetric spectral property of the odd-colorable $r$-graphs given in that same paper by V. Nikiforov. We show that the Laplacian spectrum and the signless Laplacian spectrum of an $r$-hypergraph $G$ are equal if and only if $G$ is odd-colorable, and then study some further applications of these spectral properties.

math.CO↗

arXiv2016

The first few unicyclic and bicyclic hypergraphs with larger spectral radii

A connected $k$-uniform hypergraph with $n$ vertices and $m$ edges is called $r$-cyclic if $n=m(k-1)-r+1$. For $r=1$ or $2$, the hypergraph is simply called unicyclic or bicyclic. In this paper we investigate hypergraphs that attain larger spectral radii among all simple connected $k$-uniform unicyclic and bicyclic hypergraphs. Specifically, by using some edge operations, the formula on power hypergraph eigenvalues, the weighted incidence matrix and a result on linear unicyclic hypergraphs, we determined the first five hypergraphs with larger spectral radius among all unicyclic hypergraphs and the first three over all bicyclic hypergraphs.

math.CO↗