Hua Xiang

Wenlong Liu, Jiahua Pan, Xingyu Zhang et al.

Product matching aims to identify identical or similar products sold on different platforms. By building knowledge graphs (KGs), the product matching problem can be converted to the Entity Alignment (EA) task, which aims to discover the equivalent entities from diverse KGs. The existing EA methods inadequately utilize both attribute triples and relation triples simultaneously, especially the interactions between them. This paper introduces a two-stage pipeline consisting of rough filter and fine filter to match products from eBay and Amazon. For fine filtering, a new framework for Entity Alignment, Relation-aware and Attribute-aware Graph Attention Networks for Entity Alignment (RAEA), is employed. RAEA focuses on the interactions between attribute triples and relation triples, where the entity representation aggregates the alignment signals from attributes and relations with Attribute-aware Entity Encoder and Relation-aware Graph Attention Networks. The experimental results indicate that the RAEA model achieves significant improvements over 12 baselines on EA task in the cross-lingual dataset DBP15K (6.59% on average Hits@1) and delivers competitive results in the monolingual dataset DWY100K. The source code for experiments on DBP15K and DWY100K is available at github (https://github.com/Mockingjay-liu/RAEA-model-for-Entity-Alignment).

Hua Xiang, Shiyang Zhang, Jun Zou

We shall propose and analyze some new preconditioners for the saddle-point systems arising from the edge element discretization of the time-harmonic Maxwell equations in three dimensions. We will first consider the saddle-point systems with vanishing wave number, for which we present an important relation between the solutions of the singular curl-curl system and the non-singular saddle-point system, then demonstrate that the saddle-point system can be efficiently solved by the Hiptmair-Xu solver. For the saddle-point systems with non-vanishing wave numbers, we will show that the PCG with a new preconditioner can apply for the non-singular system when wave numbers are small, while the methods like preconditioned MINRES may apply for some existing and new preconditioners when wave numbers are large. The spectral behaviors of the resulting preconditioned systems for the existing and new preconditioners are analyzed and compared, and numerical experiments are presented to demonstrate and compare the efficiencies of these preconditioners.

Kazufumi Ito, Hua Xiang, Jun Zou

We propose an inexact Uzawa algorithm with two variable relaxation parameters for solving the generalized saddle-point system. The saddle-point problems can be found in a wide class of applications, such as the augmented Lagrangian formulation of the constrained minimization, the mixed finite element method, the mortar domain decomposition method and the discretization of elliptic and parabolic interface problems. The two variable parameters can be updated at each iteration, requiring no a priori estimates on the spectrum of two preconditioned subsystems involved. The convergence and convergence rate of the algorithm are analysed. Both symmetric and nonsymmetric saddle-point systems are discussed, and numerical experiments are presented to demonstrate the robustness and effectiveness of the algorithm.

Changpeng Shao, Hua Xiang

We consider the quantum implementations of the two classical iterative solvers for a system of linear equations, including the Kaczmarz method which uses a row of coefficient matrix in each iteration step, and the coordinate descent method which utilizes a column instead. These two methods are widely applied in big data science due to their very simple iteration schemes. In this paper we use the block-encoding technique and propose fast quantum implementations for these two approaches, under the assumption that the quantum states of each row or each column can be efficiently prepared. The quantum algorithms achieve exponential speed up at the problem size over the classical versions, meanwhile their complexity is nearly linear at the number of steps.

Changpeng Shao, Hua Xiang

In this paper we propose a quantum algorithm to determine the Tikhonov regularization parameter and solve the ill-conditioned linear equations, for example, arising from the finite element discretization of linear or nonlinear inverse problems. For regularized least squares problem with a fixed regularization parameter, we use the HHL algorithm and work on an extended matrix with smaller condition number. For the determination of the regularization parameter, we combine the classical L-curve and GCV function, and design quantum algorithms to compute the norms of regularized solution and the corresponding residual in parallel and locate the best regularization parameter by Grover's search. The quantum algorithm can achieve a quadratic speedup in the number of regularization parameters and an exponential speedup in the dimension of problem size.

Yuting Hu, Lei Zhuang, Hua Xiang et al.

As integrated circuit (IC) dimensions shrink below the lithographic wavelength, optical lithography faces growing challenges from diffraction and process variability. Model-based optical proximity correction (OPC) and inverse lithography technique (ILT) remain indispensable but computationally expensive, requiring repeated simulations that limit scalability. Although deep learning has been applied to mask optimization, existing datasets often rely on synthetic layouts, disregard standard-cell hierarchy, and neglect the surrounding contexts around the mask optimization targets, thereby constraining their applicability to practical mask optimization. To advance deep learning for cell- and context-aware mask optimization, we present MaskOpt, a large-scale benchmark dataset constructed from real IC designs at the 45$\mathrm{nm}$ node. MaskOpt includes 104,714 metal-layer tiles and 121,952 via-layer tiles. Each tile is clipped at a standard-cell placement to preserve cell information, exploiting repeated logic gate occurrences. Different context window sizes are supported in MaskOpt to capture the influence of neighboring shapes from optical proximity effects. We evaluate state-of-the-art deep learning models for IC mask optimization to build up benchmarks, and the evaluation results expose distinct trade-offs across baseline models. Further context size analysis and input ablation studies confirm the importance of both surrounding geometries and cell-aware inputs in achieving accurate mask generation.

Nianci Wu, Hua Xiang

In this paper, we describe the randomized QLP (RQLP) algorithm and its enhanced version (ERQLP) for computing the low rank approximation to $A$ of size $m\times n$ efficiently such that $A\approx QLP$, where $L$ is the rank-$k$ lower-triangular matrix, $Q$ and $P$ are column orthogonal matrices. The theoretical cost of the implementation of RQLP and ERQLP only needs $\mathcal{O}(mnk)$. Moreover, we derive the upper bounds of the expected approximation error $\mathbb{E}\left [ (σ_{j}(A) - σ_{j} (L))/ σ_{j}(A) \right] $ for $j=1,\cdots, k$, and prove that the $L$-values of the proposed methods can track the singular values of $A$ accurately. These claims are supported by extensive numerical experiments.

Hailun Shen, Hua Xiang

In this paper, we extend the inexact Uzawa algorithm in [Q. Hu, J. Zou, SIAM J. Matrix Anal., 23(2001), pp. 317-338] to the nonsymmetric generalized saddle point problem. The techniques used here are similar to those in [Bramble \emph{et al}, Math. Comput. 69(1999), pp. 667-689], where the convergence of Uzawa type algorithm for solving nonsymmetric case depends on the spectrum of the preconditioners involved. The main contributions of this paper focus on a new linear Uzawa type algorithm for nonsymmetric generalized saddle point problems and its convergence. This new algorithm can always converge without any prior estimate on the spectrum of two preconditioned subsystems involved, which may not be easy to achieve in applications. Numerical results of the algorithm on the Navier-Stokes problem are also presented.

Yu-Qiu Liu, Hefeng Wang, Hua Xiang

Quantum signal processing (QSP) and generalized quantum signal processing (GQSP) are essential tools for implementing the block encoding of matrix functions. The achievable polynomials of QSP have restrictions on parity, while GQSP eliminates these restrictions. But GQSP only constructs functions of unitary matrices. In this paper, we further investigate GQSP and extend it to general matrices. Compared with the quantum singular value transformation (QSVT), our proposed method relaxes the requirements on the parity of polynomials. We refer to this extension as generalized quantum singular value transformation (GQSVT). Subsequently, by utilizing the relationship between generalized matrix functions and standard matrix functions, we propose a classical-quantum hybrid quantum conjugate gradient least squares (CGLS) algorithm using GQSVT.

Yuting Hu, Lei Zhuang, Chen Wang et al.

As feature sizes shrink to the nanometer scale, accurately transferring circuit patterns from photomasks to silicon wafers becomes increasingly challenging. Optical proximity correction (OPC) is widely used to ensure pattern fidelity and manufacturability. Recent generative mask optimization models based on encoder-decoder architecture can synthesize near-optimal masks, serving as fast machine learning (ML) surrogates for traditional OPC. However, these models often fail to capture the geometric transformations from target layouts to mask patterns, leading to suboptimal quality. In this work, we formulate mask generation as a sequence of morphological operations on local layout features and propose \textit{MorphOPC}, a multi-scale hierarchical model with neural morphological modules to learn these transformations. Experiments on edge-based OPC and ILT benchmarks across metal and via layers show that \textit{MorphOPC} consistently outperforms state-of-the-art methods, achieving higher printing fidelity and lower manufacturing cost, demonstrating strong potential for scalable mask optimization.

Hua Xiang, Lin Zhang

We use a unified framework to summarize sixteen randomized iterative methods including Kaczmarz method, coordinate descent method, etc. Some new iterative schemes are given as well. Some relationships with \textsc{mg} and \textsc{ddm} are also discussed. We analyze the convergence properties of the iterative schemes by using the matrix integrals associated with alternating projectors, and demonstrate the convergence behaviors of the randomized iterative methods by numerical examples.

Hua Xiang, Jun Zou

We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then apply randomized algorithms to reduce large-scale systems of standard form to much smaller-scale systems and seek their regularized solutions in combination with some popular choice rules for regularization parameters. Then we will propose a second approach to solve large-scale ill-posed systems with general regularizations. This involves a new randomized generalized SVD algorithm that can essentially reduce the size of the original large-scale ill-posed systems. The reduced systems can provide approximate regularized solutions with about the same accuracy as the ones by the classical generalized SVD, and more importantly, the new approach gains obvious robustness, stability and computational time as it needs only to work on problems of much smaller size. Numerical results are given to demonstrated the efficiency of the algorithms.

Pengpeng Xie, Yimin Wei, Hua Xiang

In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular probabilistic algorithms for low-rank approximations, we develop randomized algorithms for the TLS and the truncated total least squares (TTLS) solutions of large-scale discrete ill-posed problems, which can greatly reduce the computational time and still keep good accuracy.