arXiv subjects

Jiang Hu

Publications and source records attributed to Jiang Hu.

At least 37 records · Page 2Linked to original sources

arXiv2026

Size Scaling Law for Radiation Losses of Modes in Photonic Crystal Surface Emitting Devices

Photonic-crystal surface-emitting lasers (PCSELs) have garnered significant attention due to their ability to generate laser beams with ultra high power and low divergence. This is because they support high power single mode lasing with volumes orders of magnitude larger than those of conventional semiconductor lasers. The finite lateral size in a PCSEL is a primary factor limiting its lasing mode volume and consequently, its output power. We demonstrate that the scaling relation between the total cavity loss $α=α_\perp + α_\parallel$ and the device size $L$ is such that the surface radiation loss scales as $α_{\perp} \sim O(L^{-2})$, while the edge radiation loss $α_{\parallel} \sim O(L^{-3})$. Both scaling relations can be explained by the second order expansions of the complex frequency $ω(k)$ of the band diagram. Our results constitute an explicit guideline for PCSEL designs to optimize various optical properties.

physics.optics↗

arXiv2026

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold

Decentralized optimization provides a fundamental framework for large-scale learning and signal processing with distributed data. We study decentralized optimization with orthogonality constraints on the Stiefel manifold and propose RF-EXTRA, a distributed retraction-free primal-dual method on static undirected networks. The method combines an approximate gradient mapping for orthogonality-constrained optimization with an EXTRA-based decentralized recursion, thereby avoiding retractions while preserving a simple communication pattern. On the theoretical side, the analysis considers \revise{the joint error} $(\mathbf{X}_k-\overline{\mathbf X}_k,\mathbf{s}_k-\overline{\mathbf s}_k)$ in the local variables and local directions, and establishes a contractive recursion for the joint error. This contractivity ensures that the joint error can be controlled using small yet constant step sizes, thus leading to an exact $\mathcal{O}(1/K)$ convergence rate of RF-EXTRA to a stationary point. Experiments on PCA and low-rank matrix completion show that RF-EXTRA compares favorably with the reported decentralized baselines and exhibits strong communication efficiency on the tested tasks on the Stiefel manifold.

math.OC↗

arXiv2026

Simultaneous Multi-die Floorplanning and Technology Assignment

In heterogeneous integration, different dies may employ distinct technologies, making floorplanning across multiple dies inherently coupled with technology assignment. By assuming a fixed technology, almost all prior floorplanning studies were developed without addressing the challenge of technology assignment. This work presents the first systematic study of multi-die floorplanning that treats technology choice as a variable. To address the challenge of variable block areas, we incorporate a recent machine learning technique for rapid PPA estimation. Our methods jointly optimize area, wirelength, performance, power, and cost, thereby highlighting the importance of technology assignment. Experimental evaluations, validated with a commercial tool for both 2.5D and 3D ICs, demonstrate that our systematic optimizations significantly outperform a greedy approach.

eess.SY↗

arXiv2026

Fast Cross-Operator Optimization of Attention Dataflow

Attention is a fundamental computational kernel that accounts for the majority of the workload in transformer and LLM computing. Optimizing dataflow is crucial for enhancing both performance and energy efficiency in attention computation. This optimization involves a range of decisions, such as tiling, computation ordering and buffer management, and can be applied at both intra-operator and inter-operator levels, resulting in a highly complex decision space. We propose a new approach to cross-operator dataflow optimization. Its centerpiece is an analytical performance model that spans a large decision space and enables matrix-based encoding of multiple candidate solutions. Built on this foundation, a vast number of solutions can be evaluated rapidly, and with the aid of an effective pruning technique, the optimal solution can be identified through exhaustive enumeration. We refer to our method as MMEE (Matrix Multiplication Encoded Enumeration). The ability to efficiently enumerate a large design space allows MMEE to deliver higher-quality solutions at a substantially faster speed compared to prior approaches. The MMEE approach is evaluated across various test cases for different accelerator configurations. For energy-driven optimization, MMEE reduces energy consumption by 48%-50% and latency by 31%-69%, compared to state-of-the-art methods. For latency-driven optimization, MMEE achieves simultaneous reductions of 40%-50% in energy consumption and 40%-69% in latency, respectively. Additionally, MMEE is $64\times$ to $343\times$ faster than previous works.

cs.AR↗

arXiv2026

Functional CLT for general sample covariance matrices

This paper studies the central limit theorems (CLTs) for linear spectral statistics (LSSs) of general sample covariance matrices, when the test functions belong to $C^3$, the class of functions with continuous third order derivatives. We consider matrices of the form $B_n=(1/n)T_p^{1/2}X_nX_n^{*}T_p^{1/2},$ where $X_n= (x_{i j} ) $ is a $p \times n$ matrix whose entries are independent and identically distributed (i.i.d.) real or complex random variables, and $T_p$ is a $p\times p$ nonrandom Hermitian nonnegative definite matrix with its spectral norm uniformly bounded in $p$. By using Bernstein polynomial approximation, we show that, under $\mathbb{E}|x_{ij}|^{8}<\infty$, the centered LSSs of $B_n$ have Gaussian limits. Under the stronger $\mathbb{E}|x_{ij}|^{10}<\infty$, we further establish convergence rates $O(n^{-1/2+κ})$ in Kolmogorov--Smirnov $O(n^{-1/2+κ})$, for any fixed $κ>0$.

math.ST↗

arXiv2026

The Spurious Factor Dilemma: Robust Inference in Heavy-Tailed Elliptical Factor Models

Standard methods for determining the number of factors often overestimate the true number when data exhibit heavy-tailed randomness, misinterpreting noise-induced outliers as genuine factors. This paper addresses this challenge within the framework of Elliptical Factor Models (EFM), which accommodate both heavy tails and potential non-linear dependencies common in real-world data. We demonstrate, both theoretically and empirically, that heavy-tailed noise generates spurious eigenvalues that mimic true factor signals. To distinguish these, we propose a novel methodology based on a fluctuation magnification algorithm. Under mild conditions, we show that, by magnifying perturbations, the eigenvalues associated with real factors exhibit significantly less fluctuation (stabilizing asymptotically) than spurious eigenvalues arising from heavy-tailed effects. We develop a formal testing procedure based on this principle and apply it to the problem of accurately selecting the number of common factors in heavy-tailed EFMs. Simulation studies and real data analysis confirm the effectiveness of our approach, particularly in scenarios with pronounced heavy-tailedness.

stat.ME↗

arXiv2025

Worth Their Weight: Randomized and Regularized Block Kaczmarz Algorithms without Preprocessing

Due to the ever growing amounts of data leveraged for machine learning and scientific computing, it is increasingly important to develop algorithms that sample only a small portion of the data at a time. In the case of linear least-squares, the randomized block Kaczmarz method (RBK) is an appealing example of such an algorithm, but its convergence is only understood under sampling distributions that require potentially prohibitively expensive preprocessing steps. To address this limitation, we analyze RBK when the data is sampled uniformly, showing that its iterates converge in a Monte Carlo sense to a $\textit{weighted}$ least-squares solution. Unfortunately, for general problems the bias of the weighted least-squares solution and the variance of the iterates can become arbitrarily large. We show that these quantities can be rigorously controlled by incorporating regularization into the RBK iterations, yielding the regularized algorithm ReBlocK. Numerical experiments including examples arising from natural gradient optimization demonstrate that ReBlocK can outperform both RBK and minibatch stochastic gradient descent for inconsistent problems with rapidly decaying singular values.

cs.LG↗

arXiv2025

A Retraction-free Method for Nonsmooth Minimax Optimization over a Compact Manifold

We study the minimax problem $\min_{x\in M} \max_y f_r(x,y):=f(x,y)-h(y)$, where $M$ is a compact submanifold, $f$ is continuously differentiable in $(x, y)$, $h$ is a closed, weakly-convex (possibly non-smooth) function and we assume that the regularized coupling function $-f_r(x,\cdot)$ is either $μ$-PL for some $μ>0$ or concave ($μ= 0$) for any fixed $x$ in the vicinity of $M$. To address the nonconvexity due to the manifold constraint, we use an exact penalty for the constraint $x \in M$, and enforcing a convex constraint $x\in X$ for some $X \supset M$, onto which projections can be computed efficiently. Building upon this new formulation for the manifold minimax problem in question, a single-loop smoothed manifold gradient descent-ascent (sm-MGDA) algorithm is proposed. Theoretically, any limit point of sm-MGDA sequence is a stationary point of the manifold minimax problem and sm-MGDA can generate an $O(ε)$-stationary point of the original problem with $O(1/ε^2)$ and $\tilde{O}(1/ε^4)$ complexity for $μ> 0$ and $μ= 0$ scenarios, respectively. Moreover, for the $μ= 0$ setting, through adopting Tikhonov regularization of the dual, one can improve the complexity to $O(1/ε^3)$ at the expense of asymptotic stationarity. The key component, common in the analysis of all cases, is to connect $ε$-stationary points between the penalized problem and the original problem by showing that the constraint $x \in X$ becomes inactive and the penalty term tends to $0$ along any convergent subsequence. To our knowledge, sm-MGDA is the first retraction-free algorithm for minimax problems over compact submanifolds, and this is a very desirable algorithmic property since through avoiding retractions, one can get away with matrix orthogonalization subroutines required for computing retractions to manifolds arising in practice, which are not GPU friendly.

math.OC↗

arXiv2025

Extended parameter shift rules with minimal derivative variance for parameterized quantum circuits

Parameter shift rules (PSRs) are useful methods for computing arbitrary-order derivatives of the cost function in parameterized quantum circuits. The basic idea of PSRs is to evaluate the cost function at different parameter shifts, then use specific coefficients to combine them linearly to obtain the exact derivatives. In this work, we propose an extended parameter shift rule (EPSR) which generalizes a broad range of existing PSRs and has the following two advantages. First, EPSR offers an infinite number of possible parameter shifts, allowing the selection of the optimal parameter shifts to minimize the final derivative variance and thereby obtaining the more accurate derivative estimates with limited quantum resources. Second, EPSR extends the scope of the PSRs in the sense that EPSR can handle arbitrary Hermitian operator $H$ in gate $U(x) = \exp (iHx)$ in the parameterized quantum circuits, while existing PSRs are valid only for simple Hermitian generators $H$ such as simple Pauli words. Additionally, we show that the widely used ``general PSR'', introduced by Wierichs et al. (2022), is a special case of our EPSR, and we prove that it yields globally optimal shifts for minimizing the derivative variance under the weighted-shot scheme. Finally, through numerical simulations, we demonstrate the effectiveness of EPSR and show that the usage of the optimal parameter shifts indeed leads to more accurate derivative estimates.

quant-ph↗

arXiv2025

Asymptotics for Reinforced Stochastic Processes on Hierarchical Networks

In this paper, we analyze the asymptotic behavior of a system of interacting reinforced stochastic processes $({\bf Z}_n, {\bf N}_n)_n$ on a directed network of $N$ agents. The system is defined by the coupled dynamics ${\bf Z}_{n+1}=(1-r_{n}){\bf Z}_{n}+r_{n}{\bf X}_{n+1}$ and ${\bf N}_{n+1}=(1-\frac{1}{n+1}){\bf N}_n+\frac{1}{n+1}{\bf X}_{n+1}$, where agent actions $\mathbb{P}(X_{n+1,j}=1\mid{\cal F}_n)=\sum_{h} w_{hj}Z_{nh}$ are governed by a column-normalized adjacency matrix ${\bf W}$, and $r_n \sim cn^{-γ}$ with $γ\in (1/2, 1]$. Existing asymptotic theory has largely been restricted to irreducible and diagonalizable ${\bf W}$. We extend this analysis to the broader and more practical class of reducible and non-diagonalizable matrices ${\bf W}$ possessing a block upper-triangular form, which models hierarchical influence. We first establish synchronization, proving $({\bf Z}^\top_n, {\bf N}^\top_n)^\top \to Z_\infty {\bf 1}$ almost surely, where the distribution of the limit $Z_\infty$ is shown to be determined solely by the internal dynamics of the leading subgroup. Furthermore, we establish a joint central limit theorem for $({\bf Z}_n,{\bf N}_n)_n$, revealing how the spectral properties and Jordan block structure of ${\bf W}$ govern second-order fluctuations. We demonstrate that the convergence rates and the limiting covariance structure exhibit a phase transition dependent on $γ$ and the spectral properties of ${\bf W}$. Crucially, we explicitly characterize how the non-diagonalizability of ${\bf W}$ fundamentally alters the asymptotic covariance and introduces new logarithmic scaling factors in the critical case ($γ=1$). These results provide a probabilistic foundation for statistical inference on such hierarchical network structures.

math.ST↗

arXiv2025

Interpolation-based coordinate descent method for parameterized quantum circuits

Parameterized quantum circuits (PQCs) are ubiquitous in the design of hybrid quantum-classical algorithms. In this work, we propose an interpolation-based coordinate descent (ICD) method to address the parameter optimization problem in PQCs. The ICD method provides a unified framework for existing structure optimization techniques such as Rotosolve, sequential minimal optimization, ExcitationSolve, and others. ICD employs interpolation to approximate the PQC cost function, effectively recovering its underlying trigonometric structure, and then performs an argmin update on a single parameter in each iteration. In contrast to previous studies on structure optimization, we determine the optimal interpolation nodes to mitigate statistical errors arising from quantum measurements. Moreover, in the common case of $r$ equidistant frequencies, we show that the optimal interpolation nodes are equidistant nodes with spacing $2π/(2r+1)$ (under constant variance assumption), and that our ICD method simultaneously minimizes the mean squared error, the condition number of the interpolation matrix, and the average variance of the approximated cost function. We perform numerical simulations and test on the MaxCut problem, the transverse field Ising model, and the XXZ model. Numerical results imply that our ICD method is more efficient than the commonly used gradient descent and random coordinate descent method.

quant-ph↗

arXiv2025

A general partial Cramér's condition for Edgeworth expansion of a function of sample means with applications

A large class of statistics can be formulated as smooth functions of sample means of random vectors. In this paper, we propose a general partial Cramér's condition (GPCC) and apply it to establish the validity of the Edgeworth expansion for the distribution function of these functions of sample means. Additionally, we apply the proposed theorems to several specific statistics. In particular, by verifying the GPCC, we demonstrate for the first time the validity of the formal Edgeworth expansion of Pearson's correlation coefficient between random variables with absolutely continuous and discrete components. Furthermore, we conduct a series of simulation studies that show the Edgeworth expansion has higher accuracy.

math.PR↗

arXiv2025

Adaptive Riemannian ADMM for Nonsmooth Optimization: Optimal Complexity without Smoothing

We study the problem of minimizing the sum of a smooth function and a nonsmooth convex regularizer over a compact Riemannian submanifold embedded in Euclidean space. By introducing an auxiliary splitting variable, we propose an adaptive Riemannian alternating direction method of multipliers (ARADMM), which, for the first time, achieves convergence without requiring smoothing of the nonsmooth term. Our approach involves only one Riemannian gradient evaluation and one proximal update per iteration. Through careful and adaptive coordination of the stepsizes and penalty parameters, we establish an optimal iteration complexity of order $\mathcal{O}(ε^{-3})$ for finding an $ε$-approximate KKT point, matching the complexity of existing smoothing technique-based Riemannian ADMM methods. Extensive numerical experiments on sparse PCA and robust subspace recovery demonstrate that our ARADMM consistently outperforms state-of-the-art Riemannian ADMM variants in convergence speed and solution quality.

math.OC↗

arXiv2025

Asymptotic distributions of four linear hypotheses test statistics under generalized spiked model

In this paper, we establish the Central Limit Theorem (CLT) for linear spectral statistics (LSSs) of large-dimensional generalized spiked sample covariance matrices, where the spiked eigenvalues may be either bounded or diverge to infinity. Building upon this theorem, we derive the asymptotic distributions of linear hypothesis test statistics under the generalized spiked model, including Wilks' likelihood ratio test statistic U, the Lawley-Hotelling trace test statistic W, and the Bartlett-Nanda-Pillai trace test statistic V. Due to the complexity of the test functions, explicit solutions for the contour integrals in our calculations are generally intractable. To address this, we employ Taylor series expansions to approximate the theoretical results in the asymptotic regime. We also derive asymptotic power functions for three test criteria above, and make comparisons with Roy's largest root test under specific scenarios. Finally, numerical simulations are conducted to validate the accuracy of our asymptotic approximations.

math.ST↗

arXiv2025

VCDiag: Classifying Erroneous Waveforms for Failure Triage Acceleration

Failure triage in design functional verification is critical but time-intensive, relying on manual specification reviews, log inspections, and waveform analyses. While machine learning (ML) has improved areas like stimulus generation and coverage closure, its application to RTL-level simulation failure triage, particularly for large designs, remains limited. VCDiag offers an efficient, adaptable approach using VCD data to classify failing waveforms and pinpoint likely failure locations. In the largest experiment, VCDiag achieves over 94% accuracy in identifying the top three most likely modules. The framework introduces a novel signal selection and statistical compression approach, achieving over 120x reduction in raw data size while preserving features essential for classification. It can also be integrated into diverse Verilog/SystemVerilog designs and testbenches.

cs.LG↗

arXiv2025

Structural Effect and Spectral Enhancement of High-Dimensional Regularized Linear Discriminant Analysis

Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear insight into how data structure affects classification performance. To address this issue, we derive a non-asymptotic approximation of the misclassification rate and thus analyze the structural effect and structural adjustment strategies of RLDA. Based on this, we propose the Spectral Enhanced Discriminant Analysis (SEDA) algorithm, which optimizes the data structure by adjusting the spiked eigenvalues of the population covariance matrix. By developing a new theoretical result on eigenvectors in random matrix theory, we derive an asymptotic approximation on the misclassification rate of SEDA. The bias correction algorithm and parameter selection strategy are then obtained. Experiments on synthetic and real datasets show that SEDA achieves higher classification accuracy and dimensionality reduction compared to existing LDA methods.

stat.ML↗

arXiv2025

BugGen: A Self-Correcting Multi-Agent LLM Pipeline for Realistic RTL Bug Synthesis

Hardware complexity continues to strain verification resources, motivating the adoption of machine learning (ML) methods to improve debug efficiency. However, ML-assisted debugging critically depends on diverse and scalable bug datasets, which existing manual or automated bug insertion methods fail to reliably produce. We introduce BugGen, a first of its kind, fully autonomous, multi-agent pipeline leveraging Large Language Models (LLMs) to systematically generate, insert, and validate realistic functional bugs in RTL. BugGen partitions modules, selects mutation targets via a closed-loop agentic architecture, and employs iterative refinement and rollback mechanisms to ensure syntactic correctness and functional detectability. Evaluated across five OpenTitan IP blocks, BugGen produced 500 unique bugs with 94% functional accuracy and achieved a throughput of 17.7 validated bugs per hour-over five times faster than typical manual expert insertion. Additionally, BugGen identified 104 previously undetected bugs in OpenTitan regressions, highlighting its utility in exposing verification coverage gaps. Compared against Certitude, BugGen demonstrated over twice the syntactic accuracy, deeper exposure of testbench blind spots, and more functionally meaningful and complex bug scenarios. Furthermore, when these BugGen-generated datasets were employed to train ML-based failure triage models, we achieved high classification accuracy (88.1%-93.2%) across different IP blocks, confirming the practical utility and realism of generated bugs. BugGen thus provides a scalable solution for generating high-quality bug datasets, significantly enhancing verification efficiency and ML-assisted debugging.

cs.SE↗

arXiv2025

On the rate of convergence in the CLT for LSS of large-dimensional sample covariance matrices

This paper investigates the rate of convergence for the central limit theorem of linear spectral statistic (LSS) associated with large-dimensional sample covariance matrices. We consider matrices of the form ${\mathbf B}_n=\frac{1}{n}{\mathbf T}_p^{1/2}{\mathbf X}_n{\mathbf X}_n^*{\mathbf T}_p^{1/2},$ where ${\mathbf X}_n= (x_{i j} ) $ is a $p \times n$ matrix whose entries are independent and identically distributed (i.i.d.) real or complex variables, and ${\mathbf T} _p$ is a $p\times p$ nonrandom Hermitian nonnegative definite matrix with its spectral norm uniformly bounded in $p$. Employing Stein's method, we establish that if the entries $x_{ij}$ satisfy $\mathbb{E}|x_{ij}|^{10}<\infty$ and the ratio of the dimension to sample size $p/n\to y>0$ as $n\to\infty$, then the convergence rate of the normalized LSS of ${\mathbf B}_n$ to the standard normal distribution, measured in the Kolmogorov-Smirnov distance, is $O(n^{-1/2+κ})$ for any fixed $κ>0$.

math.PR↗