arXiv subjects

Jiang Hu

Publications and source records attributed to Jiang Hu.

At least 55 records · Page 3Linked to original sources

arXiv2025

Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity

We consider decentralized optimization over a compact Riemannian submanifold in a network of $n$ agents, where each agent holds a smooth, nonconvex local objective defined by its private data. The goal is to collaboratively minimize the sum of these local objective functions. In the presence of data heterogeneity across nodes, existing algorithms typically require communicating both local gradients and iterates to ensure exact convergence with constant step sizes. In this work, we propose REXTRA, a Riemannian extension of the EXTRA algorithm [Shi et al., SIOPT, 2015], to address this limitation. On the theoretical side, we leverage proximal smoothness to overcome the challenges of manifold nonconvexity and establish a global sublinear convergence rate of $\mathcal{O}(1/k)$, matching the best-known results. To our knowledge, REXTRA is the first algorithm to achieve a global sublinear convergence rate under a constant step size while requiring only a single round of local iterate communication per iteration. Numerical experiments show that REXTRA achieves superior performance compared to state-of-the-art methods, while supporting larger step sizes and reducing total communication by over 50\%.

math.OC↗

arXiv2025

Spec2Assertion: Automatic Pre-RTL Assertion Generation using Large Language Models with Progressive Regularization

SystemVerilog Assertions (SVAs) play a critical role in detecting and debugging functional bugs in digital chip design. However, generating SVAs has traditionally been a manual, labor-intensive, and error-prone process. Recent advances in automatic assertion generation, particularly those using machine learning and large language models (LLMs), have shown promising potential, though most approaches remain in the early stages of development. In this work, we introduce Spec2Assertion, a new technique for automatically generating assertions from design specifications prior to RTL implementation. It leverages LLMs with progressive regularization and incorporates Chain-of-Thought (CoT) prompting to guide assertion synthesis. Additionally, we propose a new evaluation methodology that assesses assertion quality across a broad range of scenarios. Experiments on multiple benchmark designs show that Spec2Assertion generates 70% more syntax-correct assertions with 2X quality improvement on average compared to a recent state-of-the-art approach.

cs.AR↗

arXiv2025

PatternPaint: Practical Layout Pattern Generation Using Diffusion-Based Inpainting

Generating diverse VLSI layout patterns is essential for various downstream tasks in design for manufacturing, as design rules continually evolve during the development of new technology nodes. However, existing training-based methods for layout pattern generation rely on large datasets. In practical scenarios, especially when developing a new technology node, obtaining such extensive layout data is challenging. Consequently, training models with large datasets becomes impractical, limiting the scalability and adaptability of prior approaches. To this end, we propose PatternPaint, a diffusion-based framework capable of generating legal patterns with limited design-rule-compliant training samples. PatternPaint simplifies complex layout pattern generation into a series of inpainting processes with a template-based denoising scheme. Furthermore, we perform few-shot finetuning on a pretrained image foundation model with only 20 design-rule-compliant samples. Experimental results show that using a sub-3nm technology node (Intel 18A), our model is the only one that can generate legal patterns in complex 2D metal interconnect design rule settings among all previous works and achieves a high diversity score. Additionally, our few-shot finetuning can boost the legality rate with 1.87X improvement compared to the original pretrained model. As a result, we demonstrate a production-ready approach for layout pattern generation in developing new technology nodes.

cs.CV↗

arXiv2025

An efficient primal dual semismooth Newton method for semidefinite programming

In this paper, we present an efficient semismooth Newton method, named SSNCP, for solving a class of semidefinite programming problems. Our approach is rooted in an equivalent semismooth system derived from the saddle point problem induced by the augmented Lagrangian duality. An additional correction step is incorporated after the semismooth Newton step to ensure that the iterates eventually reside on a manifold where the semismooth system is locally smooth. Global convergence is achieved by carefully designing inexact criteria and leveraging the $α$-averaged property to analyze the error. The correction steps address challenges related to the lack of smoothness in local convergence analysis. Leveraging the smoothness established by the correction steps and assuming a local error bound condition, we establish the local superlinear convergence rate without requiring the stringent assumptions of nonsingularity or strict complementarity. Furthermore, we prove that SSNCP converges to an $\varepsilon$-stationary point with an iteration complexity of $\widetilde{\mathcal{O}}(\varepsilon^{-3/2})$. Numerical experiments on various datasets, especially the Mittelmann benchmark, demonstrate the high efficiency and robustness of SSNCP compared to state-of-the-art solvers.

math.OC↗

arXiv2025

Lorecast: Layout-Aware Performance and Power Forecasting from Natural Language

In chip design planning, obtaining reliable performance and power forecasts for various design options is of critical importance. Traditionally, this involves using system-level models, which often lack accuracy, or trial synthesis, which is both labor-intensive and time-consuming. We introduce a new methodology, called Lorecast, which accepts English prompts as input to rapidly generate layout-aware performance and power estimates. This approach bypasses the need for HDL code development and synthesis, making it both fast and user-friendly. Experimental results demonstrate that Lorecast achieves accuracy within a few percent of error compared to post-layout analysis, while significantly reducing turnaround time.

cs.AR↗

arXiv2025

Non-convex composite federated learning with heterogeneous data

We propose an innovative algorithm for non-convex composite federated learning that decouples the proximal operator evaluation and the communication between server and clients. Moreover, each client uses local updates to communicate less frequently with the server, sends only a single d-dimensional vector per communication round, and overcomes issues with client drift. In the analysis, challenges arise from the use of decoupling strategies and local updates in the algorithm, as well as from the non-convex and non-smooth nature of the problem. We establish sublinear and linear convergence to a bounded residual error under general non-convexity and the proximal Polyak-Lojasiewicz inequality, respectively. In the numerical experiments, we demonstrate the superiority of our algorithm over state-of-the-art methods on both synthetic and real datasets.

cs.LG↗

arXiv2025

A Survey of Research in Large Language Models for Electronic Design Automation

Within the rapidly evolving domain of Electronic Design Automation (EDA), Large Language Models (LLMs) have emerged as transformative technologies, offering unprecedented capabilities for optimizing and automating various aspects of electronic design. This survey provides a comprehensive exploration of LLM applications in EDA, focusing on advancements in model architectures, the implications of varying model sizes, and innovative customization techniques that enable tailored analytical insights. By examining the intersection of LLM capabilities and EDA requirements, the paper highlights the significant impact these models have on extracting nuanced understandings from complex datasets. Furthermore, it addresses the challenges and opportunities in integrating LLMs into EDA workflows, paving the way for future research and application in this dynamic field. Through this detailed analysis, the survey aims to offer valuable insights to professionals in the EDA industry, AI researchers, and anyone interested in the convergence of advanced AI technologies and electronic design.

cs.LG↗

arXiv2024

Vertical Emission of Blue Light from a Symmetry Breaking Plasmonic Nanocavity-Emitter System Supporting Bound States in the Continuum

The concept of photonic bound states in the continuum (BICs), introduced in structured metallic surface cavities, provides a crucial mechanism for designing plasmonic open-resonant cavities with high quality (high-Q) factors, making significant advances in plasmonic nanophotonics. However, the two major bottlenecks for plasmonic nanocavities: enhancing emission and big beam divergence for quantum emitters, due to the strong intrinsic Ohmic losses of metals. Here, we propose and realize a σh symmetry-breaking plasmonic honeycomb nanocavities (PHC) that support quasi-BIC resonance modes with high-Q factors. Our anodic oxidation-engineered strategy breaks out-of-plane symmetry while preserving in-plane symmetry, enabling the PHC to exhibit collective plasmonic lattice resonances (PLR) couplings and achieve Q-factors exceeding 106. Experimentally, we couple perovskite quantum dots (PQDs) to the PHC, demonstrating effective tuning of their emission properties and beam quality in the blue spectral region, achieving a 32-fold emission enhancement by suppress Ohmic loss and the life time of quantum emitters, simultaneously realize vertical emission in the 2.556 - 2.638 eV region, with a far-field hexagonal beam shape and a full width at half maximum of 12.6 degree under optimal coupling conditions. Furthermore, we demonstrate topological band inversion characterized by Zak phase transitions by continuously tuning the system parameters, confirming that the PHC supports topologically non-trivial q-BIC due to PLR coupling. The PHC presents itself as a promising next-generation, high-brightness nanoscale light source matrix, which can be directly scaled up to cover a wide wavelength range from UV to IR.

physics.optics↗

arXiv2024

A revisit of the circular law

Consider a complex random $n\times n$ matrix ${\bf X}_n=(x_{ij})_{n\times n}$, whose entries $x_{ij}$ are independent random variables with zero means and unit variances. It is well-known that Tao and Vu (Ann Probab 38: 2023-2065, 2010) resolved the circular law conjecture, establishing that if the $x_{ij}$'s are independent and identically distributed random variables with zero mean and unit variance, the empirical spectral distribution of $\frac{1}{\sqrt{n}}{\bf X}_n$ converges almost surely to the uniform distribution over the unit disk in the complex plane as $n \to \infty$. This paper demonstrates that the circular law still holds under the more general Lindeberg's condition: $$ \frac1{n^2}\sum_{i,j=1}^n\mathbb{E}|x_{ij}^2|I(|x_{ij}|>η\sqrt{n})\to 0,\mbox{as $n \to \infty$}. $$ This paper is a revisit of the proof procedure of the circular law by Bai in (Ann Probab 25: 494-529, 1997). The key breakthroughs in the paper are establishing a general strong law of large numbers under Lindeberg's condition and the uniform upper bound for the integral with respect to the smallest eigenvalues of random matrices. These advancements significantly streamline and clarify the proof of the circular law, offering a more direct and simplified approach than other existing methodologies.

math.PR↗

arXiv2024

Identifying Smart Contract Security Issues in Code Snippets from Stack Overflow

Smart contract developers frequently seek solutions to developmental challenges on Q&A platforms such as Stack Overflow (SO). Although community responses often provide viable solutions, the embedded code snippets can also contain hidden vulnerabilities. Integrating such code directly into smart contracts may make them susceptible to malicious attacks. We conducted an online survey and received 74 responses from smart contract developers. The results of this survey indicate that the majority (86.4%) of participants do not sufficiently consider security when reusing SO code snippets. Despite the existence of various tools designed to detect vulnerabilities in smart contracts, these tools are typically developed for analyzing fully-completed smart contracts and thus are ineffective for analyzing typical code snippets as found on SO. We introduce SOChecker, the first tool designed to identify potential vulnerabilities in incomplete SO smart contract code snippets. SOChecker first leverages a fine-tuned Llama2 model for code completion, followed by the application of symbolic execution methods for vulnerability detection. Our experimental results, derived from a dataset comprising 897 code snippets collected from smart contract-related SO posts, demonstrate that SOChecker achieves an F1 score of 68.2%, greatly surpassing GPT-3.5 and GPT-4 (20.9% and 33.2% F1 Scores respectively). Our findings underscore the need to improve the security of code snippets from Q&A websites.

cs.SE↗

arXiv2024

Improving the communication in decentralized manifold optimization through single-step consensus and compression

We are concerned with decentralized optimization over a compact submanifold, where the loss functions of local datasets are defined by their respective local datasets. A key challenge in decentralized optimization is mitigating the communication bottleneck, which primarily involves two strategies: achieving consensus and applying communication compression. Existing projection/retraction-type algorithms rely on multi-step consensus to attain both consensus and optimality. Due to the nonconvex nature of the manifold constraint, it remains an open question whether the requirement for multi-step consensus can be reduced to single-step consensus. We address this question by carefully elaborating on the smoothness structure and the asymptotic 1-Lipschitz continuity associated with the manifold constraint. Furthermore, we integrate these insights with a communication compression strategy to propose a communication-efficient gradient algorithm for decentralized manifold optimization problems, significantly reducing per-iteration communication costs. Additionally, we establish an iteration complexity of $\mathcal{O}(ε^{-1})$ to find an $ε$-stationary point, which matches the complexity in the Euclidean setting. Numerical experiments demonstrate the efficiency of the proposed method in comparison to state-of-the-art approaches.

math.OC↗

arXiv2024

Asymptotic properties of a multicolored random reinforced urn model with an application to multi-armed bandits

The random self-reinforcement mechanism, characterized by the principle of ``the rich get richer'', has demonstrated significant utility across various domains. One prominent model embodying this mechanism is the random reinforcement urn model. This paper investigates a multicolored, multiple-drawing variant of the random reinforced urn model. We establish the limiting behavior of the normalized urn composition and demonstrate strong convergence upon scaling the counts of each color. Additionally, we derive strong convergence estimators for the reinforcement means, i.e., for the expectations of the replacement matrix's diagonal elements, and prove their joint asymptotic normality. It is noteworthy that the estimators of the largest reinforcement mean are asymptotically independent of the estimators of the other smaller reinforcement means. Additionally, if a reinforcement mean is not the largest, the estimators of these smaller reinforcement means will also demonstrate asymptotic independence among themselves. Furthermore, we explore the parallels between the reinforced mechanisms in random reinforced urn models and multi-armed bandits, addressing hypothesis testing for expected payoffs in the latter context.

math.ST↗

arXiv2024

Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Data

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for manifold optimization in the centralized setting, there are currently very few works addressing the federated setting. In this paper, we consider nonconvex federated learning over a compact smooth submanifold in the setting of heterogeneous client data. We propose an algorithm that leverages stochastic Riemannian gradients and a manifold projection operator to improve computational efficiency, uses local updates to improve communication efficiency, and avoids client drift. Theoretically, we show that our proposed algorithm converges sub-linearly to a neighborhood of a first-order optimal solution by using a novel analysis that jointly exploits the manifold structure and properties of the loss functions. Numerical experiments demonstrate that our algorithm has significantly smaller computational and communication overhead than existing methods.

cs.LG↗

arXiv2024

A spectral based goodness-of-fit test for stochastic block models

Community detection is a fundamental problem in complex network data analysis. Though many methods have been proposed, most existing methods require the number of communities to be the known parameter, which is not in practice. In this paper, we propose a novel goodness-of-fit test for the stochastic block model. The test statistic is based on the linear spectral of the adjacency matrix. Under the null hypothesis, we prove that the linear spectral statistic converges in distribution to $N(0,1)$. Some recent results in generalized Wigner matrices are used to prove the main theorems. Numerical experiments and real world data examples illustrate that our proposed linear spectral statistic has good performance.

stat.ME↗

arXiv2024

An Augmented Lagrangian Primal-Dual Semismooth Newton Method for Multi-Block Composite Optimization

In this paper, we develop a novel primal-dual semismooth Newton method for solving linearly constrained multi-block convex composite optimization problems. First, a differentiable augmented Lagrangian (AL) function is constructed by utilizing the Moreau envelopes of the nonsmooth functions. It enables us to derive an equivalent saddle point problem and establish the strong AL duality under the Slater's condition. Consequently, a semismooth system of nonlinear equations is formulated to characterize the optimality of the original problem instead of the inclusion-form KKT conditions. We then develop a semismooth Newton method, called ALPDSN, which uses purely second-order steps and a nonmonotone line search based globalization strategy. Through a connection to the inexact first-order steps when the regularization parameter is sufficiently large, the global convergence of ALPDSN is established. Under the regularity conditions, partial smoothness, the local error bound, and the strict complementarity, we show that both the primal and the dual iteration sequences possess a superlinear convergence rate and provide concrete examples where these regularity conditions are met. Numerical results on the image restoration with two regularization terms and the corrected tensor nuclear norm problem are presented to demonstrate the high efficiency and robustness of our ALPDSN.

math.OC↗

arXiv2024

The Asymptotic Properties of the Extreme Eigenvectors of High-dimensional Generalized Spiked Covariance Model

In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block diagonal structure in the population covariance matrix. Moreover, there is no requirement for the spiked eigenvalues and the 4th moment to be bounded. Specifically, we apply random matrix theory to derive the convergence and limiting distributions of certain projections of the extreme eigenvectors in a large sample covariance matrix within a generalized spiked population model. Furthermore, our techniques are robust and effective, even when spiked eigenvalues differ significantly in magnitude from nonspiked ones. Finally, we propose a powerful statistic for hypothesis testing for the eigenspaces of covariance matrices.

math.ST↗

arXiv2024

Oracle complexities of augmented Lagrangian methods for nonsmooth manifold optimization

In this paper, we present two novel manifold inexact augmented Lagrangian methods, \textbf{ManIAL} for deterministic settings and \textbf{StoManIAL} for stochastic settings, solving nonsmooth manifold optimization problems. By using the Riemannian gradient method as a subroutine, we establish an $\mathcal{O}(ε^{-3})$ oracle complexity result of \textbf{ManIAL}, matching the best-known complexity result. Our algorithm relies on the careful selection of penalty parameters and the precise control of termination criteria for subproblems. Moreover, for cases where the smooth term follows an expectation form, our proposed \textbf{StoManIAL} utilizes a Riemannian recursive momentum method as a subroutine, and achieves an oracle complexity of $\tilde{\mathcal{O}}(ε^{-3.5})$, which surpasses the best-known $\mathcal{O}(ε^{-4})$ result. Numerical experiments conducted on sparse principal component analysis and sparse canonical correlation analysis demonstrate that our proposed methods outperform an existing method with the previously best-known complexity result. To the best of our knowledge, these are the first complexity results of the augmented Lagrangian methods for solving nonsmooth manifold optimization problems.

math.OC↗

arXiv2024

AdaFish: Fast low-rank parameter-efficient fine-tuning by using second-order information

Recent advancements in large-scale pretrained models have significantly improved performance across a variety of tasks in natural language processing and computer vision. However, the extensive number of parameters in these models necessitates substantial memory and computational resources for full training. To adapt these models for downstream tasks or specific application-oriented datasets, parameter-efficient fine-tuning methods leveraging pretrained parameters have gained considerable attention. However, it can still be time-consuming due to lots of parameters and epochs. In this work, we introduce AdaFish, an efficient algorithm of the second-order type designed to expedite the training process within low-rank decomposition-based fine-tuning frameworks. Our key observation is that the associated generalized Fisher information matrix is either low-rank or extremely small-scaled. Such a generalized Fisher information matrix is shown to be equivalent to the Hessian matrix. Moreover, we prove the global convergence of AdaFish, along with its iteration/oracle complexity. Numerical experiments show that our algorithm is quite competitive with the state-of-the-art AdamW method.

cs.LG↗