arXiv subjects

Jiani Wang

Publications and source records attributed to Jiani Wang.

13 recordsLinked to original sources

arXiv2026

A Stochastic Implicit Proximal Point Algorithm for Solving Linearly Constrained Stochastic Minimax Problems

This paper presents a novel approach to solving large-scale minimax problems with nonsmooth regularizers. We propose a stochastic implicit proximal point algorithm with variance reduction techniques where stochastic oracles are selected in two cases -- with or without replacement. The semismooth Newton methods with Armijo line search is used to solve the implicit proximal point update subproblem in each iteration. The algorithm efficiently handles the strongly-convex-strongly-concave objective function with nonsmooth regularizers and coupling linear equations, which is proved to exhibit global q-linear convergence of the iterations to the saddle point and global r-linearly convergence of the multipliers to the multiplier set in expectation. Numerical experiments on machine learning problems demonstrate the superiority of the proposed method over state-of-the-art algorithms in terms of both computational efficiency and selection of the step sizes.

math.OC↗

arXiv2026

Optimality Conditions and Numerical Algorithms for a Class of Minimax Bilevel Optimization Problems

In many applications, including Stackelberg games, machine learning, and power systems \cite{Mackay2018Selftuning,Heinrich1952The,Wang2021Bi-Level}, the decisions in a minimax optimization problem can be constrained by a solution to an optimization problem. In this paper, we introduce optimality conditions of this novel minimax bilevel optimization problem and develops efficient first-order algorithms for this class of problems. Firstly, we establish the optimality conditions for minimax bilevel problems by reconstructing the lower-level problem through its Karush-Kuhn-Tucker (KKT) conditions and value function. Secondly, we develop a penalty method framework to approximately solve the minimax bilevel problem by transforming it into a single-level minimax problem. Thirdly, we design a projected gradient multi-step ascent descent method to solve the resulting minimax problem, which can find an $\epsilon$-KKT solution for the original minimax bilevel problem within $\mathcal{O}(\epsilon^{-3} \log(\epsilon^{-1}))$ iterations. To improve {the convergence rate} of the algorithm, we provide its Nesterov accelerated extension with $\mathcal{O}(\epsilon^{-3} \log(\epsilon^{-1}))$ iteration complexity. Finally, we demonstrate the effectiveness of our model and algorithms through numerical experiments on various minimax bilevel optimization problems and a bilevel economic dispatch in the power system.

math.OC↗

arXiv2026

SPA: A Simple but Tough-to-Beat Baseline for Knowledge Injection

While large language models (LLMs) are pretrained on massive amounts of data, their knowledge coverage remains incomplete in specialized, data-scarce domains, motivating extensive efforts to study synthetic data generation for knowledge injection. We propose SPA (Scaling Prompt-engineered Augmentation), a simple but tough-to-beat baseline that uses a small set of carefully designed prompts to generate large-scale synthetic data for knowledge injection. Through systematic comparisons, we find that SPA outperforms several strong baselines. Furthermore, we identify two key limitations of prior approaches: (1) while RL-based methods may improve the token efficiency of LLM-based data augmentation at small scale, they suffer from diversity collapse as data scales, leading to diminishing returns; and (2) while multi-stage prompting may outperform simple augmentation methods, their advantages can disappear after careful prompt tuning. Our results suggest that, for knowledge injection, careful prompt design combined with straightforward large-scale augmentation can be surprisingly effective, and we hope SPA can serve as a strong baseline for future studies in this area. Our code is available at https://github.com/Tangkexian/SPA.

cs.LG↗

arXiv2025

Hierarchical Multi-Stage BERT Fusion Framework with Dual Attention for Enhanced Cyberbullying Detection in Social Media

Detecting and classifying cyberbullying in social media is hard because of the complex nature of online language and the changing nature of content. This study presents a multi-stage BERT fusion framework. It uses hierarchical embeddings, dual attention mechanisms, and extra features to improve detection of cyberbullying content. The framework combines BERT embeddings with features like sentiment and topic information. It uses self-attention and cross-attention to align features and has a hierarchical classification head for multi-category classification. A dynamic loss balancing strategy helps optimize learning and improves accuracy, precision, recall, and F1-score. These results show the model's strong performance and potential for broader use in analyzing social media content.

cs.CL↗

arXiv2025

Integral formulas and Teodorescu transform for generalized partial-slice monogenic functions

The theory of generalized partial-slice monogenic functions is considered as a syhthesis of the classical Clifford analysis and the theory of slice monogenic functions. In this paper, we investigate the Cauchy integral formula and the Plemelj formula for generalized partial-slice monogenic functions. Further, we study some properties of the Teodorescu transform in this context. A norm estimation for the Teodorescu transform is discussed as well.

math.CV↗

arXiv2025

A Hybrid Attention Framework for Fake News Detection with Large Language Models

With the rapid growth of online information, the spread of fake news has become a serious social challenge. In this study, we propose a novel detection framework based on Large Language Models (LLMs) to identify and classify fake news by integrating textual statistical features and deep semantic features. Our approach utilizes the contextual understanding capability of the large language model for text analysis and introduces a hybrid attention mechanism to focus on feature combinations that are particularly important for fake news identification. Extensive experiments on the WELFake news dataset show that our model significantly outperforms existing methods, with a 1.5\% improvement in F1 score. In addition, we assess the interpretability of the model through attention heat maps and SHAP values, providing actionable insights for content review strategies. Our framework provides a scalable and efficient solution to deal with the spread of fake news and helps build a more reliable online information ecosystem.

cs.CL↗

arXiv2025

Enhancing User Intent for Recommendation Systems via Large Language Models

Recommendation systems play a critical role in enhancing user experience and engagement in various online platforms. Traditional methods, such as Collaborative Filtering (CF) and Content-Based Filtering (CBF), rely heavily on past user interactions or item features. However, these models often fail to capture the dynamic and evolving nature of user preferences. To address these limitations, we propose DUIP (Dynamic User Intent Prediction), a novel framework that combines LSTM networks with Large Language Models (LLMs) to dynamically capture user intent and generate personalized item recommendations. The LSTM component models the sequential and temporal dependencies of user behavior, while the LLM utilizes the LSTM-generated prompts to predict the next item of interest. Experimental results on three diverse datasets ML-1M, Games, and Bundle show that DUIP outperforms a wide range of baseline models, demonstrating its ability to handle the cold-start problem and real-time intent adaptation. The integration of dynamic prompts based on recent user interactions allows DUIP to provide more accurate, context-aware, and personalized recommendations. Our findings suggest that DUIP is a promising approach for next-generation recommendation systems, with potential for further improvements in cross-modal recommendations and scalability.

cs.IR↗

arXiv2025

The Application of Large Language Models in Recommendation Systems

The integration of Large Language Models into recommendation frameworks presents key advantages for personalization and adaptability of experiences to the users. Classic methods of recommendations, such as collaborative filtering and content-based filtering, are seriously limited in the solution of cold-start problems, sparsity of data, and lack of diversity in information considered. LLMs, of which GPT-4 is a good example, have emerged as powerful tools that enable recommendation frameworks to tap into unstructured data sources such as user reviews, social interactions, and text-based content. By analyzing these data sources, LLMs improve the accuracy and relevance of recommendations, thereby overcoming some of the limitations of traditional approaches. This work discusses applications of LLMs in recommendation systems, especially in electronic commerce, social media platforms, streaming services, and educational technologies. This showcases how LLMs enrich recommendation diversity, user engagement, and the system's adaptability; yet it also looks into the challenges connected to their technical implementation. This can also be presented as a study that shows the potential of LLMs for changing user experiences and making innovation possible in industries.

cs.IR↗

arXiv2024

Stochastic Approximation Proximal Subgradient Method for Stochastic Convex-Concave Minimax Optimization

This paper presents a stochastic approximation proximal subgradient (SAPS) method for stochastic convex-concave minimax optimization. By accessing unbiased and variance bounded approximate subgradients, we show that this algorithm exhibits ${\rm O}(N^{-1/2})$ expected convergence rate of the minimax optimality measure if the parameters in the algorithm are properly chosen, where $N$ denotes the number of iterations. Moreover, we show that the algorithm has ${\rm O}(\log(N)N^{-1/2})$ minimax optimality measure bound with high probability. Further we study a specific stochastic convex-concave minimax optimization problems arising from stochastic convex conic optimization problems, which the the bounded subgradient condition is fail. To overcome the lack of the bounded subgradient conditions in convex-concave minimax problems, we propose a linearized stochastic approximation augmented Lagrange (LSAAL) method and prove that this algorithm exhibits ${\rm O}(N^{-1/2})$ expected convergence rate for the minimax optimality measure and ${\rm O}(\log^2(N)N^{-1/2})$ minimax optimality measure bound with high probability as well. Preliminary numerical results demonstrate the effect of the SAPS and LSAAL methods.

math.OC↗

arXiv2023

FlaCGEC: A Chinese Grammatical Error Correction Dataset with Fine-grained Linguistic Annotation

Chinese Grammatical Error Correction (CGEC) has been attracting growing attention from researchers recently. In spite of the fact that multiple CGEC datasets have been developed to support the research, these datasets lack the ability to provide a deep linguistic topology of grammar errors, which is critical for interpreting and diagnosing CGEC approaches. To address this limitation, we introduce FlaCGEC, which is a new CGEC dataset featured with fine-grained linguistic annotation. Specifically, we collect raw corpus from the linguistic schema defined by Chinese language experts, conduct edits on sentences via rules, and refine generated samples manually, which results in 10k sentences with 78 instantiated grammar points and 3 types of edits. We evaluate various cutting-edge CGEC methods on the proposed FlaCGEC dataset and their unremarkable results indicate that this dataset is challenging in covering a large range of grammatical errors. In addition, we also treat FlaCGEC as a diagnostic dataset for testing generalization skills and conduct a thorough evaluation of existing CGEC models.

cs.CL↗

arXiv2022

Optimality Conditions and Numerical Algorithms for A Class of Linearly Constrained Minimax Optimization Problems

It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constraints are very rare. This paper aims to discuss optimality conditions and develop practical numerical algorithms for minimax problems with joint linear constraints. First of all, we use the properties of proximal mapping and KKT system to establish optimality conditions. Secondly, we propose a framework of alternating coordinate algorithm for the minimax problem and analyze its convergence properties. Thirdly, we develop a proximal gradient multi-step ascent decent method (PGmsAD) as a numerical algorithm and demonstrate that the method can find an $ε$-stationary point for this kind of nonsmooth nonconvex-nonconcave problem in ${\cal O}(ε^{-2}\logε^{-1})$ iterations. Finally, we apply PGmsAD to generalized absolute value equations, generalized linear projection equations and linear regression problems and report the efficiency of PGmsAD on large-scale optimization.

math.OC↗

arXiv2021

New insights in smoothness and strong convexity with improved convergence of gradient descent

The starting assumptions to study the convergence and complexity of gradient-type methods may be the smoothness (also called Lipschitz continuity of gradient) and the strong convexity. In this note, we revisit these two basic properties from a new perspective that motivates their definitions and equivalent characterizations, along with an improved linear convergence of the gradient descent method.

math.OC↗

arXiv2020

Majorized Semi-proximal Alternating Coordinate Method for Nonsmooth Convex-Concave Minimax Optimization

Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research areas. While there have been many numerical algorithms for solving smooth convex-concave minimax problems, numerical algorithms for nonsmooth convex-concave minimax problems are very rare. This paper aims to develop an efficient numerical algorithm for a structured nonsmooth convex-concave minimax problem. A majorized semi-proximal alternating coordinate method (mspACM) is proposed, in which a majorized quadratic convex-concave function is adopted for approximating the smooth part of the objective function and semi-proximal terms are added in each subproblem. This construction enables the subproblems at each iteration are solvable and even easily solved when the semiproximal terms are cleverly chosen. We prove the global convergence of the algorithm mspACM under mild assumptions, without requiring strong convexity-concavity condition. Under the locally metrical subregularity of the solution mapping, we prove that the algorithm mspACM has the linear rate of convergence. Preliminary numerical results are reported to verify the efficiency of the algorithm mspACM.

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