arXiv subjects

Xu Yuan

Publications and source records attributed to Xu Yuan.

At least 19 recordsLinked to original sources

arXiv2026

Construction of three-solitons with logarithmic distance for the mass-critical gKdV equations

For the mass-critical generalized Korteweg-de Vries equation, \begin{equation*} \partial_{t}u+\partial_{x}\left( \partial_{x}^{2}u+u^{5}\right)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}, \end{equation*} we prove the existence of three-soliton solutions with logarithmic relative distance and with the choice of signs $(+,-,-)$. The choice of the number three and the signs of solitons are related to the solvability of the ODE system generated by the nonlinear interactions between the three solitons and some non-localized profiles. In particular, these special behaviors are due to strong interactions between the three solitons. That is, the dynamics of each soliton is perturbed at leading order by the presence of other solitons.

math.AP↗

arXiv2026

FashionKG-RAG: Knowledge Graph-Enhanced Retrieval-Augmented Generation for Fashion Question Answering

Fashion is a knowledge-intensive domain in which effective decision-making depends on integrating multiple types of knowledge. Although Large Language Models (LLMs) have transformed many areas, their application in fashion remains limited by hallucinations and weak domain specialization. Knowledge Graph (KG)-based Retrieval-Augmented Generation (RAG) offers a promising way to add structured knowledge to LLMs. However, existing fashion KGs are typically restricted to product-level attributes or item relations, and fail to capture the broader fashion ecosystem. To bridge these gaps, we propose \textbf{FashionEcoKG}, a comprehensive, domain-wide knowledge graph built with expert-level precision and professionalism. It is constructed through a three-stage agentic pipeline that extracts high-fidelity knowledge cores from authoritative textbooks and strengthens structural connectivity through cross-domain augmentation and generative expansion. To leverage this resource, we further develop \textbf{PG-RAG} (Pruning-Grounding RAG), a training-free framework designed to handle the conceptual density and linguistic noise of fashion queries. Specifically, we introduce a Dual-Granularity Path Re-Ranking (DGPR) module of two stages. The Pruning-based Semantic Ranking (PSR) module distills each query into a skeleton form to improve retrieval recall, while the Grounding-based Agentic Ranking (GAR) performs point-wise scrutiny of candidate paths against the original full query to ensure global relevance. Experiments on a curated fashion QA dataset show that PG-RAG effectively leverages FashionEcoKG to improve retrieval and answer accuracy, outperforming both non-RAG and existing KG-RAG baselines.

cs.IR↗

arXiv2026

Quantitative observability for one-dimensional Schrödinger equations with potentials

In this note, we prove the quantitative observability with an explicit control cost for the 1D Schrödinger equation over $\mathbb{R}$ with real-valued, bounded continuous potential on thick sets. Our proof relies on different techniques for low-frequency and high-frequency estimates. In particular, we extend the large time observability result for the 1D free Schrodinger equation in Theorem 1.1 of Huang-Wang-Wang [20] to any short time. As another byproduct, we extend the spectral inequality of Lebeau-Moyano [27] for real-analytic potentials to bounded continuous potentials in the one-dimensional case.

math.AP↗

arXiv2026

mKG-RAG: Leveraging Multimodal Knowledge Graphs in Retrieval-Augmented Generation for Knowledge-intensive VQA

Retrieval-Augmented Generation (RAG) has emerged as an effective paradigm for expanding the knowledge capacity of Multimodal Large Language Models (MLLMs) by incorporating external knowledge sources into the generation process, and has been widely adopted for knowledge-based Visual Question Answering (VQA). Despite impressive advancements, vanilla RAG-based VQA methods that rely on unstructured documents and overlook the structural relations among knowledge elements frequently introduce irrelevant or misleading content, degrading answer accuracy and reliability. To overcome these challenges, a promising solution is to integrate multimodal knowledge graphs (KGs) into RAG-based VQA frameworks, thereby enhancing generation through structured multimodal knowledge. To this end, this paper proposes mKG-RAG, a novel retrieval-augmented generation framework built upon multimodal KGs for knowledge-intensive VQA tasks. Specifically, mKG-RAG leverages MLLM-driven graph extraction and vision-text matching to distill semantically consistent, modality-complementary entities and relations from multimodal documents, constructing high-quality multimodal KGs as structured knowledge representations. Furthermore, a dual-stage retrieval strategy equipped with a query-aware multimodal retriever is introduced to improve retrieval efficiency while progressively refining precision. Comprehensive experiments demonstrate that our approach significantly outperforms existing approaches and sets new state-of-the-art results for knowledge-based VQA. The code is available at https://github.com/xandery-geek/mKG-RAG.

cs.CV↗

arXiv2026

Beyond Static Collision Handling: Adaptive Semantic ID Learning for Multimodal Recommendation at Industrial Scale

Modern recommendation systems involve massive catalogs of multimodal items, where scalable item identification must balance compactness, semantic fidelity, and downstream effectiveness. Semantic IDs (SIDs) address this need by representing items as short discrete token sequences derived from multimodal signals, providing a compact interface for retrieval, ranking, and generative recommendation. However, effective SID learning is hindered by collisions, where different items are assigned identical or highly confusable codes. Existing methods mainly rely on improved quantization or fixed overlap regularization, but they do not adaptively distinguish whether an overlap should be suppressed or preserved. We propose AdaSID, an adaptive semantic ID learning framework for recommendation. AdaSID regulates SID overlaps through a two-stage process. First, it relaxes repulsion for observed overlaps when the involved items are semantically compatible, preserving admissible sharing rather than uniformly separating all collisions. Second, it allocates the remaining regulation pressure according to local collision load and training progress, strengthening control in congested regions while gradually rebalancing optimization toward recommendation alignment. This design adaptively decides which overlaps to penalize, how strongly to regulate them, and when to shift the learning focus. Extensive offline and online experiments validate AdaSID. On two public benchmarks, AdaSID improves Recall and NDCG by about 4.5% on average over strong baselines, while improving codebook utilization and SID diversity. In Kuaishou e-commerce, an online A/B test on short-video retrieval covering tens of millions of users achieves statistically significant gains, including a 0.98% GMV improvement, and industrial ranking evaluation shows consistent AUC improvements.

cs.IR↗

arXiv2026

M3R: Localized Rainfall Nowcasting with Meteorology-Informed MultiModal Attention

Accurate and timely rainfall nowcasting is crucial for disaster mitigation and water resource management. Despite recent advances in deep learning, precipitation prediction remains challenging due to limitations in effectively leveraging diverse multimedia data sources. We introduce M3R, a Meteorology-informed MultiModal attention-based architecture for direct Rainfall prediction that synergistically combines visual NEXRAD radar imagery with numerical Personal Weather Station (PWS) measurements, using a comprehensive pipeline for temporal alignment of heterogeneous meteorological data. With specialized multimodal attention mechanisms, M3R novelly leverages weather station time series as queries to selectively attend to spatial radar features, enabling focused extraction of precipitation signatures. Experimental results for three spatial areas of 100 km * 100 km centered at NEXRAD radar stations demonstrate that M3R outperforms existing approaches, achieving substantial improvements in accuracy, efficiency, and precipitation detection capabilities. Our work establishes new benchmarks for multimedia-based precipitation nowcasting and provides practical tools for operational weather prediction systems. The source code is available at https://github.com/Sanjeev97/M3Rain

cs.LG↗

arXiv2026

SUPERGLASSES: Benchmarking Vision Language Models as Intelligent Agents for AI Smart Glasses

The rapid advancement of AI-powered smart glasses-one of the hottest wearable devices-has unlocked new frontiers for multimodal interaction, with Visual Question Answering (VQA) over external knowledge sources emerging as a core application. Existing Vision Language Models (VLMs) adapted to smart glasses are typically trained and evaluated on traditional multimodal datasets; however, these datasets lack the variety and realism needed to reflect smart glasses usage scenarios and diverge from their specific challenges, where accurately identifying the object of interest must precede any external knowledge retrieval. To bridge this gap, we introduce SUPER- GLASSES, the first comprehensive VQA benchmark built on real-world data entirely collected by smart glasses devices. SUPERGLASSES comprises 2,422 egocentric image-question pairs spanning 14 image domains and 8 query categories, enriched with full search trajectories and reasoning annotations. We evaluate 26 representative VLMs on this benchmark, revealing significant performance gaps. To address the limitations of existing models, we further propose the SUPERLENS, a multimodal smart glasses agent that enables retrieval-augmented answer generation by integrating automatic object detection, query decoupling, and multimodal web search. SUPERLENS achieves state-of-the-art performance, outperforming GPT-4o by 2.19%, underscoring the need for task-specific solutions in smart glasses VQA. Our dataset is publicly available at https://huggingface.co/datasets/xandery/SuperGlasses.

cs.CV↗

arXiv2026

Construction of two-bubble blow-up solutions for the mass-critical gKdV equations

For the mass-critical generalized Korteweg-de Vries equation, $$ \partial_{t}u+\partial_{x}\left( \partial_{x}^{2}u+u^{5}\right)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}.$$ We prove the existence of a global solution that blows up in infinite time and approaches the sum of two decoupled bubbles with opposite signs. The proof is inspired by the techniques developed for the two-dimensional mass-critical NLS equation in a similar context by Martel-Raphaël [37]. The main difficulty originates from the fact that the unstable directions related to scaling are excited by the nonlinear interactions. To overcome this difficulty, a refined approximate solution that involves some non-localized profiles is needed. In particular, a sharp understanding for the interactions between solitons and such profiles is also required.

math.AP↗

arXiv2026

QA-Dragon: Query-Aware Dynamic RAG System for Knowledge-Intensive Visual Question Answering

Retrieval-Augmented Generation (RAG) has been introduced to mitigate hallucinations in Multimodal Large Language Models (MLLMs) by incorporating external knowledge into the generation process, and it has become a widely adopted approach for knowledge-intensive Visual Question Answering (VQA). However, existing RAG methods typically retrieve from either text or images in isolation, limiting their ability to address complex queries that require multi-hop reasoning or up-to-date factual knowledge. To address this limitation, we propose QA-Dragon, a Query-Aware Dynamic RAG System for Knowledge-Intensive VQA. Specifically, QA-Dragon introduces a domain router to identify the query's subject domain for domain-specific reasoning, along with a search router that dynamically selects optimal retrieval strategies. By orchestrating both text and image search agents in a hybrid setup, our system supports multimodal, multi-turn, and multi-hop reasoning, enabling it to tackle complex VQA tasks effectively. We evaluate our QA-Dragon on the Meta CRAG-MM Challenge at KDD Cup 2025, where it significantly enhances the reasoning performance of base models under challenging scenarios. Our framework achieves substantial improvements in both answer accuracy and knowledge overlap scores, outperforming baselines by 5.06% on the single-source task, 6.35% on the multi-source task, and 5.03% on the multi-turn task.

cs.AI↗

arXiv2026

FedACT: Concurrent Federated Intelligence across Heterogeneous Data Sources

Federated Learning (FL) enables collaborative intelligence across decentralized data source devices in a privacy-preserving way. While substantial research attention has been drawn to optimizing the learning process for an individual task, real-world applications increasingly require multiple machine learning tasks simultaneously training their models across a shared pool of devices. Naively applying single-FL optimization techniques in multi-FL systems results in suboptimal system performance, particularly due to device heterogeneity and resource inefficiency. To address such a critical open challenge, we introduce {\em FedACT}, a novel resource heterogeneity-aware device scheduling approach designed to efficiently schedule heterogeneous devices across multiple concurrent FL jobs, with the goal of minimizing their average job completion time (JCT). {\em FedACT} dynamically assigns devices to FL jobs based on an alignment scoring mechanism that evaluates the compatibility between available resources of devices and resource demands of jobs. Additionally, it incorporates participation fairness to ensure balanced contributions from devices across jobs, further enhancing the accuracy levels of learned global models. An optimal scheduling plan is formulated in {\em FedACT} by prioritizing devices with higher alignment scores, while ensuring fair participation across jobs. To evaluate the effectiveness of the proposed scheduling algorithm, we carried out comprehensive experiments using diverse FL jobs and benchmark datasets. Experimental results demonstrate that {\em FedACT} reduces the average JCT by up to 8.3$\times$ and improves model accuracy by up to 44.5\%, compared to the state-of-the-art baselines.

cs.LG↗

arXiv2026

Stop Treating Collisions Equally: Qualification-Aware Semantic ID Learning for Recommendation at Industrial Scale

Semantic IDs (SIDs) are compact discrete representations derived from multimodal item features, serving as a unified abstraction for ID-based and generative recommendation. However, learning high-quality SIDs remains challenging due to two issues. (1) Collision problem: the quantized token space is prone to collisions, in which semantically distinct items are assigned identical or overly similar SID compositions, resulting in semantic entanglement. (2) Collision-signal heterogeneity: collisions are not uniformly harmful. Some reflect genuine conflicts between semantically unrelated items, while others stem from benign redundancy or systematic data effects. To address these challenges, we propose Qualification-Aware Semantic ID Learning (QuaSID), an end-to-end framework that learns collision-qualified SIDs by selectively repelling qualified conflict pairs and scaling the repulsion strength by collision severity. QuaSID consists of two mechanisms: Hamming-guided Margin Repulsion, which translates low-Hamming SID overlaps into explicit, severity-scaled geometric constraints on the encoder space; and Conflict-Aware Valid Pair Masking, which masks protocol-induced benign overlaps to denoise repulsion supervision. In addition, QuaSID incorporates a dual-tower contrastive objective to inject collaborative signals into tokenization. Experiments on public benchmarks and industrial data validate QuaSID. On public datasets, QuaSID consistently outperforms strong baselines, improving top-K ranking quality by 5.9% over the best baseline while increasing SID composition diversity. In an online A/B test on Kuaishou e-commerce with a 5% traffic split, QuaSID increases ranking GMV-S2 by 2.38% and improves completed orders on cold-start retrieval by up to 6.42%. Finally, we show that the proposed repulsion loss is plug-and-play and enhances a range of SID learning frameworks across datasets.

cs.IR↗

arXiv2026

Generically sharp decay and blowing up at infinity for a weak null wave system

We study a system of semilinear wave equations satisfying the weak null condition, which can be regarded as a simplified model for the Einstein vacuum equations. The main objective is to establish precise pointwise decay estimates, as both lower and upper bounds of decay, for small data solutions. Specifically, we show that the difference between the solution and its leading-order term is dominated by lower-order terms that decay faster in the retarded time variable $u=t-r$. Moreover, we prove that these pointwise decay estimates are sharp for a generic class of small initial data decaying sufficiently fast. As applications of these estimates, we demonstrate that the energy of one component of the solution admits a lower bound that generically grows to infinity as $t\to +\infty$, which can be interpreted as ``blowing up at infinity." Furthermore, we verify that this component generically exhibits an energy cascade from high to low frequencies.

math.AP↗

arXiv2026

Revisiting the Seasonal Trend Decomposition for Enhanced Time Series Forecasting

Time series forecasting presents significant challenges in real-world applications across various domains. Building upon the decomposition of the time series, we enhance the architecture of machine learning models for better multivariate time series forecasting. To achieve this, we focus on the trend and seasonal components individually and investigate solutions to predict them with less errors. Recognizing that reversible instance normalization is effective only for the trend component, we take a different approach with the seasonal component by directly applying backbone models without any normalization or scaling procedures. Through these strategies, we successfully reduce error values of the existing state-of-the-art models and finally introduce dual-MLP models as more computationally efficient solutions. Furthermore, our approach consistently yields positive results with around 10% MSE average reduction across four state-of-the-art baselines on the benchmark datasets. We also evaluate our approach on a hydrological dataset extracted from the United States Geological Survey (USGS) river stations, where our models achieve significant improvements while maintaining linear time complexity, demonstrating real-world effectiveness. The source code is available at https://github.com/Sanjeev97/Time-Series-Decomposition

cs.LG↗

arXiv2026

Cross-Domain Transfer and Few-Shot Learning for Personal Identifiable Information Recognition

Accurate recognition of personally identifiable information (PII) is central to automated text anonymization. This paper investigates the effectiveness of cross-domain model transfer, multi-domain data fusion, and sample-efficient learning for PII recognition. Using annotated corpora from healthcare (I2B2), legal (TAB), and biography (Wikipedia), we evaluate models across four dimensions: in-domain performance, cross-domain transferability, fusion, and few-shot learning. Results show legal-domain data transfers well to biographical texts, while medical domains resist incoming transfer. Fusion benefits are domain-specific, and high-quality recognition is achievable with only 10% of training data in low-specialization domains.

cs.CL↗

arXiv2025

Long-Tailed Recognition via Information-Preservable Two-Stage Learning

The imbalance (or long-tail) is the nature of many real-world data distributions, which often induces the undesirable bias of deep classification models toward frequent classes, resulting in poor performance for tail classes. In this paper, we propose a novel two-stage learning approach to mitigate such a majority-biased tendency while preserving valuable information within datasets. Specifically, the first stage proposes a new representation learning technique from the information theory perspective. This approach is theoretically equivalent to minimizing intra-class distance, yielding an effective and well-separated feature space. The second stage develops a novel sampling strategy that selects mathematically informative instances, able to rectify majority-biased decision boundaries without compromising a model's overall performance. As a result, our approach achieves the state-of-the-art performance across various long-tailed benchmark datasets, validated via extensive experiments. Our code is available at https://github.com/fudong03/BNS_IPDPP.

cs.LG↗

arXiv2025

Designing Coherent Optical Environment for Dynamic Optical Manipulation with a Simple Control Beam

We propose a framework for designing coherent optical environments that enable versatile and dynamic optical manipulation. In contrast to conventional material-based near-field platforms, our approach employs a structured coherent light field -- optimized via a back-propagation-based inverse design algorithm -- as the manipulation environment. This light-based platform allows a simple control beam, such as a single plane wave or a low-numerical-aperture Gaussian beam, to steer micro-objects effectively. By establishing a one-to-one correspondence between control beam parameters (e.g., phase/polarization of a plane wave) and particle trapping positions, our method enables real-time and versatile control of particles. A wide range of two- and three-dimensional trajectories -- including circles, squares, tree-like paths, and epicycle-deferent curves -- can be achieved solely by modulating the phase of the control beam. This design strategy for the structured-light environments offers a dynamically reconfigurable, all-optical, and contact-free platform for advanced optical manipulation in free space, with promising applications in nanorobotics, biological probing, and beyond.

physics.optics↗

arXiv2025

Hierarchical Multi-Interest Co-Network For Coarse-Grained Ranking

In this era of information explosion, a personalized recommendation system is convenient for users to get information they are interested in. To deal with billions of users and items, large-scale online recommendation services usually consist of three stages: candidate generation, coarse-grained ranking, and fine-grained ranking. The success of each stage depends on whether the model accurately captures the interests of users, which are usually hidden in users' behavior data. Previous research shows that users' interests are diverse, and one vector is not sufficient to capture users' different preferences. Therefore, many methods use multiple vectors to encode users' interests. However, there are two unsolved problems: (1) The similarity of different vectors in existing methods is too high, with too much redundant information. Consequently, the interests of users are not fully represented. (2) Existing methods model the long-term and short-term behaviors together, ignoring the differences between them. This paper proposes a Hierarchical Multi-Interest Co-Network (HCN) to capture users' diverse interests in the coarse-grained ranking stage. Specifically, we design a hierarchical multi-interest extraction layer to update users' diverse interest centers iteratively. The multiple embedded vectors obtained in this way contain more information and represent the interests of users better in various aspects. Furthermore, we develop a Co-Interest Network to integrate users' long-term and short-term interests. Experiments on several real-world datasets and one large-scale industrial dataset show that HCN effectively outperforms the state-of-the-art methods. We deploy HCN into a large-scale real world E-commerce system and achieve extra 2.5\% improvements on GMV (Gross Merchandise Value).

cs.IR↗

arXiv2025

Construction of blow-up solution with minimal mass for 2D cubic Zakharov--Kuznetsov equation

In this article, we construct a minimal mass blow-up solution of the two-dimensional cubic (mass-critical) Zakharov--Kuznetsov equation: \begin{equation*} \partial_t ϕ+\partial_{x_1}(Δϕ+ϕ^3)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}^2. \end{equation*} Let $s>\frac{3}{4}$. Bhattacharya-Farah-Roudenko [2] show that $H^{s}$ solutions with $\|ϕ\|_{L^{2}}<\|Q\|_{L^{2}}$ are global in time. For such low regularity solutions, we study the dynamics at the threshold $\|ϕ\|_{L^{2}}=\|Q\|_{L^{2}}$ and demonstrate that finite time blow-up singularity formation may occur. This result and its proof are inspired by the recent blow-up result [29] for the mass-critical gKdV equation. This result is also complement of previous result [6] for nonexistence of minimal mass blow-up element in the energy space $H^{1}(\mathbb{R}^{2})$ of the two-dimensional cubic Zakharov--Kuznetsov equation.

math.AP↗