arXiv subjects

Weimin Zhang

Publications and source records attributed to Weimin Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Comparison principles and symmetry for subquadratic fractional $p$-Laplacian equations

This paper establishes a new comparison principle framework for the subquadratic fractional $p$-Laplacian, i.e.~$1 < p < 2$ under minimal regularity assumptions, that has remained a significant challenging issue due to the singularity of the operator. Our results provide the essential analytical tools required for the moving plane method in this setting. We prove first a weak comparison principle for $(-Δ)_p^s u = f(u)$ in bounded domains with sufficiently small measure, where only the boundedness of the weak solution is required. More importantly, we establish a strong comparison principle for continuous weak solutions in the parameter range $s \in (0, \frac{1}{2})$ and $\frac{1}{1-s} < p < 2$. Our proof introduces a localized barrier function and does not require any Hölder regularity of the weak solution, nor any smoothness of the domain. This presents a substantial contrast over previous study, which relied heavily on Hölder or even $C^{1,1}$ regularity. As a direct application, we employ these comparison principles to prove the symmetry of weak solutions to $(-Δ)_p^s u = f(u)$ under mild assumptions, which significantly extend existing symmetry theories for nonlocal quasilinear equations.

math.AP↗

arXiv2026

World Narrative Model for Highly Controllable Video Generation: A Paradigm Shift from Pixel Sampling to Physical World Orchestration

The fundamental obstacle to industrial grade video generation is the lack of controllability: existing models treat video as a pixel distribution sampling problem, bypassing the explicit, instance level $4D$ $(3D + T)$ physical world. Consequently, content creators cannot specify geometry, motion, camera parameters, or lighting in a deterministic, quantitative way, leading to the infamous ''gacha'' loop that makes professional content creation prohibitively inefficient and expensive. To address this, we introduce the World Narrative Model (WNM), a paradigm that decouples what to render -- the structured physical narrative -- from how to render -- the pixel generation process. WNM replaces end-to-end black-box sampling with orchestrated $4D$ pre-visualization for media generation. Collaborative agents translate sparse multimodal inputs, including text, reference videos, and sketches, into a fully editable world representation with scene geometry, object layouts, character/animal skeleton motion, trajectories, camera motion, and lighting at quantitative, physically meaningful granularity. This representation acts as a deterministic structural blueprint that drives existing video foundation models, either frozen or lightly adapted, to render final footage, turning the base model into a faithful neural shader. Built on this engine, our human-AI platform supports automatic world generation and pre-visualization aligned with professional filmmaking pipelines, while director consoles enable seamless human refinement. Experiments show that WNM greatly reduces probabilistic ``gacha'' calls and produces videos whose layout, motion, and cinematography closely follow creator intent. The framework is open and modular, allowing each component, such as world representation, control agents, and adapters, to be independently improved. Project website: https://glassroom.sjtu.edu.cn/WNM/.

cs.CV↗

arXiv2026

Existence and nonexistence of normalized solutions for nonlinear Schrödinger equation involving combined nonlinearities in bounded domain

In this paper, we consider the existence, multiplicity and nonexistence of solutions for the following equation \begin{equation*} \begin{cases} \begin{aligned} &-Δu+ωu=μu^{p-1}+u^{q-1},~ u>0 \quad &&\text { in } Ω, \\ &u=0 &&\text { on } \partialΩ, \\ \end{aligned} \end{cases} \end{equation*} with prescribed $L^2$-norm $\|u\|_2^2=ρ$, where $N\ge 1$, $ρ>0$, $μ\in \mathbb{R}$, $1<p\le q$, and $Ω\subset\mathbb{R}^N$ is a bounded smooth domain. The parameter $ω\in\mathbb{R}$ arises as a Lagrange multiplier. Firstly, when $2<p\le q\le \frac{2N}{(N-2)^+}$ and $ρ$ is small, we establish the existence of a local minimizer of energy. Furthermore, when $μ\ge 0$ and $Ω$ is a star-shaped domain, using the monotonicity trick and the Pohozaev identity, we show that there exists a second solution which is of mountain pass type. Secondly, when $μ\ge 0$, $N\ge 3$, $1<p\le 2$, $q\ge \max\left\{\frac{2N}{N-2}, 3\right\}$ and $Ω$ is a convex domain, using the moving-plane method, we prove the nonexistence of normalized solutions for large $ρ$. Finally, when $μ=0$, $N\ge 3$, $q=\frac{2N}{N-2}$ and $Ω$ is a ball, we give a dichotomy result of normalized solutions for the Brézis-Nirenberg problem by continuation arguments.

math.AP↗

arXiv2026

RQ-GMM: Residual Quantized Gaussian Mixture Model for Multimodal Semantic Discretization in CTR Prediction

Multimodal content is crucial for click-through rate (CTR) prediction. However, directly incorporating continuous embeddings from pre-trained models into CTR models yields suboptimal results due to misaligned optimization objectives and convergence speed inconsistency during joint training. Discretizing embeddings into semantic IDs before feeding them into CTR models offers a more effective solution, yet existing methods suffer from limited codebook utilization, reconstruction accuracy, and semantic discriminability. We propose RQ-GMM (Residual Quantized Gaussian Mixture Model), which introduces probabilistic modeling to better capture the statistical structure of multimodal embedding spaces. Through Gaussian Mixture Models combined with residual quantization, RQ-GMM achieves superior codebook utilization and reconstruction accuracy. Experiments on public datasets and online A/B tests on a large-scale short-video platform serving hundreds of millions of users demonstrate substantial improvements: RQ-GMM yields a 1.502% gain in Advertiser Value over strong baselines. The method has been fully deployed, serving daily recommendations for hundreds of millions of users.

cs.IR↗

arXiv2026

XiChen: A global weather observation-to-forecast machine learning system via four-dimensional variational gradient-guided flexible assimilation

Machine Learning (ML) has shown great promise in revolutionizing weather forecasting, yet most ML systems still rely on initial conditions generated by Numerical Weather Prediction (NWP) systems. End-to-end ML models aim to eliminate this dependency, but they often rely on observation-specific encoders and require redesign or retraining when observation sources change, thereby limiting their operational robustness. Here, we introduce XiChen, a global weather observation-to-forecast ML system via four-dimensional variational (4DVar) gradient-guided flexible assimilation. We demonstrate that the gradient of the 4DVar cost function serves as a physically grounded interface that maps heterogeneous observations into a common state space. This novel formulation enables XiChen to flexibly assimilate diverse conventional and raw satellite observations while preserving physical consistency. Experiments show that the system achieves forecasting metrics competitive with operational NWP systems. This work provides a practical and physically consistent route toward operational ML-based global weather forecasting systems with heterogeneous and evolving observations.

cs.LG↗

arXiv2026

Distribution-Aware End-to-End Embedding for Streaming Numerical Features in Click-Through Rate Prediction

This paper explores effective numerical feature embedding for Click-Through Rate prediction in streaming environments. Conventional static binning methods rely on offline statistics of numerical distributions; however, this inherently two-stage process often triggers semantic drift during bin boundary updates. While neural embedding methods enable end-to-end learning, they often discard explicit distributional information. Integrating such information end-to-end is challenging because streaming features often violate the i.i.d. assumption, precluding unbiased estimation of the population distribution via the expectation of order statistics. Furthermore, the critical context dependency of numerical distributions is often neglected. To this end, we propose DAES, an end-to-end framework designed to tackle numerical feature embedding in streaming training scenarios by integrating distributional information with an adaptive modulation mechanism. Specifically, we introduce an efficient reservoir-sampling-based distribution estimation method and two field-aware distribution modulation strategies to capture streaming distributions and field-dependent semantics. DAES significantly outperforms existing approaches as demonstrated by extensive offline and online experiments and has been fully deployed on a leading short-video platform with hundreds of millions of daily active users.

cs.IR↗

arXiv2025

Normalized solutions to mixed dispersion nonlinear Schrödinger system with coupled nonlinearity

In this paper, we consider the existence of normalized solutions for the following biharmonic nonlinear Schrödinger system \begin{equation*} \begin{cases} Δ^2u+α_{1}Δu+λu=βr_{1}|u|^{r_{1}-2}|v|^{r_{2}} u & \text { in } \mathbb{R}^{N}, \\ Δ^2v+α_{2}Δv+λv=βr_{2}|u|^{r_{1}}|v|^{r_{2}-2} v & \text { in } \mathbb{R}^{N}, \\ \int_{\mathbb{R}^{N}} (u^{2}+v^{2})\ud x=ρ^{2}, \end{cases} \end{equation*} where $Δ^2u=Δ(Δu)$ is the biharmonic operator, $α_{1}$, $α_{2}$, $β>0$, $r_{1}$, $r_{2}>1$, $N\geq 1$. $ρ^2$ stands for the prescribed mass, and $λ\in\mathbb{R}$ arises as a Lagrange multiplier. Such single constraint permits mass transformation in two materials. When $r_{1}+r_{2}\le 2+\frac{8}{N}$, we obtain a dichotomy result with respect to the mass for the existence of nontrivial ground states. Especially when $α_1=α_2$, the ground state exists for all $ρ>0$ if and only if $r_1+r_2<\min\left\{\max\left\{4, 2+\frac{8}{N+1}\right\}, 2+\frac{8}{N}\right\}$. When $r_{1}+r_{2}\in\left(2+\frac{8}{N}, \frac{2N}{(N-4)^{+}}\right)$ and $N\geq 2$, we obtain the existence of radial nontrivial mountain pass solution for sufficiently small $ρ>0$.

math.AP↗

arXiv2025

Infinitely many solutions for elliptic system with Hamiltonian type

In this paper, we use Legendre-Fenchel transform and a space decomposition to carry out Fountain theorem and dual Fountain theorem for the following elliptic system of Hamiltonian type: \[ \begin{cases} \begin{aligned} -Δu&=H_v(u, v) \,\quad&&\text{in}~Ω,\\ -Δv&=H_u(u, v) \,\quad&&\text{in}~Ω,\\ u,\,v&=0~~&&\text{on} ~ \partialΩ,\\ \end{aligned} \end{cases} \] where $N\ge 1$, $Ω\subset \mathbb{R}^N$ is a bounded domain and $H\in C^1( \mathbb{R}^2)$ is strictly convex, even and subcritical. We mainly present two results: (i) When $H$ is superlinear, the system has infinitely many solutions, whose energies tend to infinity. (ii) When $H$ is sublinear, the system has infinitely many solutions, whose energies are negative and tend to 0. As a byproduct, the Lane-Emden system under subcritical growth has infinitely many solutions.

math.AP↗

arXiv2025

SWEA: Updating Factual Knowledge in Large Language Models via Subject Word Embedding Altering

The general capabilities of large language models (LLMs) make them the infrastructure for various AI applications, but updating their inner knowledge requires significant resources. Recent model editing is a promising technique for efficiently updating a small amount of knowledge of LLMs and has attracted much attention. In particular, local editing methods, which directly update model parameters, are proven suitable for updating small amounts of knowledge. Local editing methods update weights by computing least squares closed-form solutions and identify edited knowledge by vector-level matching in inference, which achieve promising results. However, these methods still require a lot of time and resources to complete the computation. Moreover, vector-level matching lacks reliability, and such updates disrupt the original organization of the model's parameters. To address these issues, we propose a detachable and expandable Subject Word Embedding Altering (SWEA) framework, which finds the editing embeddings through token-level matching and adds them to the subject word embeddings in Transformer input. To get these editing embeddings, we propose optimizing then suppressing fusion method, which first optimizes learnable embedding vectors for the editing target and then suppresses the Knowledge Embedding Dimensions (KEDs) to obtain final editing embeddings. We thus propose SWEA$\oplus$OS method for editing factual knowledge in LLMs. We demonstrate the overall state-of-the-art (SOTA) performance of SWEA$\oplus$OS on the CounterFact and zsRE datasets. To further validate the reasoning ability of SWEA$\oplus$OS in editing knowledge, we evaluate it on the more complex RippleEdits benchmark. The results demonstrate that SWEA$\oplus$OS possesses SOTA reasoning ability.

cs.CL↗

arXiv2025

Stable solution and extremal solution for fractional $p$-Laplacian

To our knowledge, this paper is the first attempt to consider the existence issue for fractional $p$-Laplacian equation: $(-Δ)_p^s u= λf(u),\; u> 0 ~\text{in}~Ω;\; u=0\;\text{in}~ \mathbb{R}^N\setminusΩ$, where $p>1$, $s\in (0,1)$, $λ>0$ and $Ω$ is a bounded domain with $C^{1, 1}$ boundary. We first propose a notion of stable solution, then we prove that when $f$ is of class $C^1$, nondecreasing and satisfying $f(0)>0$ and $\underset{t\to \infty}{\lim}\frac{f(t)}{t^{p-1}}=\infty$, there exists an extremal parameter $λ^*\in (0, \infty)$ such that a bounded minimal solution $u_λ\in W_0^{s,p}(Ω)$ exists if $λ\in (0, λ^*)$, and no bounded solution exists if $λ>λ^*$. Moreover, no $W_0^{s,p}(Ω)$ solution exists for $λ> λ^*$ if in addition $f(t)^{\frac{1}{p-1}}$ is convex. To handle our problems, we show a Kato-type inequality for fractional $p$-Laplacian. We show also $L^r$ estimates for the equation $(-Δ)_p^su=g$ with $g\in W_0^{s, p}(Ω)^*\cap L^q(Ω)$ for $q \geq 1$, especially for $q \le \frac{N}{sp}$. We believe that these general results have their own interests. Finally, using the stability of minimal solutions $u_λ$, under the polynomial growth or convexity assumption on $f$, we show that the extremal function $u_* =\lim_{λ\toλ^*}u_λ\in W_0^{s,p}(Ω)$ in all dimensions, and $u^*\in L^{\infty}(Ω)$ in some low dimensional cases.

math.AP↗

arXiv2025

How to Bridge the Gap between Modalities: Survey on Multimodal Large Language Model

We explore Multimodal Large Language Models (MLLMs), which integrate LLMs like GPT-4 to handle multimodal data, including text, images, audio, and more. MLLMs demonstrate capabilities such as generating image captions and answering image-based questions, bridging the gap towards real-world human-computer interactions and hinting at a potential pathway to artificial general intelligence. However, MLLMs still face challenges in addressing the semantic gap in multimodal data, which may lead to erroneous outputs, posing potential risks to society. Selecting the appropriate modality alignment method is crucial, as improper methods might require more parameters without significant performance improvements. This paper aims to explore modality alignment methods for LLMs and their current capabilities. Implementing effective modality alignment can help LLMs address environmental issues and enhance accessibility. The study surveys existing modality alignment methods for MLLMs, categorizing them into four groups: (1) Multimodal Converter, which transforms data into a format that LLMs can understand; (2) Multimodal Perceiver, which improves how LLMs percieve different types of data; (3) Tool Learning, which leverages external tools to convert data into a common format, usually text; and (4) Data-Driven Method, which teaches LLMs to understand specific data types within datasets.

cs.CL↗

arXiv2024

Model Editing for LLMs4Code: How Far are We?

Large Language Models for Code (LLMs4Code) have been found to exhibit outstanding performance in the software engineering domain, especially the remarkable performance in coding tasks. However, even the most advanced LLMs4Code can inevitably contain incorrect or outdated code knowledge. Due to the high cost of training LLMs4Code, it is impractical to re-train the models for fixing these problematic code knowledge. Model editing is a new technical field for effectively and efficiently correcting erroneous knowledge in LLMs, where various model editing techniques and benchmarks have been proposed recently. Despite that, a comprehensive study that thoroughly compares and analyzes the performance of the state-of-the-art model editing techniques for adapting the knowledge within LLMs4Code across various code-related tasks is notably absent. To bridge this gap, we perform the first systematic study on applying state-of-the-art model editing approaches to repair the inaccuracy of LLMs4Code. To that end, we introduce a benchmark named CLMEEval, which consists of two datasets, i.e., CoNaLa-Edit (CNLE) with 21K+ code generation samples and CodeSearchNet-Edit (CSNE) with 16K+ code summarization samples. With the help of CLMEEval, we evaluate six advanced model editing techniques on three LLMs4Code: CodeLlama (7B), CodeQwen1.5 (7B), and Stable-Code (3B). Our findings include that the external memorization-based GRACE approach achieves the best knowledge editing effectiveness and specificity (the editing does not influence untargeted knowledge), while generalization (whether the editing can generalize to other semantically-identical inputs) is a universal challenge for existing techniques. Furthermore, building on in-depth case analysis, we introduce an enhanced version of GRACE called A-GRACE, which incorporates contrastive learning to better capture the semantics of the inputs.

cs.SE↗

arXiv2024

XiHe: A Data-Driven Model for Global Ocean Eddy-Resolving Forecasting

The leading operational Global Ocean Forecasting Systems (GOFSs) use physics-driven numerical forecasting models that solve the partial differential equations with expensive computation. Recently, specifically in atmosphere weather forecasting, data-driven models have demonstrated significant potential for speeding up environmental forecasting by orders of magnitude, but there is still no data-driven GOFS that matches the forecasting accuracy of the numerical GOFSs. In this paper, we propose the first data-driven 1/12° resolution global ocean eddy-resolving forecasting model named XiHe, which is established from the 25-year France Mercator Ocean International's daily GLORYS12 reanalysis data. XiHe is a hierarchical transformer-based framework coupled with two special designs. One is the land-ocean mask mechanism for focusing exclusively on the global ocean circulation. The other is the ocean-specific block for effectively capturing both local ocean information and global teleconnection. Extensive experiments are conducted under satellite observations, in situ observations, and the IV-TT Class 4 evaluation framework of the world's leading operational GOFSs from January 2019 to December 2020. The results demonstrate that XiHe achieves stronger forecast performance in all testing variables than existing leading operational numerical GOFSs including Mercator Ocean Physical SYstem (PSY4), Global Ice Ocean Prediction System (GIOPS), BLUElinK OceanMAPS (BLK), and Forecast Ocean Assimilation Model (FOAM). Particularly, the accuracy of ocean current forecasting of XiHe out to 60 days is even better than that of PSY4 in just 10 days. Additionally, XiHe is able to forecast the large-scale circulation and the mesoscale eddies. Furthermore, it can make a 10-day forecast in only 0.35 seconds, which accelerates the forecast speed by thousands of times compared to the traditional numerical GOFSs.

physics.ao-ph↗

arXiv2024

Variational method for fractional Hamiltonian system in bounded domain

Here we consider the following fractional Hamiltonian system \begin{equation*} \begin{cases} \begin{aligned} (-Δ)^{s} u&=H_v(u,v) \;\;&&\text{in}~Ω,\\ (-Δ)^{s} v&=H_u(u,v) &&\text{in}~Ω,\\ u &= v = 0 &&\text{in} ~ \mathbb{R}^N\setminusΩ, \end{aligned} \end{cases} \end{equation*} where $s\in (0,1)$, $N>2s$, $H \in C^1(\mathbb{R}^2, \mathbb{R})$ and $Ω\subset \mathbb{R}^N$ is a smooth bounded domain. %As the problem remains unchanged if $H(u, v)$ is replaced by $H(u, v)-H(0, 0)$, hence we always assume $H(0,0)=0$. To apply the variational method for this problem, the key question is to find a suitable functional setting. Instead of usual fractional Sobolev spaces, we use the solutions space of $(-Δ)^{s}u=f\in L^r(Ω)$ for $r\ge 1$, for which we show the (compact) embedding properties. When $H$ has subcritical and superlinear growth, we construct two frameworks, respectively with interpolation space method and dual method, to show the existence of nontrivial solution. As byproduct, we revisit the fractional Lane-Emden system, i.e. $H(u, v)=\frac{1}{p+1}|u|^{p+1}+\frac{1}{q+1}|v|^{q+1}$, and consider the existence, uniqueness of (radial) positive solutions under subcritical assumption.

math.AP↗

arXiv2024

Long-Term Prediction Accuracy Improvement of Data-Driven Medium-Range Global Weather Forecast

Long-term stability stands as a crucial requirement in data-driven medium-range global weather forecasting. Spectral bias is recognized as the primary contributor to instabilities, as data-driven methods difficult to learn small-scale dynamics. In this paper, we reveal that the universal mechanism for these instabilities is not only related to spectral bias but also to distortions brought by processing spherical data using conventional convolution. These distortions lead to a rapid amplification of errors over successive long-term iterations, resulting in a significant decline in forecast accuracy. To address this issue, a universal neural operator called the Spherical Harmonic Neural Operator (SHNO) is introduced to improve long-term iterative forecasts. SHNO uses the spherical harmonic basis to mitigate distortions for spherical data and uses gated residual spectral attention (GRSA) to correct spectral bias caused by spurious correlations across different scales. The effectiveness and merit of the proposed method have been validated through its application for spherical Shallow Water Equations (SWEs) and medium-range global weather forecasting. Our findings highlight the benefits and potential of SHNO to improve the accuracy of long-term prediction.

cs.LG↗

arXiv2024

Posterior Probability Matters: Doubly-Adaptive Calibration for Neural Predictions in Online Advertising

Predicting user response probabilities is vital for ad ranking and bidding. We hope that predictive models can produce accurate probabilistic predictions that reflect true likelihoods. Calibration techniques aim to post-process model predictions to posterior probabilities. Field-level calibration -- which performs calibration w.r.t. to a specific field value -- is fine-grained and more practical. In this paper we propose a doubly-adaptive approach AdaCalib. It learns an isotonic function family to calibrate model predictions with the guidance of posterior statistics, and field-adaptive mechanisms are designed to ensure that the posterior is appropriate for the field value to be calibrated. Experiments verify that AdaCalib achieves significant improvement on calibration performance. It has been deployed online and beats previous approach.

cs.LG↗

arXiv2023

Normalized solutions for nonlinear Schrödinger equation involving potential and Sobolev critical exponent

In this paper, we consider the existence of positive solutions with prescribed $L^2$-norm for the following nonlinear Schrödinger equation involving potential and Sobolev critical exponent \begin{equation*} \begin{cases} -Δu+V(x)u=λu+μ|u|^{p-2}u+|u|^{\frac{4}{N-2}}u \;\;\text { in } \mathbb{R}^N, \\ \|u\|_2=a>0,\\ \end{cases} \end{equation*} where $N\ge 3$, $μ>0$, $p\in [2+\frac{4}{N}, \frac{2N}{N-2})$ and $V\in C^1(\mathbb{R}^N)$. Under different assumptions on $V$, we derive two different Pohozaev identities. Based on these two cases, we respectively obtain the existence of positive solution. As far as we are aware, we did not find any works on normalized solutions with Sobolev critical growth and potential $V \not\equiv 0$. Our results extend some results of Wei and Wu [J. Funct. Anal. 283(2022)] to the potential case.

math.AP↗

arXiv2023

Existence and Multiplicity of Solutions for Fractional $p$-Laplacian Equation Involving Critical Concave-convex Nonlinearities

We investigate the following fractional $p$-Laplacian equation \[ \begin{cases} \begin{aligned} (-Δ)_p^s u&=λ|u|^{q-2}u+|u|^{p_s^*-2}u &&\text{in}~Ω,\\ u &=0 &&\text{in}~ \mathbb{R}^n\setminusΩ, \end{aligned} \end{cases} \] where $s\in (0,1)$, $p>q>1$, $n>sp$, $λ>0$, $p_s^*=\frac{np}{n-sp}$ and $Ω$ is a bounded domain (with $C^{1, 1}$ boundary). Firstly, we get a dichotomy result for the existence of positive solution with respect to $λ$. For $p\ge 2$, $p-1 \frac{sp(q+1)}{q+1-p}$, we provide two positive solutions for small $λ$. Finally, without sign constraint, for $λ$ sufficiently small, we show the existence of infinitely many solutions.

math.AP↗