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Jian Zhang

Publications and source records attributed to Jian Zhang.

At least 181 records · Page 10Linked to original sources
arXiv2025

Another look at quasilinear Schrödinger equations with prescribed mass via dual method

In this paper, we aim to study the existence of ground state normalized solutions for the following quasilinear Schrödinger equation $-Δu-Δ(u^2)u=h(u)+λu,\,\, x\in\R^N$, under the mass constraint $\int_{\R^N}|u|^2\text{d}x=a,$ where $N\geq2$, $a>0$ is a given mass, $λ$ is a Lagrange multiplier and $h$ is a nonlinear reaction term with some suitable conditions. By employing a suitable transformation $u=f(v)$, we reformulate the original problem into the equivalent form $-Δv =h(f(v))f'(v)+λf(v)f'(v),\,\, x\in\R^N,$ with prescribed mass $ \int_{\R^N}|f(v)|^2\text{d}x=a. $ To address the challenge posed by the $L^2$-norm $\|f(v)\|^2_2$ not necessarily equaling $a$, we introduce a novel stretching mapping: $ v_t(x):=f^{-1}(t^{N/2}f(v(tx))). $ This construction, combined with a dual method and detailed analytical techniques, enables us to establish the following existence results: (1)Existence of solutions via constrained minimization using dual methods; (2) Existence of ground state normalized solutions under general $L^2$-supercritical growth conditions, along with nonexistence results, analyzed via dual methods; (3)Existence of normalized solutions under critical growth conditions, treated via dual methods. Additionally, we analyze the asymptotic behavior of the ground state energy obtained in {\bf(P2)}. Our results extend and refine those of Colin-Jeanjean-Squassina [Nonlinearity 20: 1353-1385, 2010], of Jeanjean-Luo-Wang [J. Differ. Equ. 259: 3894-3928, 2015], of Li-Zou [Pacific J. Math. 322: 99-138, 2023], of Zhang-Li-Wang [Topol. Math. Nonl. Anal. 61: 465-489, 2023] and so on. We believe that the methodology developed here can be adapted to study related problems concerning the existence of normalized solutions for quasilinear Schrödinger equations via the dual method.

math.AP↗
arXiv2025

DynamicVerse: A Physically-Aware Multimodal Framework for 4D World Modeling

Understanding the dynamic physical world, characterized by its evolving 3D structure, real-world motion, and semantic content with textual descriptions, is crucial for human-agent interaction and enables embodied agents to perceive and act within real environments with human-like capabilities. However, existing datasets are often derived from limited simulators or utilize traditional Structurefrom-Motion for up-to-scale annotation and offer limited descriptive captioning, which restricts the capacity of foundation models to accurately interpret real-world dynamics from monocular videos, commonly sourced from the internet. To bridge these gaps, we introduce DynamicVerse, a physical-scale, multimodal 4D world modeling framework for dynamic real-world video. We employ large vision, geometric, and multimodal models to interpret metric-scale static geometry, real-world dynamic motion, instance-level masks, and holistic descriptive captions. By integrating window-based Bundle Adjustment with global optimization, our method converts long real-world video sequences into a comprehensive 4D multimodal format. DynamicVerse delivers a large-scale dataset consisting of 100K+ videos with 800K+ annotated masks and 10M+ frames from internet videos. Experimental evaluations on three benchmark tasks, namely video depth estimation, camera pose estimation, and camera intrinsics estimation, demonstrate that our 4D modeling achieves superior performance in capturing physical-scale measurements with greater global accuracy than existing methods.

cs.CV↗
arXiv2025

PanFoMa: A Lightweight Foundation Model and Benchmark for Pan-Cancer

Single-cell RNA sequencing (scRNA-seq) is essential for decoding tumor heterogeneity. However, pan-cancer research still faces two key challenges: learning discriminative and efficient single-cell representations, and establishing a comprehensive evaluation benchmark. In this paper, we introduce PanFoMa, a lightweight hybrid neural network that combines the strengths of Transformers and state-space models to achieve a balance between performance and efficiency. PanFoMa consists of a front-end local-context encoder with shared self-attention layers to capture complex, order-independent gene interactions; and a back-end global sequential feature decoder that efficiently integrates global context using a linear-time state-space model. This modular design preserves the expressive power of Transformers while leveraging the scalability of Mamba to enable transcriptome modeling, effectively capturing both local and global regulatory signals. To enable robust evaluation, we also construct a large-scale pan-cancer single-cell benchmark, PanFoMaBench, containing over 3.5 million high-quality cells across 33 cancer subtypes, curated through a rigorous preprocessing pipeline. Experimental results show that PanFoMa outperforms state-of-the-art models on our pan-cancer benchmark (+4.0\%) and across multiple public tasks, including cell type annotation (+7.4\%), batch integration (+4.0\%) and multi-omics integration (+3.1\%). The code is available at https://github.com/Xiaoshui-Huang/PanFoMa.

q-bio.GN↗
arXiv2025

Small Language Models Reshape Higher Education: Courses, Textbooks, and Teaching

While large language models (LLMs) have introduced novel paradigms in science and education, their adoption in higher education is constrained by inherent limitations. These include a tendency to produce inaccuracies and high computational requirements, which compromise the strict demands for accurate and reliable knowledge essential in higher education. Small language models (MiniLMs), by contrast, offer distinct advantages in professional education due to their lightweight nature and precise retrieval capabilities. This research takes "Atmospheric Physics" as an example. We established a specialized corpus and image repository by gathering over 550,000 full-text PDFs from over 130 international well-respected journals in Earth and environmental science. From this collection, we extracted over 100 million high-quality sentence-level corpus and more than 3 million high-resolution academic images. Using MiniLMs, these resources were organized into a high-dimensional vector library for precise retrieval and efficient utilization of extensive educational content. Consequently, we systematically redesigned the courses, textbooks, and teaching strategies for "Atmospheric Physics" based on MiniLMs. The course is designed as a "interdisciplinary-frontier" system, breaking down traditional boundaries between atmospheric science, space science, hydrology, and remote sensing. Teaching materials are transformed from static, lagging text formats into a dynamic digital resource library powered by MiniLM. For teaching methods, we have designed a question-based learning pathway. This paradigm promotes a shift from passive knowledge transfer to active cognitive development. Consequently, this MiniLM-driven "Atmospheric Physics" course demonstrates a specific avenue for "AI for education".

physics.ed-ph↗
arXiv2025

DreamO: A Unified Framework for Image Customization

Recently, extensive research on image customization (e.g., identity, subject, style, background, etc.) demonstrates strong customization capabilities in large-scale generative models. However, most approaches are designed for specific tasks, restricting their generalizability to combine different types of condition. Developing a unified framework for image customization remains an open challenge. In this paper, we present DreamO, an image customization framework designed to support a wide range of tasks while facilitating seamless integration of multiple conditions. Specifically, DreamO utilizes a diffusion transformer (DiT) framework to uniformly process input of different types. During training, we construct a large-scale training dataset that includes various customization tasks, and we introduce a feature routing constraint to facilitate the precise querying of relevant information from reference images. Additionally, we design a placeholder strategy that associates specific placeholders with conditions at particular positions, enabling control over the placement of conditions in the generated results. Moreover, we employ a progressive training strategy consisting of three stages: an initial stage focused on simple tasks with limited data to establish baseline consistency, a full-scale training stage to comprehensively enhance the customization capabilities, and a final quality alignment stage to correct quality biases introduced by low-quality data. Extensive experiments demonstrate that the proposed DreamO can effectively perform various image customization tasks with high quality and flexibly integrate different types of control conditions.

cs.CV↗
arXiv2025

Towards Generalizable Deepfake Detection via Forgery-aware Audio-Visual Adaptation: A Variational Bayesian Approach

The widespread application of AIGC contents has brought not only unprecedented opportunities, but also potential security concerns, e.g., audio-visual deepfakes. Therefore, it is of great importance to develop an effective and generalizable method for multi-modal deepfake detection. Typically, the audio-visual correlation learning could expose subtle cross-modal inconsistencies, e.g., audio-visual misalignment, which serve as crucial clues in deepfake detection. In this paper, we reformulate the correlation learning with variational Bayesian estimation, where audio-visual correlation is approximated as a Gaussian distributed latent variable, and thus develop a novel framework for deepfake detection, i.e., Forgery-aware Audio-Visual Adaptation with Variational Bayes (FoVB). Specifically, given the prior knowledge of pre-trained backbones, we adopt two core designs to estimate audio-visual correlations effectively. First, we exploit various difference convolutions and a high-pass filter to discern local and global forgery traces from both modalities. Second, with the extracted forgery-aware features, we estimate the latent Gaussian variable of audio-visual correlation via variational Bayes. Then, we factorize the variable into modality-specific and correlation-specific ones with orthogonality constraint, allowing them to better learn intra-modal and cross-modal forgery traces with less entanglement. Extensive experiments demonstrate that our FoVB outperforms other state-of-the-art methods in various benchmarks.

cs.MM↗
arXiv2025

Toward Real-world Text Image Forgery Localization: Structured and Interpretable Data Synthesis

Existing Text Image Forgery Localization (T-IFL) methods often suffer from poor generalization due to the limited scale of real-world datasets and the distribution gap caused by synthetic data that fails to capture the complexity of real-world tampering. To tackle this issue, we propose Fourier Series-based Tampering Synthesis (FSTS), a structured and interpretable framework for synthesizing tampered text images. FSTS first collects 16,750 real-world tampering instances from five representative tampering types, using a structured pipeline that records human-performed editing traces via multi-format logs (e.g., video, PSD, and editing logs). By analyzing these collected parameters and identifying recurring behavioral patterns at both individual and population levels, we formulate a hierarchical modeling framework. Specifically, each individual tampering parameter is represented as a compact combination of basis operation-parameter configurations, while the population-level distribution is constructed by aggregating these behaviors. Since this formulation draws inspiration from the Fourier series, it enables an interpretable approximation using basis functions and their learned weights. By sampling from this modeled distribution, FSTS synthesizes diverse and realistic training data that better reflect real-world forgery traces. Extensive experiments across four evaluation protocols demonstrate that models trained with FSTS data achieve significantly improved generalization on real-world datasets. Dataset is available at \href{https://github.com/ZeqinYu/FSTS}{Project Page}.

cs.CV↗
arXiv2025

Orthogonalization and polarization of Yangians

For every family of orthogonal polynomials, we define a new realization of the Yangian of ${\mathfrak{gl}}_n$. Except in the case of Dickson polynomials, the new realizations do not satisfy the RTT relation. We obtain an analogue of the Christoffel-Darboux formula. Similar construction can be made for any family of functions satisfying certain recurrence relations, for example, $q$-Pochhhammer symbols and Bessel functions. Furthermore, using an analogue of the Jordan-Schwinger map, we define the ternary Yangian for a Lie algebra as a flat deformation of the current algebra of certain ternary extension of the given Lie algebra.

math.CA↗
arXiv2025

MARS: Multi-Agent Adaptive Reasoning with Socratic Guidance for Automated Prompt Optimization

Large language models (LLMs) typically operate in a question-answering paradigm, where the quality of the input prompt critically affects the response. Automated Prompt Optimization (APO) aims to overcome the cognitive biases of manually crafted prompts and explore a broader prompt design space. However, existing APO methods often suffer from rigid template structures and inefficient exploration in the prompt space. To this end, we propose a Multi-Agent Adaptive Reasoning with Socratic guidance framework (MARS) for APO. MARS consists of five complementary agents and formulates the optimization process as a Partially Observable Markov Decision Process (POMDP), enabling adaptive prompt refinement through explicit state modeling and interactive feedback. Specifically, a Planner agent generates flexible optimization trajectories, a Teacher-Critic-Student triad engages in Socratic-style dialogue to iteratively optimize the prompt based on pseudo-gradient signals in the text space, and a Target agent executes the prompt in downstream tasks to provide performance feedback. MARS integrates reasoning, feedback, and state transition into a unified hidden-state evolution process, improving both the effectiveness and interpretability of optimization. Extensive experiments on multiple datasets demonstrate that MARS outperforms existing APO methods in terms of optimization performance, search efficiency, and interpretability.

cs.CL↗
arXiv2025

MAPS: Multi-Agent Personality Shaping for Collaborative Reasoning

Collaborative reasoning with multiple agents offers the potential for more robust and diverse problem-solving. However, existing approaches often suffer from homogeneous agent behaviors and lack of reflective and rethinking capabilities. We propose Multi-Agent Personality Shaping (MAPS), a novel framework that enhances reasoning through agent diversity and internal critique. Inspired by the Big Five personality theory, MAPS assigns distinct personality traits to individual agents, shaping their reasoning styles and promoting heterogeneous collaboration. To enable deeper and more adaptive reasoning, MAPS introduces a Critic agent that reflects on intermediate outputs, revisits flawed steps, and guides iterative refinement. This integration of personality-driven agent design and structured collaboration improves both reasoning depth and flexibility. Empirical evaluations across three benchmarks demonstrate the strong performance of MAPS, with further analysis confirming its generalizability across different large language models and validating the benefits of multi-agent collaboration.

cs.AI↗
arXiv2025

AutoG: Towards automatic graph construction from tabular data

Recent years have witnessed significant advancements in graph machine learning (GML), with its applications spanning numerous domains. However, the focus of GML has predominantly been on developing powerful models, often overlooking a crucial initial step: constructing suitable graphs from common data formats, such as tabular data. This construction process is fundamental to applying graph-based models, yet it remains largely understudied and lacks formalization. Our research aims to address this gap by formalizing the graph construction problem and proposing an effective solution. We identify two critical challenges to achieve this goal: 1. The absence of dedicated datasets to formalize and evaluate the effectiveness of graph construction methods, and 2. Existing automatic construction methods can only be applied to some specific cases, while tedious human engineering is required to generate high-quality graphs. To tackle these challenges, we present a two-fold contribution. First, we introduce a set of datasets to formalize and evaluate graph construction methods. Second, we propose an LLM-based solution, AutoG, automatically generating high-quality graph schemas without human intervention. The experimental results demonstrate that the quality of constructed graphs is critical to downstream task performance, and AutoG can generate high-quality graphs that rival those produced by human experts. Our code can be accessible from https://github.com/amazon-science/Automatic-Table-to-Graph-Generation.

cs.LG↗
arXiv2025

LLM-Driven Completeness and Consistency Evaluation for Cultural Heritage Data Augmentation in Cross-Modal Retrieval

Cross-modal retrieval is essential for interpreting cultural heritage data, but its effectiveness is often limited by incomplete or inconsistent textual descriptions, caused by historical data loss and the high cost of expert annotation. While large language models (LLMs) offer a promising solution by enriching textual descriptions, their outputs frequently suffer from hallucinations or miss visually grounded details. To address these challenges, we propose $C^3$, a data augmentation framework that enhances cross-modal retrieval performance by improving the completeness and consistency of LLM-generated descriptions. $C^3$ introduces a completeness evaluation module to assess semantic coverage using both visual cues and language-model outputs. Furthermore, to mitigate factual inconsistencies, we formulate a Markov Decision Process to supervise Chain-of-Thought reasoning, guiding consistency evaluation through adaptive query control. Experiments on the cultural heritage datasets CulTi and TimeTravel, as well as on general benchmarks MSCOCO and Flickr30K, demonstrate that $C^3$ achieves state-of-the-art performance in both fine-tuned and zero-shot settings.

cs.CV↗
arXiv2025

ReNiL: Event-Driven Pedestrian Bayesian Localization Using IMU for Real-World Applications

Pedestrian inertial localization is key for mobile and IoT services because it provides infrastructure-free positioning. Yet most learning-based methods depend on fixed sliding-window integration, struggle to adapt to diverse motion scales and cadences, and yield inconsistent uncertainty, limiting real-world use. We present ReNiL, a Bayesian deep-learning framework for accurate, efficient, and uncertainty-aware pedestrian localization. ReNiL introduces Inertial Positioning Demand Points (IPDPs) to estimate motion at contextually meaningful waypoints instead of dense tracking, and supports inference on IMU sequences at any scale so cadence can match application needs. It couples a motion-aware orientation filter with an Any-Scale Laplace Estimator (ASLE), a dual-task network that blends patch-based self-supervision with Bayesian regression. By modeling displacements with a Laplace distribution, ReNiL provides homogeneous Euclidean uncertainty that integrates cleanly with other sensors. A Bayesian inference chain links successive IPDPs into consistent trajectories. On RoNIN-ds and a new WUDataset covering indoor and outdoor motion from 28 participants, ReNiL achieves state-of-the-art displacement accuracy and uncertainty consistency, outperforming TLIO, CTIN, iMoT, and RoNIN variants while reducing computation. Application studies further show robustness and practicality for mobile and IoT localization, making ReNiL a scalable, uncertainty-aware foundation for next-generation positioning.

cs.RO↗
arXiv2025

NVIDIA Nemotron Nano V2 VL

We introduce Nemotron Nano V2 VL, the latest model of the Nemotron vision-language series designed for strong real-world document understanding, long video comprehension, and reasoning tasks. Nemotron Nano V2 VL delivers significant improvements over our previous model, Llama-3.1-Nemotron-Nano-VL-8B, across all vision and text domains through major enhancements in model architecture, datasets, and training recipes. Nemotron Nano V2 VL builds on Nemotron Nano V2, a hybrid Mamba-Transformer LLM, and innovative token reduction techniques to achieve higher inference throughput in long document and video scenarios. We are releasing model checkpoints in BF16, FP8, and FP4 formats and sharing large parts of our datasets, recipes and training code.

cs.LG↗
arXiv2025

Monotonicity Conjectures and Sharp Stability for Solitons of the Cubic-Quintic NLS on R^3

This paper deals with the cubic-quintic nonlinear Schrödinger equation on R^3. Two monotonicity conjectures for solitons posed by Killip, Oh, Pocovnicu and Visan are completely resolved: one concerning frequency monotonicity, and the other concerning mass monotonicity. Uniqueness of the energy minimizer is proved. Then sharp stability of the solitons is established. And classification of normalized solutions is first presented.

math.AP↗
arXiv2025

Sharp Stability of Solitons for the Cubic-Quintic NLS on R^2

This paper concerns with the cubic-quintic nonlinear Schrödinger equation on R^2. A family of new variational problems related to the solitons are introduced and solved. Some key monotonicity and uniqueness results are obtained. Then the orbital stability of solitons at every frequency are proved in terms of the Cazenave and Lions' argument. And classification of normalized ground states is first presented. Our results settle the questions raised by Lewin and Rota Nodari as well as Carles and Sparber.

math.AP↗
arXiv2025

Uniqueness and stability of normalized ground states for Hartree equation with a harmonic potential

The dynamic properties of normalized ground states for the Hartree equation with a harmonic potential are addressed. The existence of normalized ground state for any prescribed mass is confirmed according to mass-energy constrained variational approach. The uniqueness is shown by the strictly convex properties of the energy functional. Moreover, the orbital stability of every normalized ground state is proven in terms of the Cazenave and Lions' argument.

math.AP↗