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Xinyu Cheng

Publications and source records attributed to Xinyu Cheng.

At least 19 recordsLinked to original sources
arXiv2026

CuSearch: Curriculum Rollout Sampling via Search Depth for Agentic RAG

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for training agentic retrieval-augmented generation (RAG) systems from outcome-only supervision. Most existing methods optimize policies from uniformly sampled rollouts, implicitly treating all trajectories as equally informative. However, trajectories differ substantially in search depth and are therefore not equally informative: deeper-search trajectories contain more retrieval decision points and provide denser direct supervision for the retrieval sub-policy. Moreover, this heterogeneity grows over training as the within-batch depth distribution shifts toward higher values, yet uniform rollout sampling remains blind to this shift. To address this, we propose CuSearch, a curriculum rollout sampling framework built on Search-Depth Greedy Allocation (SDGA), a batch-level operator that reallocates a fixed update budget toward deeper-search trajectories. SDGA-Auto always targets the deepest available trajectories in the current batch, yielding an implicit training-aligned curriculum as the depth distribution shifts upward. SDGA-Phase explicitly advances the curriculum threshold as deeper trajectories become sufficiently abundant. Experiments across model types and retrieval frameworks show that CuSearch consistently improves performance, achieving up to 11.8 exact-match points over standard GRPO on ZeroSearch. These results establish per-trajectory search depth as a reliable, annotation-free proxy for retrieval supervision density in RLVR-based agentic RAG training.

cs.AI↗
arXiv2026

DEIG: Detail-Enhanced Instance Generation with Fine-Grained Semantic Control

Multi-Instance Generation has advanced significantly in spatial placement and attribute binding. However, existing approaches still face challenges in fine-grained semantic understanding, particularly when dealing with complex textual descriptions. To overcome these limitations, we propose DEIG, a novel framework for fine-grained and controllable multi-instance generation. DEIG integrates an Instance Detail Extractor (IDE) that transforms text encoder embeddings into compact, instance-aware representations, and a Detail Fusion Module (DFM) that applies instance-based masked attention to prevent attribute leakage across instances. These components enable DEIG to generate visually coherent multi-instance scenes that precisely match rich, localized textual descriptions. To support fine-grained supervision, we construct a high-quality dataset with detailed, compositional instance captions generated by VLMs. We also introduce DEIG-Bench, a new benchmark with region-level annotations and multi-attribute prompts for both humans and objects. Experiments demonstrate that DEIG consistently outperforms existing approaches across multiple benchmarks in spatial consistency, semantic accuracy, and compositional generalization. Moreover, DEIG functions as a plug-and-play module, making it easily integrable into standard diffusion-based pipelines.

cs.CV↗
arXiv2025

A Besov-based integration-by-parts method for the incompressible Navier-Stokes equations

This note introduces a novel numerical analysis framework for the incompressible Navier-Stokes equations based on Besov spaces. The key contribution of this note is to establish the stability and convergence of a semi-implicit time-stepping scheme by deriving precise error estimates in the $B^0_{\infty,1}$ and $B^0_{\infty,2}$ spaces. Another contribution of our analysis is the detailed treatment of the $B^0_{\infty,2}$ case, where a crucial integration-by-parts technique is employed to adeptly handle the nonlinear advection term. This technique allows for a refined estimate that effectively transfers derivatives onto the test functions, mitigating the inherent analytical challenges posed by the low regularity of these spaces. Our results provide sharper, more localized error bounds than in classical Sobolev spaces, directly linking the scheme's convergence to the critical regularity of the continuous solution. This work underscores the advantage of Besov spaces for the numerical analysis of nonlinear fluid PDEs.

math.NA↗
arXiv2025

ViseGPT: Towards Better Alignment of LLM-generated Data Wrangling Scripts and User Prompts

Large language models (LLMs) enable the rapid generation of data wrangling scripts based on natural language instructions, but these scripts may not fully adhere to user-specified requirements, necessitating careful inspection and iterative refinement. Existing approaches primarily assist users in understanding script logic and spotting potential issues themselves, rather than providing direct validation of correctness. To enhance debugging efficiency and optimize the user experience, we develop ViseGPT, a tool that automatically extracts constraints from user prompts to generate comprehensive test cases for verifying script reliability. The test results are then transformed into a tailored Gantt chart, allowing users to intuitively assess alignment with semantic requirements and iteratively refine their scripts. Our design decisions are informed by a formative study (N=8) that explores user practices and challenges. We further evaluate the effectiveness and usability of ViseGPT through a user study (N=18). Results indicate that ViseGPT significantly improves debugging efficiency for LLM-generated data-wrangling scripts, enhances users' ability to detect and correct issues, and streamlines the workflow experience.

cs.HC↗
arXiv2024

Global well-posedness and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model

In this paper, we consider global strong solutions and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model in R^d, where d=2 and 3. The well-recognized problem of the global existence of smooth solutions for the 2D inviscid Oldroyd-B model without smallness assumptions is open due to the complex structure of Q. Therefore improving the smallness assumptions, especially in lower regularity class, is the core question in the area of fluid models. On the other hand, long-time behaviors of solutions including temporal decay and uniform-in-time damping stability are also of deep significance. These problems have been widely studied, however, the existing results are not regularity critical and the (uniform) vanishing damping limit has not been discussed. The goal of this work is to dig deeper in this direction. In this work we first establish the local well-posedness in the sense of Hadamard with critical regularity. Then, by virtue of the sharp commutator estimate for Calderon-Zygmund operator, we establish the global existence of solutions for d=2 with damping in the low regularity class, which to our best knowledge, is novel in the literature. Furthermore, in both 2D and 3D cases, we prove the global existence of the solutions to the inviscid Oldroyd-B model independent of the damping parameters. In addition, we obtain the optimal temporal decay rates and time integrability by improving the existing Fourier splitting method and developing a novel decomposition strategy. One of the major contributions of the presenting paper is to prove the uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model and discover the correlation between sharp vanishing damping rate and the temporal decay rate. Finally, we will support our findings by providing numerical evidence regarding the vanishing damping limit in the periodic domain T^d.

math.AP↗
arXiv2024

GTSinger: A Global Multi-Technique Singing Corpus with Realistic Music Scores for All Singing Tasks

The scarcity of high-quality and multi-task singing datasets significantly hinders the development of diverse controllable and personalized singing tasks, as existing singing datasets suffer from low quality, limited diversity of languages and singers, absence of multi-technique information and realistic music scores, and poor task suitability. To tackle these problems, we present GTSinger, a large global, multi-technique, free-to-use, high-quality singing corpus with realistic music scores, designed for all singing tasks, along with its benchmarks. Particularly, (1) we collect 80.59 hours of high-quality singing voices, forming the largest recorded singing dataset; (2) 20 professional singers across nine widely spoken languages offer diverse timbres and styles; (3) we provide controlled comparison and phoneme-level annotations of six commonly used singing techniques, helping technique modeling and control; (4) GTSinger offers realistic music scores, assisting real-world musical composition; (5) singing voices are accompanied by manual phoneme-to-audio alignments, global style labels, and 16.16 hours of paired speech for various singing tasks. Moreover, to facilitate the use of GTSinger, we conduct four benchmark experiments: technique-controllable singing voice synthesis, technique recognition, style transfer, and speech-to-singing conversion. The demos can be found at http://aaronz345.github.io/GTSingerDemo/. We provide the dataset and the code for processing data and conducting benchmarks at https://huggingface.co/datasets/AaronZ345/GTSinger and https://github.com/AaronZ345/GTSinger.

eess.AS↗
arXiv2024

Leveraging Contrastive Learning and Self-Training for Multimodal Emotion Recognition with Limited Labeled Samples

The Multimodal Emotion Recognition challenge MER2024 focuses on recognizing emotions using audio, language, and visual signals. In this paper, we present our submission solutions for the Semi-Supervised Learning Sub-Challenge (MER2024-SEMI), which tackles the issue of limited annotated data in emotion recognition. Firstly, to address the class imbalance, we adopt an oversampling strategy. Secondly, we propose a modality representation combinatorial contrastive learning (MR-CCL) framework on the trimodal input data to establish robust initial models. Thirdly, we explore a self-training approach to expand the training set. Finally, we enhance prediction robustness through a multi-classifier weighted soft voting strategy. Our proposed method is validated to be effective on the MER2024-SEMI Challenge, achieving a weighted average F-score of 88.25% and ranking 6th on the leaderboard. Our project is available at https://github.com/WooyoohL/MER2024-SEMI.

cs.SD↗
arXiv2024

On semi-implicit schemes for the incompressible Euler equations via the vanishing viscosity limit

A new type of systematic approach to study the incompressible Euler equations numerically via the vanishing viscosity limit is proposed in this work. We show the new strategy is unconditionally stable that the $L^2$-energy dissipates and $H^s$-norm is uniformly bounded in time without any restriction on the time step. Moreover, first-order convergence of the proposed method is established including both low regularity and high regularity error estimates. The proposed method is extended to full discretization with a newly developed iterative Fourier spectral scheme. Another main contributions of this work is to propose a new integration by parts technique to lower the regularity requirement from $H^4$ to $H^3$ in order to perform the $L^2$-error estimate. To our best knowledge, this is one of the very first work to study incompressible Euler equations by designing stable numerical schemes via the inviscid limit with rigorous analysis. Furthermore, we will present both low and high regularity errors from numerical experiments and demonstrate the dynamics in several benchmark examples.

math.NA↗
arXiv2023

Unconditionally stable exponential integrator schemes for the 2D Cahn-Hilliard equation

Phase field models are gradient flows with their energy naturally dissipating in time. In order to preserve this property, many numerical schemes have been well-studied. In this paper we consider a well-known method, namely the exponential integrator method (EI). In the literature a few works studied several EI schemes for various phase field models and proved the energy dissipation by either requiring a strong Lipschitz condition on the nonlinear source term or certain $L^\infty$ bounds on the numerical solutions (maximum principle). However for phase field models such as the (non-local) Cahn-Hilliard equation, the maximum principle no longer exists. As a result, solving such models via EI schemes remains open for a long time. In this paper we aim to give a systematic approach on applying EI-type schemes to such models by solving the Cahn-Hilliard equation with a first order EI scheme and showing the energy dissipation. In fact second order EI schemes can be handled similarly and we leave the discussion in a subsequent paper. To our best knowledge, this is the first work to handle phase field models without assuming any strong Lipschitz condition or $L^\infty$ boundedness. Furthermore, we will analyze the $L^2$ error and present some numerical simulations to demonstrate the dynamics.

math.NA↗
arXiv2023

Global well-posedness of a two dimensional wave-Klein-Gordon system with small non-compactly supported data

In this paper we are interested in the coupled wave and Klein-Gordon equations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the global solution without any compactness assumptions on the initial data. In addition, we also demonstrate the pointwise asymptotic behavior of the solution pair. In order to achieve that we apply a modified Alinhac's ghost weight method together with a newly developed normal-form framework to remedy the lack of the space-time scaling vector field. Finally we show the global solutions scatter linearly strongly for the Klein-Gordon field $\phi$ and weakly for the wave field $n$ as $t\to+\infty$. To our best knowledge such scattering phenomenon is novel in the literature.

math.AP↗
arXiv2022

On the global well-posedness and scattering of the 3D Klein-Gordon-Zakharov system

In this paper we are interested in the global well-posedness of the 3D Klein-Gordon-Zakharov equations with small initial data. We show the uniform boundedness of the energy for the global solution without any compactness assumptions on the initial data. The main novelty of our proof is to apply a modified Alinhac's ghost weight method together with a newly developed normal-form type estimate to remedy the lack of the space-time scaling vector field; moreover, we give a clear description of the smallness conditions on the initial data.

math.AP↗
arXiv2022

Localization for general Helmholtz

In \cite{gmw2022}, Guan, Murugan and Wei established the equivalence of the classical Helmholtz equation with a ``fractional Helmholtz" equation in which the Laplacian operator is replaced by the nonlocal fractional Laplacian operator. More general equivalence results are obtained for symbols which are complete Bernstein and satisfy additional regularity conditions. In this work we introduce a novel and general set-up for this Helmholtz equivalence problem. We show that under very mild and easy-to-check conditions on the Fourier multiplier, the general Helmholtz equation can be effectively reduced to a localization statement on the support of the symbol.

math.AP↗
arXiv2022

Switching modulation of spin transport in ferromagnetic tetragonal silicene

We study the band structure and transport properties of ferromagnetic tetragonal silicene nanoribbons by using the non-equilibrium Green's function method. The band structure and spin-dependent conductance are discussed under the combined effect of the external electric field, potential energy, exchange field and the spin-orbit coupling. One can easily realize a phase transition from a semimetallic to a semiconducting state by changing the transverse width of the nanoribbon. Separation of spin-dependent conductances arises from the effect of exchange field and the spin-orbit coupling, while zero-conductance behaviors exhibit spin-dependent band gaps induced by the electric field. We propose a device configuration of four-terminal tetragonal silicene nanoribbon with two central channels. It is found that spin current can be controlled by utilizing two switches. The switch with a high potential barrier can block electrons flowing from the central scattering region into other terminals. Interestingly, applying only one switch can realize spin-dependent zero conductance and large spin polarization. Two switches can provide multiple operations for controlling spin-dependent transport properties. The two-channel ferromagnetic tetragonal silicene nanoribbon can realize an effective separation of spin current, which may be a potential candidate for spintronic devices.

cond-mat.mes-hall↗
arXiv2021

On a sinc-type MBE model

We introduce a new sinc-type molecular beam epitaxy model which is derived from a cosine-type energy functional. The landscape of the new functional is remarkably similar to the classical MBE model with double well potential but has the additional advantage that all its derivatives are uniformly bounded. We consider first order IMEX and second order BDF2 discretization schemes. For both cases we quantify explicit time step constraints for the energy dissipation which is in good accord with the practical numerical simulations. Furthermore we introduce a new theoretical framework and prove unconditional uniform energy boundedness with no size restrictions on the time step. This is the first unconditional (i.e. independent of the time step size) result for semi-implicit methods applied to the phase field models without introducing any artificial stabilization terms or fictitious variables.

math.NA↗
arXiv2021

On a parabolic sine-Gordon model

We consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the one-dimensional case we classify all bounded steady states and exhibit some explicit solutions. For the numerical discretization we employ first order IMEX, and second order BDF2 discretization without any additional stabilization term. We rigorously prove the energy stability of the numerical schemes under nearly sharp and quite mild time step constraints. We demonstrate the striking similarity of the parabolic sine-Gordon model with the standard Allen-Cahn equations with double well potentials.

math.AP↗
arXiv2021

Equivalent formulations of the oxygen depletion problem, other implicit free boundary value problems, and implications for numerical approximation

The Oxygen Depletion problem is an implicit free boundary value problem. The dynamics allow topological changes in the free boundary. We show several mathematical formulations of this model from the literature and give a new formulation based on a gradient flow with constraint. All formulations are shown to be equivalent. We explore the possibilities for the numerical approximation of the problem that arise from the different formulations. We show a convergence result for an approximation based on the gradient flow with constraint formulation that applies to the general dynamics including topological changes. More general (vector, higher order) implicit free boundary value problems are discussed. Several open problems are described.

math.AP↗