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Xiaoyan Su

Publications and source records attributed to Xiaoyan Su.

17 recordsLinked to original sources
arXiv2026

PosterText: Towards Unified Visual Text Generation and Editing for E-commerce Poster

Automated e-commerce poster design requires both high-quality poster generation and flexible editing of existing designs. However, most existing methods either target end-to-end poster generation or follow multi-stage design pipelines, with limited capability for flexible and precise editing of existing posters. To enable unified generation and editing of e-commerce posters, we introduce Text Patch Generation and Editing, a unified task formulation that treats text patches as atomic units and covers four operations: poster generation, patch addition, patch deletion, and patch modification, with optional reference-guided style control. Based on this, we propose PosterText, a unified model trained with a four-stage curriculum, including text rendering pretraining, instruction-following training, reinforcement learning for preference alignment, and spatial guidance self-distillation for execution refinement. We further construct a large-scale dataset with patch-level annotations and a comprehensive benchmark for evaluation. Extensive experiments demonstrate that PosterText achieves competitive performance against existing generation and editing approaches, validating the effectiveness of the proposed framework.

cs.CV↗
arXiv2026

TransAnyText: Translating Arbitrary Text in E-commerce Images via Structured Visual Generation

Cross-border e-commerce image translation is essential for global retail, where product images, banners, and detail pages need to be produced in different languages. Existing methods struggle to achieve accurate translation, faithful visual identity preservation, and easy-to-edit outputs, simultaneously. To address these challenges, we introduce TransAnyText, a structured visual code framework that reformulates image text translation as generating renderable HTML patches from source images and target languages. Our framework decouples semantic generation from pixel rendering: a vision-language model (VLM) handles visual understanding, cross-lingual translation, and structured visual generation, while a diffusion model performs background inpainting and pixel-level refinement, followed by deterministic rendering to synthesize the final image. Based on this formulation, we develop a three-stage post-training framework, where supervised fine-tuning (SFT) establishes the image-to-code mapping, privilege-gap weighted self-distillation (PWSD) improves the learning of style and layout tokens, and reinforcement learning with verifiable rewards (RLVR) further optimizes task-level performance. We further introduce TransAnyDataset and TransAnyBench, a multilingual dataset and benchmark for e-commerce image translation. Extensive experiments demonstrate competitive performance against cascaded pipelines, open-source end-to-end models, and closed-source image editing systems, providing an effective, controllable, and editable solution for cross-border e-commerce image translation.

cs.CV↗
arXiv2026

VCG-Bench: Towards A Unified Visual-Centric Benchmark for Structured Generation and Editing

Despite the rapid advancements in Vision-Language Models (VLMs), a critical gap remains in their ability to handle structured, controllable diagrammatic tasks essential for professional workflows. Existing methods predominantly rely on pixel-based synthesis, which operates in probabilistic pixel spaces and is inherently limited in editability and fidelity. Instead, we propose a new Diagram-as-Code paradigm with symbolic logic that leverages mxGraph Extensible Markup Language (XML) for precise diagram generation and editing. We present VCG-Bench, a unified benchmark for visual-centric \texttt{mxGraph} tasks. VCG-Bench comprises: (1) a taxonomized dataset of 1,449 diverse diagrams spanning 6 domains and 15 sub-domains, (2) a paradigm definition that integrates Generation (Vision-to-Code) and Editability (Code-to-Code), (3) a Tailored Evaluation Protocol employing multi-dimensional metrics such as \texttt{mxGraph} Execution Success Rate, Style Consistency Score (SCS), etc. Experimental results highlight the challenges faced by current State-of-the-Art (SOTA) VLMs in structured fidelity and instruction compliance, reflecting their vision and reasoning capabilities.

cs.CL↗
arXiv2026

Orthonormal Spectral Cluster Bounds on Manifolds with Nonpositive Curvature

Let $(M,g)$ be a closed $n$-dimensional Riemannian manifold with nonpositive sectional curvature. We prove sharp, logarithmically improved spectral cluster bounds for orthonormal systems in the supercritical range. More precisely, for spectral windows of size $(\log λ)^{-1}$, we obtain the orthonormal analogue of the logarithmically improved $L^q$ estimates of Hassell-Tacy. Our argument combines the universal orthonormal spectral cluster bounds of Frank-Sabin with Bérard-type kernel estimates and a generalization of the Bourgain-Shao-Sogge-Yao multiplier estimate to the orthonormal setting.

math.AP↗
arXiv2025

Riesz transforms and Sobolev spaces associated to the partial harmonic oscillator

In this paper, our goal is to establish the Sobolev space associated to the partial harmonic oscillator. Based on its heat kernel estimate, we firstly give the definition of the fractional powers of the partial harmonic oscillator $$\AH=-\partial_ρ^2-Δ_x+|x|^2,$$ and show that its negative powers are well defined on $L^p(\mathbb R^{d+1})$ for $p\in [1,\infty]$. We then define associated Riesz transforms and show that they are bounded on classical Sobolev spaces by the calculus of symbols. Secondly, by a factorization of the operator $\AH$, we define two families of Sobolev spaces with positive integer indices, and show the equivalence between them by the boundedness of Riesz transforms. Moreover, the adapted symbolic calculus also implies the boundedness of Riesz type transforms on the Sobolev spaces associated to the partial harmonic oscillator $\AH$. Lastly, as applications of our results, we obtain the revised Hardy-Littlewood-Sobolev inequality, the Gagliardo-Nirenberg-Sobolev inequality, and Hardy's inequality in the potential space $L_{\AH}^{α, p}$.

math.AP↗
arXiv2024

Intertwining operators beyond the Stark Effect

The main mathematical manifestation of the Stark effect in quantum mechanics is the shift and the formation of clusters of eigenvalues when a spherical Hamiltonian is perturbed by lower order terms. Understanding this mechanism turned out to be fundamental in the description of the large-time asymptotics of the associated Schrödinger groups and can be responsible for the lack of dispersion in Fanelli, Felli, Fontelos and Primo [Comm. Math. Phys., 324(2013), 1033-1067; 337(2015), 1515-1533]. Recently, Miao, Su, and Zheng introduced in [Tran. Amer. Math. Soc., 376(2023), 1739--1797] a family of spectrally projected intertwining operators, reminiscent of the Kato's wave operators, in the case of constant perturbations on the sphere (inverse-square potential), and also proved their boundedness in $L^p$. Our aim is to establish a general framework in which some suitable intertwining operators can be defined also for non constant spherical perturbations in space dimensions 2 and higher. In addition, we investigate the mapping properties between $L^p$-spaces of these operators. In 2D, we prove a complete result, for the Schrödinger Hamiltonian with a (fixed) magnetic potential an electric potential, both scaling critical, allowing us to prove dispersive estimates, uniform resolvent estimates, and $L^p$-bounds of Bochner--Riesz means. In higher dimensions, apart from recovering the example of inverse-square potential, we can conjecture a complete result in presence of some symmetries (zonal potentials), and open some interesting spectral problems concerning the asymptotics of eigenfunctions.

math.AP↗
arXiv2024

Your Network May Need to Be Rewritten: Network Adversarial Based on High-Dimensional Function Graph Decomposition

In the past, research on a single low dimensional activation function in networks has led to internal covariate shift and gradient deviation problems. A relatively small research area is how to use function combinations to provide property completion for a single activation function application. We propose a network adversarial method to address the aforementioned challenges. This is the first method to use different activation functions in a network. Based on the existing activation functions in the current network, an adversarial function with opposite derivative image properties is constructed, and the two are alternately used as activation functions for different network layers. For complex situations, we propose a method of high-dimensional function graph decomposition(HD-FGD), which divides it into different parts and then passes through a linear layer. After integrating the inverse of the partial derivatives of each decomposed term, we obtain its adversarial function by referring to the computational rules of the decomposition process. The use of network adversarial methods or the use of HD-FGD alone can effectively replace the traditional MLP+activation function mode. Through the above methods, we have achieved a substantial improvement over standard activation functions regarding both training efficiency and predictive accuracy. The article addresses the adversarial issues associated with several prevalent activation functions, presenting alternatives that can be seamlessly integrated into existing models without any adverse effects. We will release the code as open source after the conference review process is completed.

cs.LG↗
arXiv2023

Growth of Sobolev norms for 2D cubic nonlinear Schrödinger equation with partial harmonic potential

In this paper, we study the $2$D cubic nonlinear Schrödinger equation (NLS) with the partial harmonic potential. First, we prove the local well-posedness in Bourgain spaces by establishing a key bilinear estimate associated with the partial harmonic oscillator. Then, we give the polynomial bound of the Sobolev norms for the solutions using the method of the Planchon, Tzvetkov, and Visciglia.

math.AP↗
arXiv2022

A Mikhlin--Hörmander multiplier theorem for the partial harmonic oscillator

We prove a Mikhlin--Hörmander multiplier theorem for the partial harmonic oscillator $H_{\textup{par}}=-\pa_ρ^2-Δ_x+|x|^2$ for $(ρ, x)\in\R\times\R^d$ by using the Littlewood--Paley $g$ and $g^\ast$ functions and the associated heat kernel estimate. The multiplier we have investigated is defined on $\mathbb R \times \mathbb N$.

math.AP↗
arXiv2022

The $W^{s,p}$-boundedness of stationary wave operators for the Schrödinger operator with inverse-square potential

In this paper, we investigate the $W^{s,p}$-boundedness for stationary wave operators of the Schrödinger operator with inverse-square potential $$\mathcal L_a=-Δ+\tfrac{a}{|x|^2}, \quad a\geq -\tfrac{(d-2)^2}{4},$$ in dimension $d\geq 2$. We construct the stationary wave operators in terms of integrals of Bessel functions and spherical harmonics, and prove that they are $W^{s,p}$-bounded for certain $p$ and $s$ which depend on $a$. As corollaries, we solve some open problems associated with the operator $\mathcal L_a$, which include the dispersive estimates and the local smoothing estimates in dimension $d\geq 2$. We also generalize some known results such as the uniform Sobolev inequalities, the equivalence of Sobolev norms and the Mikhlin multiplier theorem, to a larger range of indices. These results are important in the description of linear and nonlinear dynamics for dispersive equations with inverse-square potential.

math.AP↗
arXiv2021

A Limiting absorption principle for high-order Schrödinger operators in critical spaces

In this paper, we prove a limiting absorption principle for high-order Schrödinger operators with a large class of potentials which generalize some results by A. Ionescu and W. Schlag. Our main idea is to handle the boundary operators by the restriction theorem of Fourier transform. Two key tools we use in this paper are the Stein--Tomas theorem in Lorentz spaces and a sharp trace lemma given by S. Agmon and L. Hörmander

math.AP↗
arXiv2019

Hölder regularity for the time fractional Schrödinger equation

In this paper, we investigate that the Hölder regularity of solutions to the time fractional Schrödinger equation of order $1<α<2$, which interpolates between the Schrödinger and wave equations. This is inspired by Hirata and Miao's work which studied the fractional diffusion-wave equation. First, we give the asymptotic behavior for the oscillatory distributional kernels and their Bessel potentials by using Fourier analytic techniques. Then, the space regularity is derived by employing some results on singular Fourier multipliers. Using the asymptotic behavior for the above kernels, we prove the time regularity. Finally, we use mismatch estimates to prove the pointwise convergence to the initial data in Hölder spaces. In addition, we also prove Hölder regularity result for the Schrödinger equation.

math.AP↗
arXiv2019

Local well-posedness of semilinear space-time fractional Schrödinger equation

The semilinear space-time fractional Schrödinger equation is considered. First, we give the explicit form for the fundamental solutions by using the Fox $H$-functions in order to to establish some $L^s$ decay estimates. After that, we give some space-time estimates for the mild solutions from which the local well-posedness is derived on some proper Banach space.

math.AP↗
arXiv2013

A generalized evidence distance

Dempster-Shafer theory of evidence (D-S theory) is widely used in uncertain information process. The basic probability assignment(BPA) is a key element in D-S theory. How to measure the distance between two BPAs is an open issue. In this paper, a new method to measure the distance of two BPAs is proposed. The proposed method is a generalized of existing evidence distance. Numerical examples are illustrated that the proposed method can overcome the shortcomings of existing methods.

cs.AI↗