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Sibei Yang

Publications and source records attributed to Sibei Yang.

At least 19 recordsLinked to original sources
arXiv2026

A Sharp Planar Fractional Isoperimetric Inequality

In this article, we prove the sharp form of the fractional isoperimetric inequality in the plane, originally posed by Maz'ya [Problem 1, Integral Equations Operator Theory, 2018]. More precisely, we show that, for any given $s\in(0,1)$ and any bounded domain $Ω\subset \mathbb{R}^2$ with $C^1$ boundary, $$ P_s(Ω) \le \frac{π^{s-\frac{1}{2}}Γ\left(\frac{3-s}{2}\right)}{s(1-s)Γ\left(\frac{4-s}{2}\right)}\left[\mathcal{H}^1(\partialΩ)\right]^{2-s}, $$ where $P_s$ denotes the fractional $s$-perimeter, $Γ$ denotes the Gamma function, and $\mathcal{H}^{1}$ denotes the $1$-dimensional Hausdorff measure on $\mathbb{R}^2$. The constant is sharp and equality is attained by the disk. The proof proceeds in three steps: reducing the fractional perimeter to a chord functional, reducing connected domains to convex bodies, and proving the sharp convex chord inequality via a fractional Willmore-type inequality, a variational formula along outer parallel bodies, and asymptotic analysis.

math.FA↗
arXiv2026

Learning Representations to Guide Pixel Diffusion Transformers

Visual representations are largely developed for understanding, yet what makes them useful for generation remains unclear. We study this question in pixel diffusion transformers and uncover two key insights. First, better representation quality does not necessarily translate into greater generative utility, as externally aligned semantics can be progressively lost during pixel synthesis. Second, architectural separation with specialized pixel decoders mainly redistributes semantic and spatial modeling, without necessarily yielding representations better suited to generation. These insights suggest that a useful generative representation must be both properly formed and actively exploited. Motivated by these insights, we introduce Representation Guidance (RG), which directly forms and exploits internal representations while retaining a plain Transformer architecture. A low-dimensional bottleneck forces generation-relevant information into a compact representation, which is then explicitly used to guide decoder generation by modifying the flow-matching target according to its induced prediction offset. RG learns clearer semantic and spatial structure while scaling efficiently in both parameters and computation. On ImageNet 256x256, RG-L/16 with only 459M parameters outperforms substantially larger pixel diffusion transformers, while RG-XL/16 achieves an FID of 1.55. RG further reaches an FID of 1.74 at 512x512 and extends to text-to-image generation, achieving 0.89 on GenEval and 87.1 on DPG-Bench.

cs.CV↗
arXiv2026

Optimal Global Sobolev Estimates for Fractional Dirichlet Problems in Bounded Lipschitz Domains

Let $n\geq2$, $s\in(0,1)$, and let $Ω\subset\mathbb{R}^n$ be a bounded Lipschitz domain. In this paper, we establish optimal global Sobolev estimates for the fractional Dirichlet problem \begin{equation*} \left\{\begin{aligned} (-Δ)^su&=f & & \text{in}\ \ Ω, u&=0 & & \text{in}\ \ \mathbb{R}^n\setminusΩ. \end{aligned}\right. \end{equation*} More precisely, for any given $t\in[s,\min\{2s,\,s+1/2\})$, we prove that there exists a small positive constant $η=η(n,s,t,Ω)$ such that the following holds. If $n=2$ and $s\in(1/2,1)$, then, for any $q\in(1,\frac{4}{1+2s}+η)$ and $p\in(1,\frac{nq}{n-(2s-t)q}]$, \begin{equation*} \|u\|_{W^{t,p}(\mathbb{R}^n)}\le C\|f\|_{L^q(Ω)}, \end{equation*} and, if either $n=2$ and $s\in(0,1/2]$ or $n\ge 3$ and $s\in(0,1)$, then, for any $q\in(1,\frac{n(2s+1)}{nt+(2s-t)(2s+1)}+η)$ and $p\in(1,\frac{nq}{n-(2s-t)q}]$, \begin{equation*} \|u\|_{W^{t,p}(\mathbb{R}^n)}\le C\|f\|_{L^q(Ω)}. \end{equation*} Here the positive constant $C$ depends only on $n$, $s$, $t$, $p$, $q$, and $Ω$. The stated universal baselines are optimal in Dahlberg's sense: for any larger target exponent $p$ there is a bounded Lipschitz domain whose solution with right-hand side identically $1$ is not in $W^{t,p}(\mathbb{R}^n)$. The counterexamples are constructed using regular Cantor sets on the boundary and, in the planar exceptional case, homogeneous solutions in sectors.

math.AP↗
arXiv2026

Full-Range $Γ$-Convergence of Weak-Type Nonlocal Functionals

Let $N\ge1$, $p\in[1,\infty)$, and $Ω\subset\mathbb R^N$ be a bounded open interval when $N=1$ or a bounded Lipschitz domain when $N\ge2$. For any given $γ\in\mathbb R\setminus\{0\}$ and $λ\in(0,\infty)$, consider the weak-type nonlocal functional \begin{align*} F_{λ,p,γ}(u;Ω):=λ^p \underset{|u(x)-u(y)|>λ|x-y|^{1+\fracγ{p}}} {\int_Ω\int_Ω}|x-y|^{γ-N}\,dy\,dx. \end{align*} In this article, we prove that, for $γ\in(0,\infty)$ as $λ\to\infty$ or for $γ\in(-\infty,-1]$ as $λ\to0^+$, the family $F_{λ,p,γ}(\cdot;Ω)$ converges, in the sense of $Γ$-convergence in $L^p(Ω)$, to the functional \begin{align*} Ψ_{p,γ}^Ω(u) :=\begin{cases} C_{N,p,γ}^{\rm cell}\displaystyle\int_Ω|\nabla u|^p\,dx, &p\in(1,\infty)\ \hbox{and}\ u\in W^{1,p}(Ω),\\[2mm] C_{N,1,γ}^{\rm cell}|Du|(Ω), &p=1\ \hbox{and}\ u\in BV(Ω),\\[1mm] \infty,&\hbox{otherwise}. \end{cases} \end{align*} where the positive constants $C_{N,p,γ}^{\mathrm{cell}}$ are independent of $Ω$. As applications, we further show that, for $γ\in(0,\infty)$ as $λ\to\infty$ or for $γ\in(-\infty,-1]$ as $λ\to0^+$, the weak-type nonlocal functional $F_{λ,p,γ}(\cdot;\mathbb R^N)$ converges, in the sense of $Γ$-convergence in $L^1_{\rm loc}(\mathbb R^N)$, to a similar functional; this gives an complete answer to the problem posed by Brezis et al. in [Section~7C, Anal. PDE 2024].

math.CA↗
arXiv2026

EvoSCM: Scientific Belief Revision Through Causal Model Evolution and Experimentation

Scientific discovery depends on the ability to form hypotheses, test them through experiments, and revise them when evidence disagrees. Existing LLM agents support this process by improving their reasoning or actions, but their scientific beliefs are often scattered across free-form reasoning and difficult to update coherently. This makes it difficult to identify what failed, what should change, and whether revisions remain consistent with prior evidence. We introduce EvoSCM, which represents scientific beliefs as a population of structural causal model (SCM) hypotheses that can be tested and revised across experiments. EvoSCM formulates scientific discovery as a closed loop in which causal hypotheses guide experimentation and experimental outcomes drive causal model evolution. Competing SCM hypotheses make falsifiable predictions and guide discriminative experiments that separate alternative explanations. When observations contradict these predictions, EvoSCM distills discrepancies into correction rules identifying which aspects of the hypotheses fail to explain the evidence. These rules guide revisions to causal dependencies, latent factors, mechanisms, and parameters. Revised hypotheses are validated against accumulated evidence and carried forward to guide subsequent experiments, allowing scientific beliefs to evolve cumulatively. We evaluate EvoSCM across physics, chemistry and materials, and biology. It consistently outperforms baseline agents and existing evolution methods, yielding more accurate explanations and predictions with more effective use of experimental budgets. The evolved SCMs also transfer across base models, suggesting reusable scientific knowledge beyond any single model's reasoning process.

cs.AI↗
arXiv2026

A Solution of Problem 2.5 by Brezis on the Planar Ginzburg--Landau Equation

Brezis, Merle, and Riviére [Arch. Rational Mech. Anal. 1994] proved that, if a smooth solution $u:\mathbb{R}^2\to\mathbb{C}$ of the planar entire Ginzburg--Landau equation $$ -Δu = u(1-|u|^2)\quad \text{in}\quad \mathbb{R}^2 $$ satisfies the finite potential energy estimate that $$ \int_{\mathbb{R}^2}\left[1-|u(x)|^2\right]^2\,dx < \infty, $$ then it has the asymptotic property that $$ |u(x)|\to 1\quad \text{as}\quad |x|\to\infty. $$ The converse problem whether the asymptotic property implies the finite potential energy estimate was originally posed in their work and later formulated by Brezis as \emph{Open Problem 2.5} in [Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 2023]. In this article, we give an affirmative answer to this question. Our proof relies on the Kelvin inversion, a Morrey-type energy decay for the translation Jacobi system, the $L^4$-integrability of the phase form, and a linearised amplitude equation; all these tools together imply the $L^2$-integrability of the function $1-|u|$ on an exterior domain, without any a priori integrability assumption.

math.AP↗
arXiv2026

$Γ$-Convergence of Weak-Type Nonlocal Functionals on Bounded Domains

Let $N\ge1$, $p\in[1,\infty)$, $γ\in(0,\infty)$, and $Ω\subset\mathbb R^N$ be a bounded open interval when $N=1$ or a bounded Lipschitz domain when $N\ge2$. For any $λ\in(0,\infty)$ and any measurable function $u$, consider the weak-type nonlocal functional \begin{align*} G_{λ,p,γ}(u;Ω) :=λ\iint_{Ω\timesΩ} \mathbf 1_{\left\{(x,y)\inΩ\timesΩ:\ x\neq y,\ \frac{|u(x)-u(y)|^p}{|x-y|^{p+γ}}\geqλ\right\}} |x-y|^{γ-N}\,dx\,dy. \end{align*} In this article, we prove that, as $λ\to\infty$, the family $G_{λ,p,γ}$ converges, in the sense of $Γ$-convergence in $L^p(Ω)$, to the functional \begin{align*} Ψ_{p,γ}^{\mathrm{cell}}(u;Ω):= \begin{cases} C_{N,p,γ}^{\mathrm{cell}}\displaystyle\int_Ω|\nabla u|^p\,dx, &p\in(1,\infty)\ \hbox{and}\ u\in W^{1,p}(Ω),\\[2mm] C_{N,1,γ}^{\mathrm{cell}}|Du|(Ω), &p=1\ \hbox{and}\ u\in BV(Ω),\\[1mm] \infty,&\hbox{otherwise}, \end{cases} \end{align*} where the positive constants $C_{N,p,γ}^{\mathrm{cell}}$ are independent of $Ω$ and characterized by a cell formula. This gives an affirmative answer to the problem posed by Brezis [Open Problem~9.3, Rend. Lincei Mat. Appl. 2023].

math.CA↗
arXiv2026

Lattice point counting in Cygan--Korányi balls on Heisenberg groups

Lattice point counting in gauge balls on the Heisenberg group $\mathbb{H}^q$ is a non-commutative analogue of the Euclidean multidimensional sphere problem, initiated by Garg, Nevo and Taylor \cite[\textit{Ann. Inst. Fourier}, 2015]{GNT15}. The case of particular interest is when the gauge is taken as the Cygan--Korányi norm and the error term reads: $$\mathcal{E}_q(t)=\#\left(\mathbb{Z}^{2 q+1} \cap \mathcal{B}_t\right)-\operatorname{vol}(\mathcal{B}_1) \, t^{2 q+2},$$ with $\mathcal{B}_t=\{(v,w)\in\mathbb{H}^q: (|v|^4 + w^2)^{1/4} \le t \}$, which is closely related to the Gauss circle problem. When $q\ge3$, Gath \cite[\textit{Ann. Sc. Norm. Super. Pisa Cl. Sci.}, 2022]{Gat22} improved upon \cite[]{GNT15} by showing that $ |\mathcal{E}_q(t)|\lesssim t^{2q-1+ 1/3}$ and proposed the conjecture that the optimal order should be $2q-1$. In this paper, through Landau's formula and the $5,6$-th Derivative Tests of van der Corput, we arrive at that $|\mathcal{E}_q(t)| \lesssim t^{2 q-1 + 241/753} $ for any $ q \geq 4$, and recover the bound of Gath for $q=3$ up to a logarithmic factor. This, via a simpler method, provides the first progress towards Gath's conjecture.

math.NT↗
arXiv2026

Sobolev--Morrey Spaces and Divergence-Form Degenerate Second-Order Elliptic Equations on Domains with Higher Co-Dimensional Boundaries

In this article, we study the weighted homogeneous Sobolev--Morrey spaces on domains in $\mathbb{R}^n$ with higher co-dimensional boundaries. Precisely, we systematically establish a real-variable theory of these spaces, including completeness, embedding theorems, Riesz potential characterizations, continuity, trace and extension theorems, and complex interpolation. Applying the boundedness of the trace and the extension operators, we obtain sharp weighted a priori estimates for solutions to the Dirichlet problem of divergence-form degenerate second-order elliptic equations on such domains in weighted Lebesgue spaces. The absence of a boundary manifold structure of these domains poses some essential difficulties, which are overcome by using some tools, such as the intrinsic properties of distance weights and the geometric structure of domains, different from those available in Lipschitz domains.

math.AP↗
arXiv2026

A Counterexample to the Necessity of the Vanishing Carleson Condition for VMO Poisson Kernels

In [Problem 3.2.23, CBMS Regional Conference Series in Mathematics 83, 1994], Kenig asked whether the vanishing Carleson condition is the necessary and sufficient for the logarithm of the Poisson kernel of a perturbation of the Laplacian on the unit ball in $\mathbb{R}^n$ belonging to the space VMO. The sufficiency was proved by Escauriaza [Israel J. Math. 1996] and extended by Milakis, Pipher, and Toro [Contemp. Math. 2014] to more general setting. In this article, using the technique of bi-Lipschitz mappings, we construct a counterexample to show that the vanishing Carleson condition is not necessary and hence give a negative answer to the aforementioned problem.

math.AP↗
arXiv2026

Bridging the Agent-World Gap: Text World Models for LLM-based Agents

Large language model (LLM)-based agents are increasingly used in interactive textual environments, from web navigation and code editing to tool use and long-horizon dialogue. Yet many remain largely reactive, mapping observations to actions without an explicit model of how these environments are structured and evolve. This motivates text world models (TWMs): transition models over textual states that, given a state and a candidate action, predict the resulting webpage, terminal output, API response, or user reply, thereby supporting planning, efficient learning, and principled evaluation. We systematically review text world models for LLM-based agents, organized around a formal framework and the agent lifecycle: (1) Foundations, defining text world models and characterizing them by state representation and grounding domain; (2) Construction, taxonomizing LLM-as-WM and code-as-WM paradigms and reviewing methods for building them; (3) Application, examining how world models support agents at training time through experience synthesis and at inference time through planning, verification, and adaptation; and (4) Evaluation, covering both evaluation of the world model itself and its use as an evaluation environment for agents. We aim to consolidate this rapidly developing area, clarify its design space, and highlight open challenges for future research.

cs.CL↗
arXiv2026

Self-Prophetic Decoding to Unlock Visual Search in LVLMs

Large Vision-Language Models (LVLMs) are rapidly evolving toward true multimodal reasoning, with visual search representing a concrete instantiation of the thinking-with-images paradigm. However, LVLM visual search faces two key challenges: incompatibility among intrinsic capabilities after post-training, and interference in long multi-step reasoning contexts. To address these, we identify two novel insights. First, self-regulation between pre- and post-training LVLMs leverages the intrinsic single-step capabilities of the pre-training model to mitigate capability deterioration and long-context interference. Second, probability-based prophetic sampling, replacing naive prompting, provides a probabilistic interface where the pre-training model acts as a prophet and the post-training model selectively accepts prophetic tokens under its output distribution, preserving coherent multi-step reasoning. Building on these insights, we introduce SeProD, a self-prophetic decoding framework that leverages intrinsic single-step capabilities to enable coherent multi-step reasoning in a training-free, plug-and-play manner. Experiments show that SeProD consistently improves multiple visual-search LVLMs across all 12 splits of 4 visual search benchmarks, as well as across general VQA benchmarks, without added computational overhead, thanks to its parallel prophetic acceptance mechanism.

cs.CV↗
arXiv2026

A Counterexample to Kenig's Interpolation Problem for Sobolev Spaces with Zero Boundary Conditions

Let $n\in \mathbb N\cap[2,\infty)$. In this article, we show that there exists a bounded $C^1$ domain $Ω\subset \mathbb R^n$ such that, for any given $s\in(1,2)\setminus\{\frac32\}$, \begin{align*} \left[H_0^1(Ω),H^2(Ω)\cap H_0^1(Ω)\right]_{s-1} =H^s(Ω)\cap H_0^1(Ω)=H_0^s(Ω) \end{align*} with equivalent norms, but \begin{align*} \left[H_0^1(Ω),H^2(Ω)\cap H_0^1(Ω)\right]_{\frac12} \subsetneqq H^{\frac32}(Ω)\cap H_0^1(Ω), \end{align*} which provides a counterexample to Problem 3.3.19 of Kenig in [CBMS Regional Conf. Ser. in Math. 83, 1994]. As applications, we prove that for such a domain $Ω$ \begin{align*} H^2(Ω)\cap H_0^1(Ω)\subsetneqq D(-Δ_D) \end{align*} (the domain of the Dirichlet Laplacian operator $-Δ_D$ on $Ω$) and construct a solution of the homogeneous heat equation with zero Dirichlet boundary condition, which does not belong to $L^2((0,T);H^2(Ω)\cap H_0^1(Ω))$ for any given $T\in(0,\infty)$.

math.AP↗
arXiv2026

EVA: Editing for Versatile Alignment against Jailbreaks

Large Language Models (LLMs) and Vision Language Models (VLMs) have demonstrated impressive capabilities but remain vulnerable to jailbreaking attacks, where adversaries exploit textual or visual triggers to bypass safety guardrails. Recent defenses typically rely on safety fine-tuning or external filters to reduce the model's likelihood of producing harmful content. While effective to some extent, these methods often incur significant computational overheads and suffer from the safety utility trade-off, degrading the model's performance on benign tasks. To address these challenges, we propose EVA (Editing for Versatile Alignment against Jailbreaks), a novel framework that pioneers the application of direct model editing for safety alignment. EVA reframes safety alignment as a precise knowledge correction task. Instead of retraining massive parameters, EVA identifies and surgically edits specific neurons responsible for the model's susceptibility to harmful instructions, while leaving the vast majority of the model unchanged. By localizing the updates, EVA effectively neutralizes harmful behaviors without compromising the model's general reasoning capabilities. Extensive experiments demonstrate that EVA outperforms baselines in mitigating jailbreaks across both LLMs and VLMs, offering a precise and efficient solution for post-deployment safety alignment.

cs.CR↗
arXiv2026

GPO-V: Jailbreak Diffusion Vision Language Model by Global Probability Optimization

Diffusion Vision-Language Models (dVLMs), built upon the non-causal foundations of Diffusion Large Language Models (dLLMs), have demonstrated remarkable efficacy in multimodal tasks by departing from the traditional autoregressive generation paradigm. While dVLMs appear inherently robust against conventional jailbreak tactics, which we categorize as Fixed Prefix Optimization (FPO) (e.g., anchoring responses with "Sure, here is"), this perceived resilience is deceptive. Our investigation into the safety landscape of dVLMs reveals a unique refusal pattern: Immediate Refusal and Progressive Refusal. We find that while FPO-based attacks often fail by triggering the latter, the progressive refinement process itself uncovers a novel, latent attack surface. To exploit this vulnerability, we propose Global Probability Optimization (GPO), a general jailbreak paradigm designed specifically for the denoising trajectory of masked diffusion models. Unlike prefix-based methods, GPO manipulates the global generative dynamics to bypass guardrails in diffusion language models. Building on this, we introduce GPO-V, the first visual-modality jailbreak framework tailored for dVLMs. Empirical results demonstrate that GPO-V produces stealthy perturbations with exceptional cross-model transferability, revealing a critical security gap in non-sequential generative architectures. Our findings underscore the critical urgency of addressing safety alignment in dVLMs. These results necessitate an immediate and fundamental re-evaluation of current defense paradigms to mitigate the unique risks of diffusion-based generation. Our code is available at: https://anonymous.4open.science/r/GPO-V-0250.

cs.CV↗
arXiv2026

Vision Transformers Need More Than Registers

Vision Transformers (ViTs), when pre-trained on large-scale data, provide general-purpose representations for diverse downstream tasks. However, artifacts in ViTs are widely observed across different supervision paradigms and downstream tasks. Through systematic analysis of artifacts in ViTs, we find that their fundamental mechanisms have yet to be sufficiently elucidated. In this paper, through systematic analysis, we conclude that these artifacts originate from a lazy aggregation behavior: ViT uses semantically irrelevant background patches as shortcuts to represent global semantics, driven by global attention and Coarse-grained semantic supervision. Our solution selectively integrates patch features into the CLS token, reducing the influence of background-dominated shortcuts and consistently improving performance across 12 benchmarks under label-, text-, and self-supervision. We hope this work offers a new perspective on ViT behavior.

cs.CV↗
arXiv2026

Chart Deep Research in LVLMs via Parallel Relative Policy Optimization

With the rapid advancement of data science, charts have evolved from simple numerical presentation tools to essential instruments for insight discovery and decision-making support. However, current chart data intelligence exhibits significant limitations in deep research capabilities, with existing methods predominantly addressing shallow tasks such as visual recognition or factual question-answering, rather than the complex reasoning and high-level data analysis that deep research requires. This limitation stems from two primary technical bottlenecks: at the training level, existing post-training techniques exhibit deficiencies in handling multi-dimensional reward signal interference and heterogeneous data gradient conflicts, preventing models from achieving balanced development across multiple capability dimensions; at the evaluation level, current methods remain limited to factual retrieval and basic computation, failing to assess end-to-end analytic reasoning and other deep research capabilities. To address the training challenge, we propose PRPO, which performs parallel optimization across reward dimensions and capability partitioning across data types, effectively disentangling conflicts between heterogeneous data and multi-dimensional reward signals while ensuring optimization stability. For the evaluation challenge, we construct MCDR-Bench based on the ``error uniqueness principle," transforming subjective generation assessment into objective error identification through controllable error injection, enabling quantifiable evaluation of deep research capabilities. Experimental validation confirms that the proposed PRPO and MCDR-Bench jointly establish a unified framework that systematically advances chart deep research through enhanced collaborative training and objective evaluation.

cs.CV↗
arXiv2026

WeaveTime: Stream from Earlier Frames into Emergent Memory in VideoLLMs

Recent advances in Multimodal Large Language Models have greatly improved visual understanding and reasoning, yet their quadratic attention and offline training protocols make them ill-suited for streaming settings where frames arrive sequentially and future observations are inaccessible. We diagnose a core limitation of current Video-LLMs, namely Time-Agnosticism, in which videos are treated as an unordered bag of evidence rather than a causally ordered sequence, yielding two failures in streams: temporal order ambiguity, in which the model cannot follow or reason over the correct chronological order, and past-current focus blindness where it fails to distinguish present observations from accumulated history. We present WeaveTime, a simple, efficient, and model agnostic framework that first teaches order and then uses order. We introduce a lightweight Temporal Reconstruction objective-our Streaming Order Perception enhancement-that instills order aware representations with minimal finetuning and no specialized streaming data. At inference, a Past-Current Dynamic Focus Cache performs uncertainty triggered, coarse-to-fine retrieval, expanding history only when needed. Plugged into exsiting Video-LLM without architectural changes, WeaveTime delivers consistent gains on representative streaming benchmarks, improving accuracy while reducing latency. These results establish WeaveTime as a practical path toward time aware stream Video-LLMs under strict online, time causal constraints. Code and weights will be made publicly available. Project Page: https://zhangyl4.github.io/publications/weavetime/

cs.CV↗