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Wen Yang

Publications and source records attributed to Wen Yang.

At least 19 recordsLinked to original sources
arXiv2026

On Brezis' open problem 2.4

We show the existence of a ``nonradial" smooth entire solution of the Ginzburg--Landau equation with degree $q\in\{8,9\}$ and modulus tending to one at infinity. This answers Brezis' Open Problem 2.4 negatively. To construct the counterexample, we vary a cone parameter $q \in [8, 9]$ and keeping the degree on the cone equal to one. Several key ingredients are needed. First, we need to compute the Morse index of radial vortex solutions at $q\in \{8, 9\}$. Second, we need to show compactness. Finally, Leray-Schauder degree theory and a homotopy argument yield the desired existence result.

math.AP↗
arXiv2026

How Well Does Mathematical Reasoning Transfer Across Languages in English-Centric LLMs?

Recent advances in Reinforcement Post-Training (RPT) have substantially improved the mathematical reasoning capabilities of large language models (LLMs), but it remains unclear how well such gains transfer across languages. In this work, we study cross-lingual mathematical reasoning transfer in English-centric LLMs under controlled multilingual evaluation. We first evaluate a range of English-centric reasoning models on multilingual mathematical reasoning benchmarks and find that transfer is highly variable across initial model choice, target language, and training paradigm. Through controlled comparative experiments, we further find that stronger English-centric initialization does not necessarily lead to stronger relative transfer efficiency, even when it yields higher multilingual reasoning accuracy. Finally, we show that the largest improvement comes from moving beyond English-only supervision: adding a single parallel language yields a substantial gain, while further gains from additional languages are smaller but consistent. Overall, our results highlight the need to evaluate multilingual mathematical reasoning directly, using both absolute performance and relative transfer-efficiency metrics.

cs.CL↗
arXiv2026

SWE-Stream: Scaling Executable Training Data for SWE Agents via Progressive Construction and Elastic Streaming

Software engineering agents have advanced rapidly, but scaling their training remains constrained by the limited availability of high-quality executable tasks. Development histories contain valuable signals for constructing such tasks, yet they often require substantial reconstruction due to incomplete environments, missing tests, and inconsistent artifacts. We present SWE-Stream, a system for scaling executable SWE training data through progressive construction and elastic streaming execution. SWE-Stream progressively validates and refines task candidates, reusing existing artifacts when possible and applying targeted completion only when necessary. An elastic scheduler asynchronously coordinates construction stages under shared resource constraints, adapting execution budgets based on observed workload demands. Using development histories from 10,728 repositories across six programming languages, SWE-Stream constructs 80,874 validated tasks and collects 118,688 successful trajectories. Fine-tuning Qwen3-30B-A3B-Thinking-2507 on these trajectories achieves resolve rates of 69.0%, 49.3%, and 45.42% on SWE-bench Verified, Multilingual, and Pro, respectively. In a controlled comparison with approximately matched training budgets, SWE-Stream achieves a 45.6% resolve rate on SWE-bench Verified, outperforming three existing data sources. Moreover, its streaming construction strategy improves efficiency, delivering $1.45\times$ the accepted-task throughput of batch construction and accepting 13.2% more tasks than fixed-limit streaming.

cs.SE↗
arXiv2026

Domain dependence of Sobolev-curl constants and structure of critical curl-curl solutions

This paper investigates intrinsic critical Sobolev-curl constants on bounded domains and the structure of finite-energy solutions to the critical curl-curl equation in R^3. First, for 1< p < 3, we prove that the intrinsic critical p-curl constant on (0, a)\times D is bounded above by a^{p/3} times a Sobolev quotient on D. The proof uses an aligned test field whose optimal curl-free correction vanishes. Consequently, these constants tend to zero along thin convex boxes. For p = 2, we construct explicit convex and nonconvex domains with intrinsic constant below the sharp scalar Sobolev constant. The nonconvex example gives an affirmative answer to the domain-existence question in Problem 5 of Mederski and Szulkin(Arch. Ration. Mech. Anal. 241 (2021), 1815-1842), while the convex example disproves the lower bound stated there for convex domains. Concerning their Problem 2, we obtain an implicit Newtonian representation of finite-energy solutions and exclude two special forms of solutions. These structural results do not yet provide an explicit ground state or an unconditional ground-state decay rate as asked in Problem 2.

math.AP↗
arXiv2026

Uniqueness and Symmetry Breaking for Singular $Q$-curvature Equations in $\R^n$

For $n\ge3$ and $γ>-1$, we study normal solutions of \begin{equation*} (-Δ)^{n/2}u=(n-1)!\,|x|^{nγ}e^{nu} \quad\hbox{in }\R^n. \end{equation*} We reformulate this problem on the cylinder via the Emden--Fowler transform. We first establish Kelvin symmetry for normal solutions. We then prove existence and uniqueness, up to dilation, of the radial normal solution and establish its radial nondegeneracy. Next, we carry out a detailed spectral analysis of the linearized operator and construct branches of nonradial normal solutions by the Crandall--Rabinowitz theorem. Finally, we prove that every normal solution is radial when $γ>0$ is sufficiently small.

math.AP↗
arXiv2026

Foundation and Small Models Coordination for Visuomotor Policy Learning

Visuomotor policy learning enables robots to perform a wide range of tasks, but small policy models often remain sensitive to changes in object and background appearance. In this work, we investigate the coordination of pretrained vision foundation models with small policy models to improve appearance generalization. We propose a framework in which a small policy model operates on task-relevant visual observations constructed through semantic repainting. A segmentation foundation model identifies the robot and target object, which are rendered with fixed role colors on a constant background. An alternative representation replaces the target's role color with normalized monocular depth predicted by a depth foundation model, providing additional geometric cues. The perception models are adapted using in-distribution data where needed and held fixed during policy training. This design combines the perceptual capabilities of foundation models with a small policy model trained on the resulting observations for action prediction. Evaluations with flow matching policies on simulation benchmarks, together with experiments on two real-world robotic tasks, demonstrate substantial improvements in task success under the evaluated appearance shifts.

cs.RO↗
arXiv2026

EDGE: Experience-Distillation for Guided Exploration in Agentic Reinforcement Learning

Reinforcement learning with outcome-based objectives such as GRPO enables LLM-based agents to solve complex, long-horizon tasks, yet the reusable exploration patterns embedded in interaction trajectories are largely discarded after a single policy update. Existing experience-augmented approaches retrieve historical guidance at inference time, but they apply experiences without accounting for the policy's evolving capability and create persistent dependencies on external retrieval. We propose EDGE (Experience-Distillation for Guided Exploration), a framework that treats retrieved experiences as temporary training-time scaffolds and progressively internalizes their benefits into the parametric policy. Concretely, EDGE partitions each rollout group into experience-conditioned and experience-free trajectories to estimate and admit only positive marginal gains without extra sampling, then distills the induced behavior into the base policy via a reverse-KL objective on its own empirical support. A co-evolutionary experience bank further synthesizes guidance from emerging failure modes and prunes obsolete entries as the policy evolves. Across embodied, web, and search-based QA tasks, EDGE improves over strong RL baselines by up to 12.5 points and remains effective without inference-time scaffolds or a proprietary reflector. The code is available at https://github.com/xvolcano02/EDGE.

cs.CL↗
arXiv2026

On Brezis' open problem 2.2

We prove that the global minimizer of the Ginzburg-Landau energy in the disk of radius $R$ with boundary value $ u(x)=\frac{x}{|x|}$ is the degree-one radial solution of the planar Ginzburg--Landau equation. This gives an affirmative answer to Open Problem~2.2 in Brezis' open-problem list. This is achieved by comparing the radial solution $f$ in the disk with the degree-one radial solution $F$ in the whole plane. Multiplying a disk competitor by $F/f$ enables us to use the known minimality of the whole-plane vortex without changing the boundary trace. The difference of the two energies can be decomposed into Fourier modes. Every nonzero mode is nonnegative, and the zero mode is then handled by a Picone type identity.

math.AP↗
arXiv2026

MEDR: Query-Independent Frame Selection via Multi-Signal Event Modeling and Dynamic Rescoring

Frame selection is a fundamental component of multimodal large language models, enabling long videos to be processed under limited visual-token and computational budgets. Uniform sampling preserves temporal coverage but may miss informative content that appears only briefly. To alleviate this limitation, query-dependent methods can retrieve question-relevant frames. However, because the selected frames depend on the current question, the same visual input cannot be directly shared across different questions, and frame selection must be repeated in multi-turn video dialogue. This motivates us to seek a query-independent frame selection method that preserves the reusability of a fixed visual input while improving the coverage of informative events beyond uniform sampling. We propose Multi-Signal Event Modeling and Dynamic Rescoring (MEDR), a training-free and query-independent frame selection method. Multi-Signal Event Modeling organizes complementary visual, motion, and text signals into signal-specific temporal events. Dynamic Rescoring then iteratively reevaluates each candidate relative to the current selected set, updating its score according to frame-level signal strength, additional event coverage, and temporal proximity. The resulting fixed frame set is constructed without observing the query and can be reused across different questions. On the standard benchmark evaluations, MEDR improves model accuracy by 0.63%-0.89% on Video-MME. On the long-video subset of LongVideoBench, it improves accuracy by up to 1.23% with Qwen3-VL-8B. MEDR further improves overall accuracy by 0.53%, while reusing exactly the same frame set for every question about a video.

cs.CV↗
arXiv2026

DialectS2S: End-to-End Speech Dialogue Modeling for Low-Resource Chinese Dialects

Current end-to-end speech dialogue models are primarily optimized for mainstream languages and remain limited in low-resource dialect scenarios due to the scarcity of dialect speech data. Moreover, during dialect adaptation, the semantic representation space of speech dialogue models continuously evolves, while conventional speech supervision remains unchanged, leading to semantic inconsistency between hidden representations and speech targets and degrading speech stability and naturalness. To address these issues, we propose DialectS2S, an end-to-end speech dialogue model for Chinese dialects. We first develop a scalable dialect speech dialogue synthesis pipeline for efficient data construction. We further introduce a two-stage post-training strategy with self-aligned speech supervision, which aligns the semantic content of speech supervision with the evolved semantic representations of the model to improve dialect speech generation quality. Experimental results show that DialectS2S consistently outperforms existing baselines across multiple Chinese dialects in speech dialogue, achieving substantial improvements in dialect consistency, response quality, and speech intelligibility. Our work provides an efficient and scalable solution for end-to-end speech dialogue modeling in low-resource dialect scenarios. To facilitate future research and practical applications, we fully open-source the DialectS2S framework, including model checkpoints, training datasets, and fine-tuning code.

cs.CL↗
arXiv2026

Bifurcation analysis of Stokes waves with piecewise smooth vorticity in deep water

In this paper, we establish the existence of Stokes waves with piecewise smooth vorticity in a two-dimensional, infinitely deep fluid domain. These waves represent traveling water waves propagating over sheared currents in a semi-infinite cylinder, where the vorticity may have jump discontinuities across internal streamlines. The analysis is carried out by applying a hodograph transformation, which reformulates the original free boundary problem into an abstract elliptic boundary value problem. Compared to previously studied steady water waves, the present setting introduces several novel features: the presence of an internal interface, an unbounded spatial domain, and a non-Fredholm linearized operator. To address these difficulties, we introduce a height function formulation, casting the problem as a transmission problem with suitable transmission conditions. A singular bifurcation approach is then employed, combining global bifurcation theory with Whyburn's topological lemma. The singular limit is taken in a natural deep-water topology based on the surface trace and the derivatives of the height function. An exact mean-flux identity controls the closing zero Fourier mode uniformly as the regularization is removed. This yields a connected global continuum of exact waves together with explicit norm, ellipticity, surface-obliqueness, and parameter-boundary alternatives.

math.AP↗
arXiv2026

Nonradial stable solutions near the Joseph--Lundgren threshold

We study positive stable solutions of the supercritical Lane--Emden equation in the first Joseph--Lundgren interval. For a family of dimensions, we construct nonradial stable entire solutions with exponent close to the upper endpoint of this interval. This disproves a radiality conjecture of Chan and Wei. The construction begins with a smooth positive nonconstant solution on the sphere, which is obtained by matching a polar cap to an inner neck. A sharp expansion of the lowest shifted eigenvalue proves that the resulting singular cone is strictly stable. Finally, a minimal-solution and rescaling argument replaces the cone by a smooth stable entire solution while preserving its sphere variation. To the best of our knowledge, this is the first nontrivial example of nonradial stable solutions for the Emden-Fowler equation.

math.AP↗
arXiv2026

Nondegeneracy and Morse Index of Ginzburg--Landau Vortices

We prove that the standard degree-two and degree-three vortex solutions of the Ginzburg-Landau equation are nondegenerate. Their Morse indices are also computed. The proof relies on new explicit upper and lower bounds of the modulus of these solutions and a comparison argument. It is expected that our method can be generalized to study higher degree solutions.

math.AP↗
arXiv2026

On Sirakov's equal-frequency uniqueness conjecture

Let $N\in\{2,3\}$, $0<μ_1\leqμ_2$, and $0<β<μ_1$. We prove that the equal-frequency two-component cubic Schrödinger system \[ -Δu+u=μ_1u^3+βuv^2, \qquad -Δv+v=μ_2v^3+βu^2v \quad\text{in }\mathbb{R}^N \] has exactly one positive solution in $H^1(\mathbb{R}^N)\times H^1(\mathbb{R}^N)$ modulo simultaneous translations. More precisely, every positive solution is a simultaneous translate of the synchronized state constructed from the unique positive radial solution of $-Δw+w=w^3$ in $\mathbb{R}^N$. This settles Sirakov's equal-frequency uniqueness conjecture throughout the weak-coupling range. The main difficulty in the proof is to exclude radial solutions for which the ratio of the normalized components is nonconstant. After normalization, the two components satisfy scalar equations with a common potential. We construct a weighted Pohozaev functional for the system together with a correction term and prove that both the corrected functional and the associated weighted functional are strictly positive. Combining these sign properties with a radial flux identity and an auxiliary quotient associated with the component ratio forces synchronization.

math.AP↗
arXiv2026

Timing and Spectral Analysis of the 2024 Outburst of 2S 1553$-$542 with NuSTAR and NICER

We report a timing and spectral study of the 2024 outburst of the Be/X-ray binary pulsar 2S~1553$-$542 using \textit{NuSTAR} and \textit{NICER} observations. From the \textit{NuSTAR} light curve we measure a pulse period of $9.285022\pm0.000001$~s. The energy-resolved pulse profiles are dominated by a single peak and show a wing-like structure most clearly in the $12$--$22$~keV band. The pulsed fraction remains above 60\% and increases with energy. The phase-averaged \textit{NuSTAR} spectrum is described by an absorbed blackbody plus cutoff power-law continuum, together with an iron emission line and a cyclotron absorption feature. Using the \texttt{cyclabs} model, we obtain a cyclotron energy of $E_{\rm cyc}\simeq24.1$~keV, corresponding to a magnetic field strength of $B\sim3\times10^{12}$~G. Phase-resolved spectroscopy shows that the continuum and cyclotron-line parameters vary with pulse phase, and that the line becomes poorly constrained around the pulse-wing phase. We also searched the short \textit{NICER} GTIs for transient mHz variability using wavelet analysis and a CEEMDAN-based Hilbert--Huang transform. Localized excesses near $\sim10$~mHz and $\sim20$~mHz are found, but the short exposures, COI effects, red-noise fluctuations, and the lack of a well-constrained Fourier peak limit their significance. We therefore treat them as candidate mHz variability rather than firm mHz QPO detections.

astro-ph.HE↗
arXiv2026

Finite Potential Energy for Entire Solutions of the Planar Ginzburg--Landau Equation

We prove that every smooth entire solution $ u\colon\mathbb{R}^2\to\mathbb{R}^2 $ of the Ginzburg--Landau equation $ -Δu=u(1-|u|^2) $ with $ |u(x)|\to1 $ as $ |x|\to\infty $ has finite potential energy, i.e., \begin{equation*} \int_{\mathbb{R}^2}(1-|u|^2)^2 \mathrm{d}x<+\infty, \end{equation*} thereby resolving Brezis' Open Problem 2.5 in [4]. The main difficulty stems from the possible presence of a curl-free mode that carries nonzero circulation and decays only like $ |x|^{-1} $; such a mode lies outside $ L^2 $ and does not admit a single-valued potential. By minimizing over $ L^2 $ gradient corrections, we construct a comparison field that solves the homogeneous equation and inherits the same circulation. The Kelvin inversion, combined with the De Giorgi--Nash--Moser theory for quasilinear elliptic equations, then produces the optimal decay $ O(|x|^{-1}) $. For a Ginzburg--Landau solution, the Bernstein estimate and the coercivity of the Jacobi form produce an $ L^2 $ forcing term in the exterior phase equation. The resulting $ L^4 $ bound on the phase field implies $1-|u|^2\in L^2(\mathbb{R}^2)$, and therefore the potential energy is finite.

math.AP↗
arXiv2026

On two-dimensional steady compactly supported Euler flows with constant vorticity

In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar flows that predominate in the existing literature on steady water waves. More precisely, we analyze three distinct classes of steady Euler flows with compact support, which correspond, respectively, to partially overdetermined, two-phase overdetermined, and (fully) overdetermined elliptic free-boundary problems. Our main contributions are threefold. For each class, we first prove a flexibility result-the existence of nontrivial admissible domains-by combining shape derivatives with local bifurcation theory. Second, we establish the corresponding rigidity results. Third, we apply the implicit function theorem to show that the standard annular flows are stable under small perturbations of the Neumann boundary condition. These results provide new perspectives on the theory of overdetermined elliptic problems.

math.AP↗
arXiv2026

Task Decomposition-Guided Reranking for Adaptive Agent Skill Retrieval

Skill usage can significantly enhance the ability of modern agent systems to complete complex tasks. However, the growing scale of skill libraries makes accurate skill selection increasingly challenging. In real-world scenarios, ambiguous semantic matching often arises between a specific task requirement and multiple generic yet semantically similar candidate skills. Moreover, existing methods tend to overlook the dynamic influence of task difficulty and skill applicability when selecting the optimal target skill set. To address these issues, we propose SkillReranker, an inference-time reranking framework for adaptive skill selection. Specifically, we first perform semantic decomposition on both the task and skill sides, yielding informative subtask and execution-state descriptions as well as transition-state descriptions that characterize each skill's functionality. These descriptions are then used to construct a directed acyclic execution graph, where intermediate task states are modeled as nodes and candidate skills as edges, thereby establishing a structured task-skill correspondence. On this basis, SkillReranker determines whether each state node satisfies the split condition to identify subtask intervals. For each task interval, we employ a cross-encoder to perform comprehensive scoring over candidate skills and select the most suitable ones to form the final target skill set. Experiments on ALFWorld and ScienceWorld with three backbone LLMs show that SkillReranker effectively improves task performance, reduces environment interaction steps, and lowers token consumption compared with existing skill selection baselines.

cs.AI↗