arXiv subjects

Hongyu Liu

Publications and source records attributed to Hongyu Liu.

At least 73 records · Page 4Linked to original sources

arXiv2026

Quantitative symmetry-breaking and nonlinear harmonic generation in plasmonics

We develop a quantitative mathematical theory that offers new perspectives on nonlinear harmonic generation in plasmonic structures arising from symmetry breaking. Focusing on second harmonic generation--the most fundamental process and the most extensively studied owing to its practical significance--we establish a theoretical framework that can be readily extended to higher-order harmonics. We investigate the plasmonic system in the static regime using a columnar nanowire with $n$-fold rotational symmetry ($n \in \mathbb{N}$) and construct a phenomenological model in which the second harmonic response originates from nonlinear sources confined to a selvedge region near the surface. By introducing a notion of symmetry degree grounded in group theory, we precisely quantify the second harmonic generation in terms of multipolar contributions. Our theory complements existing physical descriptions of this practically important phenomenon and provides a rigorous account of how nonlinear optical efficiency depends on shape, size, symmetry, and defects in plasmonic structures.

math.AP↗

arXiv2026

RouteLMT: Learned Sample Routing for Hybrid LLM Translation Deployment

Large Language Models (LLMs) have achieved remarkable performance in Machine Translation (MT), but deploying them at scale remains prohibitively expensive. A widely adopted remedy is the hybrid system paradigm, which balances cost and quality by serving most requests with a small model and selectively routing a fraction to a large model. However, existing routing strategies often rely on heuristics, external predictors, or absolute quality estimation, which fail to capture whether the large model actually provides a worthwhile improvement over the small one. In this paper, we formulate routing as a budget allocation problem and identify marginal gain, i.e., the large model's improvement over the small model, as the optimal signal for budgeted decisions. Building on this, we propose \textbf{RouteLMT} (routing for LLM-based MT), an efficient in-model router that predicts this expected gain by probing the small translators prompt-token representation, without requiring external models or hypothesis decoding. Extensive experiments demonstrate that our RouteLMT outperforms heuristics, quality/difficulty estimation baselines, achieving a superior quality-budget Pareto frontier. Furthermore, we analyze regression risks and show that a simple guarded variant can mitigate severe quality losses.

cs.CL↗

arXiv2026

Mathematical analysis of transverse EM field concentration for adjacent obstacles with nonlocal boundary conditions in the quasistatic regime

This paper presents a rigorous mathematical analysis of transverse electromagnetic (EM) field concentration between two adjacent obstacles within the framework of the quasi-static approximation. We investigate three degenerate conductivity models recently introduced in [22], two of these incorporating nonlocal boundary conditions to capture fundamental physical phenomena, such as surface nonlocality and thin-layer interactions. Our primary results establish sharp conditions for gradient blowup and derive the corresponding optimal blowup rates. These findings elucidate how nonlocal boundary conditions modify classical gradient estimates. Furthermore, we analyze the influence of wave frequency, demonstrating that it mitigates the severity of field concentration even in the limit of a vanishing gap distance. Consequently, this work extends the classical theory of field enhancement in plasmonic and metamaterial systems to incorporate nonlocal surface effects, yielding precise asymptotic formulas that are essential for the quantitative design of nanophotonic devices.

math.AP↗

arXiv2026

AvatarPointillist: AutoRegressive 4D Gaussian Avatarization

We introduce AvatarPointillist, a novel framework for generating dynamic 4D Gaussian avatars from a single portrait image. At the core of our method is a decoder-only Transformer that autoregressively generates a point cloud for 3D Gaussian Splatting. This sequential approach allows for precise, adaptive construction, dynamically adjusting point density and the total number of points based on the subject's complexity. During point generation, the AR model also jointly predicts per-point binding information, enabling realistic animation. After generation, a dedicated Gaussian decoder converts the points into complete, renderable Gaussian attributes. We demonstrate that conditioning the decoder on the latent features from the AR generator enables effective interaction between stages and markedly improves fidelity. Extensive experiments validate that AvatarPointillist produces high-quality, photorealistic, and controllable avatars. We believe this autoregressive formulation represents a new paradigm for avatar generation, and we will release our code inspire future research.

cs.CV↗

arXiv2026

VoxSafeBench: Not Just What Is Said, but Who, How, and Where

As speech language models (SLMs) transition from personal devices into shared, multi-user environments, their responses must account for far more than the words alone. Who is speaking, how they sound, and where the conversation takes place can each turn an otherwise benign request into one that is unsafe, unfair, or privacy-violating. Existing benchmarks, however, largely focus on basic audio comprehension, study individual risks in isolation, or conflate content that is inherently harmful with content that only becomes problematic due to its acoustic context. We introduce VoxSafeBench, among the first benchmarks to jointly evaluate social alignment in SLMs across three dimensions: safety, fairness, and privacy. VoxSafeBench adopts a Two-Tier design: Tier1 evaluates content-centric risks using matched text and audio inputs, while Tier2 targets audio-conditioned risks in which the transcript is benign but the appropriate response hinges on the speaker, paralinguistic cues, or the surrounding environment. To validate Tier2, we include intermediate perception probes and confirm that frontier SLMs can successfully detect these acoustic cues yet still fail to act on them appropriately. Across 22 tasks with bilingual coverage, we find that safeguards appearing robust on text often degrade in speech: safety awareness drops for speaker- and scene-conditioned risks, fairness erodes when demographic differences are conveyed vocally, and privacy protections falter when contextual cues arrive acoustically. Together, these results expose a pervasive speech grounding gap: current SLMs frequently recognize the relevant social norm in text but fail to apply it when the decisive cue must be grounded in speech. Code and data are publicly available at: https://amphionteam.github.io/VoxSafeBench_demopage/

cs.SD↗

arXiv2026

Uncovering the Fragility of Trustworthy LLMs through Chinese Textual Ambiguity

In this work, we study a critical research problem regarding the trustworthiness of large language models (LLMs): how LLMs behave when encountering ambiguous narrative text, with a particular focus on Chinese textual ambiguity. We created a benchmark dataset by collecting and generating ambiguous sentences with context and their corresponding disambiguated pairs, representing multiple possible interpretations. These annotated examples are systematically categorized into 3 main categories and 9 subcategories. Through experiments, we discovered significant fragility in LLMs when handling ambiguity, revealing behavior that differs substantially from humans. Specifically, LLMs cannot reliably distinguish ambiguous text from unambiguous text, show overconfidence in interpreting ambiguous text as having a single meaning rather than multiple meanings, and exhibit overthinking when attempting to understand the various possible meanings. Our findings highlight a fundamental limitation in current LLMs that has significant implications for their deployment in real-world applications where linguistic ambiguity is common, calling for improved approaches to handle uncertainty in language understanding. The dataset and code are publicly available at this GitHub repository: https://github.com/ictup/LLM-Chinese-Textual-Disambiguation.

cs.CL↗

arXiv2026

Construction of Solutions with Extraordinary Gradient Amplification and Localization for Schrödinger Equations

This paper constructs solutions to linear and nonlinear Schrödinger-type equations in two and three spatial dimensions that exhibit prescribed, extraordinary gradient amplification and localization. For any finite time interval $[0,T]$, any prescribed collection of $n\in\mathbb{N}$ distinct points on $\partial D$, where $D$ is the compact support of the anisotropic coefficients, lower-order terms, or nonlinearities, and any amplitude threshold $\mathcal{M}>0$, we show that one can design smooth initial and/or boundary data such that the spatial gradients of the resulting solutions exceed $\mathcal{M}$ in neighborhoods of these points outside $D$ for almost every $t\in[0,T]$. Moreover, the ratio between the local $C^{1,\frac12}$-norm of the solution near each prescribed point outside $D$ and the $C^{1,\frac12}$-norm inside $D$ is bounded from below by $\mathcal{M}/2$ for almost every $t\in[0,T]$. We further prove that the spatial measure of the regions where the gradient magnitude exceeds $\mathcal{M}$ tends to zero as $\mathcal{M}\to\infty$, demonstrating that the amplification phenomenon is highly localized. This effect arises from the structure of the Schrödinger-type equation combined with carefully designed input profiles. From a physical perspective, the results provide a deterministic analogue of localization phenomena observed in quantum scattering and Anderson localization. In addition, the observed trade-off between extreme spatial localization and large gradient amplification is fully consistent with the spirit of the Heisenberg uncertainty principle: while the latter is traditionally formulated in a global $L^2$ space--frequency framework, our results offer a complementary deterministic manifestation at the level of localized spatial gradients in Schrödinger dynamics.

math.AP↗

arXiv2026

Stably Determining a generalised Impedance Obstacle from a Single Far-Field Pattern

Inverse scattering focuses on recovering unknown scatterers from wave measurements. A fundamental challenge is determining whether an inverse obstacle problem can be resolved from a single far-field measurement, a task particularly demanding for non-convex polytope obstacles under generalized impedance boundary conditions and closely linked to the long-standing Schiffer problem. In this paper, we develop a novel \emph{Artificial Test Domain} (ATD) framework for single-measurement inverse scattering of impenetrable polytope obstacles. Based on microlocal analysis near exterior-visible flat boundary patches, this approach transcends traditional methods reliant on observable corners. The ATD framework establishes two primary conceptual advancements: a unified \emph{generalized impedance hyperplane (GIH) exclusion mechanism}, which clarifies the structural role of uniqueness mechanisms, and a unified \emph{qualitative--quantitative principle} for the generalized impedance setting. Quantitatively, the method yields a \emph{far-field--geometry relation} where geometric discrepancy is controlled by far-field error, scaled by a leading ATD coefficient. Qualitatively, the non-vanishing of this coefficient reduces to the exclusion of exterior generalized impedance hyperplanes. Once uniqueness is established, this relation produces sharp stability estimates. Within this framework, the classical stability estimates for the sound-soft and sound-hard cases are recovered as special instances of a much more general stability theory. At the same time, we obtain several new sharp stability results that are of significant importance. These results unify currently available single-measurement uniqueness regimes for polytope geometry and provide new insights into the Schiffer problem across multiple generalized impedance settings.

math.AP↗

arXiv2026

FastVMT: Eliminating Redundancy in Video Motion Transfer

Video motion transfer aims to synthesize videos by generating visual content according to a text prompt while transferring the motion pattern observed in a reference video. Recent methods predominantly use the Diffusion Transformer (DiT) architecture. To achieve satisfactory runtime, several methods attempt to accelerate the computations in the DiT, but fail to address structural sources of inefficiency. In this work, we identify and remove two types of computational redundancy in earlier work: motion redundancy arises because the generic DiT architecture does not reflect the fact that frame-to-frame motion is small and smooth; gradient redundancy occurs if one ignores that gradients change slowly along the diffusion trajectory. To mitigate motion redundancy, we mask the corresponding attention layers to a local neighborhood such that interaction weights are not computed unnecessarily distant image regions. To exploit gradient redundancy, we design an optimization scheme that reuses gradients from previous diffusion steps and skips unwarranted gradient computations. On average, FastVMT achieves a 3.43x speedup without degrading the visual fidelity or the temporal consistency of the generated videos.

cs.CV↗

arXiv2026

LACON: Training Text-to-Image Model from Uncurated Data

The success of modern text-to-image generation is largely attributed to massive, high-quality datasets. Currently, these datasets are curated through a filter-first paradigm that aggressively discards low-quality raw data based on the assumption that it is detrimental to model performance. Is the discarded bad data truly useless, or does it hold untapped potential? In this work, we critically re-examine this question. We propose LACON (Labeling-and-Conditioning), a novel training framework that exploits the underlying uncurated data distribution. Instead of filtering, LACON re-purposes quality signals, such as aesthetic scores and watermark probabilities as explicit, quantitative condition labels. The generative model is then trained to learn the full spectrum of data quality, from bad to good. By learning the explicit boundary between high- and low-quality content, LACON achieves superior generation quality compared to baselines trained only on filtered data using the same compute budget, proving the significant value of uncurated data.

cs.CV↗

arXiv2026

Group Editing: Edit Multiple Images in One Go

In this paper, we tackle the problem of performing consistent and unified modifications across a set of related images. This task is particularly challenging because these images may vary significantly in pose, viewpoint, and spatial layout. Achieving coherent edits requires establishing reliable correspondences across the images, so that modifications can be applied accurately to semantically aligned regions. To address this, we propose GroupEditing, a novel framework that builds both explicit and implicit relationships among images within a group. On the explicit side, we extract geometric correspondences using VGGT, which provides spatial alignment based on visual features. On the implicit side, we reformulate the image group as a pseudo-video and leverage the temporal coherence priors learned by pre-trained video models to capture latent relationships. To effectively fuse these two types of correspondences, we inject the explicit geometric cues from VGGT into the video model through a novel fusion mechanism. To support large-scale training, we construct GroupEditData, a new dataset containing high-quality masks and detailed captions for numerous image groups. Furthermore, to ensure identity preservation during editing, we introduce an alignment-enhanced RoPE module, which improves the model's ability to maintain consistent appearance across multiple images. Finally, we present GroupEditBench, a dedicated benchmark designed to evaluate the effectiveness of group-level image editing. Extensive experiments demonstrate that GroupEditing significantly outperforms existing methods in terms of visual quality, cross-view consistency, and semantic alignment.

cs.CV↗

arXiv2026

BIRD-INTERACT: Re-imagining Text-to-SQL Evaluation for Large Language Models via Lens of Dynamic Interactions

Large language models (LLMs) have demonstrated remarkable performance on single-turn text-to-SQL tasks, but real-world database applications predominantly require multi-turn interactions to handle ambiguous queries, execution errors, and evolving user requirements. Existing multi-turn benchmarks fall short by treating conversation histories as static context or limiting evaluation to read-only operations, failing to reflect production-grade database assistant challenges. We introduce BIRD-INTERACT, a benchmark that restores this realism through: (1) a comprehensive interaction environment coupling each database with a hierarchical knowledge base, metadata files, and a function-driven user simulator, enabling models to solicit clarifications, retrieve knowledge, and recover from errors without human supervision; (2) two evaluation settings consisting of a pre-defined conversational protocol (c-Interact) and an open-ended agentic setting (a-Interact) where models autonomously decide when to query the user simulator or explore the environment; (3) a challenging task suite covering the full CRUD spectrum for business-intelligence and operational use cases, guarded by executable test cases. Each task features ambiguous and follow-up sub-tasks requiring dynamic interaction. The suite comprises BIRD-INTERACT-FULL (600 tasks, up to 11,796 interactions) for comprehensive performance assessment, and BIRD-INTERACT-LITE (300 tasks with simplified databases) for detailed behavioral analysis and rapid method development. Our empirical results highlight BIRD-INTERACT's difficulty: GPT-5 completes only 8.67% of tasks in c-Interact and 17.00% in a-Interact. Analysis via memory grafting and Interaction Test-time Scaling validates the importance of effective interaction for complex, dynamic text-to-SQL tasks.

cs.AI↗

arXiv2026

Spectral properties of surface-localized transmission eigenmodes and applications to inverse scattering problems

This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp spectral density estimates--establishing both lower and upper bounds--to demonstrate that a significant proportion of transmission eigenfunctions manifest this surface-localizing behavior. Our analysis elucidates the connection between the geometric rigidity of eigenfunctions and their spectral properties. Though primarily explored within a radially symmetric framework, this study provides rigorous theoretical insights, advances new perspectives in this emerging field, and offers meaningful implications for inverse scattering theory.

math.AP↗

arXiv2026

The Sommerfeld-Rellich Framework for Scattering on Hyperbolic Space: Far-Field Patterns and Inverse Problems

This paper establishes a complete time-harmonic scattering theory for hyperbolic space, formulating it within the classical Sommerfeld-Rellich paradigm centered on far-field patterns--a foundational framework that has been absent despite the well-developed spectral and time-dependent theories for this geometry. We explicitly construct the ingoing and outgoing fundamental solutions for the Helmholtz operator and perform a precise asymptotic analysis at the conformal boundary to derive a {hyperbolic Sommerfeld radiation condition}. This condition, which is a local criterion at infinity, uniquely selects physically admissible outgoing solutions. We prove a {hyperbolic Rellich theorem} guaranteeing the uniqueness of the scattered field and its far-field pattern from asymptotic data. Within this rigorous framework, we solve the direct scattering problem for compact sources, penetrable media, and impenetrable obstacles, providing explicit representations for the corresponding {far-field patterns}. As a principal application and demonstration of the framework's utility, we initiate the study of inverse scattering on hyperbolic space, formulating both the inverse obstacle and inverse medium problems where the objective is to reconstruct the scatterer from measurements of its far-field pattern. Our work lays the groundwork for a far-field-based approach to scattering and inversion in hyperbolic geometry. Due to the local feature of the {hyperbolic Sommerfeld radiation condition}, our study can be readily extended to the broader asymptotically hyperbolic manifolds.

math.AP↗

arXiv2026

Follow-Your-Shape: Shape-Aware Image Editing via Trajectory-Guided Region Control

While recent flow-based image editing models demonstrate general-purpose capabilities across diverse tasks, they often struggle to specialize in challenging scenarios -- particularly those involving large-scale shape transformations. When performing such structural edits, these methods either fail to achieve the intended shape change or inadvertently alter non-target regions, resulting in degraded background quality. We propose Follow-Your-Shape, a training-free and mask-free framework that supports precise and controllable editing of object shapes while strictly preserving non-target content. Motivated by the divergence between inversion and editing trajectories, we compute a Trajectory Divergence Map (TDM) by comparing token-wise velocity differences between the inversion and denoising paths. The TDM enables precise localization of editable regions and guides a Scheduled KV Injection mechanism that ensures stable and faithful editing. To facilitate a rigorous evaluation, we introduce ReShapeBench, a new benchmark comprising 120 new images and enriched prompt pairs specifically curated for shape-aware editing. Experiments demonstrate that our method achieves superior editability and visual fidelity, particularly in tasks requiring large-scale shape replacement.

cs.CV↗

arXiv2026

HeadLighter: Disentangling Illumination in Generative 3D Gaussian Heads via Lightstage Captures

Recent 3D-aware head generative models based on 3D Gaussian Splatting achieve real-time, photorealistic and view-consistent head synthesis. However, a fundamental limitation persists: the deep entanglement of illumination and intrinsic appearance prevents controllable relighting. Existing disentanglement methods rely on strong assumptions to enable weakly supervised learning, which restricts their capacity for complex illumination. To address this challenge, we introduce HeadLighter, a novel supervised framework that learns a physically plausible decomposition of appearance and illumination in head generative models. Specifically, we design a dual-branch architecture that separately models lighting-invariant head attributes and physically grounded rendering components. A progressive disentanglement training is employed to gradually inject head appearance priors into the generative architecture, supervised by multi-view images captured under controlled light conditions with a light stage setup. We further introduce a distillation strategy to generate high-quality normals for realistic rendering. Experiments demonstrate that our method preserves high-quality generation and real-time rendering, while simultaneously supporting explicit lighting and viewpoint editing. We will publicly release our code and dataset.

cs.CV↗

arXiv2026

FUGC: Benchmarking Semi-Supervised Learning Methods for Cervical Segmentation

Accurate segmentation of cervical structures in transvaginal ultrasound (TVS) is critical for assessing the risk of spontaneous preterm birth (PTB), yet the scarcity of labeled data limits the performance of supervised learning approaches. This paper introduces the Fetal Ultrasound Grand Challenge (FUGC), the first benchmark for semi-supervised learning in cervical segmentation, hosted at ISBI 2025. FUGC provides a dataset of 890 TVS images, including 500 training images, 90 validation images, and 300 test images. Methods were evaluated using the Dice Similarity Coefficient (DSC), Hausdorff Distance (HD), and runtime (RT), with a weighted combination of 0.4/0.4/0.2. The challenge attracted 10 teams with 82 participants submitting innovative solutions. The best-performing methods for each individual metric achieved 90.26\% mDSC, 38.88 mHD, and 32.85 ms RT, respectively. FUGC establishes a standardized benchmark for cervical segmentation, demonstrates the efficacy of semi-supervised methods with limited labeled data, and provides a foundation for AI-assisted clinical PTB risk assessment.

eess.IV↗

arXiv2026

Controllable Video Generation: A Survey

With the rapid development of AI-generated content (AIGC), video generation has emerged as one of its most dynamic and impactful subfields. In particular, the advancement of video generation foundation models has led to growing demand for controllable video generation methods that can more accurately reflect user intent. Most existing foundation models are designed for text-to-video generation, where text prompts alone are often insufficient to express complex, multi-modal, and fine-grained user requirements. This limitation makes it challenging for users to generate videos with precise control using current models. To address this issue, recent research has explored the integration of additional non-textual conditions, such as camera motion, depth maps, and human pose, to extend pretrained video generation models and enable more controllable video synthesis. These approaches aim to enhance the flexibility and practical applicability of AIGC-driven video generation systems. In this survey, we provide a systematic review of controllable video generation, covering both theoretical foundations and recent advances in the field. We begin by introducing the key concepts and commonly used open-source video generation models. We then focus on control mechanisms in video diffusion models, analyzing how different types of conditions can be incorporated into the denoising process to guide generation. Finally, we categorize existing methods based on the types of control signals they leverage, including single-condition generation, multi-condition generation, and universal controllable generation. For a complete list of the literature on controllable video generation reviewed, please visit our curated repository at https://github.com/mayuelala/Awesome-Controllable-Video-Generation.

cs.GR↗