arXiv subjects

Tianyi Zheng

Publications and source records attributed to Tianyi Zheng.

At least 19 recordsLinked to original sources

arXiv2026

Stable determination of coefficients for the nonlinear third-order acoustic equations

In this paper, we study an inverse boundary value problem for a generalized Jordan-Moore-Gibson-Thompson equation with Westervelt-type nonlinearity and space-dependent coefficients. This third-order (in time) hyperbolic equation models nonlinear ultrasound propagation in viscous and thermally relaxing media. Assuming that the diffusivity and the sound speed are known a priori, we investigate the simultaneous stable determination of the friction coefficient, the weak damping coefficient, the potential, and the nonlinear coefficient from the associated Dirichlet-to-Neumann map. The proof combines the finite-difference linearization method with the construction of Gaussian beam and geometric optics solutions. These arguments reduce the inverse problem to stability estimates for (attenuated) geodesic ray transforms under the foliation condition. As a consequence, we obtain Hölder-type stability estimates of recovering the linear and nonlinear coefficients.

math.AP↗

arXiv2026

Inverse problems for nonlinear Kirchhoff plate equations with multiple unknown parameters

This paper provides a comprehensive treatment of inverse boundary value problems for (nonlinear) Kirchhoff plate equations under diverse general settings. We begin by establishing the global well-posedness of the nonlinear forward equations, which not only underpins the subsequent inverse analysis but also holds independent theoretical significance. The inverse problems are then examined for both passive and active measurement regimes. With a single passive boundary measurement, we establish the stable recovery of the unknown initial data. In the active regime with infinitely many boundary measurements, our results are twofold. For linear equations featuring generic time-dependent potentials-allowing for spatial unboundedness, we demonstrate the simultaneous recovery of both initial data and coefficients. For nonlinear equations, where both the nonlinearity and initial data are unknown, we develop a novel Runge approximation approach, together with carefully constructed geometric optics solutions and higher-order linearization around nonzero solutions, to prove their simultaneous determination. Furthermore, we introduce a delicate cut-off technique that provides an alternative means of addressing the scenario of vanishing initial data. Notably, the methodologies and results developed herein are readily generalizable to other boundary conditions and plate models, including the classical Euler-Bernoulli equation.

math.AP↗

arXiv2026

MIEScore: Human-Aligned Evaluation for Multi-Source Image Editing

Recent advances in unified multimodal models have significantly improved text-guided image editing abilities. In particular, models such as Nano-Banana-Pro and GPT-Image-2 demonstrate emerging capabilities in multi-source image editing (MIE), including tasks such as object synthesis, person-background composition, and cross-image style fusion. However, existing benchmarks and image editing assessment (IEQA) methods remain primarily focused on single-image editing tasks and largely overlook the more challenging setting of MIE. This highlights the urgent need for a comprehensive and human-aligned benchmark for MIE. To this end, we introduce MIE-Bench, the first large-scale multiple image editing benchmark with fine-grained human preference annotations. Specifically, MIE-Bench includes 3,000 editing instances across 16 tasks, each involving more than two source images and an editing prompt, together with 36K edited images produced by 12 state-of-the-art editing models and over 108K mean opinion scores (MOSs) covering visual quality, instruction following, and attribute preservation. Based on MIE-Bench, we propose MIEScore, a multimodal large language model (MLLM)-based evaluation model enhanced with skill optimization and multi-dimensional supervised fine-tuning, to provide human-aligned feedback for MIE. Extensive experiments show that MIEScore achieves state-of-the-art performance in aligning with human preferences and generalizes well across other IEQA datasets. Both the dataset and the model are available at https://github.com/IntMeGroup/MIEScore.

cs.CV↗

arXiv2026

Commensurating actions and self-similar groups

Commensurating actions govern how a group can act on non-positively curved cube complexes. We obtain a complete picture of them for a class of finitely generated groups acting on rooted trees: contracting self-similar branch groups. The main application is a proof of Property FW for the iterated monodromy group of the subdivision rule generating the classical square Sierpiński carpet. This is the first example of an infinite finitely generated amenable group with Property FW, answering a question of Cornulier. As another application, we show that a contracting self-similar regular branch group does not have Property PW. In particular, the Grigorchuk group does not have Property PW, answering another question in the literature.

math.GR↗

arXiv2026

$L_1$ Actions and Embeddings of Property A Spaces

We provide several new characterizations of Property A for bounded degree graphs. In particular, we show that $(X,d)$ has Property A if and only if there is a proper gauge $ω$ such that the Lipschitz free space $\operatorname{LF}(X,ω\circ d)$ is isomorphic to $\ell_1$. As a consequence, all finitely generated groups with Property A admit proper uniformly Lipschitz affine actions on $\ell_1$. Moreover, for groups with finite Nagata dimension, we obtain actions with compression exponent 1. This result applies to higher rank lattices, such as $\operatorname{SL}(3,\mathbb{Z})$. We also show that a countable discrete group coarsely embeds into $L_1$ if and only if it admits a proper uniformly Lipschitz affine action on a subspace of $L_1$.

math.GR↗

arXiv2026

Quasi-isometric rigidity for random subsets in products of trees

In this article, we prove a rigidity result for quasi-isometric embeddings from a random subset $D$ of the product $\mathbb{X}$ of two regular trees into $\mathbb{X}$ itself. This can be seen as an extension of Eskin's quasi-isometric rigidity of higher-rank nonuniform lattices to random subsets. As a consequence, we give a description of the self-quasi-isometric embeddings of a random sample. We also show that two independent samples are almost surely non-quasi-isometric, confirming that such a phenomenon occurs in the higher-rank setting, as suggested by Abért. This result contrasts with the result on quasi-isometric equivalence between random sequences by Basu and Sly.

math.MG↗

arXiv2026

C$^2$FG: Control Classifier-Free Guidance via Score Discrepancy Analysis

Classifier-Free Guidance (CFG) is a cornerstone of modern conditional diffusion models, yet its reliance on the fixed or heuristic dynamic guidance weight is predominantly empirical and overlooks the inherent dynamics of the diffusion process. In this paper, we provide a rigorous theoretical analysis of the Classifier-Free Guidance. Specifically, we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a principled foundation for time-dependent guidance. Motivated by this insight, we introduce \textbf{Control Classifier-Free Guidance (C$^2$FG)}, a novel, training-free, and plug-in method that aligns the guidance strength with the diffusion dynamics via an exponential decay control function. Extensive experiments demonstrate that C$^2$FG is effective and broadly applicable across diverse generative tasks, while also exhibiting orthogonality to existing strategies.

cs.LG↗

arXiv2026

EditRefiner: A Human-Aligned Agentic Framework for Image Editing Refinement

Recent text-guided image editing (TIE) models have made remarkable progress, yet edited images still frequently suffer from fine-grained issues such as unnatural objects, lighting mismatch, and unexpected changes. Existing refinement approaches either rely on costly iterative regeneration or employ vision-language models (VLMs) with weak spatial grounding, often resulting in semantic drift and unreliable local corrections. To address these limitations, we first construct EditFHF-15K, a dataset of fine-grained human feedback for edited images, comprising (1) 15K images from 12 TIE models spanning 43 editing tasks, (2) 60K annotated artifact regions and 80K editing failure regions, each accompanied by textual reasoning, and (3) 45K mean opinion scores (MOSs) assessing perceptual quality, instruction following, and visual consistency. Based on EditFHF-15K, we propose EditRefiner, a hierarchical, interpretable, and human-aligned agentic framework that reformulates post-editing correction as a human-like perception-reasoning-action-evaluation loop. Specifically, we introduce: (1) a perception agent that detects contextual saliency maps of artifacts and editing failures, (2) a reasoning agent that interprets these perceptual cues to perform human-aligned diagnostic inference, (3) an action agent that uses the reasoning output to plan and execute localized re-editing, and (4) an evaluation agent that assesses the re-edited image and guides the action agent on whether further refinements are required. Extensive experiments demonstrate that EditRefiner consistently outperforms state-of-the-art methods in distortion localization, diagnose accuracy and human perception alignment, establishing a new paradigm for self-corrective and perceptually reliable image editing. The code is available at https://github.com/IntMeGroup/EditRefiner.

cs.CV↗

arXiv2026

Visual Text Compression as Measure Transport

Visual text compression (VTC) promises efficient long-context processing by rendering text into an image and re-encoding it with a vision-language model, often producing $3$--$20\times$ fewer decoder tokens than subword tokenization. Yet token savings do not translate predictably into downstream utility: on some tasks the visual path matches or exceeds the text path, on others it collapses, and the compression ratio itself does not predict which regime will occur. The missing quantity is therefore not another summary of efficiency, but a principled measure of task-relevant information loss induced by visual encoding. We address this problem by formulating VTC in the language of measure transport. Treating text and visual tokens as empirical probability measures, we show that the ViT patch encoder induces a push-forward map whose transport cost decomposes into a precision cost from within-patch aggregation and a coverage cost from cross-patch fragmentation. Both terms are estimable from downstream-label-free probes. This formulation yields two operational consequences: a downstream-label-free routing criterion that selects whether to use the visual path for a given input or benchmark instance, and a transport-informed foveation mechanism that re-encodes high-cost regions at higher resolution. Across $24$ NLP datasets at Qwen3-4B, our label-free rule matches the per-dataset oracle on $17/24$ datasets ($70.8\%$), and improves the average task score by $+3.3\%$ with $-10.3\%$ average tokens relative to a pure-LLM.

cs.CV↗

arXiv2026

InfoTok: Information-Theoretic Regularization for Capacity-Constrained Shared Visual Tokenization in Unified MLLMs

Unified multimodal large language models (MLLMs) aim to unify image understanding and image generation within a single framework, where a shared visual tokenizer serves as the sole interface that maps high-dimensional images into a limited token budget for downstream multimodal reasoning and synthesis. However, existing shared-token designs are largely architecture-driven and lack an explicit criterion for what information should be preserved to simultaneously support semantic abstraction and visual detail. In this paper, we adopt a capacity-constrained perspective, viewing the shared tokenizer as a compute-bounded learner whose finite representational budget should prioritize reusable structure over hard-to-exploit high-entropy variations and redundancy. Motivated by this view, we propose \textbf{\textit{InfoTok}}, an information-regularized tokenization mechanism grounded in the Information Bottleneck (IB) principle. InfoTok explicitly controls information flow from images to shared tokens to multimodal outputs by imposing mutual-information (MI) constraints that enforce a principled trade-off between compression and task relevance, while also encouraging cross-modal consistency. Because MI is intractable for high-dimensional visual representations, we instantiate InfoTok with practical, differentiable dependence estimators, including a variational IB formulation and a Hilbert Schmidt Independence Criterion (HSIC) based alternative. Integrated into three representative unified MLLMs without introducing any additional training data, InfoTok consistently improves both image understanding and generation performance. These results support information-regularized visual tokenization as a sound basis for token learning in unified MLLMs.

cs.LG↗

arXiv2026

Concentration inequalities for maximal displacement of random walks on groups of polynomial growth

We prove Gaussian concentration inequalities for maximal displacement of compactly supported random walks on a compactly generated locally compact group with polynomial growth. Concentration inequalities with different exponents hold for non-centred random walks as well, after correction by the drift. When the support of the measure generates a virtually nilpotent group, we provide an effective version of this result. These more refined estimates rely on the existence of a ``quantitative splitting'' of a virtually simply connected nilpotent group, a result which may be of independent interest. As applications, we deduce that the same concentration inequalities hold for centred random walks on the following classes of groups: amenable connected Lie groups (including non-unimodular ones), polycyclic and more generally finitely generated solvable groups with finite Prüfer rank. This shows in particular that centred random walk are diffusive on such groups. For polycyclic groups, this strengthens and completes partial results previously obtained by Russ Thompson in 2011.

math.PR↗

arXiv2025

Victim as a Service: Designing a System for Engaging with Interactive Scammers

Pig butchering, and similar interactive online scams, lower their victims' defenses by building trust over extended periods of conversation - sometimes weeks or months. They have become increasingly public losses (at least $75B by one recent study). However, because of their long-term conversational nature, they are extremely challenging to investigate at scale. In this paper, we describe the motivation, design, implementation, and experience with CHATTERBOX, an LLM-based system that automates long-term engagement with online scammers, making large-scale investigations of their tactics possible. We describe the techniques we have developed to attract scam attempts, the system and LLM-engineering required to convincingly engage with scammers, and the necessary capabilities required to satisfy or evade "milestones" in scammers' workflow.

cs.CR↗

arXiv2025

Infinite stationary measures of co-compact group actions

Let $Γ$ be a finitely generated group, and let $μ$ be a nondegenerate, finitely supported probability measure on $Γ$. We show that every co-compact $Γ$ action on a locally compact Hausdorff space admits a nonzero $μ$-stationary Radon measure. The main ingredient of the proof is a stationary analogue of Tarski's theorem: we show that for every nonempty subset $A \subseteq Γ$ there is a $μ$-stationary, finitely additive measure on $Γ$ that assigns unit mass to $A$.

math.GR↗

arXiv2025

Liouville property for groups and conformal dimension

Conformal dimension is a fundamental invariant of metric spaces, particularly suited to the study of self-similar spaces, such as spaces with an expanding self-covering (e.g. Julia sets of complex rational functions). The dynamics of these systems are encoded by the associated iterated monodromy groups, which are examples of contracting self-similar groups. Their amenability is a well-known open question. We show that if $G$ is an iterated monodromy group, and if the (Alfhors-regular) conformal dimension of the underlying space is strictly less than 2, then every symmetric random walk with finite second moment on $G$ has the Liouville property. As a corollary, every such group is amenable. This criterion applies to all examples of contracting groups previously known to be amenable, and to many new ones. In particular, it implies that for every sub-hyperbolic complex rational function $f$ whose Julia set is not the whole sphere, the iterated monodromy group of $f$ is amenable.

math.GR↗

arXiv2025

Pruning for Sparse Diffusion Models based on Gradient Flow

Diffusion Models (DMs) have impressive capabilities among generation models, but are limited to slower inference speeds and higher computational costs. Previous works utilize one-shot structure pruning to derive lightweight DMs from pre-trained ones, but this approach often leads to a significant drop in generation quality and may result in the removal of crucial weights. Thus we propose a iterative pruning method based on gradient flow, including the gradient flow pruning process and the gradient flow pruning criterion. We employ a progressive soft pruning strategy to maintain the continuity of the mask matrix and guide it along the gradient flow of the energy function based on the pruning criterion in sparse space, thereby avoiding the sudden information loss typically caused by one-shot pruning. Gradient-flow based criterion prune parameters whose removal increases the gradient norm of loss function and can enable fast convergence for a pruned model in iterative pruning stage. Our extensive experiments on widely used datasets demonstrate that our method achieves superior performance in efficiency and consistency with pre-trained models.

cs.LG↗

arXiv2024

Prime orbit theorems for expanding Thurston maps: Lattès maps and split Ruelle operators

We obtain an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption. More precisely, we show that the number of primitive periodic orbits, ordered by a weight on each point induced by a non-constant (eventually) positive real-valued Hölder continuous function on $S^2$ satisfying the $α$-strong non-integrability condition, is asymptotically the same as the well-known logarithmic integral, with an exponential error bound. In particular, our results apply to postcritically-finite rational maps for which the Julia set is the whole Riemann sphere. Moreover, a stronger result is obtained for Lattès maps.

math.DS↗

arXiv2024

Prime orbit theorems for expanding Thurston maps: Genericity of strong non-integrability condition

In the second paper [LZ24b] of this series, we obtained an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption. More precisely, the number of primitive periodic orbits, ordered by a weight on each point induced by a non-constant (eventually) positive real-valued Hölder continuous function on $S^2$ satisfying the $α$-strong non-integrability condition, is asymptotically the same as the well-known logarithmic integral, with an exponential error bound. In this third and last paper of the series, we show that the $α$-strong non-integrability condition is generic in the class of $α$-Hölder continuous functions.

math.DS↗

arXiv2024

Confined subgroups in groups with contracting elements

In this paper, we study the growth of confined subgroups through boundary actions of groups with contracting elements. We establish that the growth rate of a confined subgroup is strictly greater than half of the ambient growth rate in groups with purely exponential growth. Along the way, several results are obtained on the Hopf decomposition for boundary actions of subgroups with respect to conformal measures. In particular, we prove that confined subgroups are conservative, and examples of subgroups with nontrivial Hopf decomposition are constructed. We show a connection between Hopf decomposition and quotient growth and provide a dichotomy on quotient growth of Schreier graphs for subgroups in hyperbolic groups.

math.GR↗