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Tianyi Zheng

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Published work

15 published item(s)

preprint2026arXiv

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.

preprint2026arXiv

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.

preprint2020arXiv

Isoperimetric profiles and random walks on some groups defined by piecewise actions

We study the isoperimetric and spectral profiles of certain families of finitely generated groups defined via actions on labelled Schreier graphs and simple {\em gluing} of such. In one of our simplest constructions---the {\em pocket-extension} of a group $G$---this leads to the study of certain finitely generated subgroups of the full permutation group $\mathbb S(G\cup \{*\})$. Some sharp estimates are obtained while many challenging questions remain.

preprint2020arXiv

On FC-central extensions of groups of intermediate growth

It is shown that FC-central extensions retain sub-exponential volume growth. A large collection of FC-central extensions of the first Grigorchuk group is provided by the constructions in the works of Erschler and Kassabov-Pak. We show that in these examples subgroup separability is preserved. We introduce two new collections of extensions of the Grigorchuk group. One collection gives first examples of intermediate growth groups with centers isomorphic to $\mathbb{Z}^{\infty}$; and the other provides groups with prescribed oscillating intermediate growth functions.

preprint2020arXiv

On rigid stabilizers and invariant random subgroups of groups of homeomorphisms

A generalization of the double commutator lemma for normal subgroups is shown for invariant random subgroups of a countable group acting faithfully on a Hausdorff space. As an application, we classify ergodic invariant random subgroups of topological full groups of Cantor minimal $\mathbb{Z}^{d}$-systems. Another corollary is that for an ergodic invariant random subgroup of a branch group, a.e. subgroup $H$ must contain derived subgroups of certain rigid stabilizers. Such results can be applied towards classification of invariant random subgroups of Grigorchuk groups.

preprint2016arXiv

Infinitely supported Liouville measures of Schreier graphs

We provide equivalent conditions for Liouville property of actions of groups. As an application, we show that there is a Liouville measure for the action of the Thompson group $F$ on dyadic rationals. This result should be compared with a recent result of Kaimanovich, where he shows that the action of the Thompson group F on dyadic rationals is not Liouville for all finitely supported measures. As another application we show that there is a Liouville measure for lamplighter actions. This gives more examples of non-amenable Liouville actions.

preprint2016arXiv

Speed of random walks, isoperimetry and compression of finitely generated groups

We give a solution to the inverse problem (given a function, find a corresponding group) for large classes of speed, entropy, isoperimetric profile, return probability and $L_p$-compression functions of finitely generated groups of exponential volume growth. For smaller classes, we give solutions among solvable groups. As corollaries, we prove a recent conjecture of Amir on joint evaluation of speed and entropy exponents and we obtain a new proof of the existence of uncountably many pairwise non-quasi-isometric solvable groups, originally due to Cornulier and Tessera. We also obtain a formula relating the $L_p$-compression exponent of a group and its wreath product with the cyclic group for $p$ in $[1,2]$.

preprint2015arXiv

Isoperimetric profiles and random walks on some permutation wreath products

We study the isoperimetric profiles of certain families of finitely generated groups defined via marked Schreier graphs and permutation wreath products. The groups we study are among the "simplest" examples within a much larger class of groups, all defined via marked Schreier graphs and/or action on rooted trees, which includes such examples as the long range group, Grigorchuck group and the basillica group. The highly non-linear structure of these groups make them both interesting and difficult to study. Because of the relative simplicity of the Schreier graphs that define the groups we study here (the key fact is that they contained very large regions that are "one dimensional"), we are able to obtain sharp explicit bounds on the $L^1$ and $L^2$ isoperimetric profiles of these groups. As usual, these sharp isoperimetric profile estimates provide sharp bounds on the probability of return of simple random walk. Nevertheless, within each of the families of groups we study there are also many cases for which the existing techniques appear inadequate and this leads to a variety of open problems.

preprint2015arXiv

Random walks and isoperimetric profiles under moment conditions

Let $G$ be a finitely generated group equipped with a finite symmetric generating set and the associated word length function $|\cdot |$. We study the behavior of the probability of return for random walks driven by symmetric measures $μ$ that are such that $\sum ρ(|x|)μ(x)<\infty$ for increasing regularly varying or slowly varying functions $ρ$, for instance, $s\mapsto (1+s)^α$, $α\in (0,2]$, or $s\mapsto (1+\log (1+s))^ε$, $ε>0$. For this purpose we develop new relations between the isoperimetric profiles associated with different symmetric probability measures. These techniques allow us to obtain a sharp $L^2$-version of Erschler's inequality concerning the Følner functions of wreath products. Examples and assorted applications are included.

preprint2015arXiv

Random walks under slowly varying moment conditions on groups of polynomial volume growth

Let $G$ be a finitely generated group of polynomial volume growth equipped with a word-length $|\cdot|$. The goal of this paper is to develop techniques to study the behavior of random walks driven by symmetric measures $μ$ such that, for any $ε>0$, $\sum|\cdot|^εμ=\infty$. In particular, we provide a sharp lower bound for the return probability in the case when $μ$ has a finite weak-logarithmic moment.

preprint2013arXiv

On some random walks driven by spread-out measures

Let $G$ be a finitely generated group equipped with a symmetric generating $% k $-tuple $S$. Let $|\cdot|$ and $V$ be the associated word length and volume growth function. Let $ν$ be a probability measure such that $% ν(g)\simeq [(1+|g|)^2V(|g|)]^{-1}$. We prove that if $G$ has polynomial volume growth then $ν^{(n)}(e) \simeq V(\sqrt{n\log n})^{-1}$. We also obtain assorted estimates for other spread-out probability measures.

preprint2012arXiv

Random walks on nilpotent groups driven by measures supported on powers of generators

We study the decay of convolution powers of a large family $μ_{S,a}$ of measures on finitely generated nilpotent groups. Here, $S=(s_1,...,s_k)$ is a generating $k$-tuple of group elements and $a= (α_1,...,α_k)$ is a $k$-tuple of reals in the interval $(0,2)$. The symmetric measure $μ_{S,a}$ is supported by $S^*=\{s_i^{m}, 1\le i\le k,\,m\in \mathbb Z\}$ and gives probability proportional to $$(1+m)^{-α_i-1}$$ to $s_i^{\pm m}$, $i=1,...,k,$ $m\in \mathbb N$. We determine the behavior of the probability of return $μ_{S,a}^{(n)}(e)$ as $n$ tends to infinity. This behavior depends in somewhat subtle ways on interactions between the $k$-tuple $a$ and the positions of the generators $s_i$ within the lower central series $G_{j}=[G_{j-1},G]$, $G_1=G$.