arXiv subjects

Zhongyang Li

Publications and source records attributed to Zhongyang Li.

At least 19 recordsLinked to original sources

arXiv2026

WebHarbor: Docking Real Websites for Evolving GUI Agent Environments

GUI web agents require realistic and interactive environments that remain stable during both evaluation and training. Live website evaluation suffers from changing content, access restrictions, and limited coverage of authenticated workflows, while existing synthetic environments for training often lack functional depth and visual fidelity. We propose WebHarbor, a suite of 153 executable and dockerized website environments that faithfully reconstruct the visual interfaces, content, and functional workflows of real-world web services under deterministic control. We build WebHarbor through task-driven human-agent collaboration, where environments evolve as new tasks expand their functional scope, coding agents implement the required changes, and human contributors audit visual fidelity, functional correctness, and task validity. The resulting suite comprises 3,518 tasks spanning multi-step and post-authentication workflows, where existing works often fail to cover. Beyond reliable evaluation, WebHarbor provides high-fidelity synthetic web environments for cost-efficient reinforcement learning (RL). We demonstrate that a Qwen 4B-level GUI agent trained with RL in WebHarbor generalizes to unseen tasks and performs competitively with leading open-source GUI web agents across four benchmarks. The code and data are publicly available at https://github.com/aiming-lab/WebHarbor.

cs.AI↗

arXiv2026

Finite-Sample Optimal Conformal Prediction Sets under Covariate Shift

We study conformal prediction under covariate shift with a known covariate density ratio, seeking prediction sets with minimum expected length under the target distribution. For every calibration sample size, we prove that the rule combining the inverse conditional-density score with randomized weighted conformal calibration minimizes this expected length among all rules valid over the full weighted-exchangeability class. We approximate the oracle using quantile and kernel histograms, including forest-weighted estimators, and select estimators and tuning parameters by resampling to estimate calibrated target length. On a bounded response domain, we bound excess length linearly in $L^1$ density error at fixed calibration size, without requiring a uniform positive lower bound on the true density. We also bound selection-pool and resampling errors. Under explicit growth conditions, the selected procedure approaches the same oracle while the calibration size remains fixed. Experiments on 36 known-density configurations and four public regression datasets compare coverage, prediction-set length, and runtime with existing methods. In targeted low-coverage and strong-shift comparisons, inverse-density selection yields shorter mean sets in most cases and lower mean runtime than the evaluated weighted baselines, with some differences in achieved coverage.

stat.ML↗

arXiv2026

QUEST: Training Frontier Deep Research Agents with Fully Synthetic Tasks

Deep research agents extend the role of search engines from retrieving keyword-matched pages to synthesizing knowledge, fundamentally changing how humans interact with information. However, frontier systems remain proprietary, while existing open agents often generalize poorly across different task types, leaving unclear how to train a broadly capable deep research agent. We release QUEST, a family of open models (ranging from 2B to 35B) that serve as general-purpose deep research agents designed to handle a wide range of long-horizon search tasks, with strong capabilities in fact seeking, citation grounding, and report synthesis. To build QUEST, we propose an effective training recipe combining mid-training, supervised fine-tuning, and reinforcement learning. Central to this recipe is a curated data synthesis pipeline based on unified rubric trees, which applies to different task types and enables synthesizing training data with verifiable rewards without human annotation. In addition, QUEST incorporates a built-in context management mechanism that enables effective long-horizon reasoning and knowledge synthesis. Using only 8K synthesized tasks, QUEST approaches or even surpasses frontier closed-source agents across eight deep research benchmarks spanning diverse task types, and achieves the best overall performance among recent open-weight agents. We released everything: models, data, and training scripts.

cs.CL↗

arXiv2026

A Randomized Approximation Algorithm for Doubly Free-Boundary Macdonald Processes

We construct an approximate sampler for finite doubly free-boundary Macdonald rail-yard processes with Macdonald, boundary, and edge parameters in $(0,1)$. The construction allows arbitrary finite sequences of additions and removals of horizontal or vertical strips and all four boundary types. It reverses a finite commutation--reflection history from a partition sequence whose entries are equal, with the common partition weighted by both boundaries. We derive local reconstruction kernels from the skew Cauchy, Littlewood, and branching identities. Bulk and boundary updates combine integer increments with conditional shape sampling at a prescribed size; same-sign swaps use finite conditional resampling. For $K$ reflection periods and an initial partition-size cutoff $M$, the algorithm terminates almost surely and samples the resulting approximating law exactly. We prove total variation convergence to the target process as $K,M\to\infty$ and give explicit bounds for both truncation errors, decaying geometrically in the cutoffs for fixed input parameters. Under fixed parameter bounds, we also bound the expected operation count of direct enumeration in a unit-cost model. We further construct an exact rejection sampler for the initial partition law without a size cutoff or evaluation of its normalizing constant. Using this sampler removes the size-truncation error, leaving only the error from the finite reflection history.

math.PR↗

arXiv2026

Asymptotics of Bounded Lecture-Hall Tableaux

We study weighted bounded $n$-lecture hall tableaux with bound $t_n$ in the joint limit $n,t_n\to\infty$ with $t_n/n\toα\in(0,\infty)$. Using their non-intersecting-path representation, we construct a Schur generating function adapted to this model and derive moment formulas for the limiting counting measures. When the normalized tail sums of the weights have a $C^2$ macroscopic profile with negative derivative, the rescaled height functions converge in probability in $L^1_{\mathrm{loc}}(\mathbb R\times(0,α))$ to a deterministic limit shape whose complex slope satisfies a Burgers equation with an explicit source term. In the uniformly weighted model of \cite{SKN21}, the source term vanishes, proving Conjecture~6.1 of that work. Under an additional interval-structure assumption on the limiting bottom boundary, and only continuity and strict monotonicity of the tail profile, the unrescaled height fluctuations converge to the Gaussian free field in the sense of joint moments of horizontal polynomial observables. The method applies although the particle configurations are not Gelfand--Tsetlin patterns and the associated dimer model is not doubly periodic.

math.PR↗

arXiv2026

Doubly Free-Boundary Macdonald Processes: Reflection Identities and Jack Asymptotics

We introduce a doubly free-boundary Macdonald process on rail-yard interlacings and develop a reflection calculus for its observables. Boundary Cauchy--Littlewood identities, combined with Negu\c t operators, yield exact multipoint contour formulas for arbitrary $L/R$ words. Under the Jack scaling \[ q=t^α,\qquad t=e^{-nβε}, \] and piecewise-periodic data, these formulas imply a Laplace-transform law of large numbers and a weak slope-measure limit shape at $L$-type columns. For arbitrary piecewise-periodic $L/R$ backgrounds and finitely many $L$-type marked columns, under the stated contour, branch, and normal-convergence hypotheses, the centered height-Laplace observables converge jointly to a Gaussian vector. Its covariance exhibits a boundary--deformation separation: the Jack parameter and the microscopic rail-yard data enter through the one-point spectral factors and the normalization, whereas the two-point interaction is the logarithmic derivative of an annular prime function generated by the two boundary reflections. Thus the deformation changes the spectral map while preserving the annular image geometry of the Schur specialization. For $β=1$, in the all-$L$ sector and under explicit signed zero--pole and root-localization hypotheses, we characterize regular liquid and frozen points through the nonreal-root structure of the characteristic equation and show that nondegenerate regular interfaces lie on the real double-root locus. The half-space Macdonald-process formulas are recovered in the continuous degeneration $v\downarrow0$, which forces the right boundary partition to be empty.

math.PR↗

arXiv2026

Tree embeddings and nonuniqueness in site percolation

We prove a nonuniqueness theorem for Bernoulli site percolation on properly embedded planar graphs (graphs that can be embedded into $\RR^2$ with no accumulation points), and we obtain a general connectivity principle beyond planarity. Let $G$ be an infinite connected graph properly embedded in $\RR^2$ with minimum degree at least $7$. Then \[ p_c^{\mathrm{site}}(G)<\tfrac12, \] and for every \[ p\in \bigl(p_c^{\mathrm{site}}(G),\,1-p_c^{\mathrm{site}}(G)\bigr), \] Bernoulli$(p)$ site percolation on $G$ has almost surely infinitely many infinite open clusters. In particular, this verifies a conjecture of Benjamini and Schramm for properly embedded planar graphs. The core new ingredient is an explicit embedded-tree separation mechanism for planar nonuniqueness. We construct embedded trees and an embedded forest whose separation properties yield exponential decay of two-point connection probabilities in the auxiliary face-completion graph obtained by joining vertices that lie on a common finite face. To treat the high-density regime, we introduce a binary-tree version of uniform percolation and prove stability of infinite clusters under edge additions, without any bounded-degree assumption. Beyond the planar theorem, we prove a general lower bound on two-point connectivity under uniqueness for arbitrary infinite locally finite graphs. As a consequence, if \[ p_c^{\mathrm{site}}(G)<p<p_{\mathrm{conn}}(G), \] then Bernoulli site percolation on $G$ has almost surely infinitely many infinite open clusters.

math.PR↗

arXiv2026

MS-Resampler: Multi-Scope Visual Resampling for Efficient Multimodal LLMs

Multimodal large language models (MLLMs) typically employ resampling-based projectors to transform dense visual features into a compact token sequence for language modeling. Most existing resamplers adopt a single, fixed aggregation scope via global cross-attention, which can blur fine-grained local evidence and limit the ability to capture both local details and global context within a fixed token budget. In this work, we propose MS-Resampler, a multi-scope visual resampling framework for MLLMs. MS-Resampler instantiates multiple scope-specific resamplers by injecting explicit spatial scope priors into the resampling attention, enabling each branch to aggregate visual information at a particular granularity from local to global. The outputs of these scope-specific resamplers are then adaptively fused to produce the final visual representations for language modeling. Extensive experiments on ten public multimodal benchmarks show that MS-Resampler consistently improves visual understanding and multimodal reasoning over conventional single-scope resamplers, while introducing only minimal computational overhead.

cs.CV↗

arXiv2026

Doubly Free-Boundary Rail-Yard Dimers and Annular Gaussian Fluctuations

We study rail-yard dimer measures with free boundary conditions at both the left and the right boundary. The double free-boundary geometry produces an infinite family of reflected Cauchy factors in the partition function and in the exact contour formulas for height Laplace observables. These factors are absent from the empty-boundary model and survive in both the deterministic and second-order asymptotics. For admissible piecewise periodic weights, we prove a Laplace-transform law of large numbers. In the natural moment variable $x=e^{-nβκ}$, the transform convergence gives a limit shape of the rescaled height function. The associated frozen-boundary satisfies the following system of equations \[ S_χ(w)^β=e^{-nβκ}, \qquad \frac{d}{dw}\log S_χ(w)=0, \qquad S_χ(w):=\mathcal G_χ(w)\prod_{r\ge1}\mathcal F_{u,v,r}(w). \] The main second-order result is a Gaussian fluctuation theorem for centered height Laplace observables. The covariance is the annular reflected-image kernel \[ \mathsf K_{LL}(z,w) = \partial_z\partial_w \log\frac{Θ_{\mathfrak q}(z/w)} {Θ_{\mathfrak q}(u^2zw)}, \qquad \mathfrak q=(uv)^2, \] with specified contour interpretation. Thus the two free boundaries do not merely alter the deterministic limit shape: they replace the usual Gaussian free field half-plane image structure by an annular prime-function covariance on the Laplace-test class. As a final exact-solvability consequence, we construct an exact growth-diagram sampler for the finite reflected truncations of the doubly free-boundary model and prove that the resulting $K$-truncated laws converge, as $K\to\infty$, in total variation to the full doubly free-boundary Gibbs measure on every fixed rail-yard graph with finitely many columns.

math.PR↗

arXiv2026

Matchings on Random Regular Hypergraphs

We study the monomer--dimer partition function on the configuration model of random $d$-regular, $l$-uniform hypergraphs. For fixed $d,l\ge2$, we prove quenched free-energy limits in explicit parameter regimes. The proof combines fixed-density first-moment asymptotics, a two-overlap second-moment variational analysis, and a subgraph-conditioning argument for the short cycles of the incidence structure. The main technical point is to identify regimes in which the replica-symmetric saddle is the unique global maximizer of the second-moment rate function. In those regimes the normalized logarithm of the total matching partition function converges in probability to an explicit variational value. We also prove the corresponding result for the weighted partition function whenever the maximizing density lies in the verified replica-symmetric region, give an additional checkable criterion for that region, and record a first-moment upper tail estimate for the maximum matching size.

math.PR↗

arXiv2026

Exact Recovery of Community Detection in dependent Gaussian Mixture Models

We study exact recovery for community detection in a Gaussian mixture model with dependent and heterogeneous Gaussian noise. The noise covariance matrix $Σ$ may be non-diagonal and, in the general formulation, singular. In the singular case, we write the Gaussian likelihood on the support of the induced measure and show that the maximum likelihood estimator (MLE) is a constrained quadratic optimization problem involving the Moore--Penrose inverse. For general covariance structures, we obtain sufficient conditions for exact recovery of the MLE when the community sizes are unknown and when they are known. These conditions are driven by the $Σ$-whitened separation $L_Σ(x,y)$ together with local one-step comparison inequalities in the near-truth regime. Under the additional assumption that $Σ$ is invertible, we derive converse results showing failure of exact recovery when a large family of local perturbations has sufficiently nondegenerate Gaussian comparison statistics. We then analyze a full-rank non-diagonal block-covariance model, prove a sharp exact-recovery threshold in the unknown-size setting, and identify a general no-gap mechanism under which the sufficient and necessary conditions coincide asymptotically.

math.ST↗

arXiv2026

EventWeave: A Dynamic Framework for Capturing Core and Supporting Events in Dialogue Systems

Large language models have improved dialogue systems, but often process conversational turns in isolation, overlooking the event structures that guide natural interactions. Hence we introduce EventWeave, a framework that explicitly models relationships between conversational events to generate more contextually appropriate dialogue responses. EventWeave constructs a dynamic event graph that distinguishes between core events (main goals) and supporting events (interconnected details), employing a multi-head attention mechanism to selectively determine which events are most relevant to the current turn. Unlike summarization or standard graph-based approaches, our method captures three distinct relationship types between events, allowing for more nuanced context modeling. Experiments on three dialogue datasets demonstrate that EventWeave produces more natural and contextually appropriate responses while requiring less computational overhead than models processing the entire dialogue history. Ablation studies confirm improvements stem from better event relationship modeling rather than increased information density. Our approach effectively balances comprehensive context understanding with generating concise responses, maintaining strong performance across various dialogue lengths through targeted optimization techniques.

cs.CL↗

arXiv2026

QMoP: Query Guided Mixture-of-Projector for Efficient Visual Token Compression

Multimodal large language models suffer from severe computational and memory bottlenecks, as the number of visual tokens far exceeds that of textual tokens. While recent methods employ projector modules to align and compress visual tokens into text-aligned features, they typically depend on fixed heuristics that limit adaptability across diverse scenarios. In this paper, we first propose Query Guided Mixture-of-Projector (QMoP), a novel and flexible framework that adaptively compresses visual tokens via three collaborative branches: (1) a pooling-based branch for coarse-grained global semantics, (2) a resampler branch for extracting high-level semantic representations, and (3) a pruning-based branch for fine-grained token selection to preserve critical visual detail. To adaptively coordinate these branches, we introduce the Query Guided Router (QGR), which dynamically selects and weights the outputs from different branches based on both visual input and textual queries. A Mixture-of-Experts-style fusion mechanism is designed to aggregate the outputs, harnessing the strengths of each strategy while suppressing noise. To systematically evaluate the effects of Visual Token Compression, we also develop VTCBench, a dedicated benchmark for evaluating the information loss induced by visual token compression. Extensive experiments demonstrate that despite relying on fundamental compression modules, QMoP outperforms strong baselines and delivers significant savings in memory, computation, and inference time.

cs.CV↗

arXiv2026

Recursive Packing Bounds for Supercritical Disconnection in Bernoulli Site Percolation

For Bernoulli site percolation on an infinite, connected, locally finite graph $G=(V,E)$, we obtain quantitative upper bounds on the supercritical disconnection probability \[ \mathbb{P}_p(S\nleftrightarrow\infty) \] for arbitrary finite or infinite sets $S\subset V$ and all $p>p^{\mathrm{site}}_c(G)$. The key quantity is a recursive packing number $\mathbf{PK}_{p,\eps,c}(S)$. It is the maximal number of vertices that can be extracted from $S$ so that, after deleting witness balls around the previously chosen vertices, each selected vertex still connects to infinity with probability at least $c$, while its failure to connect to infinity is already detected, up to a factor $1+\eps$, by failure to reach the inner boundary of its witness ball. Thus $\mathbf{PK}_{p,\eps,c}(S)$ counts essentially independent local witnesses for the global event $\{S\nleftrightarrow\infty\}$. We prove the structural estimate \[ \mathbb{P}_p(S\nleftrightarrow\infty) \le \frac{\eps(1-c)}{c} +(1-c)^{\mathbf{PK}_{p,\eps,c}(S)}. \] Combining this bound with the local functional characterization of $p^{\mathrm{site}}_c(G)$ from \cite{ZL24} yields an explicit supercritical estimate valid on every infinite, connected, locally finite graph. We also illustrate the packing number on ray-homogeneous trees. In particular, sparse finite subsets of a distinguished ray have packing number equal to their cardinality, both for regular trees and for a non-regular decorated spine. This shows that the packing number is explicit on concrete graph families.

math.PR↗

arXiv2026

Independent GUE minor processes of perfect matchings on rail-yard graphs

We study perfect matchings on the rail-yard graphs in which the right boundary condition is given by the empty partition and the left boundary can be divided into finitely many alternating line segments where all the vertices along each line segment are either removed or remained. When the edge weights satisfy certain conditions, we show that the distributions of the locations of certain types of dimers near the right boundary converge to the spectra of independent GUE minor processes. The proof is based on new quantitative analysis of a formula to compute Schur functions at general points discovered in \cite{ZL18}.

math.PR↗

arXiv2026

Self-avoiding walks on cubic graphs and local transformations

Despite its elementary definition, the self-avoiding walk (SAW) poses notoriously hard enumerative problems: exact connective constants are known for only a handful of infinite graphs, notably the honeycomb lattice \cite{ds}. We establish a general substitution principle for SAWs on infinite connected quasi-transitive cubic graphs under port-transitive vertex replacements, where each degree-$3$ vertex is replaced by a fixed finite three-port gadget. Writing $g(x)$ for the associated two-port SAW series, we prove that for $G_1=ϕ(G)$, \[ μ(G)^{-1}=g\bigl(μ(G_1)^{-1}\bigr), \] equivalently $μ(G_1)^{-1}$ is the unique solution $x\in(0,1)$ of $g(x)=μ(G)^{-1}$, thereby extending the Fisher-triangle relation of Grimmett--Li to arbitrary symmetric three-port gadgets. We also obtain the corresponding identity for bipartite graphs when one or both colour classes are transformed, and show that the critical exponents $γ$ and $η$ (and $ν$ under a standard regularity hypothesis) are invariant. For explicit gadget families, including complete-graph gadgets $K_N$ and Fisher-type constructions, these identities turn base graphs with known $μ$ into infinite families of new quasi-transitive graphs whose connective constants are determined exactly as the unique roots of explicit algebraic equations.

math.CO↗

arXiv2026

Planar Site Percolation, End Structure, and the Benjamini-Schramm Conjecture

Let $G$ be an infinite, connected, locally finite planar graph and consider i.i.d.\ Bernoulli$(p)$ site percolation. Write $p_c^{\mathrm{site}}(G)$ and $p_u^{\mathrm{site}}(G)$ for the critical and uniqueness thresholds. Using a well--separated Freudenthal embedding $G\hookrightarrow\mathbb S^2$, we introduce a cycle--separation equivalence on ends and associated ``directional'' thresholds $p^{\mathrm{site}}_{c,F}(G)$. When the set of end--equivalence classes is countable, we show that $p_c^{\mathrm{site}}(G)=\inf_F p^{\mathrm{site}}_{c,F}(G)$ and that for every $p\in\bigl(\tfrac12,\,1-p_c^{\mathrm{site}}(G)\bigr)$ there are almost surely infinitely many infinite open clusters. Combined with the $0/\infty$ theorem of Glazman--Harel--Zelesko for $p\le \tfrac12$, this yields non--uniqueness throughout the full coexistence interval $\bigl(p_c^{\mathrm{site}}(G),\,1-p_c^{\mathrm{site}}(G)\bigr)$, and hence $p_u^{\mathrm{site}}(G)\ge 1-p_c^{\mathrm{site}}(G)$ in this setting. This resolves the extension problem posed by Glazman--Harel--Zelesko for the upper half of the coexistence regime under a natural countability hypothesis. In contrast, for graphs with uncountably many end--equivalence classes we give criteria guaranteeing infinitely many infinite clusters above criticality, and we construct an explicit locally finite planar graph of minimum degree at least $7$ for which $p_u^{\mathrm{site}}(G)<1-p_c^{\mathrm{site}}(G)$. Consequently, the Benjamini--Schramm conjecture (Conjecture 7 in \cite{bs96}) that planarity together with minimal vertex degree at least 7 forces infinitely many infinite clusters for all $p\in(p_c,1-p_c)$ does not hold in full generality. Our proofs combine a cutset characterization of $p_c^{\mathrm{site}}$ with a planar alternating--arm exploration organized by an end--adapted boundary decomposition.

math.PR↗

arXiv2026

Scene-Aware Memory Discrimination: Deciding Which Personal Knowledge Stays

Intelligent devices have become deeply integrated into everyday life, generating vast amounts of user interactions that form valuable personal knowledge. Efficient organization of this knowledge in user memory is essential for enabling personalized applications. However, current research on memory writing, management, and reading using large language models (LLMs) faces challenges in filtering irrelevant information and in dealing with rising computational costs. Inspired by the concept of selective attention in the human brain, we introduce a memory discrimination task. To address large-scale interactions and diverse memory standards in this task, we propose a Scene-Aware Memory Discrimination method (SAMD), which comprises two key components: the Gating Unit Module (GUM) and the Cluster Prompting Module (CPM). GUM enhances processing efficiency by filtering out non-memorable interactions and focusing on the salient content most relevant to application demands. CPM establishes adaptive memory standards, guiding LLMs to discern what information should be remembered or discarded. It also analyzes the relationship between user intents and memory contexts to build effective clustering prompts. Comprehensive direct and indirect evaluations demonstrate the effectiveness and generalization of our approach. We independently assess the performance of memory discrimination, showing that SAMD successfully recalls the majority of memorable data and remains robust in dynamic scenarios. Furthermore, when integrated into personalized applications, SAMD significantly enhances both the efficiency and quality of memory construction, leading to better organization of personal knowledge.

cs.CL↗