arXiv subjects
Publications and source records attributed to Xiaoqing Wu.
In this paper, we investigate the almost-periodic solutions for the one-dimensional nonlinear Klein-Gordon equation within the non-relativistic limit under periodic boundary conditions. Specifically, by employing the method introduced in \cite{Bourgain2005JFA}, we establish the existence and linear stability of full-dimensional tori with subexponential decay for the equation.
Based on the work of Chen and Its [{\em J. Approx. Theory} {\bf 162} ({2010}) {270--297}], we further study orthogonal polynomials with respect to the singularly perturbed Laguerre weight $w(x;t,α) = {x^α}{\mathrm e^{- x-\frac{t}{x}}}, \; x\in\mathbb{R}^{+},\;α> -1,\; t\geq 0$. By using the ladder operators and associated compatibility conditions for orthogonal polynomials with general Laguerre-type weights, we derive the second-order differential equation satisfied by the orthogonal polynomials, a system of difference equations and a system of differential-difference equations for the recurrence coefficients. We also investigate the properties of the zeros of the orthogonal polynomials. Using Dyson's Coulomb fluid approach together with the discrete system, we obtain the large $n$ asymptotic expansions of the recurrence coefficients, the sub-leading coefficient of the monic orthogonal polynomials, the Hankel determinant and the normalized constant for fixed $t>0$. It is found that all the asymptotic expansions are singular at $t=0$. We also study the long-time ($t\rightarrow+\infty$) asymptotics of these quantities explicitly for fixed $n\in\mathbb{N}$ from the Toda-type system.
Tool-calling agents infer task state from accumulated dialogue and tool traces. In persistent interactions, however, historical traces may remain structurally valid and semantically plausible after they cease to be authoritative for the current request. We show that such history can hijack a policy the model already possesses: on Qwen3-1.7B, pollution flips 32.1% of decisions that are correct under the original trajectory and frequently induces reuse of corrupted entities or interface conventions. We introduce bench, a paired benchmark with synchronized Original, Polluted, and Oracle State views that preserve the system policy, current tools, latest request, and gold next action. Eleven gold-preserving interventions isolate failures in decision state, entity binding, and interface execution across complete calls and non-call decisions. We further propose ours, which transfers an Oracle-conditioned teacher policy to a student observing only polluted history through soft supervision on student-generated prefixes. On Qwen3-1.7B, ours achieves 87.0% Balanced Tool-Use Accuracy, outperforming Gold-SFT (66.3%), Oracle sequence distillation (82.3%), and off-policy token distillation (85.0%). The method scales consistently: an 8B teacher raises the same compact 1.7B student to 91.9%, while an 8B student reaches 93.0%. The resulting policies further transfer to clean histories, unseen functions, independently regenerated evaluation contexts, external tool-use benchmarks, and noisy multi-hop question answering. These results establish history reliability as a distinct tool-use bottleneck and demonstrate reliable-state policy transfer as an effective and scalable solution.
LLM-curated hierarchical knowledge bases, namely a tree-structured wiki whose nodes summarize an underlying corpus, have become a dominant substrate for retrieval-augmented applications, yet their storage layer is still treated as an implementation detail. This workload is hierarchical, query-intensive, and continuously evolving, and no existing storage model natively captures all three properties at once. We present WikiKV, a path-indexed key-value storage model purpose-built for this workload, comprising three components: (i) a data-driven schema that bootstraps the hierarchy via Intent-Anchored Schema Induction and refines it through Continuous Evolution Operators; (ii) a consistency protocol for the path-indexed storage model that precludes partial-read observations under concurrent offline rewrites without read-path locking; and (iii) a budgeted navigation operator whose search-accelerated routing reduces the expected number of LLM-assisted descent steps from d to O(1) while preserving anytime semantics with progressively refined answers. We evaluate WikiKV through real-world deployment for the WeChat Official Account AI Assistant and benchmark it against diverse baselines on the AuthTrace dataset, where it achieves balanced low per-operator latency across four query operators against relational, graph, and FS backends, and reaches 63.2% end-to-end answer correctness, exceeding multiple RAG baselines, with the gap widening on low- and high-fan-in multi-document questions. Ablation study further confirms the effectiveness of WikiKV's components.
We consider the Hankel determinant and orthogonal polynomials with respect to the deformed Laguerre weight $w(x; t) = {x^α}{\mathrm e^{ - x}}{(x + t)^λ},\; x\in \mathbb{R}^{+} $ with parameters $α> -1,\; t > 0$ and $λ\in \mathbb{R}$. This problem originates from the information theory of single-user multiple-input multiple-output (MIMO) systems studied by Chen and McKay [{\em IEEE Trans. Inf. Theory} {\bf 58} ({2012}) {4594--4634}]. By using the ladder operators for orthogonal polynomials with general Laguerre-type weights, we obtain a system of difference equations and a system of differential-difference equations for the recurrence coefficients $α_n(t)$ and $β_n(t)$. We also show that the orthogonal polynomials satisfy a second-order ordinary differential equation. By using Dyson's Coulomb fluid approach, we obtain the large $n$ asymptotic expansions of the recurrence coefficients $α_n(t)$ and $β_n(t)$, the sub-leading coefficient $\mathrm p(n, t)$ of the monic orthogonal polynomials, the Hankel determinant $D_n(t)$ and the normalized constant $h_n(t)$ for fixed $t\in\mathbb{R}^{+}$. We also discuss the long-time asymptotics of these quantities as $t\rightarrow\infty$ for fixed $n\in\mathbb{N}$. The large $n$ and large $t$ asymptotics of the above quantities are very important for the study of the asymptotics of the mutual information distribution and two fundamental quantities (the outage capacity and the error probability) for single-user MIMO systems.
Evidence construction--the stage that determines which passages reach the language model before generation begins--is evaluated paradigm by paradigm, leaving practitioners with no principled way to diagnose which organization strategy fails, where, or why. We introduce AuthTrace, a diagnostic benchmark built on thematically dense single-author corpora where near-miss distractors share style, topic, and vocabulary with the required evidence. AuthTrace provides explicit quoted evidence, exact fan-in annotation, and a unified pack-level protocol measuring evidence recall, evidence precision, and answer correctness. A fan-in gradient--the number of source documents required to support the answer--serves as the primary diagnostic axis, enabling controlled comparison across retrieval, memory, graph, and structured-evidence paradigms. Evaluating eight systems across two QA models, we find that evidence recall is the strongest observed predictor of answer correctness under the primary reader-judge pair (r = 0.96); most failures stem from missing evidence rather than answer synthesis. Fan-in further exposes paradigm-specific collapse patterns: flat retrieval degrades 2-3x faster than thematically organized evidence construction. These results show fan-in decomposition to be a reusable diagnostic lens for identifying where evidence-construction systems fail and which paradigm best serves a given workload.
LLM agents require retrieval to behave less like one-shot context fetching and more like reasoning: searching, reading, traversing, and deciding when evidence is sufficient. Yet current Retrieval-Augmented Generation (RAG) systems organize external knowledge as flat chunks retrieved by embedding similarity, exposing a retrieval-as-lookup interface ill-suited to iterative reasoning agents. We propose LLM-Wiki, an agent-native retrieval system that operationalizes the Retrieval-as-Reasoning paradigm by treating external knowledge as a compilable, composable, and self-evolving structure rather than a static retrieval index. LLM-Wiki compiles documents into structured Wiki pages with bidirectional links, exposes search, read, and link-following operations through standard tool-calling interfaces, and introduces an Error Book for persistent structural and semantic self-correction. LLM-Wiki achieves state-of-the-art results on HotpotQA, MuSiQue, and 2WikiMultiHopQA, outperforming HippoRAG 2, LightRAG, and GraphRAG by 2.0-8.1 F1 points. On AuthTrace, LLM-Wiki achieves the best overall accuracy, with especially strong gains on multi-document structured queries, confirming that compilation-based retrieval generalizes beyond chain-style multi-hop reasoning.
Inpatient medication recommendation requires clinicians to repeatedly select specific medications, doses, and routes as a patient's condition evolves. Existing benchmarks formulate this task as admission-level prediction over coarse drug codes with multi-hot diagnostic and procedure code inputs, failing to capture the per-timepoint, information-rich nature of real prescribing. We propose RxEval, a prescription-level benchmark that evaluates LLM prescribing capability by multiple-choice questions: each question presents a detailed patient profile and time-ordered clinical trajectory, requiring selection of specific medication-dose-route triples from real prescriptions and patient-specific distractors generated via reasoning-chain perturbation. RxEval comprises 1,547 questions spanning 584 patients, 18 diagnostic categories, and 969 unique medications. Evaluation of 16 LLMs shows that RxEval is both challenging and discriminative: F1 ranges from 45.18 to 77.10 across models, and the best Exact Match is only 46.10%. Error analysis reveals that even frontier models may overlook stated patient information and fail to derive clinical conclusions.
Reactions between cyano radical and aromatic hydrocarbons are believed to be important pathways for the formation of aromatic nitriles in the interstellar medium (ISM) including those identified in the Taurus molecular cloud (TMC-1). Aromatic nitriles might participate in the formation of polycyclic aromatic nitrogen containing hydrocarbons (PANHs) in Titan's atmosphere. Here, ab initio kinetics simulations reveal a high efficiency of $\rm \sim10^{-10}~cm^{3}~s^{-1}$ and the competition of the different products of 30-1800 K and $10^{-7}$-100 atm of the CN + toluene reaction. In the star-forming region of TMC-1 environment, the product yields of benzonitrile and tolunitriles for CN reacting with toluene may be approximately 17$\%$ and 83$\%$, respectively. The detection of main products, tolunitriles, can serve as proxies for the undetected toluene in the ISM due to their much larger dipole moments. The competition between bimolecular and unimolecular products is extremely intense under the warmer and denser PANH forming region of Titan's stratosphere. The computational results show that the fractions of tolunitriles, adducts, and benzonitrile are 19$\%$-68$\%$, 15$\%$-64$\%$ and 17$\%$, respectively, at 150-200 K and 0.0001-0.001 atm (Titan's stratosphere). Then, benzonitrile and tolunitriles may contribute to the formation of PANHs by consecutive $\rm C_{2}H$ additions. Kinetic information of aromatic nitriles for the CN + toluene reaction calculated here helps to explain the formation mechanism of polycyclic aromatic hydrocarbons (PAHs) or PANHs under different interstellar environments and constrains corresponding astrochemical models.
In this paper, we prove the existence of full dimensional tori for $d$-dimensional nonlinear Schr$\ddot{\mbox{o}}$dinger equation with periodic boundary conditions \begin{equation*}\label{L1} \sqrt{-1}u_{t}+Δu+V*u\pmε|u|^2u=0,\hspace{12pt}x\in\mathbb{T}^d,\quad d\geq 1, \end{equation*} where $V*$ is the convolution potential. Here the radius of the invariant torus satisfies a slower decay, i.e. \begin{equation*}\label{031601} I_{\textbf n}\sim e^{-r\ln^σ\left\|\textbf n\right\|},\qquad \mbox{as}\ \left\|\textbf n\right\|\rightarrow\infty, \end{equation*}for any $σ>2$ and $r\geq 1$. This result confirms a conjecture by Bourgain [J. Funct. Anal. 229 (2005), no. 1, 62-94].