arXiv subjects

Mingyan Wu

Publications and source records attributed to Mingyan Wu.

14 recordsLinked to original sources

arXiv2026

When Knowledge Is Not Free: Cost-Aware Evidence Selection in Retrieval-Augmented Generation

Retrieval-Augmented Generation (RAG) typically assumes that external knowledge is free, but many high-quality sources are paywalled, licensed, restricted, or otherwise costly to access. We introduce cost-aware RAG, a setting where retrieved evidence is assigned access-cost tiers and systems must answer under an explicit evidence-access budget. We instantiate this setting by augmenting MS MARCO v2.1 with access-friction tiers and evaluate budgeted evidence selection across general-domain and domain-specific QA benchmarks. Our results show that static selection is brittle: no fixed selector uniformly dominates, and larger budgets do not reliably improve answer quality, even when costly evidence is domain-matched. We then study agentic cost-aware RAG, where an LLM decides when to retrieve, which tier to access, and when to stop. Agents show strong promise as adaptive evidence-acquisition controllers, but their behavior remains highly model- and task-dependent. These findings suggest that cost-aware evidence acquisition is a central challenge for the next generation of RAG systems. All code and data are available at https://github.com/Mignonmy/Cost-Aware.

cs.CL↗

arXiv2026

Stein's Method for Convergence Rates of Invariant Measures in the Nonlocal-to-Local Limit

We utilize Stein's method to establish quantitative bounds on the total variation distance between the invariant measure of a drifted nonlocal Markov operator and that of its local counterpart under minimal assumptions on the drifts. The main ingredient is a reduction via Stein's method that transforms the original problem into analyzing growth estimates for solutions to a nonlocal Poisson equation and decay estimates for the invariant measure of the local operator.

math.PR↗

arXiv2026

Reasoning Compression with Mixed-Policy Distillation

Reasoning-centric large language models (LLMs) achieve strong performance by generating intermediate reasoning trajectories, but often incur excessive token usage and high inference-time decoding cost. We observe that, when solving the same problems, larger reasoning models can often produce more concise traces, whereas smaller reasoning models tend to generate longer and more redundant trajectories. This is especially problematic in real-world deployment, where memory, latency, and serving-cost constraints often favor smaller models. Our observations suggest that reasoning compression can be transferred from large models to small ones rather than enforced through explicit length constraints. Based on this insight, we propose Mixed-Policy Distillation (MPD), a reasoning compression framework that transfers concise reasoning behavior from a larger-sized teacher to a smaller student by distilling teacher-compressed student trajectories. Unlike on-policy distillation, which aligns the student with teacher distributions over verbose student trajectories, or off-policy distillation, which relies on teacher-generated trajectories and may suffer from distribution mismatch, MPD combines the strengths of both. Given a student-sampled trajectory, the teacher rewrites it into a more concise reasoning trace, and the student is trained via KL-based alignment on the compressed trajectory. This preserves student-policy exploration while injecting teacher-guided compression. Experiments on Qwen3-1.7B show that MPD reduces token usage by up to 27.1% while improving performance across multiple reasoning benchmarks, demonstrating an effective approach to efficient small-model reasoning.

cs.AI↗

arXiv2026

The Euler-Maruyama method for invariant measures of McKean-Vlasov stochastic differential equations

This paper investigates the approximation of invariant measures for McKean-Vlasov stochastic differential equations (SDEs) using the Euler-Maruyama (EM) scheme under a monotonicity condition. Firstly, the convergence of the numerical solution from the EM scheme to its continuous-time counterpart is established. Secondly, we show that the numerical solution admits a unique invariant measure and derive its convergence rate under the Wasserstein metric. In parallel, it is demonstrated that the associated particle system also possesses these properties.

math.PR↗

arXiv2026

Euler--Maruyama scheme for $\alpha$-stable SDE with distributional drift

In this paper, we consider a class of stochastic differential equations driven by symmetric non-degenerate $\alpha$-stable processes (including cylindrical ones) with $\alpha \in (1,2)$. We first establish a quantitative estimate for the Euler scheme under bounded drift $b(x)$, with an explicit dependence on $ \| b \|_{L^\infty}$. Then we obtain the weak convergence rates for the case where the drift coefficient belongs to a Besov space of negative order.

math.PR↗

arXiv2026

EigentSearch-Q+: Enhancing Deep Research Agents with Structured Reasoning Tools

Deep research requires reasoning over web evidence to answer open-ended questions, and it is a core capability for AI agents. Yet many deep research agents still rely on implicit, unstructured search behavior that causes redundant exploration and brittle evidence aggregation. Motivated by Anthropic's "think" tool paradigm and insights from the information-retrieval literature, we introduce Q+, a set of query and evidence processing tools that make web search more deliberate by guiding query planning, monitoring search progress, and extracting evidence from long web snapshots. We integrate Q+ into the browser sub-agent of Eigent, an open-source, production-ready multi-agent workforce for computer use, yielding EigentSearch-Q+. Across four benchmarks (SimpleQA-Verified, FRAMES, WebWalkerQA, and XBench DeepSearch), Q+ improves Eigent's browser agent benchmark-size-weighted average accuracy by 3.0, 3.8, and 0.6 percentage points (pp) for GPT-4.1, GPT-5.1, and Minimax M2.5 model backends, respectively. Case studies further suggest that EigentSearch-Q+ produces more coherent tool-calling trajectories by making search progress and evidence handling explicit.

cs.AI↗

arXiv2026

The Non-Gaussian to Gaussian Transition: Pointwise Heat Kernel Estimates and Optimal Convergence Rates

We establish uniform pointwise estimates for the densities of a family of $\alpha$-stable processes with respect to the index $\alpha \in [\alpha_0,2]$ for some $\alpha_0>0$. In addition, we estimate the difference between the heat kernels of non-local and local operators, showing that it is controlled by the rate $2-\alpha$. Both estimates (see Proposition 2.4) are new to the literature. Furthermore, as an application, we achieve the optimal rate $2-\alpha$ for the pointwise estimate between the transition probabilities, as well as for the (weighted) total variation and Kantorovich distances between the invariant measures, of non-Gaussian and Gaussian diffusion. These results are obtained under the assumption that the drifts are locally $\beta$-H\"older continuous, with the latter additionally requiring dissipativity. The results on transition probabilities (see Theorem 2.3) are novel, while those on invariant measures (see Theorem 2.7) significantly extend the existing literature.

math.PR↗

arXiv2026

Finding What Matters: Anchoring Context Knowledge with Evolving Indices for Iterative Retrieval

Retrieval-Augmented Generation (RAG) has become a dominant paradigm for mitigating hallucinations in Large Language Models (LLMs) by incorporating external knowledge. However, existing RAG systems often struggle to effectively integrate and reason over key evidence scattered across noisy retrieved documents, particularly in multi-hop scenarios. In this paper, we propose KAIR, a Knowledge Anchoring framework for Iterative Retrieval that anchors knowledge within retrieved knowledge to guide LLMs to locate the key information. During iterative retrieval, KAIR progressively updates the knowledge index to anchor salient evidence from retrieved documents. The evolving index serves as a navigational anchoring index that enables the LLM to assess knowledge sufficiency and formulate subsequent retrieval queries. Finally, KAIR generates answers by jointly leveraging the retrieved documents and the finalized anchoring index. Experiments on four multi-hop question answering benchmarks demonstrate that KAIR consistently outperforms strong RAG baselines. Further analysis shows that KAIR effectively anchors key knowledge and alleviates the context noise during iterative retrieval, improving the LLM's ability to associate and reason over dispersed evidence across retrieved documents. All code and data are available at https://github.com/NEUIR/KAIR.

cs.CL↗

arXiv2025

RankCoT: Refining Knowledge for Retrieval-Augmented Generation through Ranking Chain-of-Thoughts

Retrieval-Augmented Generation (RAG) enhances the performance of Large Language Models (LLMs) by incorporating external knowledge. However, LLMs still encounter challenges in effectively utilizing the knowledge from retrieved documents, often being misled by irrelevant or noisy information. To address this issue, we introduce RankCoT, a knowledge refinement method that incorporates reranking signals in generating CoT-based summarization for knowledge refinement based on given query and all retrieval documents. During training, RankCoT prompts the LLM to generate Chain-of-Thought (CoT) candidates based on the query and individual documents. It then fine-tunes the LLM to directly reproduce the best CoT from these candidate outputs based on all retrieved documents, which requires LLM to filter out irrelevant documents during generating CoT-style summarization. Additionally, RankCoT incorporates a self-reflection mechanism that further refines the CoT outputs, resulting in higher-quality training data. Our experiments demonstrate the effectiveness of RankCoT, showing its superior performance over other knowledge refinement models. Further analysis reveals that RankCoT can provide shorter but effective refinement results, enabling the generator to produce more accurate answers. All code and data are available at https://github.com/NEUIR/RankCoT.

cs.CL↗

arXiv2024

Supercritical McKean-Vlasov SDE driven by cylindrical $\alpha$-stable process

In this paper, we study the following supercritical McKean-Vlasov SDE, driven by a symmetric non-degenerate cylindrical $\alpha$-stable process in $\mathbb{R}^d$ with $\alpha \in (0,1)$: $$ \mathord{{\rm d}} X_t = (K * \mu_{t})(X_t)\mathord{{\rm d}}t + \mathord{{\rm d}} L_t^{(\alpha)}, \quad X_0 = x \in \mathbb{R}^d, $$ where $K: \mathbb{R}^d \to \mathbb{R}^d$ is a $\beta$-order H\"older continuous function, and $\mu_t$ represents the time marginal distribution of the solution $X$. We establish both strong and weak well-posedness under the conditions $\beta \in (1 - \alpha/2, 1)$ and $\beta \in (1 - \alpha, 1)$, respectively. Additionally, we demonstrate strong propagation of chaos for the associated interacting particle system, as well as the convergence of the corresponding Euler approximations. In particular, we prove a commutation property between the particle approximation and the Euler approximation.

math.PR↗

arXiv2023

SDE driven by cylindrical $\alpha$-stable process with distributional drift

For $\alpha \in (1,2)$, we study the following stochastic differential equation driven by a non-degenerate symmetric $\alpha$-stable process in $\mathbb{R}^d$: \begin{align*} {\rm d} X_t=b(t,X_t){\mathord{{\rm d}}} t+\sigma(t,X_{t-}){\mathord{{\rm d}}} L_t^{(\alpha)},\ \ X_0 =x \in \mathbb{R}^d, \end{align*} where $b$ belongs to $ L^\infty(\mathbb{R}_+;\mathbf{C}^{-\beta}(\mathbb{R}^d))$ with some $\beta\in(0,\alpha-1)$, and $\mathbf{C}^\beta$ denotes a Besov space (see Definition (2.2) below). The coefficient $\sigma:\mathbb{R}_+\times \mathbb{R}^d \to \mathbb{R}^d \otimes \mathbb{R}^d$ is a measurable matrix-valued function. The noise $L_t^{(\alpha)}=(L_t^{(\alpha),1},...,L_t^{(\alpha),d})$ consists of independent $1$-dimensional symmetric $\alpha$-stable processes, and is referred to as a cylindrical $\alpha$-stable process. We establish the well-posedness of weak solutions to the SDE, and provide quantitative stability estimates with respect to the drift coefficients.

math.PR↗

arXiv2021

Well-posedness of density dependent SDE driven by $α$-stable process with Hölder drifts

In this paper, we show the weak and strong well-posedness of density dependent stochastic differential equations driven by $α$-stable processes with $α\in(1,2)$. The existence part is based on Euler's approximation as \cite{HRZ20}, while, the uniqueness is based on the Schauder estimates in Besov spaces for nonlocal Fokker-Planck equations. For the existence, we only assume the drift being continuous in the density variable. For the weak uniqueness, the drift is assumed to be Lipschitz in the density variable, while for the strong uniqueness, we also need to assume the drift being $β_0$-order Hölder continuous in the spatial variable, where $β_0\in(1-α/2,1)$.

math.PR↗

arXiv2020

Schauder's estimates for nonlocal equations with singular Lévy measures

In this paper, we establish Schauder's estimates for the following non-local equations in \mR^d : $$ \partial_tu=\mathscr L^{(α)}_{κ,σ} u+b\cdot\nabla u+f,\ u(0)=0, $$ where $α\in(1/2,2)$ and $ b:\mathbb R_+\times\mathbb R^d\to\mathbb R$ is an unbounded local $β$-order Hölder function in $ x $ uniformly in $ t $, and $\mathscr L^{(α)}_{κ,σ}$ is a non-local $α$-stable-like operator with form: \begin{align*} {\mathscr L}^{(α)}_{κ,σ}u(t,x):=\int_{\mathbb R^d}\Big(u(t,x+σ(t,x)z)-u(t,x)-σ(t,x)z^{(α)}\cdot\nabla u(t,x)\Big)κ(t,x,z)ν^{(α)}(\mathord{\rm d} z), \end{align*} where $z^{(α)}=z\mathbf{1}_{α\in(1,2)}+z\mathbf{1}_{|z|\leq 1}\mathbf{1}_{α=1}$, $ κ:\mathbb R_+\times\mathbb R^{2d}\to\mathbb R_+ $ is bounded from above and below, $ σ:\mathbb R_+\times\mathbb R^{d}\to \mathbb R^d\otimes \mathbb R^d$ is a $ γ$-order Hölder continuous function in $ x $ uniformly in $ t $, and $ ν^{(α)} $ is a singular non-degenerate $ α$-stable Lévy measure.

math.PR↗

arXiv2019

Schauder's estimate for nonlocal kinetic equations and its applications

In this paper we develop a new method based on Littlewood-Paley's decomposition and heat kernel estimates of integral form, to establish Schauder's estimate for the following degenerate nonlocal equation in $\mathbb R^{2d}$ with Hölder coefficients: $$ \partial_tu=\mathscr L^{(α)}_{κ;{\rm v}} u+b\cdot\nabla u+f,\ u_0=0, $$ where $u=u(t,x,{\rm v})$ and $\mathscr L^{(α)}_{κ;{\rm v}}$ is a nonlocal $α$-stable-like operator with $α\in(1,2)$ and kernel function $κ$, which acts on the variable ${\rm v}$. As an application, we show the strong well-posedness to the following degenerate stochastic differential equation with Hölder drift $b$: $$ {\rm d}Z_t=b(t,Z_t){\rm d}t+(0,σ(t,Z_t){\rm d}L^{(α)}_t),\ \ Z_0=(x,{\rm v})\in\mathbb R^{2d}, $$ where $L^{(α)}_t$ is a $d$-dimensional rotationally invariant and symmetric $α$-stable process with $α\in(1,2)$, and $b:\mathbb R_+\times\mathbb R^{2d}\to\mathbb R^{2d}$ is a $(γ,β)$-Hölder continuous function in $(x,{\rm v})$ with $γ\in\big(\frac{2+α}{2(1+α)},1\big)$ and $β\in\big(1-\fracα{2},1\big)$, $σ:\mathbb R_+\times\mathbb R^{2d}\to\mathbb R^d\otimes\mathbb R^d$ is a Lipschitz function. Moreover, we also show that for almost all $ω$, the following random transport equation has a unique $C^1_b$-solution: $$ \partial_tu(t,x,ω)+(b(t,x)+L^{(α)}_t(ω))\cdot\nabla_x u(t,x,ω)=0,\ \ u(0,x)=φ(x), $$ where $φ\in C^1_b(\mathbb R^d)$ and $b:\mathbb R_+\times\mathbb R^d\to\mathbb R^d$ is a bounded continuous function in $(t,x)$ and $γ$-order Hölder continuous in $x$ uniformly in $t$ with $γ\in\big(\frac{2+α}{2(1+α)},1\big)$.

math.AP↗