arXiv subjects

Fei Wei

Publications and source records attributed to Fei Wei.

At least 19 recordsLinked to original sources

arXiv2026

Joint moments of characteristic polynomials in the circular Jacobi ensemble and Painlev\'e equations

In this paper, we establish a connection between joint moments of characteristic polynomials and their derivatives in the Circular Jacobi Ensemble, a generalisation of the Circular Unitary Ensemble, and solutions of nonlinear Painlev\'e equations. For finite $N$, we show that these joint moments are characterised by a solution of the $\sigma$-Painlev\'e V equation for all real moment exponents in their admissible range. Under an appropriate large-$N$ scaling limit, we further prove that the limiting joint moments admit a representation in terms of a solution of the $\sigma$-Painlev\'e III$'$ equation for a certain range of moment exponents. As applications, we answer a question posed by Assiotis et al. in [Math. Physics. Anal. Geom. 25 (2022), no.2, Paper No. 15, 24pp, Remark 1.7] by showing that the characteristic function of a distinguished random variable is connected with the $\sigma$-Painlev\'e III$'$ equation for complex parameters. Furthermore, we investigate joint moments involving higher-order derivatives of characteristic polynomials in the Circular Jacobi Ensemble. As a consequence, we extend a result of Assiotis et al. in [Comm. Pure Appl. Math. 79 (2026), no. 7, 1771-1827, Theorem 1.11] concerning the joint moments of a sequence of random variables arising from the ergodic decomposition of Hua-Pickrell measures, from real parameters to complex parameters.

math-ph↗

arXiv2026

Private Direct Preference Optimization for LLM Alignment

Direct preference optimization (DPO) is now a standard method for aligning large language models (LLMs) using human preference data. Each DPO example contains a prompt and a pair of candidate model responses. While prompts and responses are often public or model-generated, the relative preference between responses reflects subjective judgments and can reveal sensitive attributes of annotators or end users. Off-the-shelf privacy-preserving approaches are not well matched to this structure, leading to unnecessary noise injection and biased updates in training. In this paper, we formalize preference privacy, a label-DP-style privacy notion for DPO that protects only the relative preference between candidate responses, assuming an adversary who already knows the prompt and responses. We then design PrivDPO, a DPO variant that enforces preference privacy while remaining compatible with large-scale LLM training. Our main observation is that, for neighboring examples differing only in their preference signal, the gradient difference lies on a one-dimensional preference axis determined solely by the text; all preference information flows through this axis. PrivDPO adds calibrated randomness only along this axis via an unbiased randomized rescaling of the DPO objective, avoiding per-example gradient operations. Our experiments on three alignment benchmarks and three LLM families show that PrivDPO consistently achieves strong privacy-utility trade-offs compared with privacy-preserving baselines.

cs.CR↗

arXiv2026

LongHorizon-Harness: Advancing Long-Horizon Agents for Real-World Tasks

Large language model (LLM) agents increasingly undertake long-horizon tasks that require sustained reasoning, tool use, and revision across many interdependent steps. However, existing agent harnesses maintain task execution, task state, and completion assessment within a growing context, making the state difficult to track and allowing incorrect self-assessments to propagate into later decisions. We reformulate long-horizon execution as a task-state management problem and propose LongHorizon-Harness, which maintains the task state explicitly outside execution and updates it only with facts independently verified from the environment. Its Manage-Execute-Audit(MEA) loop uses a manager to maintain the task state and determine the next subtask, a fresh-context executor to perform it, and a read-only auditor to verify the resulting environment state before the next round. A lightweight AgentAdapter supports interchangeable model and harness backends without modifying their native agent loops. LongHorizon-Harness improves Qwen~3.7-Plus from 51.8% to 80.7% on WeaveBench, from 69.7% to 77.2% on Terminal-Bench~2.1, and from 2.8% to 8.3% on OSWorld~2.0. It also raises Claude Opus~4.7 from 20.0% to 34.3% on an OSWorld2.0 subset, demonstrating consistent gains across models, harnesses, and interaction domains.

cs.CV↗

arXiv2026

Can a Robot Walk the Robotic Dog: Triple-Zero Collaborative Navigation for Heterogeneous Multi-Agent Systems

We present Triple Zero Path Planning (TZPP), a collaborative framework for heterogeneous multi-robot systems that requires zero training, zero prior knowledge, and zero simulation. TZPP employs a coordinator--explorer architecture: a humanoid robot handles task coordination, while a quadruped robot explores and identifies feasible paths using guidance from a multimodal large language model. We implement TZPP on Unitree G1 and Go2 robots and evaluate it across diverse indoor and outdoor environments, including obstacle-rich and landmark-sparse settings. Experiments show that TZPP achieves robust, human-comparable efficiency and strong adaptability to unseen scenarios. By eliminating reliance on training and simulation, TZPP offers a practical path toward real-world deployment of heterogeneous robot cooperation. Our code and video are provided at: https://github.com/triple-zeropp/Triple-zero-robot-agent

cs.RO↗

arXiv2026

A note on "Higher order linear differential equations for unitary matrix integrals: applications and generalisations"

In this note, we briefly introduce the background and motivation of the collaborative work [arXiv:2508.20797], and provide an outline of the main results. The latter relates to matrix and higher order scalar differential equations satisfied by certain Hankel and Toeplitz determinants involving I-Bessel functions, or equivalently certain unitary matrix integrals, and moreover puts this property in a broader context. We also investigate large gaps between zeros of the derivatives of the Hardy $\mathsf{Z}$-function, assuming the validity of a certain joint moments conjecture in random matrix theory.

math-ph↗

arXiv2026

Accurate Table Question Answering with Accessible LLMs

Given a table T in a database and a question Q in natural language, the table question answering (TQA) task aims to return an accurate answer to Q based on the content of T. Recent state-of-the-art solutions leverage large language models (LLMs) to obtain high-quality answers. However, most rely on proprietary, large-scale LLMs with costly API access, posing a significant financial barrier. This paper instead focuses on TQA with smaller, open-weight LLMs that can run on a desktop or laptop. This setting is challenging, as such LLMs typically have weaker capabilities than large proprietary models, leading to substantial performance degradation with existing methods. We observe that a key reason for this degradation is that prior approaches often require the LLM to solve a highly sophisticated task using long, complex prompts, which exceed the capabilities of small open-weight LLMs. Motivated by this observation, we present Orchestra, a multi-agent approach that unlocks the potential of accessible LLMs for high-quality, cost-effective TQA. Orchestra coordinates a group of LLM agents, each responsible for a relatively simple task, through a structured, layered workflow to solve complex TQA problems -- akin to an orchestra. By reducing the prompt complexity faced by each agent, Orchestra significantly improves output reliability. We implement Orchestra on top of AgentScope, an open-source multi-agent framework, and evaluate it on multiple TQA benchmarks using a wide range of open-weight LLMs. Experimental results show that Orchestra achieves strong performance even with small- to medium-sized models. For example, with Qwen2.5-14B, Orchestra reaches 72.1% accuracy on WikiTQ, approaching the best prior result of 75.3% achieved with GPT-4; with larger Qwen, Llama, or DeepSeek models, Orchestra outperforms all prior methods and establishes new state-of-the-art results across all benchmarks.

cs.DB↗

arXiv2025

Asymptotic analysis of a Family of Painlev\'e Functions with Applications to CUE Derivative Moments

The Riemann-Hilbert method is employed to carry out an asymptotic analysis of a family of $\sigma$-Painlev\'e V functions associated with Hankel determinants involving the confluent hypergeometric function of the second kind. In the large-matrix limit, this family degenerates to a family of $\sigma$-Painlev\'e III$'$ functions, whose precise asymptotic behavior is also obtained. Both families of Painlev\'e functions arise in the study of the joint moments of the derivative of the characteristic polynomial of a CUE random matrix and the polynomial itself, whose asymptotics are closely related to the moments of the Riemann zeta function and the Hardy $\mathsf{Z}$-function on the critical line. One of our main results establishes a representation of the leading coefficients of these joint moments in terms of $\sigma$-Painlev\'e III$'$ functions for general real exponents. The other main result resolves a question of Assiotis et al. in [Probab. Math. Physics. 2(2021), 613-642, Remark 2.5] concerning the existence of a probability density for a random variable arising in the ergodic decomposition of Hua-Pickrell measures.

math-ph↗

arXiv2025

AdaCuRL: Adaptive Curriculum Reinforcement Learning with Invalid Sample Mitigation and Historical Revisiting

Reinforcement learning (RL) has demonstrated considerable potential for enhancing reasoning in large language models (LLMs). However, existing methods suffer from Gradient Starvation and Policy Degradation when training directly on samples with mixed difficulty. To mitigate this, prior approaches leverage Chain-of-Thought (CoT) data, but the construction of high-quality CoT annotations remains labor-intensive. Alternatively, curriculum learning strategies have been explored but frequently encounter challenges, such as difficulty mismatch, reliance on manual curriculum design, and catastrophic forgetting. To address these issues, we propose AdaCuRL, a Adaptive Curriculum Reinforcement Learning framework that integrates coarse-to-fine difficulty estimation with adaptive curriculum scheduling. This approach dynamically aligns data difficulty with model capability and incorporates a data revisitation mechanism to mitigate catastrophic forgetting. Furthermore, AdaCuRL employs adaptive reference and sparse KL strategies to prevent Policy Degradation. Extensive experiments across diverse reasoning benchmarks demonstrate that AdaCuRL consistently achieves significant performance improvements on both LLMs and MLLMs.

cs.LG↗

arXiv2025

Grounded in Reality: Learning and Deploying Proactive LLM from Offline Logs

Large Language Models (LLMs) excel as passive responders, but teaching them to be proactive, goal-oriented partners, a critical capability in high-stakes domains, remains a major challenge. Current paradigms either myopically optimize single-turn attributes or rely on brittle, high-cost user simulators, creating a persistent ``reality gap''. To bridge this gap, we introduce \texttt{Learn-to-Ask}, a general, simulator-free framework for learning and deploying proactive dialogue agents \textit{directly from offline expert data}, bypassing the need to model complex user dynamics. Our key insight is to reframe the offline policy learning problem by leveraging the \textbf{observed future} of each expert trajectory. This allows us to infer a dense, turn-by-turn reward signal grounded in the expert's revealed strategy, decomposing the intractable long-horizon problem into a series of supervised learning tasks, and training a policy to output a structured \texttt{(action, state_assessment)} tuple, governing both \textbf{what to ask} and, crucially, \textbf{when to stop}. To ensure reward fidelity, our Automated Grader Calibration pipeline systematically purges noise from the LLM-based reward model with minimal human supervision. Empirically, we demonstrate the efficacy of \texttt{Learn-to-Ask} in a real-world medical dataset, using LLMs of varying sizes up to 32B. Our approach culminates in the successful deployment of LLMs into a live, large-scale online AI service. In rigorous in-house evaluations, our model was launched and achieved performance even superior to human experts, proving our framework's ability to translate offline data into tangible, real-world impact. We hope this work provides a practical and economically viable blueprint for transforming passive LLMs into proactive, goal-oriented LLM applications.

cs.CL↗

arXiv2025

Higher-Order Linear Differential Equations for Unitary Matrix Integrals: Applications and Generalisations

In this paper, we consider characterisations of the class of unitary matrix integrals $\big\langle (\det U)^q {\rm e}^{s^{1/2} \operatorname{Tr}(U + U^\dagger)} \big\rangle_{U(l)}$ in terms of a first-order matrix linear differential equation for a vector function of size $l+1$, and in terms of a scalar linear differential equation of degree ${l+1}$. It will be shown that the latter follows from the former. The matrix linear differential equation provides an efficient way to compute the power series expansion of the matrix integrals, which with $q=0$ and $q=l$ are of relevance to the enumeration of longest increasing subsequences for random permutations, and to the question of the moments of the first and second derivative of the Riemann zeta function on the critical line, respectively. This procedure is compared against that following from known characterisations involving the $\sigma$-Painlev&\'e III$'$ second-order nonlinear differential equation. We show too that the natural $\beta$ generalisation of the unitary group integral permits characterisation by the same classes of linear differential equations.

math-ph↗

arXiv2025

Joint Moments of Characteristic Polynomials from the Orthogonal and Unitary Symplectic Groups

We establish asymptotic formulae for general joint moments of characteristic polynomials and their higher-order derivatives associated with matrices drawn randomly from the groups $\mathrm{USp}(2N)$ and $\mathrm{SO}(2N)$ in the limit as $N\to\infty$. This relates the leading-order asymptotic contribution in each case to averages over the Laguerre ensemble of random matrices. We uncover an exact connection between these joint moments and a solution of the $\sigma$-Painlev\'{e} V equation, valid for finite matrix size, as well as a connection between the leading-order asymptotic term and a solution of the $\sigma$-Painlev\'{e} III$'$ equation in the limit as $N \rightarrow \infty$. These connections enable us to derive exact formulae for joint moments for finite matrix size and for the joint moments of certain random variables arising from the Bessel point process in a recursive way. As an application, we provide a positive answer to a question proposed by Altu\u{g} et al.

math-ph↗

arXiv2025

UPRE: Zero-Shot Domain Adaptation for Object Detection via Unified Prompt and Representation Enhancement

Zero-shot domain adaptation (ZSDA) presents substantial challenges due to the lack of images in the target domain. Previous approaches leverage Vision-Language Models (VLMs) to tackle this challenge, exploiting their zero-shot learning capabilities. However, these methods primarily address domain distribution shifts and overlook the misalignment between the detection task and VLMs, which rely on manually crafted prompts. To overcome these limitations, we propose the unified prompt and representation enhancement (UPRE) framework, which jointly optimizes both textual prompts and visual representations. Specifically, our approach introduces a multi-view domain prompt that combines linguistic domain priors with detection-specific knowledge, and a visual representation enhancement module that produces domain style variations. Furthermore, we introduce multi-level enhancement strategies, including relative domain distance and positive-negative separation, which align multi-modal representations at the image level and capture diverse visual representations at the instance level, respectively. Extensive experiments conducted on nine benchmark datasets demonstrate the superior performance of our framework in ZSDA detection scenarios. Code is available at https://github.com/AMAP-ML/UPRE.

cs.CV↗

arXiv2025

AutoMat: Enabling Automated Crystal Structure Reconstruction from Microscopy via Agentic Tool Use

Reconstructing atomistic crystal structures from a single noisy STEM projection is an ill-posed inverse problem: multiple lattices can explain similar contrast, and purely feed-forward models cannot verify physical validity. We present AutoMat, a failure-aware agentic controller that performs inference-time hypothesis search with closed-loop verification to convert Scanning Transmission Electron Microscopy (STEM) images into simulation-ready crystal structures and downstream properties. AutoMat composes perception and physics modules---pattern-adaptive denoising, physics-guided template retrieval as a state-dependent auxiliary branch, symmetry-constrained atomic reconstruction, and MLIP-based relaxation/validation---and triggers rollback-and-retry when verification fails. For systematic evaluation, we introduce STEM2Mat-Bench, a benchmark dataset containing 450+ annotated samples. Performance is assessed using lattice root-mean-square deviation (RMSD), formation energy mean absolute error (MAE), and structure matching accuracy. Results demonstrate that AutoMat outperforms existing approaches including SOTA models, specialized domain tools, and closed-source multimodal large models. This work establishes a direct pathway from microscopic characterization to atomic-scale modeling, addressing a fundamental challenge in materials science.

cs.CV↗

arXiv2025

GPG: A Simple and Strong Reinforcement Learning Baseline for Model Reasoning

Reinforcement Learning (RL) can directly enhance the reasoning capabilities of large language models without extensive reliance on Supervised Fine-Tuning (SFT). In this work, we revisit the traditional Policy Gradient (PG) mechanism and propose a minimalist RL approach termed Group Policy Gradient (GPG). Unlike conventional methods, GPG directly optimize the original RL objective, thus obviating the need for surrogate loss functions. By eliminating the critic and reference models, avoiding KL divergence constraints, and addressing the advantage and gradient estimation bias, our approach significantly simplifies the training process compared to Group Relative Policy Optimization (GRPO). Our approach achieves superior performance without relying on auxiliary techniques or adjustments. As illustrated in Figure 1, extensive experiments demonstrate that our method not only reduces computational costs but also consistently outperforms GRPO across various unimodal and multimodal tasks. Our code is available at https://github.com/AMAP-ML/GPG.

cs.LG↗

arXiv2025

Towards Anthropomorphic Conversational AI Part I: A Practical Framework

Large language models (LLMs), due to their advanced natural language capabilities, have seen significant success in applications where the user interface is usually a conversational artificial intelligence (AI) agent and engages the user through multi-round conversations. However, many scenarios require the agents to exhibit stronger social and conversational intelligence and demonstrate more human-like (anthropomorphic) reactions. This is an aspect that foundational LLMs have yet to fully address such that a single call of foundational models might be insufficient. To bridge this gap, we propose a two-stage solution. In this work, we focus on the first stage, introducing a multi-module framework designed to replicate the key aspects of human intelligence involved in conversations. This framework comprises thinking modules for reasoning, resource modules for managing knowledge and external information, and response modules for generating contextually appropriate interactions. With all the modules cooperating, the framework would empower the agents to provide a better human-like conversation experience. In the second stage of our approach, these conversational data, after filtering and labeling, can serve as training and testing data for reinforcement learning, enabling AI to better capture human preferences. This stage is left for future work. In our experiments, volunteers engaged in over 3000 rounds of conversation with the same AI character powered by a standalone LLM and our framework which integrates the same LLM. A separate group of evaluators rated the conversation samples, revealing that our framework significantly enhanced the social and conversational intelligence, even without fine-tuning the LLM.

cs.CL↗

arXiv2025

KIMAs: A Configurable Knowledge Integrated Multi-Agent System

Knowledge-intensive conversations supported by large language models (LLMs) have become one of the most popular and helpful applications that can assist people in different aspects. Many current knowledge-intensive applications are centered on retrieval-augmented generation (RAG) techniques. While many open-source RAG frameworks facilitate the development of RAG-based applications, they often fall short in handling practical scenarios complicated by heterogeneous data in topics and formats, conversational context management, and the requirement of low-latency response times. This technical report presents a configurable knowledge integrated multi-agent system, KIMAs, to address these challenges. KIMAs features a flexible and configurable system for integrating diverse knowledge sources with 1) context management and query rewrite mechanisms to improve retrieval accuracy and multi-turn conversational coherency, 2) efficient knowledge routing and retrieval, 3) simple but effective filter and reference generation mechanisms, and 4) optimized parallelizable multi-agent pipeline execution. Our work provides a scalable framework for advancing the deployment of LLMs in real-world settings. To show how KIMAs can help developers build knowledge-intensive applications with different scales and emphases, we demonstrate how we configure the system to three applications already running in practice with reliable performance.

cs.AI↗

arXiv2025

Talk to Right Specialists: Iterative Routing in Multi-agent Systems for Question Answering

Retrieval-augmented generation (RAG) agents are increasingly deployed to answer questions over local knowledge bases that cannot be centralized due to knowledge-sovereignty constraints. This results in two recurring failures in production: users do not know which agent to consult, and complex questions require evidence distributed across multiple agents. To overcome these challenges, we propose RIRS, a training-free orchestration framework to enable a multi-agent system for question answering. In detail, RIRS summarizes each agent's local corpus in an embedding space, enabling a user-facing server to route queries only to the most relevant agents, reducing latency and avoiding noisy "broadcast-to-all" contexts. For complicated questions, the server can iteratively aggregate responses to derive intermediate results and refine the question to bridge the gap toward a comprehensive answer. Extensive experiments demonstrate the effectiveness of RIRS, including its ability to precisely select agents and provide accurate responses to single-hop queries, and its use of an iterative strategy to achieve accurate, multi-step resolutions for complex queries.

cs.MA↗

arXiv2024

On moments of the derivative of CUE characteristic polynomials and the Riemann zeta function

We study the derivative of the characteristic polynomial of $N \times N$ Haar distributed unitary matrices. We obtain the first explicit formulae for complex-valued moments when the spectral variable is inside the unit disc, in the limit $N \to \infty$. These formulae are expressed in terms of the confluent hypergeometric function of the first kind. As an application, we provide an alternative method to re-obtain Mezzadri's result [J. Phys. A, 36(12):2945-2962, 2003] on the asymptotic density of zeros of the derivative as $N \to \infty$. We explore the connection between these moments and those of the derivative of the Riemann zeta function away from the critical line. Under the Lindel\"of hypothesis, we prove that all positive integer moments agree with our random matrix results up to an arithmetic factor. Inspired by this finding, we propose a conjecture on the asymptotics of non-integer moments of the derivative of the Riemann zeta function off the critical line. Within random matrix theory, we also investigate the microscopic regime where the spectral variable $z$ satisfies $|z|^{2}=1-\frac{c}{N}$ for a fixed constant $c$. We obtain an asymptotic formula for the moments in this regime as a determinant involving the finite temperature Bessel kernel, which reduces to the Bessel kernel when $c=0$. For finite matrix size, we provide an exact formula for the moments of the derivative inside the unit disc, expressed as polynomials of the inverse of the distance from the circle, with coefficients given by combinatorial sums.

math.PR↗