arXiv subjects

Kun Chen

Publications and source records attributed to Kun Chen.

At least 37 records · Page 2Linked to original sources

arXiv2026

Residual bounds for Schur-stable polynomials

Let $r_n$ be the infimum of \[ \frac{\lVert P'-P'(0)P\rVert_{H^2}}{\lVert P\rVert_{H^2}} \] over all degree-$n$ polynomials $P$ satisfying $P(0)=1$ whose zeros lie in the closed unit disk. We prove the quantitative residual bound \[ r_n\geq \exp\!\bigl(-(1+o(1))\sqrt n\log n\bigr) \qquad(n\to\infty). \] As an application, we answer Erdős Problem 973 on exterior power sums in the negative, in a form quantitatively stronger than the answer first obtained by Luo, Yang, and Zhu.

math.CV↗

arXiv2026

Complementary Quantum Correlations Are Universal for Qubits

Extracting total correlations from a quantum system usually requires reconstructing its state, whereas many experiments access only a few measurement settings. A possible shortcut is to add the mutual informations obtained from complementary measurements; in dimensions above two, however, this procedure can count the same classical correlation twice. We establish that qubits are protected from such overcounting. For every two-qubit state, the correlations observed in two complementary local bases are bounded by the premeasurement quantum mutual information. The proof traces this protection to binary-entropy curvature on the Bloch ball and combines a qubit information-exclusion tradeoff with data processing under local dephasing. Consequently, two correlation tables give a tomography-free lower bound on total correlation. A score above one bit also certifies a quantitative one-way entanglement-distillation rate; when applied to the Choi state of a qubit channel, the same data lower bound its quantum capacity. The theorem therefore identifies both an operational use of complementarity and the trusted two-dimensional setting in which its correlation accounting is valid.

quant-ph↗

arXiv2026

SciCode-Verified: How Benchmark Defects Underestimated the Scientific-Coding Ability of Language Models

SciCode is the standard measure of the scientific-coding ability of language models: research-level problems that demand both frontier scientific theory and its implementation as working numerical code. It is a component of the Artificial Analysis Intelligence Index and a standing evaluation in government and national-laboratory suites. Yet its scores have recently plateaued: the strongest 2026 models cluster tightly around 60\% subproblem accuracy, and a successor model ties its predecessor. We trace this stagnation to defects in the benchmark itself. A per-problem, domain-expert audit of all 65 test problems uncovers 263 defects; 192 of them, spread across 91\% of the main problems, cause correct, instruction-following solutions to be wrongly rejected---through non-reproducible gold answers, over-tight tolerances, or self-contradictory specifications. Critically, 78\% of these score-suppressing defects require specialized physics or mathematics knowledge to detect, not mere clerical proofreading. We corrected every confirmable defect to produce SciCode-Verified. The corrections add only the specifications a well-posed problem requires, repair grading, and tighten the tests that were too lenient; every change is recorded with its justification and independently re-checked by a second domain expert. We re-evaluate twelve frontier model snapshots on the corrected benchmark and find a substantial recovery: subproblem accuracy rises from 45--60\% to 84--98\%, and main-problem accuracy from 9--27\% to 69--92\%. State-of-the-art models are far more proficient in scientific coding than SciCode has suggested---the bottleneck was not model capability, but the quality of the evaluation instrument. We release SciCode-Verified with its complete audit trail as the corrected public standard.

cs.SE↗

arXiv2026

Dissecting Microbial Community Structure and Heterogeneity via Multivariate Covariate-Adjusted Clustering

In microbiome studies, it is often of great interest to identify clusters or partitions of microbiome profiles within a study population and to characterize the distinctive attributes of each resulting microbial community. While raw counts or relative compositions are commonly used for such analysis, variations between clusters may be driven or distorted by subject-level covariates, reflecting underlying biological and clinical heterogeneity across individuals. Simultaneously detecting latent communities and identifying covariates that differentiate them can enhance our understanding of the microbiome and its association with health outcomes. To this end, we propose a Dirichlet-multinomial mixture regression (DMMR) model that enables joint clustering of microbiome profiles while accounting for covariates with either homogeneous or heterogeneous effects across clusters. A novel symmetric link function is introduced to facilitate covariate modeling through the compositional parameters. We develop efficient algorithms with convergence guarantees for parameter estimation and establish theoretical properties of the proposed estimators. Extensive simulation studies demonstrate the effectiveness of the method in clustering, feature selection, and heterogeneity detection. We illustrate the utility of DMMR through a comprehensive application to upper-airway microbiota data from a pediatric asthma study, uncovering distinct microbial subtypes and their associations with clinical characteristics.

stat.ME↗

arXiv2026

PCGD: Physics-Guided Conditional Graph Diffusion for TCAD Device Simulation

Technology computer-aided design (TCAD) semiconductor device simulation is fundamentally constrained by the high computational cost of iteratively solving coupled drift-diffusion equations. Existing ML surrogates either reduce internal physics to macroscopic scalar regressions, or rely on single-step mappings that lack the iterative refinement required to resolve stiff, coupled fields. To address this, we introduce PCGD, a Physics-Guided Conditional Graph Diffusion framework operating natively on unstructured TCAD meshes to predict coupled electrostatic and carrier density fields. PCGD employs a Condition-Aware MeshGraphNet denoiser that explicitly injects boundary conditions and device structure context via global cross-attention. By augmenting data-driven denoising with a physics-guided hybrid objective that integrates exponent-free quasi-Fermi gradient matching with noise-aware PDE residuals, PCGD progressively enforce physical constraints in the iterative diffusion trajectory. This strategy successfully bypasses the numerical instabilities typical of stiff drift-diffusion equations. Evaluated on a challenging mixed PN/MOS benchmark, PCGD significantly outperforms deterministic one-step regression (1.207% error) and local diffusion (1.585% error) baselines by achieving a sub-percent mean relative field error of 0.835%, while concurrently reducing maximum PDE residual errors by nearly three orders of magnitude compared to pure diffusion. It also transfers robustly to unseen SOI topologies (0.815% error) via LoRA adaptation, using 5.30$\times$ less data and 14.34$\times$ fewer parameters than full fine-tuning. Ultimately, PCGD bridges the computational efficiency of generative surrogates with the rigorous physical fidelity of traditional TCAD, unlocking highly scalable, field-level analysis for robust device engineering.

cs.LG↗

arXiv2026

Perturbative Renormalization and Universality Diagram for Long-Range Quantum Criticality

Experimental progress in quantum simulators highlights the role of long-range (LR) interactions in reshaping quantum criticality and stabilizing exotic phases beyond the short-range (SR) paradigm. We study ferromagnetic long-range quantum $O(n)$ models with interactions decaying as $1/r^{d+σ}$ and develop a perturbative renormalization-group expansion around the LR--SR boundary by setting $d=3-ε$ and $σ=2-δ$. In this parametrization, the full interacting LR window $2d/3<σ<2$ becomes $0<δ<2ε/3$, and is therefore perturbatively controlled. A two-loop calculation yields explicit expressions, in terms of $ε$, $δ$, and $n$, for the correlation-length exponent $ν$ and for the frequency and momentum anomalous dimensions $η_ω$ and $η_k$. The resulting exponents reduce to long-range Gaussian scaling at $σ=2d/3$ and to SR quantum Wilson-Fisher scaling in the $σ\to 2$ limit, thereby identifying $σ_*=2$ as the LR--SR boundary within the controlled $3-ε$ expansion. Combining the RG results with scaling boundaries and classical LR analogies, we propose a $(d,σ)$ universality diagram for ferromagnetic long-range quantum $O(n)$ criticality and use it as an organizing framework for the phase diagram of long-range quantum spin chains.

cond-mat.stat-mech↗

arXiv2026

Two-Electron Correlations in the Metallic Electron Gas

We present high-precision \emph{ab initio} calculations of the four-point vertex function for the three-dimensional uniform electron gas using variational diagrammatic Monte Carlo. From these results, we extract Landau parameters that reveal a density-driven crossover from underscreening to overscreening, and obtain the full two-electron scattering amplitude on the Fermi surface with controlled accuracy. A residual analysis of the scattering amplitude against the charge-channel Kukkonen--Overhauser (KO$^+$) interaction shows that only a minimal s-wave correction in the antiparallel-spin channel is needed, defining the sKO$^+$ ansatz: KO$^+$ within the local-density approximation plus this short-range correction. Using both our direct VDMC amplitudes and the sKO$^+$ ansatz, we compute the electron-electron contribution to the thermal resistivity, obtaining quantitative agreement with experiments on simple metals (Al, Na, K, Rb). sKO$^+$ thus provides a controlled UEG-based effective interaction for simple-metal transport and future first-principles extensions.

cond-mat.str-el↗

arXiv2026

Guidelines for the Annotation and Visualization of Legal Argumentation Structures in Chinese Judicial Decisions

This Guideline presents a systematic and operationalizable annotation framework for representing legal argumentation structures in judicial decisions. Grounded in theories of legal reasoning and argumentation, the framework aims to reveal the logical organization of judicial reasoning and provide a reliable foundation for computational analysis. At the element level, the Guideline distinguishes between the non-propositional layer and the propositional layer. The non-propositional layer consists of two elements: Issue and Non-argumentative Component. At the propositional level, the Guideline defines four proposition types: General Normative Judgment, Particular Normative Judgment, General Factual Judgment, and Particular Factual Judgment. At the relational level, five relation types are defined to represent argumentative structures: Support, Attack, Joint, Match, and Identity. These relations capture positive and negative argumentative connections, conjunctive reasoning structures, correspondences between legal norms and case facts, and identity or semantic equivalence between propositions. The Guideline further specifies formal representation rules and visualization conventions for both basic and nested structures, enabling consistent visualization of complex argumentation patterns. In addition, it establishes a standardized annotation workflow and consistency control mechanisms to ensure the reproducibility and reliability of annotated data. By providing a clear conceptual model, formal representation rules, and practical annotation procedures, this Guideline supports large-scale analysis of judicial reasoning and future research in legal argument mining, computational modeling of legal reasoning, and AI-assisted legal analysis.

cs.CL↗

arXiv2026

Universality for Products of Random Matrices with i.i.d. Entries and the Fuss--Catalan Number

Let $(w_{ij})_{i,j\ge1}$ be a single infinite array of independent identically distributed real- or complex-valued entries of mean zero, variance $σ^2$, and finite fourth moment. Set $W_n=(w_{ij})_{1\le i,j\le n}$ and $X_n=n^{-1/2}W_n$. For every fixed $k\ge1$, we identify the almost sure limiting operator norm of several fixed products built from this family. Define the $k$-th freeness coefficient by \[ γ_k:=\sqrt{\frac{(k+1)^{k+1}}{k^k}}. \] Then we prove \[ \|X_n^k\|\toσ^kγ_k \qquad \text{almost surely}. \] The same limit holds for products sampled with replacement from any fixed finite pool of independent copies of $X_n$; in particular, it holds for the product of $k$ independent copies. Thus, the freeness coefficient captures the non-commuting characteristic between large random matrices %powers and independent or fixed-pool sampled products under the finite fourth moment assumption. The improvement of the classical Bai--Yin-type power estimate from the scale $σ^k(k{+}1)$ to $σ^k \sqrt{k{+}1}$ is a direct corollary of our result. The main technical challenge is to prove the upper bound using a high-moment expansion of %the upper bound is proved by a high-moment expansion of $\E\Tr((X_n^kX_n^{*k})^m)$. The leading zero-defect trace words are tree-like and are counted by the Fuss--Catalan number \[ F_{k,m}= \frac1{km+1}\binom{(k+1)m}{m}. \] The combinatorial tool helps to devise a defect-sensitive global enumeration: if $L=km$ and \[ r=(L+1-v)+(L-q), \] then the number of admissible word classes with defect $r$ is at most $F_{k,m}(Cm)^{Dr}$. This polynomial-in-$m$ loss, with degree proportional to the defect, is summable in the logarithmic moment range.

math.ST↗

arXiv2026

Harnessing Source Heterogeneity for Cluster-Structured Transfer Learning

Transfer learning is a natural strategy when a target population has limited data but multiple related auxiliary sources are available. A central difficulty is source heterogeneity: auxiliary sources may not be equally useful, and their usefulness may vary in a structured, cluster-like fashion. Existing transfer-learning methods often reduce source selection to a binary informative/non-informative decision, overlooking subgroups of sources with differential transferability. Motivated by a suicide-risk study using data from the Connecticut Hospital Information Management Exchange (CHIME), comprising 636,758 patients across 27 hospitals, we propose Trans-GLMC, a cluster-structured transfer-learning procedure for generalized linear models. The CHIME setting illustrates the core challenge: hospital-specific risk models are unstable because suicide attempts are rare at any single facility, whereas indiscriminate pooling across hospitals can obscure facility-level differences in patient mix and risk profiles. Trans-GLMC first constructs a coefficient-based distance among the target and candidate sources to recover latent source clusters. It then combines global fusion, within-cluster refinement, and target debiasing to produce an estimator that adapts to the detected structure. We establish a non-asymptotic error bound that improves over its unclustered counterpart whenever a meaningful target cluster exists and matches the unclustered rate up to constants otherwise. In simulations and in the CHIME study, Trans-GLMC improves facility-specific prediction, identifies interpretable communities of hospitals with mutual transferability, and recovers clinically coherent suicide-risk factors.

stat.ML↗

arXiv2026

Scalable Counterfactual Risk Estimation for Rare Events in Longitudinal Data

Estimating the causal effect of time-varying treatments on survival outcomes in large observational studies is computationally demanding, particularly when outcomes are rare. While g-formula-based methods such as the iterative conditional expectation (ICE) estimator provide a principled framework for longitudinal causal inference, they become computationally expensive, especially when bootstrap-based variance estimation is required. In addition, outcome rarity at each time point induces severe class imbalance, leading to instability and convergence issues in logistic regression and related models. To address these challenges, we propose a principled subsampling and reweighting strategy for longitudinal survival data that can be applied to a range of existing causal effect estimators in this setting, including the ICE estimator. The proposed method substantially reduces computational burden while preserving consistency and improving estimation stability in rare-outcome settings. We evaluate the method through simulations and validate it using a large-scale EHR cohort study on social and behavioral determinants of health (SBDH) and suicide risk, demonstrating its effectiveness for modeling rare outcomes in longitudinal data.

stat.ME↗

arXiv2026

PuzzleClone: A DSL-Powered Framework for Synthesizing Verifiable Data

High-quality mathematical and logical datasets with verifiable answers are essential for strengthening the reasoning capabilities of large language models (LLMs). While recent data augmentation techniques have facilitated the creation of large-scale benchmarks, existing LLM-generated datasets often suffer from limited reliability, diversity, and scalability. To address these challenges, we introduce PuzzleClone, a formal framework for synthesizing verifiable data at scale using a novel DSL-driven approach. Our approach features three key innovations: (1) encoding seed puzzles into structured logical specifications, (2) generating scalable variants through systematic variable and constraint randomization, and (3) ensuring validity via a reproduction mechanism. Applying PuzzleClone, we construct PC-83K, a benchmark comprising over 83K diverse and programmatically validated puzzles. The generated puzzles span a wide spectrum of difficulty and formats, posing significant challenges to current state-of-the-art models. Experimental results show that post training (SFT and RL) on PC-83K yields substantial improvements not only on the testset but also on various logic and mathematical benchmarks. Post training raises average performance on PC-83K from 14.5 to 66.0 and delivers consistent improvements across 7 logic and mathematical benchmarks up to 18.4 absolute percentage points (SATBench from 51.6 to 70.0). Our code and data are available at https://github.com/HiThink-Research/PuzzleClone.

cs.AI↗

arXiv2026

APEX-Searcher: Refining Credit Assignment with Subgoaling for Agentic Retrieval-Augmented Generation

Retrieval-augmented generation (RAG) connects large language models (LLMs) to external knowledge, but single-round retrieval is often insufficient for complex multi-hop questions. To enhance search capabilities for complex tasks, most existing works integrate multi-round iterative retrieval with reasoning processes via end-to-end training. While these approaches improve problem-solving performance, they still face challenges in task reasoning and model training, especially ambiguous retrieval execution paths and sparse rewards in end-to-end reinforcement learning (RL), which can lead to inaccurate retrieval results and lower performance. We attribute these failures to hierarchical credit entanglement: a single final reward updates planning and execution together, so the model cannot clearly separate plan errors from retrieval errors. We propose APEX-Searcher, which uses a Refining Credit Assignment paradigm: planning is optimized by RL with a plan-level reward, while execution is learned by SFT. Extensive experiments show consistent gains in both multi-hop RAG and task planning across benchmarks.

cs.CL↗

arXiv2026

Scientific Logicality Enriched Methodology for LLM Reasoning: A Practice in Physics

With the continuous advancement of reasoning abilities in Large Language Models (LLMs), their application to scientific reasoning tasks has gained significant research attention. Current research primarily emphasizes boosting LLMs' performance on scientific QA benchmarks by training on larger, more comprehensive datasets with extended reasoning chains. However, these approaches neglect the essence of the scientific reasoning process -- logicality, which is the rational foundation to ensure the validity of reasoning steps leading to reliable conclusions. In this work, we make the first systematic investigation into the internal logicality underlying LLM scientific reasoning, and develop a scientific logicality-enriched methodology, including a set of assessment criteria and data sampling methods for logicality-guided training, to improve the logical faithfulness as well as task performance. Further, we take physics, characterized by its diverse logical structures and formalisms, as an exemplar discipline to practise the above methodology. For data construction, we extract scientific problems from academic literature and sample a high-quality dataset exhibiting strong logicality. Experiments based on three different backbone LLMs reveal that: 1) the training data we constructed can effectively improve the scientific logicality in LLM reasoning; and 2) the enriched scientific logicality plays a critical role in solving scientific problems. Code is available at \href{https://github.com/ScienceOne-AI/PhysLogic}{https://github.com/ScienceOne-AI/PhysLogic}.

cs.AI↗

arXiv2026

A Persistence-Aware Framework for Age Violation Control in Wireless Status Update Systems

Timely and reliable status updates are essential for emerging QoS-sensitive wireless applications. Common age of information (AoI)-based metrics, such as average AoI and age violation rate (AVR), characterize time-averaged freshness or violation frequency but do not explicitly capture the temporal persistence of consecutive age violations, which can be critical in safety-sensitive wireless applications. We develop a persistence-aware reliability framework based on the consecutive age violation rate (C-AVR) vector, whose components quantify AoI threshold violations over consecutive time windows of different lengths. Through flexible weighting schemes, the proposed framework unifies reliability objectives ranging from average persistence to tail-sensitive performance. Optimizing weighted C-AVR objectives is challenging because consecutive violations are temporally correlated, leading to sparse learning signals. To address this issue, we develop a distributional reinforcement learning approach based on a quantile regression dueling double deep Q-network (QR-D3QN). By modeling a quantile-based return distribution rather than only a scalar expected return, QR-D3QN provides richer value-estimation signals for rare but prolonged violation sequences under stochastic packet arrivals, unreliable channels, and transmission cost constraints. Simulation results show that QR-D3QN consistently outperforms expectation-based baselines across a wide range of weighting schemes and system settings, with particularly significant gains under tail-sensitive persistence objectives. Component-wise analysis further shows that distributional value learning substantially improves reliability across multiple persistence scales, especially for long consecutive violation sequences. Overall, our results establish the proposed C-AVR framework as an effective foundation for persistence-aware reliability evaluation.

cs.NI↗

arXiv2026

Decentralized Heterogeneous Multi-Robot Collaborative Exploration for Indoor and Outdoor 3D Environments

Heterogeneous multi-robot systems feature significant adaptability for complex environments. However, effective collaboration that fully exploits the robots' potential remains a core challenge. This paper proposes a decentralized collaborative framework for heterogeneous multi-robot systems to autonomously explore indoor and outdoor 3D environments. First, a basic perception map that integrates terrain and observation metrics is designed. Improved supervoxel segmentation is developed to simplify the map structure and form a high-level representation that supports lightweight communication. Second, the traversal and observation capabilities of heterogeneous robots are modeled to evaluate the requirements of task views derived from incomplete supervoxels. These task views are grouped by requirements and clustered to streamline assignment. Subsequently, the view-cluster assignment is formulated as a heterogeneous multi-depot multi-traveling salesman problem (HMDMTSP) that incorporates constraints between view-cluster requirements and robot capabilities. An improved genetic algorithm is developed to efficiently solve this problem while ensuring global consistency. Based on the assignments, redundant views within clusters are eliminated to refine exploration routes. Finally, conflicts between robots' motion paths are resolved. Simulations and field experiments in cluttered indoor and outdoor environments demonstrate that our approach effectively coordinates exploration tasks among heterogeneous robots, achieving superior exploration efficiency and communication savings compared to state-of-the-art approaches.

cs.RO↗

arXiv2026

Flexible Entropy Control in RLVR with a Gradient-Preserving Perspective

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a critical method for enhancing the reasoning capabilities of Large Language Models (LLMs). However, continuous training often leads to policy entropy collapse, characterized by a rapid decay in entropy that results in premature overconfidence, reduced output diversity, and vanishing gradient norms that inhibit learning. Gradient-Preserving Clipping is a primary factor influencing these dynamics, but existing mitigation strategies are largely static and lack a framework connecting clipping mechanisms to precise entropy control. This paper proposes reshaping entropy control in RL from the perspective of Gradient-Preserving Clipping. We first theoretically and empirically verify the contributions of specific importance sampling ratio regions to entropy growth and reduction. Leveraging these findings, we introduce a novel regulation mechanism using dynamic clipping thresholds to precisely manage entropy. Furthermore, we design and evaluate dynamic entropy control strategies, including increase-then-decrease, decrease-increase-decrease, and oscillatory decay. Experimental results demonstrate that these strategies effectively mitigate entropy collapse and achieve superior performance across multiple benchmarks.

cs.LG↗

arXiv2026

Emergent Slow Thinking in LLMs as Inverse Tree Freezing

Reinforcement learning with verifiable rewards (RLVR) enables large language models to acquire slow, multi-step reasoning from sparse final-answer signals. We provide a statistical-physics picture of this emergence. We show that an autoregressive model's finite capacity forces it to compress its exponentially large prefix space into a Markov network of predictive states, on which slow thinking unfolds as a random walk -- the Concept Network (CoNet) picture. Within CoNet, RLVR dynamics are governed by two mechanisms: merging of compatible paths and frustrated competition among incompatible ones. Together they drive the network through nucleation, growth, and freezing into multi-input, single-output directed inverse trees. The picture reproduces the training dynamics of a 1.5-billion-parameter LLM and yields three predictions: reasoning chains lengthen as a geometric necessity of sparse topology; SFT induces catastrophic forgetting through bridge-node rupture; and frustration drives policy collapse. Building on the structural timing inherent in inverse-tree freezing, we propose Annealed-RLVR -- a brief SFT intervention at the moment of maximum frustration. It outperforms standard RLVR on both in- and out-of-distribution benchmarks, with the largest gains at high sampling budgets where standard RLVR collapses. The same SFT applied after the trees freeze instead triggers catastrophic forgetting, isolating timing as the active ingredient.

cs.AI↗