arXiv subjects

Wei Xie

Publications and source records attributed to Wei Xie.

At least 19 recordsLinked to original sources

arXiv2026

Variance Reduction Based Experience Replay for Policy Optimization

Effective reinforcement learning (RL) for complex stochastic systems requires leveraging historical data to improve sample efficiency and accelerate policy optimization. However, classical experience replay treats all past observations uniformly and fails to account for their varying contributions to learning. To address this limitation, we propose Variance Reduction Experience Replay (VRER), a principled framework that selectively reuses informative samples to reduce the variance of policy gradient estimates. VRER is algorithm-agnostic and can be integrated with existing policy optimization methods, yielding the sample-efficient off-policy algorithm, Policy Gradient with VRER (PG-VRER). To provide rigorous theoretical guarantees, we develop a novel analysis framework for experience replay that explicitly accounts for dependencies induced by Markovian dynamics and behavior-policy interactions. Using this framework, we establish finite-time convergence guarantees for PG-VRER and characterize a fundamental bias-variance trade-off: reusing older samples reduces gradient variance but may introduce greater estimation bias. Extensive experiments show that VRER consistently accelerates learning and outperforms state-of-the-art policy optimization algorithms

stat.ML↗

arXiv2026

Complete Bernstein functions and real powers of P-matrices

We classify the nonzero complete Bernstein functions whose matrix functions preserve every real P-matrix in every order. They are precisely $f(z)=a+bz$, with $a,b\ge0$ and $a+b>0$, and $f(z)=a+cz/(z+s)$, with $a\ge0$ and $c,s>0$. For each fixed order $n\ge4$, the preservers vanishing at zero are exactly $cz$ and $cz/(z+s)$; every other such function admits a strictly totally positive counterexample. For a finite positive measure $μ$ on $(0,\infty)$, put $g(z)=\int z/(z+s)\,μ(ds)$ and $M_t=\int s^t\,μ(ds)$. In every fixed order $n\ge4$, a finite constant shift restores preservation on all real P-matrices if and only if $M_{r_n}$ and $M_{-r_n}$ are finite, where $r_n=\lfloor n/2\rfloor-1$. Every $a>c_n\sqrt{M_{r_n}M_{-r_n}}$ is sufficient, with $c_n$ depending only on $n$. A complete Bernstein function vanishing at zero admits a possibly different repairing constant in every order exactly when it is linear, or is a pure kernel mixture with all positive and negative integer moments finite. For principal real powers, the preserving exponents are $\mathbb R$ in order one, $[-1,1]$ in orders two and three, and $\{-1,0,1\}$ in every higher order. An explicit rational determinant-one totally positive family gives negative principal minors uniformly on prescribed compact subsets of $(-1,0)\cup(0,1)$.

math.RA↗

arXiv2026

Bias-Aware Adjoint Calibration and Optimal Control of Stochastic Multiscale Bioprocess Digital Twins

We develop a bias-aware digital-twin calibration and control framework for multiscale bioprocess models within a biological systems-of-systems (Bio-SoS) paradigm. The digital twin is represented by a stochastic differential equation (SDE) model and calibrated from sparse observations using quasi-likelihood estimation and adjoint sensitivity analysis. SDE generator-based moment expansions characterize truncation-induced parameter bias, while forward-backward adjoints quantify how calibration uncertainty propagates to value functions and policy performance. The resulting parameter-error distribution supports both policy-directed data acquisition and uncertainty-aware policy optimization through a second-order Gaussian-averaged objective. We characterize the asymptotic behavior of the resulting exploration criterion and derive a physical-system performance under the optimized policy. To implement these ideas, we develop an Actor-Simulator algorithm that jointly updates model parameters, selects informative experiments, and optimizes control policies. Numerical studies demonstrate improved calibration accuracy, sample efficiency, and control performance relative to state-of-the-art baselines.

stat.ML↗

arXiv2026

Primary components and large prime factors of cyclotomic values

Let $Φ_r(a,b)$ denote the homogeneous cyclotomic value. For sufficiently large $A$, uniformly for $1/2\leq B\leq A$, $r\geq3$ and $Z\geq2$, the number of coprime pairs in $(A,2A]\times(B,2B]$ whose greatest prime factor $P(Φ_r(a,b))$ is at most $Z$ is $O(AB/φ(r)+\sqrt{r/φ(r)}\,π(Z;r,1))$, where $π(Z;r,1)$ counts primes at most $Z$ congruent to $1$ modulo $r$. If $n=n(A)\to\infty$ through positive integers and $1\leq H(A)=o(\log A)$, then $P(a^{2^n}+1)>2^nAH(A)$ for almost all $a\in(A,2A]$, and $P(a^{2^n}+b^{2^n})>2^nA^2H(A)$ for almost all coprime pairs in $(A,2A]^2$, with no further restriction on $n$. For every fixed $α>0$ and every $r\geq A^α$, pairwise distinct primitive prime divisors of $Φ_r(a)$ can be selected for all but $O_α(A^{1-c_α})$ bases in $(A,2A]$, where $c_α>0$. For coprime positive integers $a,b$ with $\max(a,b)\geq2$ and $r\geq3$, put $C=Φ_r(a,b)$ and $S=φ(r)^2\log\max(a,b)$. Uniformly as $S\to\infty$, $\max_{p\mid C}p^{v_p(C)}\geq(5/16-o(1))S$. For every positive function $h(S)\to\infty$, $\sum_{p\mid C,\;p^{v_p(C)}>S/h(S)}v_p(C)\log p =(1-o(1))\log C$ uniformly in the same limit.

math.RA↗

arXiv2026

ReTerm: Recovery Training for Self-Improving Terminal Agents

Terminal agents have shown strong abilities in complex coding tasks. However, they often struggle to recover from errors during long-running execution (e.g., command errors, faulty implementations), eventually leading to task failures. To this end, we present ReTerm, a self-improving terminal agent trained by learning how to recover from its own failed terminal tasks. To support its training, we construct a customized data pipeline and produce ReTerm-10K, a high-quality dataset that provides effective recovery demonstrations for SFT cold start. Furthermore, we propose ReTerm-GRPO, an online RL algorithm that forks from the agent's own failure states to generate multiple independent self-recovery attempts. By learning from whether these attempts successfully complete the task, the agent self-improves through its own recovery experience. Built on Qwen3.5-9B, our ReTerm-9B achieves 34.8% Pass@1 on Terminal-Bench 2.0, improving over the base model by 14.6 points. Further analysis shows that our method achieves consistently higher recovery rates across diverse error categories compared with standard GRPO training. All code, data and model are released at https://github.com/twothsnd/ReTerm.

cs.AI↗

arXiv2026

EvoProbe: Evaluation-Driven Benchmark Evolution for LLM Agents

Static benchmarks for large language model (LLM) agents face saturation and data contamination risks, motivating continual updates to evaluation tasks. However, aggregate scores and success rates offer limited insight into specific problem-solving bottlenecks and provide limited guidance for subsequent task design. We propose EvoProbe, an evaluation-driven benchmark evolution framework that integrates task generation, diagnostic evaluation, and feedback-driven regeneration into a closed loop. It combines verifiable subtask outcome scoring with evidence-supported multi-judge trajectory evaluation and distills phase-level bottlenecks, success patterns, and failure patterns into diagnostic feedback for generating new executable tasks. Across two rounds of cybersecurity experiments, evaluations of eight models on 66 tasks reveal phase-level performance differences and common failure patterns beyond aggregate scores. In a cross-round comparison with the Examiner model set and solver configuration held fixed, all eight models achieve lower Outcome scores on the updated tasks, with relative decreases of 11.8\% in mean Outcome and 40.0\% in mean Pass\textasciicircum{}3. These results support using fine-grained diagnostics to guide iterative task updates and probe agents' current capabilities and limitations.

cs.AI↗

arXiv2026

Quantum circuit representation and incomplete Bell measurements in Compton scattering

We formulate massless tree-level Compton scattering as an effective two-qubit operation on electron and photon helicities. In the Bell basis, the scattering map separates into two parity sectors and admits a simple quantum circuit representation with one nonunitary filter. After Kraus normalization, this filter defines an unsharp incomplete Bell measurement that distinguishes the two Bell-parity sectors but not the relative Bell label within each sector. We further show that the incomplete measurement alone does not surpass the classical teleportation threshold, whereas a subsequent complete Bell-basis readout enables unit conditional teleportation fidelity.

hep-ph↗

arXiv2026

Positive Eigenvalues of Hadamard Square Roots on Finite Abelian Groups

For a finite abelian group $G$, let $μ_2(G)$ be the minimum number of positive eigenvalues of an entrywise positive real symmetric group-circulant matrix whose entrywise square is positive definite. We prove that $μ_2(G)\le5$ precisely when $|G|\le15$, and that $μ_2(G)=6$ precisely when $|G|=16$ or $G$ is cyclic of order $18$, $20$ or $22$. For the noncyclic groups of order at most fifteen, the minimum is three for $C_2^2$ and five otherwise. If the positive Fourier support of such a matrix is $\{0,\pm r_1,\ldots,\pm r_d\}$, where $d\ge1$ and all $2d+1$ displayed elements are distinct, then there are integers $α_1,\ldots,α_d$, not all zero, such that $\sum_iα_i r_i=0$ and $\sum_i|α_i|\le\max\{5,d+2\}$. The bound five is sharp for $d=2$ and $d=3$.

math.RA↗

arXiv2026

Absence of universal backscattering immunity in reciprocal photonic waveguides

Suppressing parasitic back-reflection caused by imperfections, such as random defects, material inhomogeneities, localized inclusions, and fabrication-induced geometric deviations, has long been a central objective in optical-waveguide engineering. In this Letter, we theoretically establish that universal immunity to backscattering from arbitrary disorder is fundamentally impossible in reciprocal optical waveguides, irrespective of whether the underlying structure is topologically trivial or nontrivial.We establish this result through two complementary constructions of physically admissible reciprocal perturbations. The first considers weak permittivity perturbations of finite spatial extent within the first Born approximation, whereas the second considers optically small dielectric perturbations of finite contrast. In each construction, an admissible realization exists that produces a nonzero leading-order backward-scattering amplitude. We trace the fundamental origin of this limitation to the absence in photons of the intrinsic spin-$\tfrac{1}{2}$ and fermionic time-reversal structure underlying Kramers protection in electronic systems. Consequently, any mechanism that enforces photonic backscattering suppression throughout a prescribed class of disorder must instead be engineered into the underlying electromagnetic structure and its constitutive response, which can itself be modified by generic reciprocal perturbations. Numerical examples in representative reciprocal topological waveguides further illustrate these limitations for random defects and sharp bends. We further identify several constructive strategies for suppressing back-reflection within certain prescribed classes of disorder.

physics.optics↗

arXiv2026

Asymptotic Entanglement Hiding under Stabilizer Restrictions

Entanglement is central to quantum information processing, while stabilizer operations underpin fault-tolerant quantum computation. We ask how much entanglement remains visible or distillable under stabilizer restrictions. We quantify stabilizer-visible entanglement by restricting the measured relative entropy of entanglement to stabilizer measurements, thereby obtaining converse bounds on entanglement distillation under stabilizer operations. We demonstrate magic-free asymptotic entanglement hiding: we construct explicit convex mixtures of pure stabilizer states on $N$ qutrits per party whose unrestricted visible entanglement and LOCC-distillable entanglement both grow as $Ω(N/\log N)$, while their stabilizer-visible and stabilizer-distillable entanglement vanish as $N\to\infty$. Thus, an unbounded amount of LOCC-distillable entanglement carried by stabilizer states can become asymptotically invisible and undistillable under stabilizer restrictions. We further prove that stabilizer-visible entanglement is $O(1)$ with high probability for Haar-random pure states despite extensive unrestricted visibility, and vanishes uniformly over entangled Werner states as the local dimension grows through odd primes. These results reveal a fundamental separation between entanglement and magic as resources, exposing intrinsic limits on entanglement extraction using stabilizer operations.

quant-ph↗

arXiv2026

SE-ADD: Self-Evolving Audio Deepfake Detection with Mistake-Driven Supervision

Audio deepfake detection (ADD) must remain effective when new spoofing attacks emerge after deployment. Emerging audio language model (ALM)-based ADD methods are built on predefined supervision from ground-truth labels or verified forensic rationales. However, this paradigm overlooks an ALM's own mistakes, which indicate where targeted supervision is most needed. To this end, we first introduce evolving spoofing environments for ALM-based ADD, where a new attack becomes dominant while previously observed attacks persist. Motivated by the above learning-from-mistakes perspective, we further propose SE-ADD, a self-evolving framework that iteratively adapts an ALM via low-rank adaptation (LoRA) using mistake-driven supervision built from its verdicts and self-generated forensic cues. All training samples receive direct authenticity supervision, while misclassified ones receive additional cue-augmented supervision. As verdicts and cues are regenerated by the updated ALM, the resulting supervision evolves accordingly. Experiments on two ALMs demonstrate the effectiveness of SE-ADD in generalizing to unseen attacks, reducing the equal error rate (EER) from $36.72\%$ to $7.52\%$ for Qwen2-Audio and from $19.93\%$ to $3.97\%$ for MOSS-Audio.

cs.SD↗

arXiv2026

SEAR: Spoofing Evidence-Grounded Audio Reasoning Benchmark for Audio Language Models

Audio language models (ALMs) are increasingly used for audio deepfake detection (ADD), yet existing benchmarks assess their verdicts or rationale plausibility without verifying the underlying acoustic evidence. To address this issue, we first introduce spoofing evidence-grounded audio reasoning (SEAR), a four-task AQA benchmark to evaluate ALM-based ADD through acoustic evidence identification and quantification, deepfake detection, and forensic rationale generation. We further propose a bona-fide-based acoustic evidence agent (BAEA), which equips a frozen ALM with controlled acoustic tools under \textsc{fixed} or \textsc{adaptive} evidence-acquisition policies. Experiments with six ALMs reveal a clear gap between plausible rationales and verifiable acoustic evidence reasoning, while BAEA-\textsc{Fixed} improves final verdicts and forensic rationales on both evaluation partitions. Controlled interventions further show that misleading evidence degrades both detection and grounding performance.

cs.SD↗

arXiv2026

Exponent Profiles of Oscillatory Matrices under Matrix and Inverse Sparsity

We classify the simultaneous half-bandwidths $p,q$ of a symmetric oscillatory matrix $A$ and its inverse. At order $n\ge2$, the possible pairs are $(1,n-1)$, $(n-1,1)$, and all pairs with $2\le p,q\le n-1$. Every pair has an integer realization of determinant one. Let $e_k(A)$ be the least positive integer $m$ for which all minors of order $k$ of $A^m$ are positive. We prove \[ e_k(A)\le \min\{\max\{k,n-p\},\max\{n-k,n-q\}\}\qquad(1\le k<n). \] When $p+q\ge n$, one realization attains all these bounds simultaneously. The maximum of $\sum_{k=1}^{n-1}e_k(A)$ is determined for every bandwidth pair. Write $A=U^TΔU$, with $U$ unit upper triangular and $Δ$ positive diagonal. Let $\ell(U)$ be the least number of positive elementary upper bidiagonal factors of $U$. At fixed $(p,q)$, its minimum is $\max\{n-1,p+q-1\}$. The bound $\sum_{k=1}^{n-1}e_k(A)+\ell(U)\le n(n-1)/2+n-1$ is sharp at each factor count; equality is characterized using $U$, $U^2$ and the zero corner minors of $A$. In particular, $\sum_{k=1}^{n-1}e_k(A)\le n(n-1)/2$, with equality exactly for basic matrices. In the basic oscillatory class, without a symmetry assumption, a positive integer vector $(f_1,\ldots,f_{n-1})$ is realizable if and only if $f_k\le\max\{k,n-k\}$ and $f_k+f_{n-k}\ge n$ for $1\le k<n$, and $\lvert f_{k+1}-f_k\rvert\le1$ for $1\le k<n-1$. Explicit factor orders realize every such vector.

math.RA↗

arXiv2026

High-Throughput Photovoltaic Screening and Spacer-Dependent Shift Current in Two-Dimensional Hybrid Perovskites

High-throughput first-principles screening of structurally diverse two-dimensional hybrid organic-inorganic perovskites (2D HOIPs) provides a route to systematically explore their photovoltaic properties. Here, we develop a computational workflow with two distinct objectives: spectroscopic limited maximum efficiency (SLME) screening to identify materials with promising photovoltaic potential and nonlinear shift current calculations to characterize their bulk photovoltaic response. Applying this workflow to a curated dataset of experimentally reported 2D HOIPs, we identify more than 25 compounds with SLME values above 25\% and more than 25 compounds exhibiting shift current responses exceeding 10~$μ$A/V$^2$. We then focus on the Pb-I-based 2D HOIPs with $n=1$ to investigate the influence of spacer chemistry on the shift current response, revealing substantial spacer-dependent variations in both its magnitude and spectral peak position. Overall, these results highlight the potential of high-throughput first-principles calculations to accelerate the discovery of experimentally relevant 2D HOIPs with promising photovoltaic properties while revealing how organic spacer chemistry influences their nonlinear shift photocurrent response.

cond-mat.mtrl-sci↗

arXiv2026

Minor-Order Exponent Profiles of Oscillatory Matrices

For an $n\times n$ oscillatory matrix $A$, let $e_k(A)$ be the least positive integer $m$ for which every minor of order $k$ of $A^m$ is positive. We determine the profile $(e_1(A),\ldots,e_n(A))$. For every nonsingular totally nonnegative matrix, the column index sets of positive entries in each compound row form an interval in the componentwise order. The endpoint maps are order-preserving and compose under multiplication. This yields a two-corner criterion for positivity of all minors of a fixed order. Consequently, $e_k(A)$ is the larger of the first positivity times of two remote corner minors. We prove the sharp inequalities $e_k(A)\leq\max{k,n-k}$ for $1\leq k<n$ and $|e_{k+1}(A)-e_k(A)|\leq1$ for $1\leq k\leq n-2$. For $D=\operatorname{diag}(1,-1,1,-1,\ldots)$, the matrix $DA^{-1}D$ is oscillatory and satisfies $e_k(DA^{-1}D)=e_{n-k}(A)$ for $1\leq k<n$; the determinant exponent remains one. The ordered positions of the positive factors in an adjacent bidiagonal factorization determine the profile independently of their values. Each one-sided factor sequence can be represented by a single permutation, giving a finite characterization of all profiles and an integer unimodular realization of each. We also obtain a compatibility condition across minor orders: if $3\leq k\leq n-3$ and $e_k(A)\leq2$, then $e_j(A)\leq2+\lceil |j-k|/2\rceil$ for $2\leq j\leq n-2$. In particular, $e_k(A)\leq2$ implies $e_{k+2}(A)\leq3$ for $3\leq k\leq n-4$, and both the constant and this range are sharp.

math.CO↗

arXiv2026

Electron-phonon coupled hydrodynamics in semimetal TaAs_2

Hydrodynamic corrections to diffusive transport can arise when momentum-conserving collisions between quasiparticles become prominent, and they have been documented for both electrons and phonons. An emerging frontier topic is coupled electron-phonon (e-ph) hydrodynamics. Here, through electrical and thermal transport measurements on TaAs2 crystals with different impurity levels, we document the emergence of an e-ph bifluid in the temperature window of 5 to 15 K. Within this range, the lattice thermal conductivity exhibits a faster-than-T^3 temperature dependence, as a consequence of non-monotonic and purity-dependent phonon mean free paths, a signature of phonon Poiseuille flow. However, strong e-ph coupling impedes the emergence of a ballistic regime. This is corroborated by the observation of quantum oscillations in the lattice thermal conductivity. Prominent phonon-mediated momentum exchange between electrons amplifies the violation of the Wiedemann-Franz law and yields a two-order-of-magnitude discrepancy between quantum and transport lifetimes, a signature of electron hydrodynamics in semimetals. Our results imply that in semimetals with optimized e-ph coupling, thanks to matching between the cryogenic phonon wave?length and the Fermi wavelength, momentum and energy flow between the electron and phonon reservoirs as frequently as within each reservoir.

cond-mat.mtrl-sci↗

arXiv2026

PrimSynth: An Agentic Approach to Discover, Validate, and Synthesize Exploit Primitives for Linux Kernel Vulnerabilities

Linux kernel vulnerabilities are critical to downstream systems. Despite extensive research on automated kernel exploitation, a fundamental challenge remains the conceptual gap between abstract exploit strategies and concrete technical operations. To fill this gap, this paper introduces a systematic characterization that formalizes six classes of exploit primitives from logical capability to validatable effect. Then, an extended exploit strategy representation is proposed, which couples primitive upgrading strategies with primitive path code synthesis rules governing object constraints, temporal sequencing, environment prerequisites, and validation constraints. Building upon this foundation, this paper presents \textsc{PrimSynth}, a multi-agent framework that encapsulates these representations through coordinated agents to discover, validate, and synthesize exploit primitives for memory corruption vulnerabilities in the Linux kernel. These agents operate in an iterative closed loop until valid primitives are found, leveraging validation signals as evidence of exploitable state transitions to ground primitive synthesis decisions. An automated method for extracting and validating primitives is also proposed based on vulnerability-directed execution and a rebootable validation environment. \textsc{PrimSynth} is evaluated on 16 real-world Linux kernel CVEs spanning 5 vulnerability types. Experimental results show that PrimSynth achieves reliable primitive extraction, maintaining a 100% primitive match rate. For primitive synthesis, PrimSynth successfully synthesizes multi-primitive exploitation chains with 82.4% strategy synthesis rate (SSR) when the public PoC is available and a 61.3% SSR without the guidance of primitive hypotheses.

cs.CR↗

arXiv2026

GlycoMAC: A Multiscale Metabolic-Glycosylation Framework for Predicting Glycosylation Across Conditions in Mammalian Cell Cultures

Antibody productivity and glycosylation quality in CHO cell cultures emerge from a dynamically evolving metabolic environment, yet existing models often work in isolation or at a single scale. Here, we present a multiscale mechanistic framework linking molecular, cellular, and process scales to predict how inputs shape bioprocess trajectories. The framework combines a single-cell kinetic model of metabolism and glycosylation with a stochastic population model that captures environment-dependent transitions among growth, production, and decline states. To characterize metabolic adaptation, we introduce the cumulative variation in oxygen uptake rate, a trajectory-based biomarker that quantifies the total metabolic adjustment experienced during culture. Unlike population-averaged approaches, the model propagates cell-resolved metabolic states (including ammonia-regulated Golgi pH, nucleotide sugar availability, manganese cofactors, and synthesis rates) into glycan processing. The framework was evaluated using CHO-K1 fed-batch cultures producing VRC01 IgG1 under targeted ammonia stress, matched control conditions, and a pyramid-feeding strategy with tighter control. It accurately reproduced trajectories of cell growth, metabolites, productivity, and harvest glycosylation, including increased G0F abundance and reduced galactosylation under ammonia stress. By mechanistically linking process conditions to cell-state dynamics and glycosylation outcomes, the framework provides a unified foundation for digital bioprocessing, predictive biomanufacturing, and advanced process control.

q-bio.CB↗