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Lingxiao Wang

Publications and source records attributed to Lingxiao Wang.

At least 19 recordsLinked to original sources
arXiv2026

Risk-matched case-control sampling and semiparametric weight calibration for efficient biomarker assessment with binary outcomes

Two-phase designs provide a cost-effective framework for biomarker studies and have been widely used to reduce the burden of collecting expensive biomarker measurements. Most methodological research has focused on efficient Phase II sampling and estimation of biomarker--outcome associations. A natural subsequent step, however, is to incorporate identified biomarkers into risk prediction models, where measures of predictive performance become important inferential targets. Even for binary outcomes, methodological developments for two-phase designs that jointly address association parameters and predictive performance remain limited. Building on classical case-control and matched case-control designs developed primarily for association inference with binary outcomes, we propose a risk-matched case-control (RMCC) design that uses a scalar disease-risk score constructed from Phase I variables to define matching strata and guide Phase II sampling. To address the limitations of existing likelihood-based approaches, which typically require correct specification of the nuisance distribution of biomarkers, we develop a unified design-based inference framework based on inverse probability weighting for both association parameters and predictive performance measures, including positive predictive value and the area under the receiver operating characteristic curve. We further introduce target-specific weight scaling and calibration procedures and derive variance estimators that account for sampling variability in both phases. Simulation studies demonstrate the efficiency and robustness of the proposed design and inference procedures, and an application to a Taiwanese oral cancer cohort illustrates their potential utility.

stat.ME↗
arXiv2026

Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory: Analytical Foundations and Numerical Scaling Tests

Gauge-equivariant diffusion models can be used to generate ensembles of field configurations in non-abelian lattice gauge theories. Previously, we demonstrated the feasibility of modeling these theories by combining L-CNN-based diffusion models with the Metropolis-adjusted annealed Langevin algorithm (MAALA). Here we focus on the underlying analytical framework. In particular, we present a rigorous derivation of the reverse-time stochastic differential equation on the group manifold, discuss the gauge invariance of the denoising loss function, and provide extensive numerical benchmarks regarding the scaling behavior with respect to the lattice volume and the inverse coupling $β$. Full analytical expressions for arbitrarily sized Wilson loops and the topological charge susceptibility during the forward process are given as well.

hep-lat↗
arXiv2026

Jianmu-Q: Bridging Quantum Field Theory and Quantum Hardware with AI Agents

Quantum computing offers a promising approach to non-perturbative simulations of quantum field theories, particularly for real-time dynamics and systems affected by the sign problem. Yet translating continuum field theories into quantum computations remains a challenging interdisciplinary task. Here we introduce \texttt{Jianmu-Q}, a multi-agent framework that transforms natural-language descriptions of quantum field theories into quantum simulation workflows. Specialized agents handle theoretical formulation, lattice discretization, qubit mapping, and circuit design, while physical consistency checks and independent numerical calculations provide validation throughout the workflow. We benchmark the framework on three field theories of increasing complexity: the $(1+1)$-dimensional Nambu--Jona-Lasinio and Schwinger models, and a $(2+1)$-dimensional $\mathbb{Z}_2$ gauge theory. Across these systems, noiseless quantum-circuit simulations converge toward independent exact-diagonalization and tensor-network results, while selected circuits are executed on IBM quantum hardware, demonstrating an end-to-end, validation-guided approach to quantum simulation of field theories.

hep-lat↗
arXiv2026

Learning Quantum Operator Dynamics from Short-Time Data

Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence. We propose a neural ordinary differential equation (Neural ODE) framework with a physics-driven neural network to reconstruct long-time operator dynamics from short-time quantum data. By expanding observables in the Pauli basis and exploiting locality and symmetry constraints, the operator evolution is reduced to a tractable set of coefficients whose dynamics are learned from the measurement data. Applied to the Ising spin chain with mixed fields, the operator learning method accurately extrapolates its long-time correlation function and resolves its excitation spectrum. We validate the framework by collecting short-time data from IBM's superconducting quantum processor and successfully reconstruct the Fourier spectrum of an $N=8$ Ising spin chain with 5 times enhanced precision. Our results demonstrate a scalable and data-efficient strategy for extracting dynamical and spectral information from practical quantum hardware.

quant-ph↗
arXiv2026

Generative Modeling of Stochastic Dynamics for Long-Time Evolution

Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar $t^{1/3}$ coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.

cond-mat.stat-mech↗
arXiv2026

Detecting Multiple Phase Transitions in Lattice Systems with Intrinsic Dimensions

Lattice systems with multiple nearby transitions pose two related challenges: resolving distinct transition scales and identifying the degrees of freedom primarily associated with each transition. We show that the intrinsic dimension of Monte Carlo configuration ensembles, estimated by the two-nearest-neighbors method, provides a geometric diagnostic for both problems. In the two-dimensional $q$-state clock model, the intrinsic dimension distinguishes the ordered, quasi-critical, and disordered regimes for both well-separated ($q=9$) and closely spaced ($q=5$) Berezinskii--Kosterlitz--Thouless transitions. In the $q=5$ case, the intermediate phase appears as a broad low-dimensional valley even when energy and magnetization do not separately resolve the two transitions. In the four-dimensional $U(1)$ Higgs model, we introduce channel-decomposed intrinsic dimensions based on gauge-invariant plaquette and Higgs variables. The dominant response of each channel tracks transitions associated with the corresponding degrees of freedom, while the combined channel retains features of both. We further show that intrinsic dimensions evaluated directly on gauge-variant fields are dominated by gauge-orbit directions, demonstrating the importance of removing gauge redundancy before interpreting configuration-space geometry. These results establish channel-decomposed intrinsic dimension as a geometric probe of lattice systems with multiple transitions and motivate its application to disentangling deconfinement and chiral crossover scales in full QCD.

hep-lat↗
arXiv2026

Solving Functional Renormalization Group Equations with Neural Networks

We employ deep neural networks to represent the field derivative of the scale-dependent effective potential in the functional renormalization group (fRG) framework for nonperturbative quantum field theory. By embedding the fRG flow equations directly into the loss function, the network parameters are determined so as to provide a continuous and differentiable representation of the scale- and field-dependent effective potential without relying on precomputed training data. Focusing on the $O(N)$ scalar field theory within the local potential approximation at finite temperature, we demonstrate that this neural network representation accurately captures the renormalization group flow across symmetric, broken, and critical regimes. A key ingredient is a decomposition of the representation into an analytically known large-$N$ contribution and a learned finite-$N$ correction, which efficiently mitigates numerical stiffness associated with convexity restoration in the broken phase. The physics-driven solutions show excellent agreement with established finite-difference and discontinuous Galerkin methods. We further apply the same strategy to the Wilson--Fisher fixed-point equation in three dimensions, illustrating that neural network representations provide a unified framework for both scale-dependent flows and fixed-point problems. For fixed points, the large-field asymptotic form alone can replace the exact large-$N$ reference, while a composite small- and large-field ansatz further improves accuracy, extending the method to problems without an analytically solvable limit. Our results indicate that physics-driven deep learning offers a robust and flexible numerical tool for functional renormalization group studies.

hep-ph↗
arXiv2026

Stochastic Quantization as Optimal Control

Stochastic quantization defines a Euclidean quantum field theory as the equilibrium of a fictitious-time Langevin dynamics, which reaches the Gibbs measure asymptotically. We show that this quantization can be formulated as a finite-time stochastic optimal control problem. A tractable reference process, naturally supplied by the free theory when available, provides an Ornstein--Uhlenbeck dynamics, while the full interaction enters as a reference-corrected terminal cost. The optimal control is a Doob-transform force that steers the path-reweighted terminal ensemble to the target at a prescribed time and for a given noise amplitude. A neural network learns the residual control, realizing this optimal stochastic quantization (OSQ). Because the path weights are exact, imperfect training increases the variance of estimators but does not introduce model bias. On multimodal potentials we recover all modes at finite time and find that the noise amplitude sets a practical diffusion-horizon window. In two-dimensional lattice scalar $ϕ^4$ theory we recover observables from hybrid Monte Carlo simulations near the critical point. Quantization is thereby formulated as control rather than equilibration.

hep-lat↗
arXiv2026

What's in a Smoothness Constant? Tighter Rates for Local SGD with Bounded Second-order Heterogeneity

Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm. Although Local SGD often outperforms alternatives such as Mini-batch SGD in practice, theory still only partially explains when and why local updates help under realistic data heterogeneity. Recent work by [Patel et al., 2025] shows that a bounded second-order heterogeneity assumption captures the efficiency of Local SGD for strongly convex objectives, and conjectures that the same principle extends to the general convex setting. In this paper, we prove this conjecture by establishing an improved convergence guarantee for Local SGD on general convex objectives under bounded second-order heterogeneity. We also improve the best-known lower bounds for Local SGD in this setting, showing that our upper bounds are nearly tight. Together, these results provide a sharper, more fine-grained convergence theory for Local SGD. As a further application of our techniques, we provide a lower bound for serial SGD with replacement, showing how second-order heterogeneity captures the impact of rare high-curvature clients.

cs.LG↗
arXiv2026

The Limits and Potentials of Local SGD for Distributed Heterogeneous Learning with Intermittent Communication

Local SGD is a popular optimization method in distributed learning, often outperforming other algorithms in practice, including mini-batch SGD. Despite this success, theoretically proving the dominance of local SGD in settings with reasonable data heterogeneity has been difficult, creating a significant gap between theory and practice. In this paper, we provide new lower bounds for local SGD under existing first-order data heterogeneity assumptions, showing that these assumptions are insufficient to prove the effectiveness of local update steps. Furthermore, under these same assumptions, we demonstrate the min-max optimality of accelerated mini-batch SGD, which fully resolves our understanding of distributed optimization for several problem classes. Our results emphasize the need for better models of data heterogeneity to understand the effectiveness of local SGD in practice. Towards this end, we consider higher-order smoothness and heterogeneity assumptions, providing new upper bounds that imply the dominance of local SGD over mini-batch SGD when data heterogeneity is low.

cs.LG↗
arXiv2026

Diffusion Models for Sampling Near Criticality in Lattice Field Theories

We investigate generative diffusion models as denoising samplers for two- and three-dimensional lattice $ϕ^4$ theory across the symmetric, near-critical, and broken phases. Validated against ensembles generated by Fourier-accelerated HMC combined with Wolff cluster updates, the reverse-SDE sampler reproduces scalar observables and the momentum-space propagator $G(|k|)$, with residual bias concentrated in the zero-mode and, in three dimensions, the action density. We introduce two local diagnostics and an HMC-referenced effective sample size (ESS), which probe the learned drift directly, through a Metropolis-adjusted Langevin acceptance rate, and through observable-level bias and variance. Exploiting a fully convolutional architecture with weights shared across different volumes ($V=L^D$), we show that cross-volume training transfers to unseen sizes, matching or slightly improving in-distribution training in the two-dimensional symmetric and broken phases. A three-dimensional model trained on $L \in \{4, 8, 16, 32\}$ reproduces the propagator and most scalar observables at the unseen lattice size $L = 64$ across the phase diagram, with the residual susceptibility excess in the broken phase as the main exception, and improves several critical observables relative to in-distribution $L = 64$ training. This establishes cross-volume generalization as a viable mechanism for large-volume sampling, and the score learned from many cheap small-lattice configurations transfers to the target volume without retraining.

hep-lat↗
arXiv2026

Improving Efficiency of Regression Analyses by Integrating Data from Population-Representative Surveys: A Model-Assisted Calibration Approach

The increasing availability of diverse data sources has motivated great interest in data integration for improving regression efficiency. Existing data integration methods primarily focus on integrating nonprobability samples and typically assume that the integrated data sources represent the same target population. While this assumption is often difficult to justify for nonprobability samples, it is naturally satisfied when integrating probability-based surveys designed to represent a common target population. Such surveys are important research data sources because they provide representative samples and collect rich information on diverse variables, making them well suited to data integration. However, existing integration methods do not accommodate complex sampling designs. We propose model-assisted calibration methods to improve regression efficiency by integrating multiple probability-based survey samples. The proposed framework accommodates settings in which either individual-level data or only summary statistics are available from external surveys while preserving valid finite-population inference without requiring correct specification of the outcome model. We establish the design consistency of the proposed estimators and develop Taylor linearization variance estimators accounting for the complex sampling designs of both surveys. Simulation studies and an application integrating National Health and Nutrition Examination Survey and National Health Interview Survey demonstrate substantial efficiency gains while maintaining valid finite-population inference.

stat.ME↗
arXiv2026

Ultra-Peripheral Collisions as a Nuclear-Structure Interferometer with Interpretable Multitask Deep Learning

Precise knowledge of nuclear structure is essential across fundamental physics, yet probing these structures is notoriously difficult. To address this challenge, ultra-peripheral collisions (UPCs) provide a femtoscopic tomography for imaging the atomic nucleus. UPCs offer a pristine electromagnetic pathway: coherent vector-meson photoproduction generates patterns of diffraction and two-source interference that directly encode the nuclear spatial density. Turning these patterns into quantitative constraints is, however, a challenging inverse problem, complicated by correlated sensitivities to deformation and neutron skin, phase smearing, and experimental backgrounds. Here we introduce an interpretable Multitask deep-learning framework that maps transverse momentum distributions to multiple nuclear-structure indicators simultaneously and identifies the kinematic regions driving each inference. We demonstrate the approach with coherent $J/ψ$ photoproduction in $^{96}_{40}\text{Zr} + ^{96}_{40}\text{Zr}$ collisions, showing that the learned features separate diffraction-dominated and interference-dominated information and provide analysis-ready observables for future high-luminosity data.

nucl-th↗
arXiv2026

Generative Criticality in Large Language Model Temperature Scaling

We propose a statistical-field framework for text generated by large language models (LLMs), treating token embeddings as continuous spin variables on a one-dimensional chain. Defining a susceptibility from the connected two-point correlator and an order parameter from the ensemble-averaged embedding field, we vary the \texttt{softmax} temperature $T$ and observe a sharp susceptibility peak near a characteristic $T_c$ with power-law-like scaling, a concurrent rapid change in the order parameter, and a collapse onto a single semantic direction below $T_c$. The intrinsic dimension estimated by the two nearest neighbor (TwoNN) method independently corroborates these findings, reaching a minimum near $T_c$. Results are robust across model scales (Qwen3: 0.6B--32B) and prompt categories. While the phenomenology closely resembles a continuous phase transition, the non-equilibrium nature of autoregressive generation warrants further investigation. Our framework provides quantitative tools for probing the collective statistical structure of LLM outputs and suggests connections between decoding strategies and critical phenomena.

cs.LG↗
arXiv2026

HoloNet: Toward a Unified Einstein-Maxwell-Dilaton Framework of QCD

We propose HoloNet, a neural-network framework that unifies lattice QCD(LQCD) thermodynamics and holographic Einstein-Maxwell-Dilaton (EMD) theory within a data-to-holography pipeline. Instead of assuming specific functional forms, HoloNet learns the metric profile $A(z)$ and the gauge-dilaton coupling $f(z)$ directly from 2+1-flavor LQCD data at $μ=0$. These learned functions are embedded into the EMD equations, enabling the model to reproduce the lattice equation of state and baryon number fluctuations with high fidelity. Once trained, HoloNet provides a fully data-driven holographic description of QCD that extends naturally to finite density, allowing us to map the phase diagram and estimate the location of the critical end point (CEP). The reconstructed potential $V(ϕ)$ and coupling $f(ϕ)$ agree quantitatively with those obtained from holographic renormalization, demonstrating that HoloNet can consistently bridge different holographic models.

hep-lat↗
arXiv2026

Reconstruction of fast-rotating neutron star observables with the neural network

Rotation can significantly affect neutron-star (NS) properties, but accurate modeling of rapidly rotating NSs requires solving a two-dimensional, axially symmetric system, making traditional calculations too expensive for inference analyses that demand a large amount of model evaluations. We develop a causal convolutional neural networks that preserve the chronological-like dependence of NS properties on the equation of state (EoS) and rapidly reconstruct observables for static, Keplerian, and rotating configurations. Using \texttt{RNS}, we generate a dataset of NS observables and use it to train our networks. We validate our networks with three representative EoS (SFHo, SLy4, and DD2) and find that the they accurately reproduce the \texttt{RNS} results. The trained networks evaluate NS configurations for a single EoS in $\sim 50$ms, providing a substantial speedup over typical \texttt{RNS} runtimes of $\sim 30$ min and enabling efficient inference analyses involving rapidly rotating NSs.

astro-ph.HE↗
arXiv2026

Quantum Simulations of Opinion Dynamics

Consensus formation is a central problem in collective behavior. In this work, we develop quantum models of opinion dynamics that can be exactly solved and implemented on current quantum hardware. By exploiting quantum superposition, measurement-induced state collapse, and entanglement, our framework captures key features of opinion evolution and allows a systematic investigation of how network connectivity shapes consensus formation. We demonstrate our approach using practical quantum circuits and validate representative cases on IBM Quantum devices for the open-chain. These findings pave the way for further exploration into quantum-enhanced social modeling, highlighting the potential of near-term quantum computers for simulating collective behavior in complex systems.

physics.soc-ph↗
arXiv2026

Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory

We demonstrate that gauge equivariant diffusion models can accurately model the physics of non-Abelian lattice gauge theory using the Metropolis-adjusted annealed Langevin algorithm (MAALA), as exemplified by computations in two-dimensional U(2) and SU(2) gauge theories. Our network architecture is based on lattice gauge equivariant convolutional neural networks (L-CNNs), which respect local and global symmetries on the lattice. Models are trained on a single ensemble generated using a traditional Monte Carlo method. By studying Wilson loops of various size as well as the topological susceptibility, we find that the diffusion approach generalizes remarkably well to larger inverse couplings and lattice sizes with negligible loss of accuracy while retaining moderately high acceptance rates.

hep-lat↗