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Zhihui Liu

Publications and source records attributed to Zhihui Liu.

At least 19 recordsLinked to original sources
arXiv2026

Uniform-in-Time Weak and Ergodic Error Estimates of a Nonlinearity-Explicit Full Discretization for Superlinear SPDEs Driven by Multiplicative Noise

For a class of superlinear SPDEs driven by multiplicative noise, we prove an (essentially) sharp uniform-in-time (UIT) weak convergence rate for the nonlinearity-explicit Galerkin tamed Euler method (GTEM). Under standard monotonicity assumptions, the proof combines Malliavin calculus with regularity theory for the associated backward Kolmogorov equation (BKE), leading to UIT moment, H\"older, and Malliavin estimates, along with regularity estimates for the BKE solution. These estimates, together with a weak error decomposition and Malliavin integration by parts (IBP) formula, then yield a UIT weak convergence rate $\tau^\rho+\lambda_N^{-(\rho+\gamma/2)}$ for any $\rho \in (0,1)$, where $\gamma\in[0,1)$ quantifies the assumed spatial Sobolev regularity. Consequently, we obtain a sharp ergodic error estimate between the exact and numerical invariant measures. Numerical experiments support the theory.

math.NA↗
arXiv2026

$2$-designs admitting a flag-transitive automorphism group with socle $PSL(2,q)$

$2$-designs admitting a flag-transitive automorphism group $G$ with socle $PSL(2,q)$, where $q=p^{f}\geq 4$, are investigated in both the point-primitive and point-imprimitive cases. In the latter case, a complete classification is achieved, and three known examples occur, namely: the complementary designs of $PG(3,2)$ and $PG(3,4)$, and the $2$-$(36,8,4)$ design constructed by Devillers and Praeger in [14]. In the point-primitive case, apart from the Witt-Bose-Shrikhande linear spaces of even order $q$, $48$ sporadic examples are classified. Surprisingly, one of these numerical examples is the linear space with $v=496$ and $k=4$ admitting $P\Gamma L(2,2^{5})$ as a flag-transitive automorphism group, which was missing in the 1990 classification by Buekenhout et al. [7,36,12].

math.CO↗
arXiv2026

Uniform-in-time Strong Error Estimates of Tamed-FEM to Superlinear SPDEs driven by Multiplicative Noise

We establish sharp, uniform-in-time strong error estimates for a nonlinearity-explicit tamed finite element method (FEM) applied to a class of superlinear stochastic partial differential equations (SPDEs) driven by multiplicative noise, including the stochastic Allen--Cahn equation with a moderately thick interface. This tamed-FEM was first introduced in [Z. Liu and J. Shen, arXiv:2502.19117] to ensure long-time unconditional stability and to preserve the Lyapunov structure of this class of SPDEs. We further prove that the scheme is exponentially ergodic and derive the convergence rate between the exact invariant measure and its numerical counterpart in the Wasserstein-2 distance. Finally, we present numerical experiments that verify the ergodicity as well as the sharpness and time-independence of the strong convergence rates for this tamed-FEM.

math.NA↗
arXiv2026

Three Creates All: You Only Sample 3 Steps

Diffusion models deliver high-fidelity generation but remain slow at inference time due to many sequential network evaluations. We find that standard timestep conditioning becomes a key bottleneck for few-step sampling. Motivated by layer-dependent denoising dynamics, we propose Multi-layer Time Embedding Optimization (MTEO), which freeze the pretrained diffusion backbone and distill a small set of step-wise, layer-wise time embeddings from reference trajectories. MTEO is plug-and-play with existing ODE solvers, adds no inference-time overhead, and trains only a tiny fraction of parameters. Extensive experiments across diverse datasets and backbones show state-of-the-art performance in the few-step sampling and substantially narrow the gap between distillation-based and lightweight methods. Code will be available.

cs.LG↗
arXiv2026

VeloEdit: Training-Free Consistent and Continuous Instruction-Based Image Editing via Velocity Field Decomposition

Instruction-based image editing aims to modify source content according to textual instructions. However, existing methods built upon flow matching often struggle to maintain consistency in non-edited regions due to denoising-induced reconstruction errors that cause drift in preserved content. Moreover, they typically lack fine-grained control over edit strength. To address these limitations, we propose VeloEdit, a training-free method that enables highly consistent and continuously controllable editing. VeloEdit dynamically identifies editing regions by quantifying the discrepancy between the velocity fields responsible for preserving source content and those driving the desired edits. Based on this partition, we enforce consistency in preservation regions by substituting the editing velocity with the source-restoring velocity, while enabling continuous modulation of edit intensity in target regions via velocity interpolation. Unlike prior works that rely on complex attention manipulation or auxiliary trainable modules, VeloEdit operates directly on the velocity fields. Extensive experiments on Flux.1 Kontext and Qwen-Image-Edit demonstrate that VeloEdit improves visual consistency and editing continuity with negligible additional computational cost. Code is available at https://github.com/xmulzq/VeloEdit.

cs.CV↗
arXiv2025

Inversions of stochastic processes from ergodic measures of Nonlinear SDEs

We introduce and analyze a novel class of inverse problems for stochastic dynamics: Given the ergodic invariant measure of a stochastic process governed by a nonlinear stochastic ordinary or partial differential equation (SODE or SPDE), we investigate the unique identifiability of the underlying process--specifically, the recovery of its drift and diffusion terms. This stands in contrast to the classical problem of statistical inference from trajectory data. We establish unique identifiability results under several key scenarios, including cases with both multiplicative and additive noise, for both finite- and infinite-dimensional systems. Our analysis leverages the intrinsic structure of the governing equations and their quantitative relationship with the ergodic measure, thereby transforming the identifiability problem into a uniqueness issue for the solutions to the associated stationary Fokker-Planck equations. This approach reveals fundamental differences between drift and diffusion inversion problems and provides counterexamples where unique recovery fails. This work lays the theoretical foundation for a new research direction with significant potential for practical application.

math.PR↗
arXiv2025

Known Meets Unknown: Mitigating Overconfidence in Open Set Recognition

Open Set Recognition (OSR) requires models not only to accurately classify known classes but also to effectively reject unknown samples. However, when unknown samples are semantically similar to known classes, inter-class overlap in the feature space often causes models to assign unjustifiably high confidence to them, leading to misclassification as known classes -- a phenomenon known as overconfidence. This overconfidence undermines OSR by blurring the decision boundary between known and unknown classes. To address this issue, we propose a framework that explicitly mitigates overconfidence caused by inter-class overlap. The framework consists of two components: a perturbation-based uncertainty estimation module, which applies controllable parameter perturbations to generate diverse predictions and quantify predictive uncertainty, and an unknown detection module with distinct learning-based classifiers, implemented as a two-stage procedure, which leverages the estimated uncertainty to improve discrimination between known and unknown classes, thereby enhancing OSR performance. Experimental results on three public datasets show that the proposed framework achieves superior performance over existing OSR methods.

cs.CV↗
arXiv2025

Ergodic Estimates of One-Step Numerical Approximations for Superlinear SODEs

This paper establishes the first-order convergence rate for the ergodic error of numerical approximations to a class of stochastic ODEs (SODEs) with superlinear coefficients and multiplicative noise. By leveraging the generator approach to the Stein method, we derive a general error representation formula for one-step numerical schemes. Under suitable dissipativity and smoothness conditions, we prove that the error between the accurate invariant measure $\pi$ and the numerical invariant measure $\pi_\tau$ is of order $\mathscr{O}(\tau)$, which is sharp. Our framework applies to several recently studied schemes, including the tamed Euler, projected Euler, and backward Euler methods.

math.NA↗
arXiv2025

Causal Variance Decompositions for Measuring Health Inequalities

Recent causal inference literature has introduced causal effect decompositions to quantify sources of observed inequalities or disparities in outcomes, but these approaches are typically limited to pairwise comparisons. In healthcare delivery settings, both the exposure of interest-hospital or healthcare unit-and sociodemographic group membership may be polytomous, making pairwise contrasts inadequate. We therefore take the observed variance in care delivery outcomes as the quantity of interest and develop a new causal variance decomposition framework for this setting. The proposed framework attributes the observed variation to eight components, including novel terms characterizing modification of hospital effects by sociodemographic group membership, hospital access or selection, and the correlation between these two sources of heterogeneity. We discuss the causal interpretation of these components, propose both parametric and nonparametric model-based estimators, and study their performance through simulation. Finally, we illustrate the method using data from the SEER program in an application to cervical cancer care delivery.

stat.ME↗
arXiv2025

LSVOS 2025 Challenge Report: Recent Advances in Complex Video Object Segmentation

This report presents an overview of the 7th Large-scale Video Object Segmentation (LSVOS) Challenge held in conjunction with ICCV 2025. Besides the two traditional tracks of LSVOS that jointly target robustness in realistic video scenarios: Classic VOS (VOS), and Referring VOS (RVOS), the 2025 edition features a newly introduced track, Complex VOS (MOSEv2). Building upon prior insights, MOSEv2 substantially increases difficulty, introducing more challenging but realistic scenarios including denser small objects, frequent disappear/reappear events, severe occlusions, adverse weather and lighting, etc., pushing long-term consistency and generalization beyond curated benchmarks. The challenge retains standard ${J}$, $F$, and ${J\&F}$ metrics for VOS and RVOS, while MOSEv2 adopts ${J\&\dot{F}}$ as the primary ranking metric to better evaluate objects across scales and disappearance cases. We summarize datasets and protocols, highlight top-performing solutions, and distill emerging trends, such as the growing role of LLM/MLLM components and memory-aware propagation, aiming to chart future directions for resilient, language-aware video segmentation in the wild.

cs.CV↗
arXiv2025

SAMSON: 3rd Place Solution of LSVOS 2025 VOS Challenge

Large-scale Video Object Segmentation (LSVOS) addresses the challenge of accurately tracking and segmenting objects in long video sequences, where difficulties stem from object reappearance, small-scale targets, heavy occlusions, and crowded scenes. Existing approaches predominantly adopt SAM2-based frameworks with various memory mechanisms for complex video mask generation. In this report, we proposed Segment Anything with Memory Strengthened Object Navigation (SAMSON), the 3rd place solution in the MOSE track of ICCV 2025, which integrates the strengths of stateof-the-art VOS models into an effective paradigm. To handle visually similar instances and long-term object disappearance in MOSE, we incorporate a long-term memorymodule for reliable object re-identification. Additionly, we adopt SAM2Long as a post-processing strategy to reduce error accumulation and enhance segmentation stability in long video sequences. Our method achieved a final performance of 0.8427 in terms of J &F in the test-set leaderboard.

cs.CV↗
arXiv2025

Weak Error Estimates of Ergodic Approximations for Monotone Jump-diffusion SODEs

We first derive the exponential ergodicity of the stochastic theta method (STM) with $\theta \in (1/2,1]$ for monotone jump-diffusion stochastic ordinary differential equations (SODEs) under a dissipative condition. Then we establish the weak error estimates of the backward Euler method (BEM), corresponding to the STM with $\theta=1$. In particular, the time-independent estimate for the BEM in the jump-free case yields a one-order convergence rate between the exact and numerical invariant measures, answering a question left in {\it Z. Liu and Z. Liu, J. Sci. Comput. (2025) 103:87}.

math.NA↗
arXiv2025

Non-asymptotic Error Analysis of Explicit Modified Euler Methods for Superlinear and Non-contractive SODEs

A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preserve the same Lyapunov structure as the continuous problems. Under a non-contractive condition, we establish a non-asymptotic error bound between the law of the numerical approximation and the target distribution in Wasserstein-1 ($\mathcal{W}_1$) distance through a time-independent weak convergence rate for the proposed schemes. As a by-product of this weak error estimate, we obtain an $\mathcal{O}(\tau|\ln \tau|)$ convergence rate between the exact and numerical invariant measures.

math.NA↗
arXiv2025

Analysis of Radiation Level and Estimation of Protection Distance of γ Mobile Flaw Detection Source

Objective To analyze the radiation dose associated with gamma-ray mobile flaw detection, estimate the extent of the supervision and control areas, and assess the associated radiation risks. Methods A combination of theoretical calculations and actual measurements was used to compare and analyze the ambient equivalent dose rates of 192 Ir and 75 Se at their nominal source strengths. Measurements were conducted at distances of 1 m, 2 m, and 5 m from the radiation source. The extents of the control and supervision areas were estimated under three working scenarios: 1 without considering air attenuation, 2 considering air attenuation, and 3 after shielding by the flaw detection workpiece, using source activities of 3.7 * 10^10 Bq and 3.7 * 10^12Bq. Results Actual measurement of radiation dose of 192 Ir and 75 Se were measured under three different nominal activities. Theoretical calculation of radiation dose estimates at various distances were obtained for both nuclides, and the results showed that the theoretical values were basically consistent with the measured values. Conclusion The estimated scope of the supervision and control areas provided in this study can serve as a reference for flaw detection companies. Technicians can use these estimates to calculate appropriate distances for safety zones based on different nuclide activities. This enables flaw detection personnel to reduce the measurement scope on-site and to quickly and accurately define area boundaries.

physics.ins-det↗
arXiv2025

Numerical Ergodicity and Optimal Strong Error Estimates for a Class of Novel Tamed Schemes to Superlinear SPDEs

We construct a class of novel tamed schemes for superlinear stochastic partial differential equations (SPDEs), including the stochastic Allen--Cahn equation driven by either multiplicative or additive noise. The schemes preserve the same Lyapunov structure as the original system, and we rigorously establish their longtime unconditional stability. Furthermore, we prove that the corresponding Galerkin-based fully discrete tamed schemes inherit the unique ergodicity of the underlying SPDEs and achieve optimal strong convergence rates in both the multiplicative and additive noise cases.

math.NA↗
arXiv2024

Geometric Ergodicity and Strong Error Estimates for Tamed Schemes of Super-linear SODEs

We construct a family of explicit tamed Euler--Maruyama (TEM) schemes, which can preserve the same Lyapunov structure for super-linear stochastic ordinary differential equations (SODEs) driven by multiplicative noise.These TEM schemes are shown to inherit the geometric ergodicity of the considered SODEs and converge with optimal strong convergence orders. Numerical experiments verify our theoretical results.

math.NA↗
arXiv2024

A Bayesian joint model for mediation analysis with matrix-valued mediators

Unscheduled treatment interruptions may lead to reduced quality of care in radiation therapy (RT). Identifying the RT prescription dose effects on the outcome of treatment interruptions, mediated through doses distributed into different organs-at-risk (OARs), can inform future treatment planning. The radiation exposure to OARs can be summarized by a matrix of dose-volume histograms (DVH) for each patient. Although various methods for high-dimensional mediation analysis have been proposed recently, few studies investigated how matrix-valued data can be treated as mediators. In this paper, we propose a novel Bayesian joint mediation model for high-dimensional matrix-valued mediators. In this joint model, latent features are extracted from the matrix-valued data through an adaptation of probabilistic multilinear principal components analysis (MPCA), retaining the inherent matrix structure. We derive and implement a Gibbs sampling algorithm to jointly estimate all model parameters, and introduce a Varimax rotation method to identify active indicators of mediation among the matrix-valued data. Our simulation study finds that the proposed joint model has higher efficiency in estimating causal decomposition effects compared to an alternative two-step method, and demonstrates that the mediation effects can be identified and visualized in the matrix form. We apply the method to study the effect of prescription dose on treatment interruptions in anal canal cancer patients.

stat.ME↗