Zhihui Liu

Yanzhao Cao, Jialin Hong, Zhihui Liu

In this paper, we analyze Galerkin approximations for stochastic evolution equations driven by an additive Gaussian noise which is temporally white and spatially fractional with Hurst index less than or equal to $1/2$. First we regularize the noise by the Wong-Zakai approximation and obtain its optimal order of convergence. Then we apply the Galerkin method to discretize the stochastic evolution equations with regularized noises. Optimal error estimates are obtained for the Galerkin approximations. In particular, our error estimates remove an infinitesimal factor which appears in the error estimates of various numerical methods for stochastic evolution equations in existing literatures.

Jianbo Cui, Jialin Hong, Zhihui Liu et al.

We prove the optimal strong convergence rate of a fully discrete scheme, based on a splitting approach, for a stochastic nonlinear Schrödinger (NLS) equation. The main novelty of our method lies on the uniform a priori estimate and exponential integrability of a sequence of splitting processes which are used to approximate the solution of the stochastic NLS equation. We show that the splitting processes converge to the solution with strong order $1/2$. Then we use the Crank--Nicolson scheme to temporally discretize the splitting process and get the temporal splitting scheme which also possesses strong order $1/2$. To obtain a full discretization, we apply this splitting Crank--Nicolson scheme to the spatially discrete equation which is achieved through the spectral Galerkin approximation. Furthermore, we establish the convergence of this fully discrete scheme with optimal strong convergence rate $\mathcal{O}(N^{-2}+τ^\frac12)$, where $N$ denotes the dimension of the approximate space and $τ$ denotes the time step size. To the best of our knowledge, this is the first result about strong convergence rates of temporally numerical approximations and fully discrete schemes for stochastic NLS equations, or even for stochastic partial differential equations (SPDEs) with non-monotone coefficients. Numerical experiments verify our theoretical result.

Jianbo Cui, Jialin Hong, Zhihui Liu et al.

We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.

Yanzhao Cao, Jialin Hong, Zhihui Liu

We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index $H\le 1/2$. We make use of a sequence of approximate solutions with the fractional noise replaced by its piecewise con- stant approximations to construct the finite element approximations for the equation. The error estimate of the approximations is derived through rigorous convergence analysis.

Jialin Hong, Lihai Ji, Zhihui Liu

In this paper, we propose a conservative local discontinuous Galerkin method for one-dimensional nonlinear Schrödinger equation. By using special upwind-biased numerical fluxes, we establish the optimal rate of convergence $\mathcal O(h^{k+1})$, with polynomial of degree $k$ and grid size $h$. Meanwhile, we show that this method preserves the charge conservation law and thus we call it a conservative local discontinuous Galerkin method. Numerical experiments verify our theoretical result.

Jialin Hong, Chuying Huang, Zhihui Liu

For semilinear stochastic evolution equations whose coefficients are more general than the classical global Lipschitz, we present results on the strong convergence rates of numerical discretizations. The proof of them provides a new approach to strong convergence analysis of numerical discretizations for a large family of second order parabolic stochastic partial differential equations driven by space-time white noises. We apply these results to the stochastic advection-diffusion-reaction equation with a gradient term and multiplicative white noise, and show that the strong convergence rate of a fully discrete scheme constructed by spectral Galerkin approximation and explicit exponential integrator is exactly $\frac12$ in space and $\frac14$ in time. Compared with the optimal regularity of the mild solution, it indicates that the spetral Galerkin approximation is superconvergent and the convergence rate of the exponential integrator is optimal. Numerical experiments support our theoretical analysis.

Zhihui Liu, Xiaoming Wu

We first derive the exponential ergodicity of the stochastic theta method (STM) with $θ\in (1/2,1]$ 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 $θ=1$. 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}.

Dongdong Zhao, Ranxin Fang, Changtian Song et al.

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.

Zongqing Li, Zhihui Liu, Yujie Xie et al.

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.

Yuren Cai, Guangyi Wang, Zongqing Li et al.

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.

Chang Liu, Henghui Ding, Kaining Ying et al.

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.

Yujie Xie, Hongyang Zhang, Zhihui Liu et al.

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.