arXiv subjects

Yuliang Wang

Publications and source records attributed to Yuliang Wang.

At least 19 recordsLinked to original sources

arXiv2026

CSG-Mamba: A Convolutional Scoring Gating Vision State Space Network for Endoscopic Polyp Segmentation

Accurate polyp segmentation is critical for computer-aided colonoscopy, yet endoscopic images often contain low-contrast boundaries, mucosal texture interference, specular highlights, and device-dependent appearance shifts. Vision State Space Models (SSMs) provide efficient long-range modeling with linear complexity, but existing Vision Mamba segmentation models typically convert 2D features into 1D scanning sequences, which may weaken local geometric continuity and over-smooth irregular contours. We propose CSG-Mamba, a convolutional scoring gating Vision State Space network for endoscopic polyp segmentation. Built on a VM-UNet-style asymmetric U-shaped encoder-decoder, CSG-Mamba inserts a Convolutional Scoring Gating (CSG) module at the semantically rich bottleneck. CSG generates a local spatial score map through pointwise and large-kernel depthwise convolutions and recalibrates state-space features by multiplicative gating. Experiments with three random seeds show that CSG-Mamba achieves 0.9220 Dice and 15.87 HD95 on Kvasir-SEG, and 0.7418 Dice and 0.6570 mIoU on CVC-ColonDB, outperforming the baselines on most overlap and recall metrics while maintaining competitive boundary accuracy.

cs.CV↗

arXiv2026

SRE-FER: Regional residual evidence learning for mitigating local evidence dilution in fine-grained facial expression recognition

Fine-grained facial expression recognition (FER) hinges on capturing subtle muscular cues that distinguish adjacent emotions. Yet capturing these cues presents a dilemma. Detector-based methods depend on fragile landmark pipelines, whereas we find that directly transferring foundation models such as DINOv3 under conventional global readouts can cause local evidence dilution: early global aggregation washes out sparse muscular signals and leaves persistent confusion between categories such as fear/surprise and sad/neutral. To recover this evidence, we propose SRE-FER, a readout-level regional residual evidence learning framework. Its core module, RERA, adds zero-initialized residual logits that refine class boundaries while preserving the backbone's global prediction. Training-time action unit (AU) guidance steers regional features toward expression-relevant areas using Facial Action Coding System (FACS)-based anatomical priors, without requiring an external facial pipeline at inference. An optional Full setting further routes sample-specific non-redundant tokens. On three benchmarks, SRE-FER attains 92.76% on RAF-DB, 91.32% on FERPlus, and 67.78% on AffectNet-7, demonstrating highly competitive performance compared to existing FER methods.

cs.CV↗

arXiv2026

Detecting Protracted Vulnerabilities in Open Source Projects

Timely resolution and disclosure of vulnerabilities are essential for maintaining the security of open-source software. However, many vulnerabilities remain unreported, unpatched, or undisclosed for extended periods, exposing users to prolonged security threats. While various vulnerability detection tools exist, they primarily focus on predicting or identifying known vulnerabilities, often failing to capture vulnerabilities that experience significant delays in resolution. In this study, we examine the vulnerability lifecycle by analyzing protracted vulnerabilities (PCVEs), which remain unresolved or undisclosed over long periods. We construct a dataset of PCVEs and conduct a qualitative analysis to uncover underlying causes of delay. To assess current automated solutions, we evaluate four state-of-the-art (SOTA) vulnerability detectors on our dataset. These tools detect only 1,059 out of 2,402 PCVEs, achieving approximately 44% coverage. To address this limitation, we propose DeeptraVul, an enhanced detection approach designed specifically for protracted cases. DeeptraVul integrates multiple development artifacts and code signals, supported by a Large Language Model (LLM)-based summarization component. For comparison, we also evaluate a standalone LLM. Our results show that DeeptraVul improves detection performance, achieving a 14% increase in coverage across all PCVEs and reaching 90% coverage on the DeeptraVul PCVE subset, outperforming existing SOTA detectors and standalone LLM based inference.

cs.CR↗

arXiv2026

A Deep Learning-Enhanced Fourier Method for the Multi-Frequency Inverse Source Problem with Sparse Far-Field Data

This paper introduces a hybrid computational framework for the multi-frequency inverse source problem governed by the Helmholtz equation. By integrating a classical Fourier method with a deep convolutional neural network, we address the challenges inherent in sparse and noisy far-field data. The Fourier method provides a physics-informed, low-frequency approximation of the source, which serves as the input to a U-Net. The network is trained to map this coarse approximation to a high-fidelity source reconstruction, effectively suppressing truncation artifacts and recovering fine-scale geometric details. To enhance computational efficiency and robustness, we propose a high-to-low noise transfer learning strategy: a model pre-trained on high-noise regimes captures global topological features, offering a robust initialization for fine-tuning on lower-noise data. Numerical experiments demonstrate that the framework achieves accurate reconstructions with noise levels up to 100%, significantly outperforms traditional spectral methods under sparse measurement constraints, and generalizes well to unseen source geometries.

math.AP↗

arXiv2025

Long-time reverse transportation inequalities for non-globally-dissipative Langevin dynamics

We establish a dimension-free, uniform-in-time reverse transportation inequality for Langevin dynamics with non-convex potentials. This inequality controls the R\'enyi divergence of arbitrary order between the process distributions starting from distinct initial points and serves as the dual version of the Harnack inequality. Notably, we prove that this inequality retains exponential decay in the long-time regime, thereby extending existing results for log-concave sampling to the non-convex setting.

math.PR↗

arXiv2025

Relative entropy estimate and geometric ergodicity for implicit Langevin Monte Carlo

We study the implicit Langevin Monte Carlo (iLMC) method, which simulates the overdamped Langevin equation via an implicit iteration rule. In many applications, iLMC is favored over other explicit schemes such as the (explicit) Langevin Monte Carlo (LMC). LMC may blow up when the drift field $\nabla U$ is not globally Lipschitz, while iLMC has convergence guarantee when the drift is only one-sided Lipschitz. Starting from an adapted continuous-time interpolation, we prove a time-discretization error bound under the relative entropy (or the Kullback-Leibler divergence), where a crucial gradient estimate for the logarithm numerical density is obtained via a sequence of PDE techniques, including Bernstein method. Based on a reflection-type continuous-discrete coupling method, we prove the geometric ergodicity of iLMC under the Wasserstein-1 distance. Moreover, we extend the error bound to a uniform-in-time one by combining the relative entropy error bound and the ergodicity. Our proof technique is universal and can be applied to other implicit or splitting schemes for simulating stochastic differential equations with non-Lipschitz drifts.

math.NA↗

arXiv2025

A modified tamed scheme for stochastic differential equations with superlinear drifts

Explicit discretizations of stochastic differential equations often encounter instability when the coefficients are not globally Lipschitz. The truncated schemes and tamed schemes have been proposed to handle this difficulty, but truncated schemes involve analyzing of the stopping times while the tamed schemes suffer from the reduced order of accuracy. We propose a modified tamed scheme by introducing an additional cut-off function in the taming, which enjoys the convenience for error analysis and preserving the original order of explicit discretization. While the strategy could be applied to any explicit discretization, we perform rigorous analysis of the modified tamed scheme for the Euler discretization as an example. Then, we apply the modified tamed scheme to the stochastic gradient Langevin dynamics for sampling with super-linear drift, and obtain a uniform-in-time near-sharp error estimate under relative entropy.

math.NA↗

arXiv2025

Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model

The Random Batch Method (RBM) [S. Jin, L. Li and J.-G. Liu, Random Batch Methods (RBM) for interacting particle systems, J. Comput. Phys. 400 (2020) 108877] is not only an efficient algorithm for simulating interacting particle systems, but also a randomly switching networked model for interacting particle system. This work investigates two RBM variants (RBM-r and RBM-1) applied to the Cucker-Smale flocking model. We establish the asymptotic emergence of global flocking and derive corresponding error estimates. By introducing a crucial auxiliary system and leveraging the intrinsic characteristics of the Cucker-Smale model, and under suitable conditions on the force, our estimates are uniform in both time and particle numbers. In the case of RBM-1, our estimates are sharper than those in Ha et al. (2021). Additionally, we provide numerical simulations to validate our analytical results.

math.NA↗

arXiv2024

On Random Batch Methods (RBM) for interacting particle systems driven by L\'evy processes

In many real-world scenarios, the underlying random fluctuations are non-Gaussian, particularly in contexts where heavy-tailed data distributions arise. A typical example of such non-Gaussian phenomena calls for L\'evy noise, which accommodates jumps and extreme variations. We propose the Random Batch Method for interacting particle systems driven by L\'evy noises (RBM-L\'evy), which can be viewed as an extension of the original RBM algorithm in [Jin et al. J Compt Phys, 2020]. In our RBM-L\'evy algorithm, $N$ particles are randomly grouped into small batches of size $p$, and interactions occur only within each batch for a short time. Then one reshuffles the particles and continues to repeat this shuffle-and-interact process. In other words, by replacing the strong interacting force by the weak interacting force, RBM-L\'evy dramatically reduces the computational cost from $O(N^2)$ to $O(pN)$ per time step. Meanwhile, the resulting dynamics converges to the original interacting particle system, even at the appearance of the L\'evy jump. We rigorously prove this convergence in Wasserstein distance, assuming either a finite or infinite second moment of the L\'evy measure. Some numerical examples are given to verify our convergence rate.

math.NA↗

arXiv2024

Time-domain direct sampling method for inverse electromagnetic scattering with a single incident source

In this paper, we consider an inverse electromagnetic medium scattering problem of reconstructing unknown objects from time-dependent boundary measurements. A novel time-domain direct sampling method is developed for determining the locations of unknown scatterers by using only a single incident source. Notably, our method imposes no restrictions on the the waveform of the incident wave. Based on the Fourier-Laplace transform, we first establish the connection between the frequency-domain and the time-domain direct sampling method. Furthermore, we elucidate the mathematical mechanism of the imaging functional through the properties of modified Bessel functions. Theoretical justifications and stability analyses are provided to demonstrate the effectiveness of the proposed method. Finally, several numerical experiments are presented to illustrate the feasibility of our approach.

math.NA↗

arXiv2024

Estimates of the numerical density for stochastic differential equations with multiplicative noise

We investigate the estimates of the density for the traditional Euler-Maruyama discretization of stochastic differential equations (SDEs) with multiplicative noise. Our estimates focus on two key aspects: (1) the $L^p$-upper bounds for derivatives of the logarithmic numerical density, (2) the sharp error order of the Euler scheme under the relative entropy (or Kullback-Leibler divergence). For the first aspect, we present estimates for the first-order and second-order derivatives of the logarithmic numerical density. The key technique is to adopt the Malliavin calculus to derive expressions of the derivatives of the logarithmic Green's function and to obtain an estimate for the inverse Malliavin matrix. Moreover, for the relative entropy error, we obtain a bound that is second order in time step, which then naturally leads to first-order error bounds under the total variation distance and Wasserstein distances. Compared with the usual weak error estimate for SDEs, such estimate can give an error bound for the worst case of a family of test functions instead of one test function.

math.NA↗

arXiv2024

Guidance for twisted particle filter: a continuous-time perspective

The particle filter (PF), also known as sequential Monte Carlo (SMC), approximates high-dimensional probability distributions and their normalizing constants in the discrete-time setting. To reduce the variance of the Monte Carlo approximation, various twisted particle filters (TPFs) have been proposed, in which a twisting function is chosen or learned to modify the Markov transition kernel. Guided by existing control-based importance sampling algorithms in the continuous-time setting, we propose a novel algorithm called the ``Twisted-Path Particle Filter'' (TPPF), in which the twisting function is parameterized by a neural network and trained to minimize a specific KL-divergence between path measures. Numerical experiments illustrate the capability of the proposed algorithm.

stat.CO↗

arXiv2024

Geometric ergodicity of SGLD via reflection coupling

We consider the geometric ergodicity of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm under nonconvexity settings. Via the technique of reflection coupling, we prove the Wasserstein contraction of SGLD when the target distribution is log-concave only outside some compact set. The time discretization and the minibatch in SGLD introduce several difficulties when applying the reflection coupling, which are addressed by a series of careful estimates of conditional expectations. As a direct corollary, the SGLD with constant step size has an invariant distribution and we are able to obtain its geometric ergodicity in terms of $W_1$ distance. The generalization to non-gradient drifts is also included.

math.PR↗

arXiv2024

From photon momentum transfer to acceleration sensing

As a typical application of photon momentum transfer, optical levitation systems are known for their ideal isolation from mechanical dissipation and thermal noise. These characters offer extraordinary potential for acceleration precision sensing and have attracted extensive attention in both fundamental and applied physics. Although considerable improvements of optical levitation accelerometers has been reported, the dynamic testing of the sensing performance remains a crucial challenge before the utilization in practical application scenarios. In this work, we present a dual-beam optical levitation accelerometer and demonstrate the test with dynamic inputs for the first time. An acceleration sensing sensitivity of $0.1μg$ and a measurement range of $ 1g$ are achieved. These advancements solidify the potential of optical levitation accelerometer for deployment in practical domains, including navigation, intelligent driving, and industrial automation, building a bridge between the laboratory systems and real-world applications.

physics.optics↗

arXiv2024

Convergence of Random Batch Method with replacement for interacting particle systems

The Random Batch Method (RBM) proposed in [Jin et al. J Comput Phys, 2020] is an efficient algorithm for simulating interacting particle systems (IPS). In this paper, we investigate the Random Batch Method with replacement (RBM-r), which is the same as the kinetic Monte Carlo (KMC) method for the pairwise interacting particle system of size $N$. In the RBM-r algorithm, one randomly picks a small batch of size $p \ll N$, and only the particles in the picked batch interact among each other within the batch for a short time, where the weak interaction (of strength $\frac{1}{N-1}$) in the original system is replaced by a strong interaction (of strength $\frac{1}{p-1}$). Then one repeats this pick-interact process. This KMC algorithm dramatically reduces the computational cost from $O(N^2)$ to $O(pN)$ per time step, and provides an unbiased approximation of the original force/velocity field of the interacting particle system. We give a rigorous proof of this approximation with an explicit convergence rate. In detail, we show that the Wasserstein-2 distance between first marginal distributions of IPS and RBM-r has an $O(\kappa^{1/4})$ upper bound, where $\kappa$ is the time step for choosing the random batch and the bound is independent of $N$. An improved $O(\kappa^{1/2})$ rate is also obtained when there is no diffusion in the system. Notably, the techniques in our analysis can potentially be applied to study KMC for other systems, including the stochastic Ising spin system.

math.NA↗

arXiv2024

Computational imaging of small-amplitude biperiodic surfaces with negative index material

This paper presents an innovative approach to computational acoustic imaging of biperiodic surfaces, exploiting the capabilities of an acoustic superlens to overcome the diffraction limit. We address the challenge of imaging physical entities in complex environments by considering the partial differential equations that govern the physics and solving the corresponding inverse problem. We focus on imaging infinite rough surfaces, specifically 2D diffraction gratings, and propose a method that leverages the transformed field expansion (TFE). We derive a reconstruction formula connecting the Fourier coefficients of the surface and the measured field, demonstrating the potential for unlimited resolution under ideal conditions. We also introduce an approximate discrepancy principle to determine the cut-off frequency for the truncated Fourier series expansion in surface profile reconstruction. Furthermore, we elucidate the resolution enhancement effect of the superlens by deriving the discrete Fourier transform of white Gaussian noise. Our numerical experiments confirm the effectiveness of the proposed method, demonstrating high subwavelength resolution even under slightly non-ideal conditions. This study extends the current understanding of superlens-based imaging and provides a robust framework for future research.

math.AP↗

arXiv2023

Propagation of chaos in path spaces via information theory

Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information theory. In our framework, the propagation of chaos is reduced to the space for driving processes with possible lower dimension. Indeed, after applying the data processing inequality, one only needs to estimate the difference between the drifts of the particle system and the mean-field Mckean stochastic differential equation. This point is particularly useful in situations where the discrepancy in the driving processes is more apparent than the investigated processes. We will take the second order system as well as other examples for the illustration of how our framework could be used. This approach allows us to focus on probability measures in path spaces for the driving processes, avoiding using the usual hypocoercivity technique or taking the pseudo-inverse of the diffusion matrix, which might be more stable for numerical computation. Our framework is different from current approaches in literature and could provide new insight into the study of interacting particle systems.

math.PR↗

arXiv2023

Inverse scattering of periodic surfaces with a superlens

We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming small amplitude. This formula suggests that unlimited resolution can be achieved for the linearized inverse problem with perfectly matched parameters. Our method requires only a single incident wave at a fixed frequency and can be efficiently implemented using fast Fourier transform. Through numerical experiments, we demonstrate that our method achieves resolution significantly surpassing the resolution limit for both smooth and non-smooth surface profiles with either perfect or marginally imperfect parameters.

math.NA↗