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Quang Huy Nguyen

Publications and source records attributed to Quang Huy Nguyen.

7 recordsLinked to original sources

Med-StepBench: A Hierarchical Reasoning Framework for Evaluating Hallucinations in Medical Vision-Language Models

Large vision-language models (VLMs) demonstrate strong performance in medical image understanding, but frequently generate clinically plausible yet incorrect statements, raising significant safety concerns. Existing medical hallucination benchmarks primarily focus on 2D imaging with one-shot diagnostic questions, offering limited insight into whether predictions are grounded in correct localization and abnormality identification, allowing critical reasoning errors to remain hidden behind seemingly correct diagnoses. We introduce Med-StepBench, the first large-scale benchmark for step-wise hallucination detection in 3D oncological PET/CT, comprising over 12,000 images and more than 1,000,000 image-statement pairs across volumetric and multi-view 2D data, which decomposes clinical reasoning into four expert-designed diagnostic stages. Using clinician-verified annotations, we perform the first step-level evaluation of general-purpose and medical VLMs, revealing systematic failure modes obscured by aggregate accuracy metrics. Furthermore, we show that current VLMs are highly susceptible to adversarial yet clinically plausible intermediate explanations, which significantly amplify hallucinations despite contradictory visual evidence. Together, our findings highlight fundamental limitations in grounding multi-step clinical reasoning and establish Med-StepBench as a rigorous benchmark for developing safer and more reliable medical VLMs.

cs.CV

A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization

This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and adjoint. This problem is shown to be equivalent to our optimal control problem. Based on fully unstructured, space-time interface-fitted meshes, we propose and analyze a Petrov-Galerkin approximation of the problem. An optimal error estimate with respect to a discrete norm is established under a specific regularity assumption on the state and adjoint. Several numerical results are presented to corroborate our theoretical results.

math.OC

Improved a priori error estimates for a space-time finite element method for parabolic problems

In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order estimates in three different norms, thereby supplementing existing research. Moreover, we obtain an optimal estimate in a norm stronger than that of the trial space. Finally, we present numerical examples to illustrate our theoretical results.

math.NA

Error analysis of the space-time interface-fitted finite element method for an inverse source problem for an advection-diffusion equation with moving subdomains

A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A space-time interface-fitted method is employed to discretize the advection-diffusion equation, where two second-order a priori error estimates are established with respect to the $L^2$-norms. Additionally, the regularized source is discretized sequentially using the variational approach, the element-wise constant discretization, and finally, the post-processing strategy. Optimal error estimates are achieved for the first two methods, while superlinear convergence is obtained for the third. Furthermore, a priori choices for the regularization parameter are proposed, depending on the mesh size and noise level. These choices ensure that the discrete and post-processing solutions strongly converge to the exact source as the mesh size and noise level tend to zero.

math.NA

A fitted space-time finite element method for an advection-diffusion problem with moving interfaces

This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution gradient across the interface. We use the Banach-Necas-Babuska theorem to show the well-posedness of the continuous variational problem. A fully discrete finite-element based scheme is analyzed using the Galerkin method and unstructured interface-fitted meshes. An optimal error estimate is established in a discrete energy norm under a globally low but locally high regularity condition. Some numerical results corroborate our theoretical results.

math.NA

Tail approximations for sums of dependent regularly varying random variables under Archimedean copula models

In this paper, we compare two numerical methods for approximating the probability that the sum of dependent regularly varying random variables exceeds a high threshold under Archimedean copula models. The first method is based on conditional Monte Carlo. We present four estimators and show that most of them have bounded relative errors. The second method is based on analytical expressions of the multivariate survival or cumulative distribution functions of the regularly varying random variables and provides sharp and deterministic bounds of the probability of exceedance. We discuss implementation issues and illustrate the accuracy of both procedures through numerical studies.

stat.CO

Strichartz estimates and local existence for the capillary water waves with non-Lipschitz initial velocity

We consider the gravity-capillary waves in any dimension and in fluid domains with general bottoms. Using the paradiferential reduction established in the companion paper, we prove Strichartz estimates for solutions to this problem, at a low regularity level such that initially, the velocity field can be non-Lipschitz up to the free surface. We then use those estimates to solve the Cauchy problem at this level of regularity.

math.AP