arXiv subjects

Tuyen Tran

Publications and source records attributed to Tuyen Tran.

15 recordsLinked to original sources

arXiv2026

A Unified Geometric Framework for Developmental Analysis of Spatial Transcriptomic Data

High-throughput single-cell and spatial transcriptomic technologies provide high-resolution snapshots of heterogeneous cellular states, but their destructive nature prevents repeated measurements of the same cells over time. Consequently, temporal and spatial dynamics must be inferred from independently sampled, unaligned cell populations, making it challenging to reconstruct developmental trajectories. Optimal transport (OT) offers a geometric framework for aligning cell populations and inferring developmental trajectories, but many existing approaches focus on modeling the evolution of distributions of cells in gene expression space rather than the relational structure encoded by gene expression networks. To address this limitation, we introduce a geometric framework for analyzing the spatiotemporal evolution of gene expression networks through embeddings in Gromov--Wasserstein (GW) space. By representing each developmental stage as a graph combining gene expression and spatial proximity, our approach enables comparisons of network structure across time, continuous interpolation between developmental stages via GW geodesics, and quantification of network-level changes using Ollivier-Ricci curvature. We evaluate our framework on a spatiotemporal transcriptomic \textit{Drosophila} dataset and show that GW geodesic interpolations reproduce main trends in curvature dynamics observed in empirical gene expression networks. Agreement with higher-order Co-Optimal Transport (COOT) distances, which jointly represent spatial and temporal information, further validates the framework and suggests that hypernetwork representations successfully record salient biological changes across time. In general, our approach provides a unified geometric approach to study dynamically evolving biological networks.

stat.ML↗

arXiv2026

New Globalized Newton-Type Methods for Nonconvex Optimization Problems

Newton's method is one of the most effective second-order algorithms for smooth optimization because of its fast local convergence. However, existing globally convergent Newton-type methods typically require convexity or strong convexity of the objective function, while approaches for nonconvex optimization often rely on Hessian regularization at every iteration. In this paper, we propose a general line-search Newton framework for unconstrained optimization that avoids repeated Hessian regularization by exploiting the Newton direction only when it is well-defined and suitable. The proposed framework encompasses several existing hybrid gradient--Newton methods as special cases and naturally yields a new extragradient Newton method. We establish global convergence under mild assumptions, including the Polyak--Lojasiewicz--Kurdyka (PLK) condition, allowing both isolated and nonisolated accumulation points. We further prove local superlinear and quadratic convergence under appropriate regularity assumptions. Finally, we apply the proposed framework to strongly quasiconvex optimization and provide, to the best of our knowledge, the first Newton-type algorithm together with a comprehensive convergence analysis for this important class of nonconvex optimization problems. Numerical experiments demonstrate the effectiveness of the proposed methods.

math.OC↗

arXiv2025

Towards Agentic AI for Multimodal-Guided Video Object Segmentation

Referring-based Video Object Segmentation is a multimodal problem that requires producing fine-grained segmentation results guided by external cues. Traditional approaches to this task typically involve training specialized models, which come with high computational complexity and manual annotation effort. Recent advances in vision-language foundation models open a promising direction toward training-free approaches. Several studies have explored leveraging these general-purpose models for fine-grained segmentation, achieving performance comparable to that of fully supervised, task-specific models. However, existing methods rely on fixed pipelines that lack the flexibility needed to adapt to the dynamic nature of the task. To address this limitation, we propose Multi-Modal Agent, a novel agentic system designed to solve this task in a more flexible and adaptive manner. Specifically, our method leverages the reasoning capabilities of large language models (LLMs) to generate dynamic workflows tailored to each input. This adaptive procedure iteratively interacts with a set of specialized tools designed for low-level tasks across different modalities to identify the target object described by the multimodal cues. Our agentic approach demonstrates clear improvements over prior methods on two multimodal-conditioned VOS tasks: RVOS and Ref-AVS.

cs.CV↗

arXiv2025

Planner-Refiner: Dynamic Space-Time Refinement for Vision-Language Alignment in Videos

Vision-language alignment in video must address the complexity of language, evolving interacting entities, their action chains, and semantic gaps between language and vision. This work introduces Planner-Refiner, a framework to overcome these challenges. Planner-Refiner bridges the semantic gap by iteratively refining visual elements' space-time representation, guided by language until semantic gaps are minimal. A Planner module schedules language guidance by decomposing complex linguistic prompts into short sentence chains. The Refiner processes each short sentence, a noun-phrase and verb-phrase pair, to direct visual tokens' self-attention across space then time, achieving efficient single-step refinement. A recurrent system chains these steps, maintaining refined visual token representations. The final representation feeds into task-specific heads for alignment generation. We demonstrate Planner-Refiner's effectiveness on two video-language alignment tasks: Referring Video Object Segmentation and Temporal Grounding with varying language complexity. We further introduce a new MeViS-X benchmark to assess models' capability with long queries. Superior performance versus state-of-the-art methods on these benchmarks shows the approach's potential, especially for complex prompts.

cs.CV↗

arXiv2025

MultiMed-ST: Large-scale Many-to-many Multilingual Medical Speech Translation

Multilingual speech translation (ST) and machine translation (MT) in the medical domain enhances patient care by enabling efficient communication across language barriers, alleviating specialized workforce shortages, and facilitating improved diagnosis and treatment, particularly during pandemics. In this work, we present the first systematic study on medical ST, to our best knowledge, by releasing MultiMed-ST, a large-scale ST dataset for the medical domain, spanning all translation directions in five languages: Vietnamese, English, German, French, and Simplified/Traditional Chinese, together with the models. With 290,000 samples, this is the largest medical MT dataset and the largest many-to-many multilingual ST among all domains. Secondly, we present the most comprehensive ST analysis in the field's history, to our best knowledge, including: empirical baselines, bilingual-multilingual comparative study, end-to-end vs. cascaded comparative study, task-specific vs. multi-task sequence-to-sequence comparative study, code-switch analysis, and quantitative-qualitative error analysis. All code, data, and models are available online: https://github.com/leduckhai/MultiMed-ST

cs.CL↗

arXiv2024

Qualitative Analysis and Adaptive Boosted DCA for Generalized Multi-Source Weber Problems

This paper has two primary objectives. First, we investigate fundamental qualitative properties of the generalized multi-source Weber problem formulated using the Minkowski gauge function. This includes proving the existence of global optimal solutions, demonstrating the compactness of the solution set, and establishing optimality conditions for these solutions. Second, we apply Nesterov's smoothing and the adaptive Boosted Difference of Convex functions Algorithm (BDCA) to solve both the unconstrained and constrained versions of the generalized multi-source Weber problems. These algorithms build upon the work presented in [6,19]. We conduct a comprehensive evaluation of the adaptive BDCA, comparing its performance to the method proposed in [19], and provide insights into its efficiency.

math.OC↗

arXiv2024

LSVOS Challenge Report: Large-scale Complex and Long Video Object Segmentation

Despite the promising performance of current video segmentation models on existing benchmarks, these models still struggle with complex scenes. In this paper, we introduce the 6th Large-scale Video Object Segmentation (LSVOS) challenge in conjunction with ECCV 2024 workshop. This year's challenge includes two tasks: Video Object Segmentation (VOS) and Referring Video Object Segmentation (RVOS). In this year, we replace the classic YouTube-VOS and YouTube-RVOS benchmark with latest datasets MOSE, LVOS, and MeViS to assess VOS under more challenging complex environments. This year's challenge attracted 129 registered teams from more than 20 institutes across over 8 countries. This report include the challenge and dataset introduction, and the methods used by top 7 teams in two tracks. More details can be found in our homepage https://lsvos.github.io/.

cs.CV↗

arXiv2024

Unified Framework with Consistency across Modalities for Human Activity Recognition

Recognizing human activities in videos is challenging due to the spatio-temporal complexity and context-dependence of human interactions. Prior studies often rely on single input modalities, such as RGB or skeletal data, limiting their ability to exploit the complementary advantages across modalities. Recent studies focus on combining these two modalities using simple feature fusion techniques. However, due to the inherent disparities in representation between these input modalities, designing a unified neural network architecture to effectively leverage their complementary information remains a significant challenge. To address this, we propose a comprehensive multimodal framework for robust video-based human activity recognition. Our key contribution is the introduction of a novel compositional query machine, called COMPUTER ($\textbf{COMP}ositional h\textbf{U}man-cen\textbf{T}ric qu\textbf{ER}y$ machine), a generic neural architecture that models the interactions between a human of interest and its surroundings in both space and time. Thanks to its versatile design, COMPUTER can be leveraged to distill distinctive representations for various input modalities. Additionally, we introduce a consistency loss that enforces agreement in prediction between modalities, exploiting the complementary information from multimodal inputs for robust human movement recognition. Through extensive experiments on action localization and group activity recognition tasks, our approach demonstrates superior performance when compared with state-of-the-art methods. Our code is available at: https://github.com/tranxuantuyen/COMPUTER.

cs.CV↗

arXiv2024

The 2nd Solution for LSVOS Challenge RVOS Track: Spatial-temporal Refinement for Consistent Semantic Segmentation

Referring Video Object Segmentation (RVOS) is a challenging task due to its requirement for temporal understanding. Due to the obstacle of computational complexity, many state-of-the-art models are trained on short time intervals. During testing, while these models can effectively process information over short time steps, they struggle to maintain consistent perception over prolonged time sequences, leading to inconsistencies in the resulting semantic segmentation masks. To address this challenge, we take a step further in this work by leveraging the tracking capabilities of the newly introduced Segment Anything Model version 2 (SAM-v2) to enhance the temporal consistency of the referring object segmentation model. Our method achieved a score of 60.40 \mathcal{J\text{\&}F} on the test set of the MeViS dataset, placing 2nd place in the final ranking of the RVOS Track at the ECCV 2024 LSVOS Challenge.

cs.CV↗

arXiv2023

Duality Theory on Vector Spaces

In this paper, we study the Fenchel-Rockafellar duality and the Lagrange duality in the general frame work of vector spaces without topological structures. We utilize the geometric approach, inspired from its successful application by B. S. Mordukhovich and his coauthors in variational and convex analysis. After revisiting coderivative calculus rules and providing the subdifferential maximum rule in vector spaces, we establish conjugate calculus rules under qualifying conditions through the algebraic interior of the function's domains. Then we develop sufficient conditions which guarantee the Fenchel-Rockafellar strong duality. Finally, after deriving some necessary and sufficient conditions for optimal solutions to convex minimization problems, under a Slater condition via the algebraic interior, we then obtain a sufficient condition for the Lagrange strong duality.

math.OC↗

arXiv2023

The Boosted DC Algorithm for Clustering with Constraints

This paper aims to investigate the effectiveness of the recently proposed Boosted Difference of Convex functions Algorithm (BDCA) when applied to clustering with constraints and set clustering with constraints problems. This is the first paper to apply BDCA to a problem with nonlinear constraints. We present the mathematical basis for the BDCA and Difference of Convex functions Algorithm (DCA), along with a penalty method based on distance functions. We then develop algorithms for solving these problems and computationally implement them, with publicly available implementations. We compare old examples and provide new experiments to test the algorithms. We find that the BDCA method converges in fewer iterations than the corresponding DCA-based method. In addition, BDCA yields faster CPU running-times in all tested problems.

math.OC↗

arXiv2020

Solving a Continuous Multifacility Location Problem by DC Algorithms

The paper presents a new approach to solve multifacility location problems, which is based on mixed integer programming and algorithms for minimizing differences of convex (DC) functions. The main challenges for solving the multifacility location problems under consideration come from their intrinsic discrete, nonconvex, and nondifferentiable nature. We provide a reformulation of these problems as those of continuous optimization and then develop a new DC type algorithm for their solutions involving Nesterov's smoothing. The proposed algorithm is computationally implemented via MATLAB numerical tests on both artificial and real data sets.

math.OC↗

arXiv2019

DNN Approximation of Nonlinear Finite Element Equations

We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the trained DNN to replace the coarse nonlinear operator thus avoiding the need to visit the fine level discretization in order to evaluate the actions of the true coarse nonlinear operator. The feasibility of the studied approach is demonstrated in a two-level FAS (full approximation scheme) used to solve a nonlinear diffusion-reaction PDE.

math.NA↗

arXiv2017

Variational Geometric Approach to Generalized Differential and Fenchel Conjugate Calculi in Convex Analysis

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their unified and simplified proofs based on the developed geometric variational schemes.

math.OC↗

arXiv2017

Nesterov's Smoothing Technique and Minimizing Differences of Convex Functions for Hierarchical Clustering

A bilevel hierarchical clustering model is commonly used in designing optimal multicast networks. In this paper, we consider two different formulations of the bilevel hierarchical clustering problem, a discrete optimization problem which can be shown to be NP-hard. Our approach is to reformulate the problem as a continuous optimization problem by making some relaxations on the discreteness conditions. Then Nesterov's smoothing technique and a numerical algorithm for minimizing differences of convex functions called the DCA are applied to cope with the nonsmoothness and nonconvexity of the problem. Numerical examples are provided to illustrate our method.

math.OC↗