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Hung Vinh Tran

Publications and source records attributed to Hung Vinh Tran.

At least 19 recordsLinked to original sources
arXiv2026

FOSTER: First-order Dataset Distillation for Text-based Sequential Recommendation

Text-based sequential recommender systems, while greatly improving recommendation accuracy by incorporating item contexts, are undeniably more expensive to train. By condensing a large dataset into a compact set of synthetic samples for model training, dataset distillation offers a promising solution. However, its adoption in text-based sequential recommendation is non-trivial given the large pool of discrete items. This challenge is further compounded by language model-based item encoding, which makes bi-level optimization commonly used in dataset distillation prohibitively expensive. To this end, we propose First-order dataset distillation for Text-based Sequential Recommendation (FOSTER), which facilitates effectiveness and efficiency via three novel components: (1) stochastic item subset sampling that replaces costly full-corpus embedding extraction at each distillation step; (2) first-order optimization with trajectory-anchored parameter reset to avoid expensive bi-level gradient computation; and (3) regularization that explicitly promotes co-occurrence between semantically similar items in the synthetic sequences. Extensive experiments on three benchmarks show that FOSTER consistently outperforms existing dataset distillation and coreset selection baselines, approximating full-dataset performance using as few as 20 synthetic interaction sequences.

cs.IR↗
arXiv2026

Quantification of ergodicity for Hamilton--Jacobi equations in a dynamic random environment

We study quantitative large-time averages for Hamilton--Jacobi equations in a dynamic random environment that is stationary ergodic and has unit-range dependence in time. Our motivation comes from stochastic growth models related to the tensionless (inviscid) KPZ equation, which can be formulated as Hamilton--Jacobi equations with random forcing. Understanding the large-time behavior of solutions is closely connected to fundamental questions concerning fluctuations and scaling in such growth processes. In this article, we establish, up to slowly varying factors, convergence rates with exponent $1/2$ for the large-time averages of both the solutions and the associated metric problem toward their ergodic limits. Our proof relies crucially on a new almost-Lipschitz regularity theory for the metric problem, which is of independent interest.

math.AP↗
arXiv2026

Efficient Content-based Recommendation Model Training via Noise-aware Coreset Selection

Content-based recommendation systems (CRSs) utilize content features to predict user-item interactions, serving as essential tools for helping users navigate information-rich web services. However, ensuring the effectiveness of CRSs requires large-scale and even continuous model training to accommodate diverse user preferences, resulting in significant computational costs and resource demands. A promising approach to this challenge is coreset selection, which identifies a small but representative subset of data samples that preserves model quality while reducing training overhead. Yet, the selected coreset is vulnerable to the pervasive noise in user-item interactions, particularly when it is minimally sized. To this end, we propose Noise-aware Coreset Selection (NaCS), a specialized framework for CRSs. NaCS constructs coresets through submodular optimization based on training gradients, while simultaneously correcting noisy labels using a progressively trained model. Meanwhile, we refine the selected coreset by filtering out low-confidence samples through uncertainty quantification, thereby avoid training with unreliable interactions. Through extensive experiments, we show that NaCS produces higher-quality coresets for CRSs while achieving better efficiency than existing coreset selection techniques. Notably, NaCS recovers 93-95\% of full-dataset training performance using merely 1\% of the training data. The source code is available at \href{https://github.com/chenxing1999/nacs}{https://github.com/chenxing1999/nacs}.

cs.LG↗
arXiv2025

Controlling Klein-Gordon Chains and Lattices

In this work, we initiate the study of controlling nonlinear Klein-Gordon chains and lattices through their emergent collective flocking behavior. By constructing appropriate feedback control mechanisms, we demonstrate that any physically admissible flock state can be achieved in finite time, meaning the chain can be driven from arbitrary initial vibrations toward a coherent traveling-wave motion. Finally, we reveal a deep connection between the flocking problem and a minimal-time control principle formulated within the framework of nonlinear Hamilton-Jacobi equations and optimal control theory, providing a unifying view-point for wave control in discrete nonlinear media.

math.OC↗
arXiv2025

Policy Iteration for Exploratory Hamilton--Jacobi--Bellman Equations

We study the policy iteration algorithm (PIA) for entropy-regularized stochastic control problems on an infinite time horizon with a large discount rate, focusing on two main scenarios. First, we analyze PIA with bounded coefficients where the controls applied to the diffusion term satisfy a smallness condition. We demonstrate the convergence of PIA based on a uniform $\mathcal{C}^{2,α}$ estimate for the value sequence generated by PIA, and provide a quantitative convergence analysis for this scenario. Second, we investigate PIA with unbounded coefficients but no control over the diffusion term. In this scenario, we first provide the well-posedness of the exploratory Hamilton--Jacobi--Bellman equation with linear growth coefficients and polynomial growth reward function. By such a well-posedess result we achieve PIA's convergence by establishing a quantitative locally uniform $\mathcal{C}^{1,α}$ estimates for the generated value sequence.

math.OC↗
arXiv2025

Policy iteration for the deterministic control problems -- a viscosity approach

This paper is concerned with the convergence rate of policy iteration for (deterministic) optimal control problems in continuous time. To overcome the problem of ill-posedness due to lack of regularity, we consider a semi-discrete scheme by adding a viscosity term via finite differences in space. We prove that PI for the semi-discrete scheme converges exponentially fast, and provide a bound on the error induced by the semi-discrete scheme. We also consider the discrete space-time scheme, where both space and time are discretized. Convergence rate of PI and the discretization error are studied.

math.OC↗
arXiv2025

Policy iteration for nonconvex viscous Hamilton--Jacobi equations

We study the convergence rates of policy iteration (PI) for nonconvex viscous Hamilton--Jacobi equations using a discrete space-time scheme, where both space and time variables are discretized. We analyze the case with an uncontrolled diffusion term, which corresponds to a possibly degenerate viscous Hamilton--Jacobi equation. We first obtain an exponential convergent result of PI for the discrete space-time schemes. We then investigate the discretization error.

math.NA↗
arXiv2025

On-device Content-based Recommendation with Single-shot Embedding Pruning: A Cooperative Game Perspective

Content-based Recommender Systems (CRSs) play a crucial role in shaping user experiences in e-commerce, online advertising, and personalized recommendations. However, due to the vast amount of categorical features, the embedding tables used in CRS models pose a significant storage bottleneck for real-world deployment, especially on resource-constrained devices. To address this problem, various embedding pruning methods have been proposed, but most existing ones require expensive retraining steps for each target parameter budget, leading to enormous computation costs. In reality, this computation cost is a major hurdle in real-world applications with diverse storage requirements, such as federated learning and streaming settings. In this paper, we propose Shapley Value-guided Embedding Reduction (Shaver) as our response. With Shaver, we view the problem from a cooperative game perspective, and quantify each embedding parameter's contribution with Shapley values to facilitate contribution-based parameter pruning. To address the inherently high computation costs of Shapley values, we propose an efficient and unbiased method to estimate Shapley values of a CRS's embedding parameters. Moreover, in the pruning stage, we put forward a field-aware codebook to mitigate the information loss in the traditional zero-out treatment. Through extensive experiments on three real-world datasets, Shaver has demonstrated competitive performance with lightweight recommendation models across various parameter budgets. The source code is available at https://github.com/chenxing1999/shaver

cs.IR↗
arXiv2025

A Thorough Performance Benchmarking on Lightweight Embedding-based Recommender Systems

Since the creation of the Web, recommender systems (RSs) have been an indispensable mechanism in information filtering. State-of-the-art RSs primarily depend on categorical features, which ecoded by embedding vectors, resulting in excessively large embedding tables. To prevent over-parameterized embedding tables from harming scalability, both academia and industry have seen increasing efforts in compressing RS embeddings. However, despite the prosperity of lightweight embedding-based RSs (LERSs), a wide diversity is seen in evaluation protocols, resulting in obstacles when relating LERS performance to real-world usability. Moreover, despite the common goal of lightweight embeddings, LERSs are evaluated with a single choice between the two main recommendation tasks -- collaborative filtering and content-based recommendation. This lack of discussions on cross-task transferability hinders the development of unified, more scalable solutions. Motivated by these issues, this study investigates various LERSs' performance, efficiency, and cross-task transferability via a thorough benchmarking process. Additionally, we propose an efficient embedding compression method using magnitude pruning, which is an easy-to-deploy yet highly competitive baseline that outperforms various complex LERSs. Our study reveals the distinct performance of LERSs across the two tasks, shedding light on their effectiveness and generalizability. To support edge-based recommendations, we tested all LERSs on a Raspberry Pi 4, where the efficiency bottleneck is exposed. Finally, we conclude this paper with critical summaries of LERS performance, model selection suggestions, and underexplored challenges around LERSs for future research. To encourage future research, we publish source codes and artifacts at \href{this link}{https://github.com/chenxing1999/recsys-benchmark}.

cs.IR↗
arXiv2024

Quenching for axisymmetric hypersurfaces under forced mean curvature flows

Here, we study the motion of axisymmetric hypersurfaces $\{Γ_t\}_{t\ge0}$ evolved by forced mean curvature flows in the periodic setting. We establish conditions that quenching occurs or does not occur in terms of the initial data and forcing term. We also study the locations where the quenching happens in some special cases.

math.AP↗
arXiv2023

Nondivergence form degenerate linear parabolic equations on the upper half space

We study a class of nondivergence form second-order degenerate linear parabolic equations in $(-\infty, T) \times {\mathbb R}^d_+$ with the homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial {\mathbb R}^d_+$, where ${\mathbb R}^d_+ = \{x =(x_1,x_2,\ldots, x_d) \in {\mathbb R}^d\,:\, x_d>0\}$ and $T\in {(-\infty, \infty]}$ is given. The coefficient matrices of the equations are the product of $μ(x_d)$ and bounded positive definite matrices, where $μ(x_d)$ behaves like $x_d^α$ for some given $α\in (0,2)$, which are degenerate on the boundary $\{x_d=0\}$ of the domain. The divergence form equations in this setting were studied in [14]. Under a partially weighted VMO assumption on the coefficients, we obtain the wellposedness and regularity of solutions in weighted Sobolev spaces. Our research program is motivated by the regularity theory of solutions to degenerate viscous Hamilton-Jacobi equations.

math.AP↗
arXiv2022

Level-set forced mean curvature flow with the Neumann boundary condition

Here, we study a level-set forced mean curvature flow with the homogeneous Neumann boundary condition. We first show that the solution is Lipschitz in time and locally Lipschitz in space. Then, under an additional condition on the forcing term, we prove that the solution is globally Lipschitz. We obtain the large time behavior of the solution in this setting and study the large time profile in some specific situations. Finally, we give two examples demonstrating that the additional condition on the forcing term is sharp, and without it, the solution might not be globally Lipschitz.

math.AP↗
arXiv2021

Degenerate linear parabolic equations in divergence form on the upper half space

We study a class of second-order degenerate linear parabolic equations in divergence form in $(-\infty, T) \times \mathbb R^d_+$ with homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial \mathbb R^d_+$, where $\mathbb R^d_+ = \{x \in \mathbb R^d\,:\, x_d>0\}$ and $T\in {(-\infty, \infty]}$ is given. The coefficient matrices of the equations are the product of $μ(x_d)$ and bounded uniformly elliptic matrices, where $μ(x_d)$ behaves like $x_d^α$ for some given $α\in (0,2)$, which are degenerate on the boundary $\{x_d=0\}$ of the domain. Under a partially VMO assumption on the coefficients, we obtain the wellposedness and regularity of solutions in weighted Sobolev spaces. Our results can be readily extended to systems.

math.AP↗
arXiv2021

On a class of divergence form linear parabolic equations with degenerate coefficients

We study a class of linear parabolic equations in divergence form with degenerate coefficients on the upper half space. Specifically, the equations are considered in $(-\infty, T) \times \mathbb{R}^d_+$, where $\mathbb{R}^d_+ = \{x \in \mathbb{R}^d\,:\, x_d>0\}$ and $T\in {(-\infty, \infty]}$ is given, and the diffusion matrices are the product of $x_d$ and bounded uniformly elliptic matrices, which are degenerate at $\{x_d=0\}$. As such, our class of equations resembles well the corresponding class of degenerate viscous Hamilton-Jacobi equations. We obtain wellposedness results and regularity type estimates in some appropriate weighted Sobolev spaces for the solutions.

math.AP↗
arXiv2019

Effective fronts of polytope shapes

We study the periodic homogenization of first order front propagations. Based on PDE methods, we provide a simple proof that for $n \geq 3$, the class of centrally symmetric polytopes with rational coordinates and nonempty interior is admissible as effective fronts, which was also established in [1,10] in the form of stable norms as an extension of Hedlund's classical result [7]. Besides, we obtain the optimal convergence rate of the homogenization problem for this class.

math.AP↗
arXiv2016

A Note on Nonconvex Mean Field Games

We introduce a nonconvex Mean Field Games system by studying a model with a large number of identical pairs of players who are all rational, and each pair plays an identical zero-sum differential game. We study existence and uniqueness of solutions for a simple system in this context.

math.AP↗
arXiv2016

Inverse problems, non-roundness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model

The main goal of this paper is to understand finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis [19]. Motivated by results in [4] and applications in turbulent combustion, we show that when the dimension is two and the flow of the ambient fluid is either weak or very strong, the level set of the effective burning velocity has flat pieces. Due to the lack of an applicable Hopf-type rigidity result, we need to identify the exact location of at least one flat piece. Implications on the effective flame front and other related inverse type problems are also discussed.

math.AP↗