arXiv subjects

Dat Ba Tran

Publications and source records attributed to Dat Ba Tran.

10 recordsLinked to original sources

arXiv2026

Diversity-Aware Reverse Kullback-Leibler Divergence for Large Language Model Distillation

Reverse Kullback-Leibler (RKL) divergence has recently emerged as the preferred objective for large language model (LLM) distillation, consistently outperforming forward KL (FKL), particularly in regimes with large vocabularies and significant teacher-student capacity mismatch, where RKL focuses learning on dominant modes rather than enforcing dense alignment. However, RKL introduces a structural limitation that drives the student toward overconfident predictions. We first provide an analysis of RKL by decomposing its gradients into target and non-target components, and show that non-target gradients consistently push the target logit upward even when the student already matches the teacher, thereby reducing output diversity. In addition, RKL provides weak supervision over non-target classes, leading to poor tail alignment. To address these issues, we propose Diversity-aware RKL (DRKL), which removes this gradient effect and strengthens non-target supervision while preserving the optimization benefits of RKL. Extensive experiments across datasets and model families demonstrate that DRKL consistently outperforms FKL, RKL, and other state-of-the-art distillation objectives, achieving better performance and a superior fidelity-diversity trade-off.

cs.LG↗

arXiv2025

Convergence of First-Order Algorithms with Momentum from the Perspective of an Inexact Gradient Descent Method

This paper introduces a novel inexact gradient descent method with momentum (IGDm) considered as a general framework for various first-order methods with momentum. This includes, in particular, the inexact proximal point method (IPPm), extragradient method (EGm), and sharpness-aware minimization (SAMm). Asymptotic convergence properies of IGDm are established under both global and local assumptions on objective functions with providing constructive convergence rates depending on the Polyak-\L ojasiewicz-Kurdyka (PLK) conditions for the objective function. Global convergence of EGm and SAMm for general smooth functions and of IPPM for weakly convex functions is derived in this way. Moreover, local convergence properties of EGm and SAMm for locally smooth functions as well as of IPPm for prox-regular functions are established. Numerical experiments for derivative-free optimization problems are conducted to confirm the efficiency of the momentum effects of the developed methods under inexactness of gradient computations

math.OC↗

arXiv2024

Understanding SAM's Robustness to Noisy Labels through Gradient Down-weighting

Sharpness-Aware Minimization (SAM) was introduced to improve generalization by seeking flat minima, yet it also exhibits robustness to label noise, a phenomenon that remains only partially understood. Prior work has mainly attributed this effect to SAM's tendency to prolong the learning of clean samples. In this work, we provide a complementary explanation by analyzing SAM at the element-wise level. We show that when noisy gradients dominate a parameter direction, their influence is reduced by the stronger amplification of clean gradients. This slows the memorization of noisy labels while sustaining clean learning, offering a more complete account of SAM's robustness. Building on this insight, we propose SANER (Sharpness-Aware Noise-Explicit Reweighting), a simple variant of SAM that explicitly magnifies this down-weighting effect. Experiments on benchmark image classification tasks with noisy labels demonstrate that SANER significantly mitigates noisy-label memorization and improves generalization over both SAM and SGD. Moreover, since SANER is designed from the mechanism of SAM, it can also be seamlessly integrated into SAM-like variants, further boosting their robustness.

cs.LG↗

arXiv2024

Fundamental Convergence Analysis of Sharpness-Aware Minimization

The paper investigates the fundamental convergence properties of Sharpness-Aware Minimization (SAM), a recently proposed gradient-based optimization method [Foret et al., 2021] that significantly improves the generalization of deep neural networks. The convergence properties, including the stationarity of accumulation points, the convergence of the sequence of gradients to the origin, the sequence of function values to the optimal value, and the sequence of iterates to the optimal solution, are established for the method. The universality of the provided convergence analysis, based on inexact gradient descent frameworks Khanh et al. [2023b], allows its extensions to efficient normalized versions of SAM such as F-SAM [Li et al., 2024], VaSSO [Li and Giannakis, 2023], RSAM [Liu et al., 2022], and to the unnormalized versions of SAM such as USAM [Andriushchenko and Flammarion, 2022]. Numerical experiments are conducted on classification tasks using deep learning models to confirm the practical aspects of our analysis.

math.OC↗

arXiv2023

General Derivative-Free Optimization Methods under Global and Local Lipschitz Continuity of Gradients

This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing such functions with either global or local Lipschitz continuous gradients. The newly developed methods use gradient approximations based on finite differences, where finite difference intervals are automatically adapted to the magnitude of the exact gradients without knowing them exactly. The suggested algorithms achieve fundamental convergence results, including stationarity of accumulation points in general settings as well as global convergence with constructive convergence rates when the Kurdyka-\L ojasiewicz property is imposed. The local convergence of the proposed algorithms to nonisolated local minimizers, along with their local convergence rates, is also analyzed under this property. Numerical experiences involving various convex, nonconvex, noiseless, and noisy functions demonstrate that the new methods exhibit essential advantages over other state-of-the-art methods in derivative-free optimization.

math.OC↗

arXiv2023

Inexact proximal methods for weakly convex functions

This paper proposes and develops inexact proximal methods for finding stationary points of the sum of a smooth function and a nonsmooth weakly convex one, where an error is present in the calculation of the proximal mapping of the nonsmooth term. A general framework for finding zeros of a continuous mapping is derived from our previous paper on this subject to establish convergence properties of the inexact proximal point method when the smooth term is vanished and of the inexact proximal gradient method when the smooth term satisfies a descent condition. The inexact proximal point method achieves global convergence with constructive convergence rates when the Moreau envelope of the objective function satisfies the Kurdyka-Lojasiewicz (KL) property. Meanwhile, when the smooth term is twice continuously differentiable with a Lipschitz continuous gradient and a differentiable approximation of the objective function satisfies the KL property, the inexact proximal gradient method achieves the global convergence of iterates with constructive convergence rates.

math.OC↗

arXiv2023

A New Inexact Gradient Descent Method with Applications to Nonsmooth Convex Optimization

The paper proposes and develops a novel inexact gradient method (IGD) for minimizing C1-smooth functions with Lipschitzian gradients, i.e., for problems of C1,1 optimization. We show that the sequence of gradients generated by IGD converges to zero. The convergence of iterates to stationary points is guaranteed under the Kurdyka- Lojasiewicz (KL) property of the objective function with convergence rates depending on the KL exponent. The newly developed IGD is applied to designing two novel gradient-based methods of nonsmooth convex optimization such as the inexact proximal point methods (GIPPM) and the inexact augmented Lagrangian method (GIALM) for convex programs with linear equality constraints. These two methods inherit global convergence properties from IGD and are confirmed by numerical experiments to have practical advantages over some well-known algorithms of nonsmooth convex optimization.

math.OC↗

arXiv2022

Inexact reduced gradient methods in nonconvex optimization

This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces. Some abstract convergence results for a broad class of linesearch methods are stablished. A general scheme for inexact reduced gradient (IRG) methods is proposed, where the errors in the gradient approximation automatically adapt with the magnitudes of the exact gradients. The sequences of iterations are shown to obtain stationary accumulation points when different stepsize selections are employed. Convergence results with constructive convergence rates for the developed IRG methods are established under the Kurdyka- Lojasiewicz property. The obtained results for the IRG methods are confirmed by encouraging numerical experiments, which demonstrate advantages of automatically controlled errors in IRG methods over other frequently used error selections.

math.OC↗

arXiv2021

Globally Convergent Coderivative-Based Generalized Newton Methods in Nonsmooth Optimization

This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are coderivative-based and employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions, which are either of class $\mathcal{C}^{1,1}$, or are represented in the form of convex composite optimization, where one of the terms may be extended-real-valued. The proposed globally convergent algorithms are of two types. The first one extends the damped Newton method and requires positive-definiteness of the generalized Hessians for its well-posedness and efficient performance, while the other algorithm is of {the regularized Newton type} being well-defined when the generalized Hessians are merely positive-semidefinite. The obtained convergence rates for both methods are at least linear, but become superlinear under the semismooth$^*$ property of subgradient mappings. Problems of convex composite optimization are investigated with and without the strong convexity assumption {on smooth parts} of objective functions by implementing the machinery of forward-backward envelopes. Numerical experiments are conducted for Lasso problems and for box constrained quadratic programs with providing performance comparisons of the new algorithms and some other first-order and second-order methods that are highly recognized in nonsmooth optimization.

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arXiv2021

Generalized Damped Newton Algorithms in Nonsmooth Optimization via Second-Order Subdifferentials

The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of second-order subdifferentials of nonsmooth functions with employing the machinery of second-order variational analysis and generalized differentiation. First we develop a globally superlinearly convergent damped Newton-type algorithm for the class of continuously differentiable functions with Lipschitzian gradients, which are nonsmooth of second order. Then we design such a globally convergent algorithm to solve a structured class of nonsmooth quadratic composite problems with extended-real-valued cost functions, which typically arise in machine learning and statistics. Finally, we present the results of numerical experiments and compare the performance of our main algorithm applied to an important class of Lasso problems with those achieved by other first-order and second-order optimization algorithms.

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