arXiv subjects

Tung Pham

Publications and source records attributed to Tung Pham.

At least 19 recordsLinked to original sources

arXiv2026

Mixture-of-Control: State-Aware Fine-Tuning for Transformer-based Models

State-based fine-tuning has emerged as a compelling alternative to weight-based adaptation for transformers, updating lightweight controls into states rather than model weights, offering substantial memory savings while retaining parameter efficiency. However, most existing state-based methods typically apply only per-block control updates, which limits inter-block information exchange and restricts representational adaptation. Meanwhile, prior mechanisms that enable cross-block communication often introduce considerable computational overhead, reducing their practicality for efficient fine-tuning. We introduce Mixture-of-Control (MoC), a lightweight fine-tuning framework that adaptively integrates local and global control signals to enhance representation learning. MoC treats block-wise control states as experts in a sparse mixture-of-experts process, enabling efficient communication across transformer blocks. Empirical results across diverse transformer-based benchmarks demonstrate that MoC outperforms state-based methods while maintaining a comparable memory and computational efficiency.

cs.LG↗

arXiv2026

Beyond the Frontier: Stochastic Backtracking for Efficient Test-Time Scaling

Test-time scaling improves language model reasoning by spending additional compute to explore multiple solution trajectories. The key challenge is to maximize accuracy while minimizing the total number of generated tokens during reasoning. Recent PRM-guided methods score intermediate prefixes to steer this search, but most are frontier-only: they keep only the current active prefixes and irreversibly prune or resample away the rest using noisy PRM scores. This can cause premature commitment, diversity collapse, and the loss of prefixes that still admit correct continuations. We introduce stochastic backtracking over a persistent pool of historical prefixes, allowing test-time compute to revisit previously generated states instead of only expanding the current frontier. To make this efficient, we propose two complementary mechanisms. Subpool Selection strengthens greedy PRM-guided search by applying Top-N selection within random subpools, giving historical prefixes a chance to bypass over-scored frontier candidates. Power Backtrack Sequential Monte Carlo extends SMC-style resampling to the persistent pool using powered PRM scores and mixture-corrected weights. Across mathematical reasoning benchmarks and model scales, our methods consistently achieve higher accuracy per token count, and the same level of accuracy using only a fraction of the token count in comparison to strong PRM-guided baselines, demonstrating that persistent-pool stochastic backtracking provides a simple and effective way to improve the accuracy-token trade-off in test-time scaling.

cs.AI↗

arXiv2025

ClozeMath: Improving Mathematical Reasoning in Language Models by Learning to Fill Equations

The capabilities of large language models (LLMs) have been enhanced by training on data that reflects human thought processes, such as the Chain-of-Thought format. However, evidence suggests that the conventional scheme of next-word prediction may not fully capture how humans learn to think. Inspired by how humans generalize mathematical reasoning, we propose a new approach named ClozeMath to fine-tune LLMs for mathematical reasoning. Our ClozeMath involves a text-infilling task that predicts masked equations from a given solution, analogous to cloze exercises used in human learning. Experiments on GSM8K, MATH, and GSM-Symbolic show that ClozeMath surpasses the strong baseline Masked Thought in performance and robustness, with two test-time scaling decoding algorithms, Beam Search and Chain-of-Thought decoding. Additionally, we conduct an ablation study to analyze the effects of various architectural and implementation choices on our approach.

cs.CL↗

arXiv2025

Explicit Eigenvalue Regularization Improves Sharpness-Aware Minimization

Sharpness-Aware Minimization (SAM) has attracted significant attention for its effectiveness in improving generalization across various tasks. However, its underlying principles remain poorly understood. In this work, we analyze SAM's training dynamics using the maximum eigenvalue of the Hessian as a measure of sharpness, and propose a third-order stochastic differential equation (SDE), which reveals that the dynamics are driven by a complex mixture of second- and third-order terms. We show that alignment between the perturbation vector and the top eigenvector is crucial for SAM's effectiveness in regularizing sharpness, but find that this alignment is often inadequate in practice, limiting SAM's efficiency. Building on these insights, we introduce Eigen-SAM, an algorithm that explicitly aims to regularize the top Hessian eigenvalue by aligning the perturbation vector with the leading eigenvector. We validate the effectiveness of our theory and the practical advantages of our proposed approach through comprehensive experiments. Code is available at https://github.com/RitianLuo/EigenSAM.

cs.LG↗

arXiv2024

On Barycenter Computation: Semi-Unbalanced Optimal Transport-based Method on Gaussians

We explore a robust version of the barycenter problem among $n$ centered Gaussian probability measures, termed Semi-Unbalanced Optimal Transport (SUOT)-based Barycenter, wherein the barycenter remains fixed while the others are relaxed using Kullback-Leibler divergence. We develop optimization algorithms on Bures-Wasserstein manifold, named the Exact Geodesic Gradient Descent and Hybrid Gradient Descent algorithms. While the Exact Geodesic Gradient Descent method is based on computing the exact closed form of the first-order derivative of the objective function of the barycenter along a geodesic on the Bures manifold, the Hybrid Gradient Descent method utilizes optimizer components when solving the SUOT problem to replace outlier measures before applying the Riemannian Gradient Descent. We establish the theoretical convergence guarantees for both methods and demonstrate that the Exact Geodesic Gradient Descent algorithm attains a dimension-free convergence rate. Finally, we conduct experiments to compare the normal Wasserstein Barycenter with ours and perform an ablation study.

cs.LG↗

arXiv2024

Principal Sub-manifolds

We propose a novel method of finding principal components in multivariate data sets that lie on an embedded nonlinear Riemannian manifold within a higher-dimensional space. Our aim is to extend the geometric interpretation of PCA, while being able to capture non-geodesic modes of variation in the data. We introduce the concept of a principal sub-manifold, a manifold passing through a reference point, and at any point on the manifold extending in the direction of highest variation in the space spanned by the eigenvectors of the local tangent space PCA. Compared to recent work for the case where the sub-manifold is of dimension one Panaretos et al. (2014)$-$essentially a curve lying on the manifold attempting to capture one-dimensional variation$-$the current setting is much more general. The principal sub-manifold is therefore an extension of the principal flow, accommodating to capture higher dimensional variation in the data. We show the principal sub-manifold yields the ball spanned by the usual principal components in Euclidean space. By means of examples, we illustrate how to find, use and interpret a principal sub-manifold and we present an application in shape analysis.

stat.ME↗

arXiv2024

Diversity-Aware Agnostic Ensemble of Sharpness Minimizers

There has long been plenty of theoretical and empirical evidence supporting the success of ensemble learning. Deep ensembles in particular take advantage of training randomness and expressivity of individual neural networks to gain prediction diversity, ultimately leading to better generalization, robustness and uncertainty estimation. In respect of generalization, it is found that pursuing wider local minima result in models being more robust to shifts between training and testing sets. A natural research question arises out of these two approaches as to whether a boost in generalization ability can be achieved if ensemble learning and loss sharpness minimization are integrated. Our work investigates this connection and proposes DASH - a learning algorithm that promotes diversity and flatness within deep ensembles. More concretely, DASH encourages base learners to move divergently towards low-loss regions of minimal sharpness. We provide a theoretical backbone for our method along with extensive empirical evidence demonstrating an improvement in ensemble generalizability.

cs.LG↗

arXiv2023

A High-Quality Robust Diffusion Framework for Corrupted Dataset

Developing image-generative models, which are robust to outliers in the training process, has recently drawn attention from the research community. Due to the ease of integrating unbalanced optimal transport (UOT) into adversarial framework, existing works focus mainly on developing robust frameworks for generative adversarial model (GAN). Meanwhile, diffusion models have recently dominated GAN in various tasks and datasets. However, according to our knowledge, none of them are robust to corrupted datasets. Motivated by DDGAN, our work introduces the first robust-to-outlier diffusion. We suggest replacing the UOT-based generative model for GAN in DDGAN to learn the backward diffusion process. Additionally, we demonstrate that the Lipschitz property of divergence in our framework contributes to more stable training convergence. Remarkably, our method not only exhibits robustness to corrupted datasets but also achieves superior performance on clean datasets.

cs.CV↗

arXiv2023

Generalization Bounds for Robust Contrastive Learning: From Theory to Practice

Contrastive Learning first extracts features from unlabeled data, followed by linear probing with labeled data. Adversarial Contrastive Learning (ACL) integrates Adversarial Training into the first phase to enhance feature robustness against attacks in the probing phase. While ACL has shown strong empirical results, its theoretical understanding remains limited. Furthermore, while a fair amount of theoretical works analyze how the unsupervised loss can support the supervised loss in the probing phase, none has examined its role to the robust supervised loss. To fill this gap, our work develops rigorous theories to identify which components in the unsupervised training can help improve the robust supervised loss. Specifically, besides the adversarial contrastive loss, we reveal that the benign one, along with a global divergence between benign and adversarial examples can also improve robustness. Proper experiments are conducted to justify our findings.

cs.LG↗

arXiv2023

Understanding the Robustness of Randomized Feature Defense Against Query-Based Adversarial Attacks

Recent works have shown that deep neural networks are vulnerable to adversarial examples that find samples close to the original image but can make the model misclassify. Even with access only to the model's output, an attacker can employ black-box attacks to generate such adversarial examples. In this work, we propose a simple and lightweight defense against black-box attacks by adding random noise to hidden features at intermediate layers of the model at inference time. Our theoretical analysis confirms that this method effectively enhances the model's resilience against both score-based and decision-based black-box attacks. Importantly, our defense does not necessitate adversarial training and has minimal impact on accuracy, rendering it applicable to any pre-trained model. Our analysis also reveals the significance of selectively adding noise to different parts of the model based on the gradient of the adversarial objective function, which can be varied during the attack. We demonstrate the robustness of our defense against multiple black-box attacks through extensive empirical experiments involving diverse models with various architectures.

cs.LG↗

arXiv2023

Sharpness-Aware Teleportation on Riemannian Manifolds

Recent studies highlight the effectiveness of flat minima in enhancing generalization, with sharpness-aware minimization (SAM) achieving state-of-the-art performance. Additionally, insights into the intrinsic geometry of the loss landscape have shown promise for improving model generalization. Building on these advancements, we introduce a novel sharpness-aware, geometry-aware teleportation mechanism to further enhance robustness and generalization. The core innovation of our approach is to decompose each iteration into a teleportation step within a local orbit and a sharpness-aware step that transitions between different orbits, leveraging the Riemannian quotient manifold. Our approach is grounded in a theoretical framework that analyzes the generalization gap between population loss and worst-case empirical loss within the context of Riemannian manifolds. To demonstrate the effectiveness of our method, we evaluate and compare our algorithm on diverse vision benchmarks with various datasets and Riemannian manifolds.

cs.LG↗

arXiv2023

Sharpness & Shift-Aware Self-Supervised Learning

Self-supervised learning aims to extract meaningful features from unlabeled data for further downstream tasks. In this paper, we consider classification as a downstream task in phase 2 and develop rigorous theories to realize the factors that implicitly influence the general loss of this classification task. Our theories signify that sharpness-aware feature extractors benefit the classification task in phase 2 and the existing data shift between the ideal (i.e., the ideal one used in theory development) and practical (i.e., the practical one used in implementation) distributions to generate positive pairs also remarkably affects this classification task. Further harvesting these theoretical findings, we propose to minimize the sharpness of the feature extractor and a new Fourier-based data augmentation technique to relieve the data shift in the distributions generating positive pairs, reaching Sharpness & Shift-Aware Contrastive Learning (SSA-CLR). We conduct extensive experiments to verify our theoretical findings and demonstrate that sharpness & shift-aware contrastive learning can remarkably boost the performance as well as obtaining more robust extracted features compared with the baselines.

cs.LG↗

arXiv2022

On Transportation of Mini-batches: A Hierarchical Approach

Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with a very high number of supports. The m-OT solves several smaller optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, the m-OT does not consider the relationship between mini-batches which leads to undesirable estimation. Moreover, the m-OT does not approximate a proper metric between probability measures since the identity property is not satisfied. To address these problems, we propose a novel mini-batch scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that finds the optimal coupling between mini-batches and it can be seen as an approximation to a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the BoMb-OT when the regularized parameter goes to infinity. Finally, we carry out experiments on various applications including deep generative models, deep domain adaptation, approximate Bayesian computation, color transfer, and gradient flow to show that the BoMb-OT can be widely applied and performs well in various applications.

stat.ML↗

arXiv2022

Improving Mini-batch Optimal Transport via Partial Transportation

Mini-batch optimal transport (m-OT) has been widely used recently to deal with the memory issue of OT in large-scale applications. Despite their practicality, m-OT suffers from misspecified mappings, namely, mappings that are optimal on the mini-batch level but are partially wrong in the comparison with the optimal transportation plan between the original measures. Motivated by the misspecified mappings issue, we propose a novel mini-batch method by using partial optimal transport (POT) between mini-batch empirical measures, which we refer to as mini-batch partial optimal transport (m-POT). Leveraging the insight from the partial transportation, we explain the source of misspecified mappings from the m-OT and motivate why limiting the amount of transported masses among mini-batches via POT can alleviate the incorrect mappings. Finally, we carry out extensive experiments on various applications such as deep domain adaptation, partial domain adaptation, deep generative model, color transfer, and gradient flow to demonstrate the favorable performance of m-POT compared to current mini-batch methods.

stat.ML↗

arXiv2022

On Multimarginal Partial Optimal Transport: Equivalent Forms and Computational Complexity

We study the multi-marginal partial optimal transport (POT) problem between $m$ discrete (unbalanced) measures with at most $n$ supports. We first prove that we can obtain two equivalence forms of the multimarginal POT problem in terms of the multimarginal optimal transport problem via novel extensions of cost tensor. The first equivalence form is derived under the assumptions that the total masses of each measure are sufficiently close while the second equivalence form does not require any conditions on these masses but at the price of more sophisticated extended cost tensor. Our proof techniques for obtaining these equivalence forms rely on novel procedures of moving mass in graph theory to push transportation plan into appropriate regions. Finally, based on the equivalence forms, we develop optimization algorithm, named ApproxMPOT algorithm, that builds upon the Sinkhorn algorithm for solving the entropic regularized multimarginal optimal transport. We demonstrate that the ApproxMPOT algorithm can approximate the optimal value of multimarginal POT problem with a computational complexity upper bound of the order $\tilde{\mathcal{O}}(m^3(n+1)^{m}/ \varepsilon^2)$ where $\varepsilon > 0$ stands for the desired tolerance.

stat.ML↗

arXiv2022

Entropic Gromov-Wasserstein between Gaussian Distributions

We study the entropic Gromov-Wasserstein and its unbalanced version between (unbalanced) Gaussian distributions with different dimensions. When the metric is the inner product, which we refer to as inner product Gromov-Wasserstein (IGW), we demonstrate that the optimal transportation plans of entropic IGW and its unbalanced variant are (unbalanced) Gaussian distributions. Via an application of von Neumann's trace inequality, we obtain closed-form expressions for the entropic IGW between these Gaussian distributions. Finally, we consider an entropic inner product Gromov-Wasserstein barycenter of multiple Gaussian distributions. We prove that the barycenter is a Gaussian distribution when the entropic regularization parameter is small. We further derive a closed-form expression for the covariance matrix of the barycenter.

math.ST↗

arXiv2021

On Robust Optimal Transport: Computational Complexity and Barycenter Computation

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost of robust optimal transport in $\widetilde{\mathcal{O}}(\frac{n^2}{\varepsilon})$ time, in which $n$ is the number of supports of the probability distributions and $\varepsilon$ is the desired error. Furthermore, we investigate a fixed-support robust barycenter problem between $m$ discrete probability distributions with at most $n$ number of supports and develop an approximating algorithm based on iterative Bregman projections (IBP). For the specific case $m = 2$, we show that this algorithm can approximate the optimal barycenter value in $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon})$ time, thus being better than the previous complexity $\widetilde{\mathcal{O}}(\frac{mn^2}{\varepsilon^2})$ of the IBP algorithm for approximating the Wasserstein barycenter.

cs.LG↗

arXiv2021

Point-set Distances for Learning Representations of 3D Point Clouds

Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer discrepancy or Earth Mover's distance, but those metrics are either ineffective in measuring the differences between point clouds or computationally expensive. In this paper, we conduct a systematic study with extensive experiments on distance metrics for 3D point clouds. From this study, we propose to use sliced Wasserstein distance and its variants for learning representations of 3D point clouds. In addition, we introduce a new algorithm to estimate sliced Wasserstein distance that guarantees that the estimated value is close enough to the true one. Experiments show that the sliced Wasserstein distance and its variants allow the neural network to learn a more efficient representation compared to the Chamfer discrepancy. We demonstrate the efficiency of the sliced Wasserstein metric and its variants on several tasks in 3D computer vision including training a point cloud autoencoder, generative modeling, transfer learning, and point cloud registration.

cs.CV↗