arXiv subjects

Viet Anh Nguyen

Publications and source records attributed to Viet Anh Nguyen.

At least 19 recordsLinked to original sources

arXiv2026

Tight Bounds for Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function

Data-driven algorithm design frames hyperparameter tuning as a statistical learning problem, but establishing generalization guarantees remains challenging due to the implicit, non-smooth dependence of model performance on hyperparameters. Existing multi-dimensional bounds under piecewise-polynomial assumptions remain theoretically loose and lack comprehensive lower bounds. We resolve this by establishing tight pseudo-dimension bounds for multi-dimensional data-driven tuning. First, we refine the learning-theoretic upper bound using real algebraic geometry; by analyzing invariant connected sign cells during block elimination rather than isolated sign vectors, we avoid topological over-counting to derive strictly sharper sample complexities. Second, we present a multi-regime lower-bound framework that disentangles combinatorial and algebraic capacities. By constructing shattered problem instances across distinct regimes, we prove our upper bounds are tightly saturated. Finally, we extend our topological framework to accommodate general bi-level validation-loss tuning and broader semi-algebraic applications.

cs.LG↗

arXiv2026

Wasserstein Projection Tests: Higher-Order Asymptotics and Connections to Empirical Likelihood

Tests of moment restrictions can be constructed by projecting the empirical distribution onto the set of laws satisfying the null. Wasserstein projection (WP) performs this projection by transporting mass in the sample space, rather than only reweighting observed atoms as in empirical likelihood (EL), and therefore incorporates both the ground geometry and the local variation of the moment function. Existing WP theory provides a first-order null limit but does not quantify finite-sample calibration or distinguish tests with the same limiting local power. We derive stochastic expansions of the rescaled WP statistic under the null and under Pitman-type local alternatives, identifying its order-$n^{-1/2}$ correction with a uniform remainder of order $\widetilde{O}_p(n^{-1})$. The resulting Edgeworth theory gives an order-$\widetilde{O}(n^{-1})$ size error for the plug-in WP test and an explicit order-$n^{-1/2}$ correction to local power. For scalar moments under local location shifts, WP, EL, and Hotelling's $T^2$ have the same first-order power, whereas their second-order ranking is determined by derivative-based curvature for WP and value-based skewness for EL. Extending the expansion by one further order, we construct two Bartlett-type corrections that improve coverage accuracy to $\widetilde{O}(n^{-3/2})$. Finally, we develop a certified localized dual algorithm that controls numerical error in the test decision. A theory-guided smooth fairness experiment using a common asymptotic chi-square reference quantile finds WP power gains over the corresponding EL and $T^2$ tests in the derivative-curvature regime predicted by the comparison theory.

math.ST↗

arXiv2026

Provably Data-driven Lagrangian Relaxation for Mixed Integer Linear Programming

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the coupling constraints, LR enables parallel subproblem solving and often yields tighter dual bounds than standard linear programming relaxations, which is crucial for efficient branch-and-bound pruning. While recent empirical work has shown promising results using machine learning to predict these multipliers, a theoretical understanding of such methods remains an open question. In this work, we bridge this gap by analyzing the problem of learning LR through the lens of Data-driven Algorithm Design, i.e., a statistical learning problem over a distribution of problem instances. Our contributions are as follows: first, we derive a generalization bound of $\mathcal{O}(s^{1.5}/\sqrt{N})$ for the learned multipliers, where $s$ is the number of coupling constraints and $N$ is the sample size. Second, we provide a minimax lower-bound of $Ω(s/\sqrt{N})$, proving that a linear dependency is unavoidable. Third, we constructively close this theoretical gap by proving that Stochastic Gradient Ascent (SGA) with averaging achieves the minimax optimal rate $Θ(s/\sqrt{N})$. Finally, we extend our framework to the learning-to-warm-start setting, proving that it achieves a fast, minimax-optimal rate of $Θ(s/N)$ and establishing a theoretical advantage over direct multiplier prediction.

stat.ML↗

arXiv2026

Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty

Ambulance response is time-critical in out-of-hospital cardiac arrest (OHCA), where dispatchers must balance timely arrivals with limited fleet capacity. Static territories and deterministic travel-time estimates are vulnerable to dynamic congestion, while always-dual dispatch adds redundancy but consumes fleet capacity. We propose IDEAL (Intelligent Dual dispatch of Emergency AmbuLances), a selective dual-dispatch framework that sends a second ambulance only when the optimistic gap between primary and secondary paths exceeds a threshold. IDEAL learns context-specific edge travel times from trip-level dispatch records, including unobserved routes, using a weakly supervised bilevel representation network. We train the nonsmooth model with mini-batch conservative gradients and prove an asymptotic convergence guarantee. IDEAL models uncertainty via Burg-divergence perturbations to a shared metric in the learned representation space, thereby inducing correlated changes in edge travel times and learning context-specific radii from historical underprediction errors. For real-time decisions, IDEAL casts optimistic-gap computation as a difference-of-convex program and derives an efficient oracle with complexity guarantees. In collaboration with the Hong Kong Fire Services Department, we evaluate IDEAL using historical OHCA records and real-time adaptive simulations. The results achieve a stronger response-time/resource trade-off relative to all region-based and Google-based baselines.

math.OC↗

arXiv2026

Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function

Data-driven algorithm design automates hyperparameter tuning, but its statistical foundations remain limited because model performance can depend on hyperparameters in implicit and highly non-smooth ways. Existing guarantees focus on the simple case of a one-dimensional (scalar) hyperparameter. This leaves the practically important, multi-dimensional hyperparameter tuning setting unresolved. We address this open question by establishing the first general framework for establishing generalization guarantees for tuning multi-dimensional hyperparameters in data-driven settings. Our approach strengthens the generalization guarantee framework for semi-algebraic function classes by exploiting tools from real algebraic geometry, yielding sharper, more broadly applicable guarantees. For completeness, we also instantiate the first lower bound for this general setting. We further extend the analysis to hyperparameter tuning using the validation loss under minimal assumptions, and derive improved bounds when additional structure is available. Finally, we demonstrate the scope of the framework with new learnability results, including data-driven weighted group lasso and weighted fused lasso.

stat.ML↗

arXiv2026

PDF Retrieval Augmented Question Answering

This paper presents an advancement in Question-Answering (QA) systems using a Retrieval Augmented Generation (RAG) framework to enhance information extraction from PDF files. Recognizing the richness and diversity of data within PDFs--including text, images, vector diagrams, graphs, and tables--poses unique challenges for existing QA systems primarily designed for textual content. We seek to develop a comprehensive RAG-based QA system that will effectively address complex multimodal questions, where several data types are combined in the query. This is mainly achieved by refining approaches to processing and integrating non-textual elements in PDFs into the RAG framework to derive precise and relevant answers, as well as fine-tuning large language models to better adapt to our system. We provide an in-depth experimental evaluation of our solution, demonstrating its capability to extract accurate information that can be applied to different types of content across PDFs. This work not only pushes the boundaries of retrieval-augmented QA systems but also lays a foundation for further research in multimodal data integration and processing.

cs.CL↗

arXiv2026

Adaptive Rollout Allocation for Online Reinforcement Learning with Verifiable Rewards

Sampling efficiency is a key bottleneck in reinforcement learning with verifiable rewards. Existing group-based policy optimization methods, such as GRPO, allocate a fixed number of rollouts for all training prompts. This uniform allocation implicitly treats all prompts as equally informative, and could lead to inefficient computational budget usage and impede training progress. We introduce VIP, a Variance-Informed Predictive allocation strategy that allocates a given rollout budget to the prompts in the incumbent batch to minimize the expected gradient variance of the policy update. At each iteration, VIP uses a lightweight Gaussian process model to predict per-prompt success probabilities based on recent rollouts. These probability predictions are translated into variance estimates, which are then fed into a convex optimization problem to determine the optimal rollout allocations under a hard compute budget constraint. Empirical results show that VIP consistently improves sampling efficiency and achieves higher performance than uniform or heuristic allocation strategies in multiple benchmarks.

cs.LG↗

arXiv2026

Retrospective Feature Estimation for Continual Learning

The intrinsic capability to continuously learn a changing data stream is a desideratum of deep neural networks (DNNs). However, current DNNs suffer from catastrophic forgetting, which interferes with remembering past knowledge. To mitigate this issue, existing Continual Learning (CL) approaches often retain exemplars for replay, regularize learning, or allocate dedicated capacity for new tasks. This paper investigates an unexplored direction for CL called Retrospective Feature Estimation (RFE). RFE learns to reverse feature changes by aligning the features from the current trained DNN backward to the feature space of the old task, where performing predictions is easier. This retrospective process utilizes a chain of small feature mapping networks called retrospector modules. Empirical experiments on several CL benchmarks, including CIFAR10, CIFAR100, and Tiny ImageNet, demonstrate the effectiveness and potential of this novel CL direction compared to existing representative CL methods, motivating further research into retrospective mechanisms as a principled alternative for mitigating catastrophic forgetting in CL. Code is available at: https://github.com/mail-research/retrospective-feature-estimation.

cs.LG↗

arXiv2026

Exploring Diverse Generation Paths via Inference-time Stiefel Activation Steering

Language models often default to a narrow set of high-probability outputs, leaving their generation paths homogeneous and prone to mode collapse. Sampling-based strategies inject randomness but still struggle to guarantee diversity across multiple concurrent generation runs. We address this limitation by introducing STARS ($\textbf{St}$iefel-based $\textbf{A}$ctivation Steering for Diverse $\textbf{R}$ea$\textbf{S}$oning), a training-free, inference-time intervention method that transforms activation steering into an exploration engine. At each token, STARS collects the hidden activations of concurrent generation runs and optimizes multiple additive steering directions jointly on the Stiefel manifold. STARS maximizes the geometric volume of the steered activations, while the Stiefel manifold induces orthogonality of the steering interventions. This formulation explicitly promotes divergent activation vectors of concurrent generation runs, and implicitly promotes divergent generation trajectories. This manifold optimization formulation can be solved using a Riemannian gradient descent algorithm with convergence guarantees, but this algorithm is too time-consuming for real-time inference. To guarantee low latency, we further design a lightweight one-step update with an aggressive, closed-form stepsize. For test case generation and scientific discovery benchmarks, STARS consistently outperforms standard sampling methods, achieving greater diversity without sacrificing qualitative performance.

cs.LG↗

arXiv2025

More Bias, Less Bias: BiasPrompting for Enhanced Multiple-Choice Question Answering

With the advancement of large language models (LLMs), their performance on multiple-choice question (MCQ) tasks has improved significantly. However, existing approaches face key limitations: answer choices are typically presented to LLMs without contextual grounding or explanation. This absence of context can lead to incomplete exploration of all possible answers, ultimately degrading the models' reasoning capabilities. To address these challenges, we introduce BiasPrompting, a novel inference framework that guides LLMs to generate and critically evaluate reasoning across all plausible answer options before reaching a final prediction. It consists of two components: first, a reasoning generation stage, where the model is prompted to produce supportive reasonings for each answer option, and then, a reasoning-guided agreement stage, where the generated reasonings are synthesized to select the most plausible answer. Through comprehensive evaluations, BiasPrompting demonstrates significant improvements in five widely used multiple-choice question answering benchmarks. Our experiments showcase that BiasPrompting enhances the reasoning capabilities of LLMs and provides a strong foundation for tackling complex and challenging questions, particularly in settings where existing methods underperform.

cs.CL↗

arXiv2025

A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either chosen heuristically - without compelling theoretical justification - or optimally in view of restrictive distributional assumptions. In this paper, we propose a principled approach to construct covariance estimators without imposing restrictive assumptions. That is, we study distributionally robust covariance estimation problems that minimize the worst-case Frobenius error with respect to all data distributions close to a nominal distribution, where the proximity of distributions is measured via a divergence on the space of covariance matrices. We identify mild conditions on this divergence under which the resulting minimizers represent shrinkage estimators. We show that the corresponding shrinkage transformations are intimately related to the geometrical properties of the underlying divergence. We also prove that our robust estimators are efficiently computable and asymptotically consistent and that they enjoy finite-sample performance guarantees. We exemplify our general methodology by synthesizing explicit estimators induced by the Kullback-Leibler, Fisher-Rao, and Wasserstein divergences. Numerical experiments based on synthetic and real data show that our robust estimators are competitive with state-of-the-art estimators.

stat.ML↗

arXiv2025

Generalized Non-Hermitian Hamiltonian for Guided Resonances in Photonic Crystal Slabs

We develop a generalized non-Hermitian Hamiltonian formalism for guided resonances in photonic crystal slabs, derived directly from Maxwell's equations through a systematic guided-mode expansion. By expanding the electromagnetic fields over the complete mode basis of an unpatterned slab and systematically integrating out radiative Fabry--Pérot channels, we obtain the analytical operator structure of the Hamiltonian, which treats guided-mode coupling and radiation losses on equal footing. The resulting Hamiltonian provides explicit expressions for both dispersive and radiative coupling terms in terms of modal overlap integrals and Fourier components of the permittivity modulation. For specific geometries, the Hamiltonian coefficients can be extracted from full-wave simulations enabling accurate modeling without phenomenological assumptions. As a case study, we investigate hexagonal lattices with both preserved and broken $C_6$ symmetry, demonstrating predictive agreement for complex band structures, near-field distributions, and far-field polarization patterns. In particular, the formalism reproduces symmetry-protected bound states in the continuum (BICs) at the $Γ$ point, accidental off-$Γ$ BICs near the $Γ$ point, and the emergence of chiral exceptional points (EPs). It also captures the tunable behavior of eigenmodes near the $K$ point, including Dirac-point shifts and the emergence of quasi-BICs or bandgap openings, depending on the nature of $C_6$ symmetry breaking. We further demonstrate in the Appendix that the same formalism extends naturally to other symmetry classes, including $C_2$ (1D grating) and $C_4$ (square lattice) photonic crystal slabs. This approach enables predictive and efficient modeling of complex photonic resonances, revealing their topological and symmetry-protected characteristics in non-Hermitian systems.

physics.optics↗

arXiv2025

SCOPE: Spectral Concentration by Distributionally Robust Joint Covariance-Precision Estimation

We propose a distributionally robust formulation for simultaneously estimating the covariance matrix and the precision matrix of a random vector.The proposed model minimizes the worst-case weighted sum of the Frobenius loss of the covariance estimator and Stein's loss of the precision matrix estimator against all distributions from an ambiguity set centered at the nominal distribution. The radius of the ambiguity set is measured via convex spectral divergence. We demonstrate that the proposed distributionally robust estimation model can be reduced to a convex optimization problem, thereby yielding quasi-analytical estimators. The joint estimators are shown to be nonlinear shrinkage estimators. The eigenvalues of the estimators are shrunk nonlinearly towards a positive scalar, where the scalar is determined by the weight coefficient of the loss terms. By tuning the coefficient carefully, the shrinkage corrects the spectral bias of the empirical covariance/precision matrix estimator. By this property, we call the proposed joint estimator the Spectral concentrated COvariance and Precision matrix Estimator (SCOPE). We demonstrate that the shrinkage effect improves the condition number of the estimator. We provide a parameter-tuning scheme that adjusts the shrinkage target and intensity that is asymptotically optimal. Numerical experiments on synthetic and real data show that our shrinkage estimators perform competitively against state-of-the-art estimators in practical applications.

stat.ML↗

arXiv2025

Provably data-driven projection method for quadratic programming

Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the projection matrix is learned from observed problem instances drawn from an application-specific distribution of problems. We analyze the generalization guarantee for the data-driven projection matrix learning for convex quadratic programs (QPs). Unlike in LPs, the optimal solutions of convex QPs are not confined to the vertices of the feasible polyhedron, and this complicates the analysis of the optimal value function. To overcome this challenge, we demonstrate that the solutions of convex QPs can be localized within a feasible region corresponding to a special active set, utilizing Caratheodory's theorem. Building on such observation, we propose the unrolled active set method, which models the computation of the optimal value as a Goldberg-Jerrum (GJ) algorithm with bounded complexities, thereby establishing learning guarantees. We then further extend our analysis to other settings, including learning to match the optimal solution and input-aware setting, where we learn a mapping from QP problem instances to projection matrices.

math.OC↗

arXiv2025

Test-time Diverse Reasoning by Riemannian Activation Steering

Best-of-$N$ reasoning improves the accuracy of language models in solving complex tasks by sampling multiple candidate solutions and then selecting the best one based on some criteria. A critical bottleneck for this strategy is the output diversity limit, which occurs when the model generates similar outputs despite stochastic sampling, and hence recites the same error. To address this lack of variance in reasoning paths, we propose a novel unsupervised activation steering strategy that simultaneously optimizes the steering vectors for multiple reasoning trajectories at test time. At any synchronization anchor along the batch generation process, we find the steering vectors that maximize the total volume spanned by all possible intervened activation subsets. We demonstrate that these steering vectors can be determined by solving a Riemannian optimization problem over the product of spheres with a log-determinant objective function. We then use a Riemannian block-coordinate descent algorithm with a well-tuned learning rate to obtain a stationary point of the problem, and we apply these steering vectors until the generation process reaches the subsequent synchronization anchor. Empirical evaluations on popular mathematical benchmarks demonstrate that our test-time Riemannian activation steering strategy outperforms vanilla sampling techniques in terms of generative diversity and solution accuracy.

cs.LG↗

arXiv2025

Reasoning Planning for Language Models

Selecting an appropriate reasoning method for a given query remains a key challenge in language model generation. Existing approaches typically generate multiple candidate responses and use an aggregation strategy to select the output answer, often assuming that more candidate answers yield higher accuracy. We revisit this assumption through a rigorous theoretical analysis, deriving accuracy bounds for standard aggregation methods under fixed generation distributions and candidate sizes. Building on these insights, we introduce EPIC, an Ensemble Planning with Contrastive learning framework to learn a shared representation space that captures both model reasoning abilities and query-method compatibility. EPIC incorporates our probability bounds as a regularizer in a utility-driven optimization that balances accuracy and computational cost. Experiments on diverse mathematical reasoning tasks show that EPIC consistently selects optimal reasoning methods, improving accuracy while reducing computational overhead. Our code can be found at https://github.com/nguyenngocbaocmt02/EPIC.

cs.LG↗

arXiv2025

Distributional Surgery for Language Model Activations

Language models, while capable of generating remarkably coherent and seemingly accurate text, can occasionally produce undesirable content, including harmful or toxic outputs. In this paper, we present a new two-stage approach to detect and mitigate undesirable content generations by rectifying activations. First, we train an ensemble of layerwise classifiers to detect undesirable content using activations by minimizing a smooth surrogate of the risk-aware score. Then, for detected undesirable contents, we propose layerwise distributional steering policies that transform the attention heads. These policies are computed through principled semidefinite programming, which aims to minimally perturb the attention distribution while probabilistically guaranteeing the effectiveness of the editions. Empirical evaluations across multiple language models and datasets show that our method outperforms baselines in reducing the generation of undesirable output.

cs.LG↗

arXiv2025

Mean-Covariance Robust Risk Measurement

We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. We find that, for a large class of risk measures, mean-covariance robust portfolio optimization boils down to the Markowitz model, subject to a regularization term given in closed form. This includes the finance standards, value-at-risk and conditional value-at-risk, and can be solved highly efficiently.

q-fin.PM↗