arXiv subjects

Na Huang

Publications and source records attributed to Na Huang.

12 recordsLinked to original sources

arXiv2026

Randomized inexact block triangular preconditioners for double saddle-point systems in PDE-constrained optimization

We develop a new class of inexact block triangular preconditioners for double saddle-point systems arising from PDE-constrained optimization. The proposed preconditioners are constructed through matrix factorization techniques while preserving the inherent block structure of the original systems. A comprehensive spectral analysis of the preconditioned matrices is provided, yielding explicit bounds for both real and nonreal eigenvalues. To enable efficient construction of the inexact preconditioners, randomized strategies are introduced to select the required subblocks. We establish high-probability bounds for the expected approximation error, with the error estimates explicitly characterized in terms of the eigenvalues of the associated matrices. Numerical experiments demonstrate the effectiveness, robustness, and scalability of the proposed preconditioners, and validate the efficiency of the randomized construction strategies.

math.NA↗

arXiv2026

Adaptive Barzilai-Borwein Proximal Gradient Method for Nonconvex Optimization

The Barzilai-Borwein (BB) method is an efficient gradient-based approach for unconstrained optimization that approximates spectral information of the Hessian matrix to capture curvature at low computational cost. In this paper, we extend the BB stepsize strategy to composite nonconvex optimization problems consisting of a smooth nonconvex term and a proper closed convex term, and propose an adaptive Barzilai-Borwein proximal gradient method for nonconvex optimization (AdaBBNC). The proposed method incorporates a flexible BB-based curvature estimate into the proximal gradient framework to enhance adaptability in nonconvex settings. Under mild assumptions, we establish that AdaBBNC achieves the optimal iteration complexity of $\mathcal{O}(\epsilon^{-2})$ for finding an $\epsilon$-stationary point, without requiring any prior knowledge of the global Lipschitz constant. Numerical experiments demonstrate the effectiveness and robustness of the proposed method. Compared with recent parameter-free and line-search-free adaptive proximal gradient methods, AdaBBNC exhibits more aggressive yet stable behavior in ill-conditioned optimization problems.

math.OC↗

arXiv2026

UniSpine-GS: An Efficient Physics-Aware Gaussian Framework for Cross-Modality Multi-view Spine Image Synthesis

The diagnosis of spinal diseases is often assisted by 3D imaging techniques in clinical practice. However, precise 3D spinal assessment is limited by the high costs of 3D imaging hardware and the challenges posed by the physical differences between imaging modalities, which hinder the generalizability of models. To address these issues, we propose UniSpine-GS, an efficient, physics-aware Gaussian framework designed for novel-view projection rendering in multi-view spine imaging via a 3D-aware representation. Instead of performing explicit 3D reconstruction, our approach learns a geometry-aware Gaussian representation that ensures anatomical consistency across different views. We introduce SPWM, a structure-guided loss reweighting strategy to improve boundary fidelity and local details. We evaluate our method on the CTSpine3D dataset and a newly constructed 3D fetal ultrasound dataset, FeSpine3D. Our results demonstrate that UniSpine-GS significantly outperforms existing methods across all metrics, offering a practical and cost-effective solution for unified multi-view medical imaging. Our code is publicly available at https://github.com/orangeisland66/UniSpine-GS.

cs.CV↗

arXiv2023

Contrastive State Augmentations for Reinforcement Learning-Based Recommender Systems

Learning reinforcement learning (RL)-based recommenders from historical user-item interaction sequences is vital to generate high-reward recommendations and improve long-term cumulative benefits. However, existing RL recommendation methods encounter difficulties (i) to estimate the value functions for states which are not contained in the offline training data, and (ii) to learn effective state representations from user implicit feedback due to the lack of contrastive signals. In this work, we propose contrastive state augmentations (CSA) for the training of RL-based recommender systems. To tackle the first issue, we propose four state augmentation strategies to enlarge the state space of the offline data. The proposed method improves the generalization capability of the recommender by making the RL agent visit the local state regions and ensuring the learned value functions are similar between the original and augmented states. For the second issue, we propose introducing contrastive signals between augmented states and the state randomly sampled from other sessions to improve the state representation learning further. To verify the effectiveness of the proposed CSA, we conduct extensive experiments on two publicly accessible datasets and one dataset collected from a real-life e-commerce platform. We also conduct experiments on a simulated environment as the online evaluation setting. Experimental results demonstrate that CSA can effectively improve recommendation performance.

cs.IR↗

arXiv2022

On GSOR, the Generalized Successive Overrelaxation Method for Double Saddle-Point Problems

We consider the generalized successive overrelaxation (GSOR) method for solving a class of block three-by-three saddle-point problems. Based on the necessary and sufficient conditions for all roots of a real cubic polynomial to have modulus less than one, we derive convergence results under reasonable assumptions. We also analyze a class of block lower triangular preconditioners induced from GSOR and derive explicit and sharp spectral bounds for the preconditioned matrices. We report numerical experiments on test problems from the liquid crystal director model and the coupled Stokes-Darcy flow, demonstrating the usefulness of GSOR.

math.NA↗

arXiv2022

Debiasing Learning for Membership Inference Attacks Against Recommender Systems

Learned recommender systems may inadvertently leak information about their training data, leading to privacy violations. We investigate privacy threats faced by recommender systems through the lens of membership inference. In such attacks, an adversary aims to infer whether a user's data is used to train the target recommender. To achieve this, previous work has used a shadow recommender to derive training data for the attack model, and then predicts the membership by calculating difference vectors between users' historical interactions and recommended items. State-of-the-art methods face two challenging problems: (1) training data for the attack model is biased due to the gap between shadow and target recommenders, and (2) hidden states in recommenders are not observational, resulting in inaccurate estimations of difference vectors. To address the above limitations, we propose a Debiasing Learning for Membership Inference Attacks against recommender systems (DL-MIA) framework that has four main components: (1) a difference vector generator, (2) a disentangled encoder, (3) a weight estimator, and (4) an attack model. To mitigate the gap between recommenders, a variational auto-encoder (VAE) based disentangled encoder is devised to identify recommender invariant and specific features. To reduce the estimation bias, we design a weight estimator, assigning a truth-level score for each difference vector to indicate estimation accuracy. We evaluate DL-MIA against both general recommenders and sequential recommenders on three real-world datasets. Experimental results show that DL-MIA effectively alleviates training and estimation biases simultaneously, and achieves state-of-the-art attack performance.

cs.IR↗

arXiv2022

A semi-conjugate gradient method for solving unsymmetric positive definite linear systems

The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We introduce an analogous semi-conjugate gradient (SCG) method for unsymmetric positive definite linear systems. Unlike CG, SCG requires the solution of a lower triangular linear system to produce each semi-conjugate direction. We prove that SCG is theoretically equivalent to the full orthogonalization method (FOM), which is based on the Arnoldi process and converges in a finite number of steps. Because SCG's triangular system increases in size each iteration, we study a sliding window implementation (SWI) to improve efficiency, and show that the directions produced are still locally semi-conjugate. A counterexample illustrates that SWI is different from the direct incomplete orthogonalization method (DIOM), which is FOM with a sliding window. Numerical experiments from the convection-diffusion equation and other applications show that SCG is robust and that the sliding window implementation SWI allows SCG to solve large systems efficiently.

math.NA↗

arXiv2020

Event triggering control for dynamical systems with designable minimum inter-event time

This paper presents a class of event-triggering rules for dynamical control systems with guaranteed positive minimum inter-event time (MIET). We first propose an event-based function design with guaranteed control performance under a clock-like variable for general nonlinear systems, and later specify them to general linear systems. Compared to the existing static and dynamic triggering mechanisms, the proposed triggering rules hold the robust global event-separation property, and can be easily implemented on practical digital platform. Namely, it is shown that the minimum inter-event time can be flexibly adapted to the various hardware limitations. Finally, several numerical simulations are given to illustrate the theoretical results.

eess.SY↗

arXiv2019

Stabilized Barzilai-Borwein method

The Barzilai-Borwein (BB) method is a popular and efficient tool for solving large-scale unconstrained optimization problems. Its search direction is the same as for the steepest descent (Cauchy) method, but its stepsize rule is different. Owing to this, it converges much faster than the Cauchy method. A feature of the BB method is that it may generate too long steps, which throw the iterates too far away from the solution. Moreover, it may not converge, even when the objective function is strongly convex. In this paper, a stabilization technique is introduced. It consists in bounding the distance between each pair of successive iterates, which often allows for decreasing the number of BB iterations. When the BB method does not converge, our simple modification of this method makes it convergent. Under suitable assumptions, we prove its global convergence, despite the fact that no line search is involved, and only gradient values are used. Since the number of stabilization steps is proved to be finite, the stabilized version inherits the fast local convergence of the BB method. The presented results of extensive numerical experiments show that our stabilization technique often allows the BB method to solve problems in a fewer iterations, or even to solve problems where the latter fails.

math.OC↗

arXiv2019

Cooperative event-based rigid formation control

This paper discusses cooperative stabilization control of rigid formations via an event-based approach. We first design a centralized event-based formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the triggering condition, event function and triggering behavior are discussed in detail, and the exponential convergence of the event-based formation system is guaranteed.

eess.SY↗

arXiv2014

Inequalities of Dirichlet eigenvalues for degenerate elliptic partial differential operators

Let ${X_j},{Y_j}(j = 1, \cdot \cdot \cdot,n)$ be vector fields satisfying Hörmander's condition and ${Δ_L} = \sum\limits_{j = 1}^n {(X_j^2 + Y_j^2)}$. In this paper, we establish some inequalities of Dirichlet eigenvalues for degenerate elliptic partial differential operator ${Δ_L}$ and $Δ_L^2$. These inequalities extend Yang's inequalities for Dirichlet eigenvalues of Laplacian to the settings here and the forms of inequalities are more general than Yang's inequalities. To obtain them, we give a generalization of the inequality by Chebyshev.

math.AP↗

arXiv2014

Some New Inequalities of Dirichlet Eigenvalues for Laplace Operator with any Order

In this paper, we establish several inequalities of Dirichlet eigenvalues for Laplace operator $Δ$ with any order on \emph{n}-dimensional Euclidean space. These inequalities are more general than known Yang's inequalities and contain new consequences. To obtain them, we borrow the approach of Illias and Makhoul, and use a generalized Chebyshev's inequality.

math.AP↗