arXiv subjects

Zekun Liu

Publications and source records attributed to Zekun Liu.

7 recordsLinked to original sources

arXiv2026

A Unified Zeroth-Order Proximal Newton-Type Framework for Composite Optimization

We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle complexity bounds for the algorithm to attain an $\epsilon$-optimal solution under both nonconvex and strongly convex settings. We also establish its local R-superlinear convergence based on the Dennis--Mor\'{e} condition, and theoretically address an open problem by showing that the BFGS scheme is more compatible with finite-difference gradient estimators than with smoothing-based ones. Numerical experiments are further presented to demonstrate the efficiency of the proposed method.

math.OC↗

arXiv2025

ITDR: An Instruction Tuning Dataset for Enhancing Large Language Models in Recommendations

Large language models (LLMs) have demonstrated outstanding performance in natural language processing tasks. However, in the field of recommender systems, due to the inherent structural discrepancy between user behavior data and natural language, LLMs struggle to effectively model the associations between user preferences and items. Although prompt-based methods can generate recommendation results, their inadequate understanding of recommendation tasks leads to constrained performance. To address this gap, we construct a comprehensive instruction tuning dataset, ITDR, which encompasses seven subtasks across two root tasks: user-item interaction and user-item understanding. The dataset integrates data from 13 public recommendation datasets and is built using manually crafted standardized templates, comprising approximately 200,000 instances. Experimental results demonstrate that ITDR significantly enhances the performance of mainstream open-source LLMs such as GLM-4, Qwen2.5, Qwen2.5-Instruct and LLaMA-3.2 on recommendation tasks. Furthermore, we analyze the correlations between tasks and explore the impact of task descriptions and data scale on instruction tuning effectiveness. Finally, we perform comparative experiments against closed-source LLMs with massive parameters. Our tuning dataset ITDR, the fine-tuned large recommendation models, all LoRA modules, and the complete experimental results are available at https://github.com/hellolzk/ITDR.

cs.IR↗

arXiv2025

Ionomeric extracellular matrices for dynamic soft robotic tissue engineering devices through protein sulfonation

Conventional tissue engineering methodologies frequently depend on pharmacological strategies to induce or expedite tissue repair. However, bioengineered strategies incorporating biophysical stimulation have emerged as promising alternatives. Electroactive materials facilitate the provision of controlled electrical, mechanical, and electromechanical stimuli, which support cell proliferation and tissue remodelling. Despite their ability to supply external electrical and mechanical stimuli to the tissue microenvironment, the electroactive polymers in use today often lack critical biochemical signals essential for native-like cell-cell and cell-scaffold interactions, thereby constraining their regenerative capabilities. To address the demand for biomimetic materials that possess enhanced capabilities in promoting cell and tissue stimulation, we present the development of a novel class of polymers called ionomeric extracellular matrices (iECMs). By utilising the linker-mediated conjugation of sulfonic acid biomolecules (taurine) to the backbone of an extracellular matrix protein (collagen), we illustrate the potential of iECMs as the first electromechanical actuating material platform derived entirely from ECM materials, paving the way for dynamic and soft-robotic platforms for a wide range of tissue engineering applications.

physics.med-ph↗

arXiv2025

Detecting Heel Strike and toe off Events Using Kinematic Methods and LSTM Models

Accurate gait event detection is crucial for gait analysis, rehabilitation, and assistive technology, particularly in exoskeleton control, where precise identification of stance and swing phases is essential. This study evaluated the performance of seven kinematics-based methods and a Long Short-Term Memory (LSTM) model for detecting heel strike and toe-off events across 4363 gait cycles from 588 able-bodied subjects. The results indicated that while the Zeni et al. method achieved the highest accuracy among kinematics-based approaches, other methods exhibited systematic biases or required dataset-specific tuning. The LSTM model performed comparably to Zeni et al., providing a data-driven alternative without systematic bias. These findings highlight the potential of deep learning-based approaches for gait event detection while emphasizing the need for further validation in clinical populations and across diverse gait conditions. Future research will explore the generalizability of these methods in pathological populations, such as individuals with post-stroke conditions and knee osteoarthritis, as well as their robustness across varied gait conditions and data collection settings to enhance their applicability in rehabilitation and exoskeleton control.

cs.RO↗

arXiv2024

An Extended ADMM for 3-Block Nonconvex Nonseparable Problems with Applications

We consider a 3-block Alternating Direction Method of Multipliers (ADMM) for solving nonconvex nonseparable problems with a linear constraint. Inspired by \cite[Sun, Toh and Yang, \textit{SIAM Journal on Optimization}, 25 (2015), pp.882-915]{wtwice}, the proposed ADMM follows the Block Coordinate Descent (BCD) cycle order $1\to 3\to 2\to 3$. We analyze its convergence based on the Kurdyka-{\L}ojasiewicz property. We also discuss two useful extensions of the proposed ADMM with $2\to 3\to 1\to 3$ Gauss-Seidel BCD cycle order, and with adding a proximal term for more general nonseparable problems, respectively. Moreover, we make numerical experiments on two nonconvex problems: robust principal component analysis and nonnegative matrix completion. Results show the efficiency and outperformance of the proposed ADMM.

math.OC↗

arXiv2023

Nonconvex ADMM for Rank-Constrained Matrix Sensing Problem

Low-rank matrix approximation (LRMA) has been arisen in many applications, such as dynamic MRI, recommendation system and so on. The alternating direction method of multipliers (ADMM) has been designed for the nuclear norm regularized least squares problem and shows a good performance. However, due to the lack of guarantees for the convergence, there are few ADMM algorithms designed directly for the rank-constrained matrix sensing problem (RCMS). Therefore, in this paper, we propose an ADMM-based algorithm for the RCMS. Based on the Kurdyka-Lojasiewicz (KL) property, we prove that the proposed algorithm globally converges. And we discuss a specific case: the rank-constrained matrix completion problem (RCMC). Numerical experiments show that specialized for the matrix completion, the proposed algorithm performs better when the sampling rate is really low in noisy case, which is the key for the matrix completion.

math.OC↗

arXiv2023

Alternating Direction Method of Multipliers Based on $\ell_{2,0}$-norm for Multiple Measurement Vector Problem

In this paper, we propose an alternating direction method of multipliers (ADMM)-based optimization algorithm to achieve better undersampling rate for multiple measurement vector (MMV) problem. The core is to introduce the $\ell_{2,0}$-norm sparsity constraint to describe the joint-sparsity of the MMV problem, which is different from the widely used $\ell_{2,1}$-norm constraint in the existing research. In order to illustrate the better performance of $\ell_{2,0}$-norm, first this paper proves the equivalence of the sparsity of the row support set of a matrix and its $\ell_{2,0}$-norm. Afterward, the MMV problem based on $\ell_{2,0}$-norm is proposed. Moreover, building on the Kurdyka-Lojasiewicz property, this paper establishes that the sequence generated by ADMM globally converges to the optimal point of the MMV problem. Finally, the performance of our algorithm and comparison with other algorithms under different conditions is studied by simulated examples.

cs.IT↗