Hing Cheung So

Zhi-Yong Wang, Hing Cheung So, Abdelhak M. Zoubir

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance.

Zhi-Yong Wang, Hing Cheung So, Abdelhak M. Zoubir

This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau envelope is convex. Moreover, the closed-form solution to its Moreau envelope, namely, the proximity operator, is derived. Compared with nonconvex regularizers like the lp-norm with 0<p<1 that requires iterations to find the corresponding proximity operator, the developed regularizer has a closed-form proximity operator. We apply our regularizer to the robust matrix completion problem, and develop an efficient algorithm based on the alternating direction method of multipliers. The convergence of the suggested method is analyzed and we prove that any generated accumulation point is a stationary point. Finally, experimental results based on synthetic and real-world datasets demonstrate that our algorithm is superior to the state-of-the-art methods in terms of restoration performance.

Yuxuan Yao, Haonan Sheng, Qingsong Lv et al.

The escalating scale of Large Language Models (LLMs) necessitates efficient adaptation techniques. Model merging has gained prominence for its efficiency and controllability. However, existing merging techniques typically serve as post-hoc refinements or focus on mitigating task interference, often failing to capture the dynamic optimization benefits of supervised fine-tuning (SFT). In this work, we propose Streaming Merging, an innovative model updating paradigm that conceptualizes merging as an iterative optimization process. Central to this paradigm is \textbf{ARM} (\textbf{A}ctivation-guided \textbf{R}otation-aware \textbf{M}erging), a strategy designed to approximate gradient descent dynamics. By treating merging coefficients as learning rates and deriving rotation vectors from activation subspaces, ARM effectively steers parameter updates along data-driven trajectories. Unlike conventional linear interpolation, ARM aligns semantic subspaces to preserve the geometric structure of high-dimensional parameter evolution. Remarkably, ARM requires only early SFT checkpoints and, through iterative merging, surpasses the fully converged SFT model. Experimental results across model scales (1.7B to 14B) and diverse domains (e.g., math, code) demonstrate that ARM can transcend converged checkpoints. Extensive experiments show that ARM provides a scalable and lightweight framework for efficient model adaptation.

Zhi-Yong Wang, Hing Cheung So

Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR with closed-form proximity operator. Besides, we specify our framework using several commonly-used loss functions, and produce the corresponding SIRs, which are then adopted as nonconvex rank surrogates for low-rank matrix completion. Furthermore, algorithms based on the alternating direction method of multipliers are developed. Extensive numerical results show the effectiveness of our methods in terms of recovery performance and runtime.

Hao Nan Sheng, Zhi-yong Wang, Mingrui Yang et al.

As large language models continue to grow in size, parameter-efficient fine-tuning (PEFT) has become increasingly crucial. While low-rank adaptation (LoRA) offers a solution through low-rank updates, its static rank allocation may yield suboptimal results. Adaptive low-rank adaptation (AdaLoRA) improves this with dynamic allocation but remains sensitive to initial and target rank configurations. We introduce AROMA, a framework that automatically constructs layer-specific updates by iteratively building up rank-one components with very few trainable parameters that gradually diminish to zero. Unlike existing methods that employ rank reduction mechanisms, AROMA introduces a dual-loop architecture for rank growth. The inner loop extracts information from each rank-one subspace, while the outer loop determines the number of rank-one subspaces, i.e., the optimal rank. We reset optimizer states to maintain subspace independence. AROMA significantly reduces parameters compared to LoRA and AdaLoRA while achieving superior performance on natural language understanding and commonsense reasoning tasks, offering new insights into adaptive PEFT. The code is available at \href{https://github.com/ShuDun23/AROMA}{AROMA}.

Yiyong Sun, Jiajun He, Zhidi Lin et al.

Accurate prediction of mmWave time-varying channels is essential for mitigating the issue of channel aging in complex scenarios owing to high user mobility. Existing channel prediction methods have limitations: classical model-based methods often struggle to track highly nonlinear channel dynamics due to limited expert knowledge, while emerging data-driven methods typically require substantial labeled data for effective training and often lack interpretability. To address these issues, this paper proposes a novel hybrid method that integrates a data-driven neural network into a conventional model-based workflow based on a state-space model (SSM), implicitly tracking complex channel dynamics from data without requiring precise expert knowledge. Additionally, a novel unsupervised learning strategy is developed to train the embedded neural network solely with unlabeled data. Theoretical analyses and ablation studies are conducted to interpret the enhanced benefits gained from the hybrid integration. Numerical simulations based on the 3GPP mmWave channel model corroborate the superior prediction accuracy of the proposed method, compared to state-of-the-art methods that are either purely model-based or data-driven. Furthermore, extensive experiments validate its robustness against various challenging factors, including among others severe channel variations and high noise levels.

Pengxing Feng, Hing Cheung So

Active noise control typically employs adaptive filtering to generate secondary noise, where the least mean square algorithm is the most widely used. However, traditional updating rules are linear and exhibit limited effectiveness in addressing nonlinear environments and nonstationary noise. To tackle this challenge, we reformulate the active noise control problem as a meta-learning problem and propose a meta-learning-based delayless subband adaptive filter with deep neural networks. The core idea is to utilize a neural network as an adaptive algorithm that can adapt to different environments and types of noise. The neural network will train under noisy observations, implying that it recognizes the optimized updating rule without true labels. A single-headed attention recurrent neural network is devised with learnable feature embedding to update the adaptive filter weight efficiently, enabling accurate computation of the secondary source to attenuate the unwanted primary noise. In order to relax the time constraint on updating the adaptive filter weights, the delayless subband architecture is employed, which will allow the system to be updated less frequently as the downsampling factor increases. In addition, the delayless subband architecture does not introduce additional time delays in active noise control systems. A skip updating strategy is introduced to decrease the updating frequency further so that machines with limited resources have more possibility to board our meta-learning-based model. Extensive multi-condition training ensures generalization and robustness against various types of noise and environments. Simulation results demonstrate that our meta-learning-based model achieves superior noise reduction performance compared to traditional methods.

Jiaxi Ying, Xi Han, Rui Zhou et al.

We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex} has uncovered the limitations of the widely used $\ell_1$-norm in learning sparse graphs under this model: empirically, the number of nonzero entries in the solution grows with the regularization parameter of the $\ell_1$-norm; theoretically, a large regularization parameter leads to a fully connected (densest) graph. To overcome these challenges, we propose a graph Laplacian estimation method incorporating the $\ell_0$-norm constraint. An efficient gradient projection algorithm is developed to solve the resulting optimization problem, characterized by sparsity and Laplacian constraints. Through numerical experiments with synthetic and financial time-series datasets, we demonstrate the effectiveness of the proposed method in network topology inference.

Xiao Peng Li, Qi Liu, Hing Cheung So

The state-of-the-art deep neural networks (DNNs) have been widely applied for various real-world applications, and achieved significant performance for cognitive problems. However, the increment of DNNs' width and depth in architecture results in a huge amount of parameters to challenge the storage and memory cost, limiting to the usage of DNNs on resource-constrained platforms, such as portable devices. By converting redundant models into compact ones, compression technique appears to be a practical solution to reducing the storage and memory consumption. In this paper, we develop a nonlinear tensor ring network (NTRN) in which both fullyconnected and convolutional layers are compressed via tensor ring decomposition. Furthermore, to mitigate the accuracy loss caused by compression, a nonlinear activation function is embedded into the tensor contraction and convolution operations inside the compressed layer. Experimental results demonstrate the effectiveness and superiority of the proposed NTRN for image classification using two basic neural networks, LeNet-5 and VGG-11 on three datasets, viz. MNIST, Fashion MNIST and Cifar-10.

Jisheng Dai, An Liu, Hing Cheung So

This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL framework. To overcome this challenge, we introduce a novel discretization enforcing prior to exploit the knowledge of the discrete nature of the signal-of-interest. By integrating the discretization enforcing prior into the SBL framework and applying the variational Bayesian inference (VBI) methodology, we devise an alternating optimization algorithm to jointly characterize the finite-alphabet feature and reconstruct the unknown signal. When the measurement matrix is i.i.d. Gaussian per component, we further embed the generalized approximate message passing (GAMP) into the VBI-based method, so as to directly adopt the ideal prior and significantly reduce the computational burden. Simulation results demonstrate substantial performance improvement of the two proposed methods over existing schemes. Moreover, the GAMP-based variant outperforms the VBI-based method with i.i.d. Gaussian measurement matrices but it fails to work for non i.i.d. Gaussian matrices.

Hao Wang, Chi-Sing Leung, Hing Cheung So et al.

The aim of this paper is to train an RBF neural network and select centers under concurrent faults. It is well known that fault tolerance is a very attractive property for neural networks. And center selection is an important procedure during the training process of an RBF neural network. In this paper, we devise two novel algorithms to address these two issues simultaneously. Both of them are based on the ADMM framework. In the first method, the minimax concave penalty (MCP) function is introduced to select centers. In the second method, an l0-norm term is directly used, and the hard threshold (HT) is utilized to address the l0-norm term. Under several mild conditions, we can prove that both methods can globally converge to a unique limit point. Simulation results show that, under concurrent fault, the proposed algorithms are superior to many existing methods.