Zhi-yong Wang

Xinjue Wang, Xiuheng Wang, Yejun Zhang et al.

Low-rank adapters are usually compared by sweeping a small set of ranks, but the rank also fixes the resolution of the parameter budget. For a $2048{\times}2048$ OPT attention projection, increasing LoRA by one rank stores $4096$ trainable scalars, leaving large gaps between feasible low-budget adapter sizes. This paper asks whether a tensorized adapter with finer capacity increments changes the observed accuracy--budget trade-off. We instantiate this question with fixed-component canonical polyadic (CP) tensor adapters. Under a $32{\times}64{\times}32{\times}64$ tensorization, one normalized CP component stores $193$ trainable scalars per projection, about $21$ times smaller than one LoRA rank step. We compare CP adapters and LoRA on OPT-1.3B across SST-2, RTE, and BoolQ under matched target modules, training protocol, data caps, and seed schedules. CP trains stably and fills the gaps between LoRA ranks, but the effect is task-dependent: SST-2 reaches an early low-budget plateau, BoolQ benefits from additional CP components before saturating slightly below LoRA, and RTE remains LoRA-favored. Finer parameter steps are therefore useful for diagnosing PEFT budget sensitivity, but they do not by themselves guarantee a better accuracy--budget curve.

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.

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}.