Aug 2026· Theoretical and Natural Science· 0 citations
TL;DR
This review covers LoRA and its main variants and pays particular attention to the linear algebra behind them, and compares the major variants: quantized LoRA (QLoRA), quantization-aware LoRA (QA-LoRA), adaptive low-rank adaptation (AdaLoRA), sparse low-rank adaptation (SoRA), and weight-decomposed low-rank adaptation (DoRA).
Abstract
Modern natural language systems rely on large language models, whose sheer size makes full fine-tuning costly in computation, graphics processing unit (GPU) memory, and storage. Low-rank adaptation (LoRA) sidesteps most of that cost. It keeps the pre-trained weights frozen and captures each task-specific change as the product of two smaller matrices, so adapting a model reduces to a low-rank decomposition. This review covers LoRA and its main variants and pays particular attention to the linear algebra behind them. It first explains why the low intrinsic dimension of fine-tuning makes low-rank updates effective, then compares the major variants: quantized LoRA (QLoRA), quantization-aware LoRA (QA-LoRA), adaptive low-rank adaptation (AdaLoRA), sparse low-rank adaptation (SoRA), and weight-decomposed low-rank adaptation (DoRA). Across published studies, these methods come close to full fine-tuning accuracy while updating well under one percent of a model's parameters in some settings. For reference, LoRA cuts the trainable parameter count of Generative Pre-trained Transformer 3 (GPT-3) by four orders of magnitude, and QLoRA brings a 65-billion-parameter model within the memory of one 48 GB card. Open problems remain in choosing the rank, comparing results across studies, limiting quantization loss, and combining multiple adapters without interference. Ultimately, an established piece of linear algebra, approximating high-dimensional objects in low-dimensional subspaces, is what keeps the adaptation of very large models affordable.
Parameter-efficient fine-tuning (PEFT) methods adapt foundation models to specific domains by selectively updating only a small subset of critical parameters, significantly reducing computational costs. Among these methods, Sparse Low-Rank Adaptation (SoRA) has emerged as an effective approach for fine-tuning large language models. This paper investigates SoRA algorithm's performance in large-scale models, particularly analyzing learning dynamics and scaling effects in wide neural networks. We find that employing a uniform learning rate across all parameter matrices limits learning efficiency. To address this, we derive an improved learning rate configuration and propose SoRA+, an enhanced variant that introduces a hyperparameter to adjust learning rates proportionally. This modification aligns with theoretical optima and mitigates the suboptimality of the original SoRA method. Experiments show that SoRA+ improves fine-tuning performance by up to 2% while accelerating convergence.
GLA-LoRA establishes a unified learning strategy that synergistically integrates multi-granular contrastive learning with knowledge distillation and establishes that explicit global-local knowledge alignment is essential for achieving high-fidelity, parameter-efficient fine-tuning across diverse language tasks.
Low-rank adaptation (LoRA) has become the standard for parameter-efficient fine-tuning of large language models. Most LoRA variants follow a uniform-LR convention, applying a single global learning rate across every rank-one component of every adapter. We show that this convention overlooks substantial within-module heterogeneity, where the rank-one components of a LoRA adapter update at highly uneven rates and low-velocity modules converge to concentrated singular spectra that underutilize the nominal rank budget. To address this, we propose an adaptive anisotropic learning-rate model that assigns each rank-one component its own effective learning rate, computed online from training-time signals and mean-normalized per module to preserve the global LR budget. AnLR-LoRA instantiates this model with two signals available during AdamW optimization, namely function-space velocity and Adam SNR, as a lightweight scheme with no extra trainable parameters. Across commonsense reasoning, natural language generation and visual instruction-tuning benchmarks, AnLR-LoRA consistently improves over LoRA while encouraging broader use of rank capacity, with gains that remain robust across a wide range of global learning rates and transfer cleanly to other LoRA variants.
Hui-Yi Wang, Daijiao Liu, Lina Yao et al.· 0 citations
This work proposes SeMi-LoRA (Separation and Mixing LoRA), a novel framework that enables complete high-rank updates while preserving mergeability and consistently outperforms strong PEFT baselines with favorable parameter efficiency.
Zhen-Fei Yang, Beiming Yu, Peiqin Lin et al.· Proceedings of the Thirty-Fi...· 0 citations
The experiments show that FrameFT achieves performance on par with/exceeding state-of-the-art PEFT techniques, but needs far fewer trainable parameters.
Harshavardhan Adepu, Li Zhang, Sanjiv Kumar et al.· 0 citations
REP-LIE leverages the gradients of LoRA low-rank matrices to estimate the importance of weights without requiring full gradient computation, and a stability score is introduced, serving as the basis for iterative pruning of unimportant model parameters.
Peng Liu, Hui-Bing Zeng, Yi-Qun Zhang et al.· IEEE Transactions on Emergin...· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
