The Primacy of Magnitude in Low-Rank Adaptation

• URL: http://arxiv.org/abs/2507.06558v1
• Date: Wed, 09 Jul 2025 05:25:24 GMT
• Title: The Primacy of Magnitude in Low-Rank Adaptation
• Authors: Zicheng Zhang, Haoran Li, Yifeng Zhang, Guoqiang Gong, Jiaxing Wang, Pengzhang Liu, Qixia Jiang, Junxing Hu,
• Abstract summary: Low-Rank Adaptation (LoRA) offers a parameter-efficient paradigm for tuning large models.<n>We propose LoRAM, a magnitude-driven "Basis & Basis" scheme that matches spectral methods without their inefficiencies.
• Score: 15.583380841988868
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Low-Rank Adaptation (LoRA) offers a parameter-efficient paradigm for tuning large models. While recent spectral initialization methods improve convergence and performance over the naive "Noise & Zeros" scheme, their extra computational and storage overhead undermines efficiency. In this paper, we establish update magnitude as the fundamental driver of LoRA performance and propose LoRAM, a magnitude-driven "Basis & Basis" initialization scheme that matches spectral methods without their inefficiencies. Our key contributions are threefold: (i) Magnitude of weight updates determines convergence. We prove low-rank structures intrinsically bound update magnitudes, unifying hyperparameter tuning in learning rate, scaling factor, and initialization as mechanisms to optimize magnitude regulation. (ii) Spectral initialization succeeds via magnitude amplification. We demystify that the presumed knowledge-driven benefit of the spectral component essentially arises from the boost in the weight update magnitude. (iii) A novel and compact initialization strategy, LoRAM, scales deterministic orthogonal bases using pretrained weight magnitudes to simulate spectral gains. Extensive experiments show that LoRAM serves as a strong baseline, retaining the full efficiency of LoRA while matching or outperforming spectral initialization across benchmarks.

Related papers

• ConsNoTrainLoRA: Data-driven Weight Initialization of Low-rank Adapters using Constraints [64.35580479051208]
  In previous works, low-rank adapters (LoRA) are randomly with a fixed rank across all attachment points.<n>In this paper, we improve convergence and final performance of LoRA fine-tuning using our proposed data-driven weight initialization method.
  arXiv  Detail & Related papers  (2025-07-09T23:52:31Z)
• GeLoRA: Geometric Adaptive Ranks For Efficient LoRA Fine-tuning [2.7446241148152253]
  Fine-tuning large language models (LLMs) is computationally intensive because it requires updating all parameters.<n>Low-Rank Adaptation (LoRA) improves efficiency by modifying only a subset of weights but introduces a trade-off between expressivity and computational cost.<n>We propose Geometric Low-Rank Adaptation (GeLoRA), a novel framework that computes the intrinsic dimensionality of hidden state representations to adaptively select LoRA ranks.
  arXiv  Detail & Related papers  (2024-12-12T13:04:54Z)
• Initialization using Update Approximation is a Silver Bullet for Extremely Efficient Low-Rank Fine-Tuning [13.823795660384262]
  We propose a method, LoRA Silver Bullet or LoRA-SB, that approximates full fine-tuning within low-rank subspaces.<n>Our findings demonstrate that it is possible to simulate full fine-tuning in low-rank subspaces without sacrificing performance.
  arXiv  Detail & Related papers  (2024-11-29T09:10:30Z)
• Less is More: Extreme Gradient Boost Rank-1 Adaption for Efficient Finetuning of LLMs [75.11449420928139]
  Fine-tuning Large Language Models (LLMs) has become a crucial technique for adapting pre-trained models to downstream tasks. Low-Rank Adaptation (LoRA) has emerged as a promising solution, but there exists a gap between the practical performance of low-rank adaptations and its theoretical optimum. We propose eXtreme Gradient Boosting LoRA, a novel framework that bridges this gap by leveraging the power of ensemble learning.
  arXiv  Detail & Related papers  (2024-10-25T17:07:13Z)
• On the Crucial Role of Initialization for Matrix Factorization [40.834791383134416]
  This work revisits the classical lowrank matrix factorization problem and unveils the critical role of initialization in shaping convergence rates.<n>We introduce Nystrom NyGD in both symmetric asymmetric matrix factorization tasks and extend this to low-rank adapters (LoRA)<n>Our approach, NoRA, demonstrates superior performance across various downstream and model scales, from 1B to 7B parameters, in large language and diffusion models.
  arXiv  Detail & Related papers  (2024-10-24T17:58:21Z)
• Randomized Asymmetric Chain of LoRA: The First Meaningful Theoretical Framework for Low-Rank Adaptation [58.288682735160585]
  Low-Rank Adaptation (LoRA) is a popular technique for finetuning models. LoRA often under performs when compared to full- parameter fine-tuning. We present a framework that rigorously analyzes the adaptation rates of LoRA methods.
  arXiv  Detail & Related papers  (2024-10-10T18:51:53Z)
• Enhancing Zeroth-order Fine-tuning for Language Models with Low-rank Structures [21.18741772731095]
  Zeroth-order (ZO) algorithms offer a promising alternative by approximating gradients using finite differences of function values. Existing ZO methods struggle to capture the low-rank gradient structure common in LLM fine-tuning, leading to suboptimal performance. This paper proposes a low-rank ZO algorithm (LOZO) that effectively captures this structure in LLMs.
  arXiv  Detail & Related papers  (2024-10-10T08:10:53Z)
• Search for Efficient Large Language Models [52.98684997131108]
  Large Language Models (LLMs) have long held sway in the realms of artificial intelligence research. Weight pruning, quantization, and distillation have been embraced to compress LLMs, targeting memory reduction and inference acceleration. Most model compression techniques concentrate on weight optimization, overlooking the exploration of optimal architectures.
  arXiv  Detail & Related papers  (2024-09-25T21:32:12Z)
• MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning [16.67302585857681]
  We propose MiLoRA, a simple yet effective LLM finetuning approach that only updates the minor singular components of the weight matrix.<n>It is observed that the minor matrix corresponds to the noisy or long-tail information, while the principal matrix contains important knowledge.<n>During finetuning, MiLoRA makes the most use of the less-optimized subspace for learning the labeled dataset.
  arXiv  Detail & Related papers  (2024-06-13T12:30:02Z)
• Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark [166.40879020706151]
  This paper proposes a shift towards BP-free, zeroth-order (ZO) optimization as a solution for reducing memory costs during fine-tuning. Unlike traditional ZO-SGD methods, our work expands the exploration to a wider array of ZO optimization techniques. Our study unveils previously overlooked optimization principles, highlighting the importance of task alignment, the role of the forward gradient method, and the balance between algorithm complexity and fine-tuning performance.
  arXiv  Detail & Related papers  (2024-02-18T14:08:48Z)
• FedNAR: Federated Optimization with Normalized Annealing Regularization [54.42032094044368]
  We explore the choices of weight decay and identify that weight decay value appreciably influences the convergence of existing FL algorithms. We develop Federated optimization with Normalized Annealing Regularization (FedNAR), a plug-in that can be seamlessly integrated into any existing FL algorithms.
  arXiv  Detail & Related papers  (2023-10-04T21:11:40Z)
• AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning [143.23123791557245]
  Fine-tuning large pre-trained language models on downstream tasks has become an important paradigm in NLP. We propose AdaLoRA, which adaptively allocates the parameter budget among weight matrices according to their importance score. We conduct extensive experiments with several pre-trained models on natural language processing, question answering, and natural language generation to validate the effectiveness of AdaLoRA.
  arXiv  Detail & Related papers  (2023-03-18T22:36:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.