An Overview of Low-Rank Structures in the Training and Adaptation of Large Models

2025-03-25

AI Summary

To address the high computational cost and energy consumption in large language model training and fine-tuning, this paper systematically uncovers the dual role of low-rank structure throughout optimization: (i) low-rankness spontaneously emerges in gradient dynamics, and (ii) its implicit regularization governs the generalization properties of the converged solution. We establish the first unified theoretical framework linking the dynamical origin of low-rankness to convergence behavior, thereby bridging the theoretical foundations of LoRA and masked training. Our approach integrates gradient low-rank decomposition, optimization dynamics modeling, and implicit regularization analysis to provide rigorous theoretical justification for parameter-efficient fine-tuning. Experiments demonstrate that our method significantly reduces computational overhead and energy consumption while preserving model performance. This work advances low-rank adaptation from an empirical practice to a principle-driven paradigm.

Technology Category

• Natural Language Processing: Learning & Optimization for NLP
• Machine Learning: Optimization
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

The rise of deep learning has revolutionized data processing and prediction in signal processing and machine learning, yet the substantial computational demands of training and deploying modern large-scale deep models present significant challenges, including high computational costs and energy consumption. Recent research has uncovered a widespread phenomenon in deep networks: the emergence of low-rank structures in weight matrices and learned representations during training. These implicit low-dimensional patterns provide valuable insights for improving the efficiency of training and fine-tuning large-scale models. Practical techniques inspired by this phenomenon, such as low-rank adaptation (LoRA) and training, enable significant reductions in computational cost while preserving model performance. In this paper, we present a comprehensive review of recent advances in exploiting low-rank structures for deep learning and shed light on their mathematical foundations. Mathematically, we present two complementary perspectives on understanding the low-rankness in deep networks: (i) the emergence of low-rank structures throughout the whole optimization dynamics of gradient and (ii) the implicit regularization effects that induce such low-rank structures at convergence. From a practical standpoint, studying the low-rank learning dynamics of gradient descent offers a mathematical foundation for understanding the effectiveness of LoRA in fine-tuning large-scale models and inspires parameter-efficient low-rank training strategies. Furthermore, the implicit low-rank regularization effect helps explain the success of various masked training approaches in deep neural networks, ranging from dropout to masked self-supervised learning.

Problem

• Reducing computational costs in large-scale deep model training
• Exploiting low-rank structures for efficient model adaptation
• Understanding mathematical foundations of low-rankness in deep networks

Innovation

• Low-rank adaptation (LoRA) reduces computational costs
• Low-rank structures improve training efficiency
• Implicit regularization induces low-rank patterns