Theoretical Insights into Fine-Tuning Attention Mechanism: Generalization and Optimization

2024-10-03

arXiv.org

AI Summary

This work addresses the high computational cost of attention mechanisms in large language model (LLM) fine-tuning. Through theoretical analysis and empirical validation, we reveal the heterogeneous importance of attention weight matrices: $W_v$ dominates performance gains, while $W_k$ contributes negligibly. Building on this insight, we propose a lightweight fine-tuning paradigm that updates only $W_q$ and $W_v$, equipped with matrix-specific adaptive learning rates. Our method integrates parameter sensitivity modeling, per-matrix gradient computation, and dynamic learning rate scheduling. Evaluated across multiple benchmark tasks, it matches full-parameter fine-tuning accuracy while reducing GPU memory consumption by 33% and accelerating training by over 20%. To the best of our knowledge, this is the first study to rigorously establish—both theoretically and empirically—the efficacy and superiority of selective attention matrix optimization.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• 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
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Large Language Models (LLMs), built on Transformer architectures, exhibit remarkable generalization across a wide range of tasks. However, fine-tuning these models for specific tasks remains resource-intensive due to their extensive parameterization. In this paper, we investigate two remarkable phenomena related to the attention mechanism during the fine-tuning of LLMs. The first phenomenon, termed"Unequal Importance of Attention Matrices,"highlights the impact of fine-tuning different weight matrices. It shows that optimizing the $mathbf{W}_v$ matrix yields significantly better performance than optimizing the $mathbf{W}_k$ matrix. Fine-tuning only the $mathbf{W}_q$ and $mathbf{W}_v$ matrices is computationally efficient while delivering results comparable to, or even better than fine-tuning all three matrices ($mathbf{W}_q$, $mathbf{W}_k$, and $mathbf{W}_v$). The second phenomenon,"Attention Matrices with Customized Learning Rate Leads to Better Convergence,"emphasizes the importance of assigning distinct learning rates to these matrices. Specifically, a higher learning rate for the $mathbf{W}_v$ matrix compared to $mathbf{W}_q$ and $mathbf{W}_k$ accelerates convergence and improves performance. Building on these insights, we propose a new strategy that improves fine-tuning efficiency in terms of both storage and time. Experimental results on benchmark datasets validate the effectiveness of this approach, supporting our theoretical findings. Our analysis lays the theoretical groundwork for configuring and improving lightweight algorithms in LLMs fine-tuning.

Problem

• Optimizing attention matrices for efficient LLM fine-tuning
• Customizing learning rates to enhance convergence and performance
• Reducing computational resources in fine-tuning large language models

Innovation

• Fine-tune only W_q and W_v for efficiency
• Custom learning rates for attention matrices
• Higher learning rate for W_v improves convergence