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

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 observed during the fine-tuning of LLMs, particularly focusing on the attention mechanism: (1) Different Impact, optimizing the $\mathbf{W}_v$ matrix significantly improves performance over optimizing the $\mathbf{W}_k$ matrix. Fine-tuning only the $\mathbf{W}_q$ and $\mathbf{W}_v$ matrices is computationally efficient, delivering results that are comparable to, or even better than, fine-tuning all three matrices $\mathbf{W}_q$, $\mathbf{W}_k$, and $\mathbf{W}_v$. (2) Efficient Convergence, employing distinct learning rates for these matrices is crucial for optimal performance, with a higher learning rate for the $\mathbf{W}_v$ matrix expediting convergence. However, theoretical analyses of these phenomena are still relatively limited. We present a theoretical analysis of these phenomena from two perspectives: (i) Generalization, where we demonstrate that fine-tuning only $\mathbf{W}_q$ and $\mathbf{W}_v$ improves generalization bounds, enhances memory efficiency, and (ii) Optimization, where we emphasize that the feature learning of the attention mechanism is efficient, particularly when using distinct learning rates for the matrices, which leads to more effective fine-tuning. 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.

Enhancing In-Context Learning Performance with just SVD-Based Weight Pruning: A Theoretical Perspective

Pre-trained large language models (LLMs) based on Transformer have demonstrated striking in-context learning (ICL) abilities. With a few demonstration input-label pairs, they can predict the label for an unseen input without any parameter updates. In this paper, we show an exciting phenomenon that SVD-based weight pruning can enhance ICL performance, and more surprising, pruning weights in deep layers often results in more stable performance improvements in shallow layers. However, the underlying mechanism of those findings still remains an open question. To reveal those findings, we conduct an in-depth theoretical analysis by presenting the implicit gradient descent (GD) trajectories of ICL and giving the mutual information based generalization bounds of ICL via full implicit GD trajectories. This helps us reasonably explain the surprising experimental findings. Besides, based on all our experimental and theoretical insights, we intuitively propose a simple, model-compression and derivative-free algorithm for downstream tasks in enhancing ICL inference. Experiments on benchmark datasets and open source LLMs display the method effectiveness\footnote{The code is available at \url{https://github.com/chen123CtrlS/EnhancingICL_SVDPruning}}.