How Transformers Utilize Multi-Head Attention in In-Context Learning? A Case Study on Sparse Linear Regression

• URL: http://arxiv.org/abs/2408.04532v1
• Date: Thu, 8 Aug 2024 15:33:02 GMT
• Title: How Transformers Utilize Multi-Head Attention in In-Context Learning? A Case Study on Sparse Linear Regression
• Authors: Xingwu Chen, Lei Zhao, Difan Zou,
• Abstract summary: In this study, we consider a sparse linear regression problem and investigate how a trained multi-head transformer performs in-context learning. We experimentally discover that the utilization of multi-heads exhibits different patterns across layers. We demonstrate that such a preprocess-then-optimize algorithm can significantly outperform naive gradient descent and ridge regression algorithms.
• Score: 19.64743851296488
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite the remarkable success of transformer-based models in various real-world tasks, their underlying mechanisms remain poorly understood. Recent studies have suggested that transformers can implement gradient descent as an in-context learner for linear regression problems and have developed various theoretical analyses accordingly. However, these works mostly focus on the expressive power of transformers by designing specific parameter constructions, lacking a comprehensive understanding of their inherent working mechanisms post-training. In this study, we consider a sparse linear regression problem and investigate how a trained multi-head transformer performs in-context learning. We experimentally discover that the utilization of multi-heads exhibits different patterns across layers: multiple heads are utilized and essential in the first layer, while usually only a single head is sufficient for subsequent layers. We provide a theoretical explanation for this observation: the first layer preprocesses the context data, and the following layers execute simple optimization steps based on the preprocessed context. Moreover, we demonstrate that such a preprocess-then-optimize algorithm can significantly outperform naive gradient descent and ridge regression algorithms. Further experimental results support our explanations. Our findings offer insights into the benefits of multi-head attention and contribute to understanding the more intricate mechanisms hidden within trained transformers.

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