How Transformers Utilize Multi-Head Attention in In-Context Learning? A Case Study on Sparse Linear Regression
<|reference_start|>How Transformers Utilize Multi-Head Attention in In-Context Learning? A Case Study on Sparse Linear Regression: 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.<|reference_end|>
@article{chen2024how,
    title={How Transformers Utilize Multi-Head Attention in In-Context Learning? A
  Case Study on Sparse Linear Regression},
    author={Xingwu Chen, Lei Zhao, Difan Zou},
    journal={arXiv preprint arXiv:2408.04532},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.04532},
    primaryClass={cs.LG}
}