Attention layers provably solve single-location regression
<|reference_start|>Attention layers provably solve single-location regression: Attention-based models, such as Transformer, excel across various tasks but lack a comprehensive theoretical understanding, especially regarding token-wise sparsity and internal linear representations. To address this gap, we introduce the single-location regression task, where only one token in a sequence determines the output, and its position is a latent random variable, retrievable via a linear projection of the input. To solve this task, we propose a dedicated predictor, which turns out to be a simplified version of a non-linear self-attention layer. We study its theoretical properties, by showing its asymptotic Bayes optimality and analyzing its training dynamics. In particular, despite the non-convex nature of the problem, the predictor effectively learns the underlying structure. This work highlights the capacity of attention mechanisms to handle sparse token information and internal linear structures.<|reference_end|>
@article{marion2024attention,
    title={Attention layers provably solve single-location regression},
    author={Pierre Marion, Rapha"el Berthier, G'erard Biau, Claire Boyer},
    journal={arXiv preprint arXiv:2410.01537},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.01537},
    primaryClass={stat.ML cs.LG}
}