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arXiv · 2410.01537

Attention layers provably solve single-location regression

Pierre Marion·Raphaël Berthier·Gérard Biau·Claire Boyer
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Abstract

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.

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Pierre Marion, Raphaël Berthier, Gérard Biau, Claire Boyer. 2024-10-02. Attention layers provably solve single-location regression. https://arxiv.org/abs/2410.01537

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