By Claire Boyer
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.
By Yannick Baraud
By Johannes Schmidt-Hieber
By Rina Foygel Barber
By Claire Boyer
By Katie Collins
By Javier Gómez-Serrano
By Riccardo Cadei
By Jack Bowden
