Transformer Learns Optimal Variable Selection in Group-Sparse Classification

• URL: http://arxiv.org/abs/2504.08638v1
• Date: Fri, 11 Apr 2025 15:39:44 GMT
• Title: Transformer Learns Optimal Variable Selection in Group-Sparse Classification
• Authors: Chenyang Zhang, Xuran Meng, Yuan Cao,
• Abstract summary: We give a case study of how transformers can be trained to learn a classic statistical model with "group sparsity"<n>We theoretically demonstrate that, a one-layer transformer trained by gradient descent can correctly leverage the attention mechanism to select variables.<n>We also demonstrate that a well-pretrained one-layer transformer can be adapted to new downstream tasks to achieve good prediction accuracy with a limited number of samples.
• Score: 14.760685658938787
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Transformers have demonstrated remarkable success across various applications. However, the success of transformers have not been understood in theory. In this work, we give a case study of how transformers can be trained to learn a classic statistical model with "group sparsity", where the input variables form multiple groups, and the label only depends on the variables from one of the groups. We theoretically demonstrate that, a one-layer transformer trained by gradient descent can correctly leverage the attention mechanism to select variables, disregarding irrelevant ones and focusing on those beneficial for classification. We also demonstrate that a well-pretrained one-layer transformer can be adapted to new downstream tasks to achieve good prediction accuracy with a limited number of samples. Our study sheds light on how transformers effectively learn structured data.

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