On the Training Convergence of Transformers for In-Context Classification of Gaussian Mixtures

• URL: http://arxiv.org/abs/2410.11778v2
• Date: Sat, 15 Feb 2025 03:41:05 GMT
• Title: On the Training Convergence of Transformers for In-Context Classification of Gaussian Mixtures
• Authors: Wei Shen, Ruida Zhou, Jing Yang, Cong Shen,
• Abstract summary: This work aims to theoretically study the training dynamics of transformers for in-context classification tasks. We demonstrate that, for in-context classification of Gaussian mixtures under certain assumptions, a single-layer transformer trained via gradient descent converges to a globally optimal model at a linear rate.
• Score: 20.980349268151546
• License:
• Abstract: While transformers have demonstrated impressive capacities for in-context learning (ICL) in practice, theoretical understanding of the underlying mechanism enabling transformers to perform ICL is still in its infant stage. This work aims to theoretically study the training dynamics of transformers for in-context classification tasks. We demonstrate that, for in-context classification of Gaussian mixtures under certain assumptions, a single-layer transformer trained via gradient descent converges to a globally optimal model at a linear rate. We further quantify the impact of the training and testing prompt lengths on the ICL inference error of the trained transformer. We show that when the lengths of training and testing prompts are sufficiently large, the prediction of the trained transformer approaches the ground truth distribution of the labels. Experimental results corroborate the theoretical findings.

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