Transformers as Unsupervised Learning Algorithms: A study on Gaussian Mixtures

• URL: http://arxiv.org/abs/2505.11918v1
• Date: Sat, 17 May 2025 09:02:18 GMT
• Title: Transformers as Unsupervised Learning Algorithms: A study on Gaussian Mixtures
• Authors: Zhiheng Chen, Ruofan Wu, Guanhua Fang,
• Abstract summary: This paper investigates the capabilities of transformers in solving unsupervised learning problems.<n>We propose a transformer-based learning framework called TGMM that simultaneously learns to solve multiple GMM tasks.<n>We prove that transformers can approximate both the EM algorithm and a core component of spectral methods.
• Score: 10.970776446566909
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The transformer architecture has demonstrated remarkable capabilities in modern artificial intelligence, among which the capability of implicitly learning an internal model during inference time is widely believed to play a key role in the under standing of pre-trained large language models. However, most recent works have been focusing on studying supervised learning topics such as in-context learning, leaving the field of unsupervised learning largely unexplored. This paper investigates the capabilities of transformers in solving Gaussian Mixture Models (GMMs), a fundamental unsupervised learning problem through the lens of statistical estimation. We propose a transformer-based learning framework called TGMM that simultaneously learns to solve multiple GMM tasks using a shared transformer backbone. The learned models are empirically demonstrated to effectively mitigate the limitations of classical methods such as Expectation-Maximization (EM) or spectral algorithms, at the same time exhibit reasonable robustness to distribution shifts. Theoretically, we prove that transformers can approximate both the EM algorithm and a core component of spectral methods (cubic tensor power iterations). These results bridge the gap between practical success and theoretical understanding, positioning transformers as versatile tools for unsupervised learning.

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