Learning Spectral Methods by Transformers

• URL: http://arxiv.org/abs/2501.01312v3
• Date: Mon, 13 Jan 2025 03:53:34 GMT
• Title: Learning Spectral Methods by Transformers
• Authors: Yihan He, Yuan Cao, Hong-Yu Chen, Dennis Wu, Jianqing Fan, Han Liu,
• Abstract summary: We show that multi-layered Transformers, given a sufficiently large set of pre-training instances, are able to learn the algorithms themselves. This learning paradigm is distinct from the in-context learning setup and is similar to the learning procedure of human brains.
• Score: 18.869174453242383
• License:
• Abstract: Transformers demonstrate significant advantages as the building block of modern LLMs. In this work, we study the capacities of Transformers in performing unsupervised learning. We show that multi-layered Transformers, given a sufficiently large set of pre-training instances, are able to learn the algorithms themselves and perform statistical estimation tasks given new instances. This learning paradigm is distinct from the in-context learning setup and is similar to the learning procedure of human brains where skills are learned through past experience. Theoretically, we prove that pre-trained Transformers can learn the spectral methods and use the classification of bi-class Gaussian mixture model as an example. Our proof is constructive using algorithmic design techniques. Our results are built upon the similarities of multi-layered Transformer architecture with the iterative recovery algorithms used in practice. Empirically, we verify the strong capacity of the multi-layered (pre-trained) Transformer on unsupervised learning through the lens of both the PCA and the Clustering tasks performed on the synthetic and real-world datasets.

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