Learning Spectral Methods by Transformers
This addresses the challenge of unsupervised learning for AI systems, offering a novel paradigm that could enhance model capabilities, though it appears incremental in extending Transformers to new tasks.
The paper tackles the problem of enabling Transformers to perform unsupervised learning by learning algorithms themselves, showing that pre-trained Transformers can learn spectral methods and achieve strong performance on tasks like PCA and clustering with synthetic and real-world datasets.
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.