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Training-Free Universal Approximation by Prompting Random Transformers
Alexander Hsu, Rongjie Lai
How expressive is prompting a transformer? Answering this question is important for separating the roles of prompting, architecture, and pretraining in transformer models, and for…
Understanding In-Context Learning for Nonlinear Regression with Transformers: Attention as Featurizer
Alexander Hsu, Zhaiming Shen, Wenjing Liao +1
Pre-trained transformers are able to learn from examples provided as part of the prompt without any weight updates, a remarkable ability known as in-context learning (ICL). Despite…
Operator Learning at Machine Precision
Aras Bacho, Aleksei G. Sorokin, Xianjin Yang +6
Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing th…
Understanding In-Context Learning on Structured Manifolds: Bridging Attention to Kernel Methods
Zhaiming Shen, Alexander Hsu, Rongjie Lai +1
While in-context learning (ICL) has achieved remarkable success in natural language and vision domains, its theoretical understanding-particularly in the context of structured geom…