<ul data-eligibleForWebStory="true"><li>A recent arXiv paper delves into the theoretical aspects of In-Context Learning (ICL) on structured geometric data.</li><li>The study focuses on regression of H"older functions on manifolds and establishes a connection between attention mechanisms and classical kernel methods.</li><li>Generalization error bounds are derived based on prompt length and the number of training tasks, showing that transformers can achieve minimax regression rates of H"older functions on manifolds.</li><li>These rates scale exponentially with the intrinsic dimension of the manifold rather than the ambient space dimension.</li><li>The research also highlights the relationship between generalization error and the number of training tasks, offering insights into the complexity of transformers as in-context learners.</li><li>The findings contribute to understanding the impact of geometry on ICL and provide new tools for studying ICL in nonlinear models.</li></ul>

Understanding In-Context Learning on Structured Manifolds: Bridging Attention to Kernel Methods

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