4 papers
A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schrödinger Equations
Frank Cole, Yulong Lu, Shaurya Sehgal
We address the following question: given a collection of independent random matrices drawn from a common distribution $…
In-Context Operator Learning on the Space of Probability Measures
Frank Cole, Dixi Wang, Yineng Chen +2
We introduce \emph{in-context operator learning on probability measure spaces} for optimal transport (OT). The goal is to learn a single solution operator that maps a pair of distr…
In-Context Learning of Linear Dynamical Systems with Transformers: Approximation Bounds and Depth-Separation
Frank Cole, Yuxuan Zhao, Yulong Lu +1
This paper investigates approximation-theoretic aspects of the in-context learning capability of the transformers in representing a family of noisy linear dynamical systems. Our fi…
In-Context Learning of Linear Systems: Generalization Theory and Applications to Operator Learning
Frank Cole, Yulong Lu, Wuzhe Xu +1
We study theoretical guarantees for solving linear systems in-context using a linear transformer architecture. For in-domain generalization, we provide neural scaling laws that bou…