1 citations · 2 across the 5 of their papers we have counts for
7 papers
Stability of Measure-to-Measure Transformers on Sub-Gaussian Data
Frank Cole, Nicholas H. Nelsen, Takashi Furuya
Transformers have exhibited impressive empirical success across various domains, but their theoretical foundations remain less developed. This work constitutes a mathematical study…
Universal Approximation of Measure-to-Measure Operators by Pushforwards
Takashi Furuya, Nicholas H. Nelsen, Frank Cole
Many learning tasks map an input distribution to an output distribution. A natural way to model such an operator is to transform each input sample using a continuous function that…
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…
Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions
Frank Cole, Yulong Lu
While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we…