Recently, a new line of works has emerged to understand and improve self-attention in
Transformers by treating it as a kernel machine. However, existing works apply the methods …

Characterizing the function spaces corresponding to neural networks can provide a way to
understand their properties. In this paper we discuss how the theory of reproducing kernel …

Linear partial differential equations (PDEs) are an important, widely applied class of
mechanistic models, describing physical processes such as heat transfer, electromagnetism …

The aim of this expository paper is to explain to graduate students and beginning
researchers in the field of mathematics, statistics and engineering the fundamental concept …

Reproducing Kernel Hilbert spaces (RKHS) have been a very successful tool in various
areas of machine learning. Recently, Barron spaces have been used to prove bounds on the …

Koopman and Perron–Frobenius operators for dynamical systems are becoming popular in
a number of fields in science recently. Properties of the Koopman operator essentially …

Asymmetric data naturally exist in real life, such as directed graphs. Different from the
common kernel methods requiring Mercer kernels, this paper tackles the asymmetric kernel …

Asymmetric kernels naturally exist in real life, eg, for conditional probability and directed
graphs. However, most of the existing kernel-based learning methods require kernels to be …

Despite their ubiquity in core AI fields like natural language processing, the mechanics of
deep attention-based neural networks like the Transformer model are not fully understood …

We provide a novel characterization of augmented balancing weights, also known as
automatic debiased machine learning (AutoDML). These popular doubly robust or double …