73 citations · 398 across the 44 of their papers we have counts for
6 papers · 1 filter
Over-parametrized neural networks as under-determined linear systems
Austin R. Benson, Anil Damle, Alex Townsend
We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural n…
Suppression of Electroconvective and Morphological Instabilities by an Imposed Cross Flow of the Electrolyte
Gaojin Li, Alex Townsend, Lynden A. Archer +1
Electroconvection and its coupling with a morphological instability are important in many applications, including electrodialysis, batteries and fuel cells. In this work, we study…
The ultraspherical spectral element method
Daniel Fortunato, Nicholas Hale, Alex Townsend
We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincaré-Steklov scheme for solving second-order linear partial differ…
Computing spectral measures of self-adjoint operators
Matthew J. Colbrook, Andrew Horning, Alex Townsend
Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The algorithm can achieve a…
Rational neural networks
Nicolas Boullé, Yuji Nakatsukasa, Alex Townsend
We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the pe…
Anderson Acceleration Based on the Sobolev Norm for Contractive and Noncontractive Fixed-Point Operators
Yunan Yang, Alex Townsend, Daniel Appelö
Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to a sequence of functions and modify the norm in i…