18 citations · 64 across the 8 of their papers we have counts for
16 papers
Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation
Josiah Park, Stephan Wojtowytsch
In this article, we prove approximation theorems in classes of deep and shallow neural networks with analytic activation functions by elementary arguments. We prove for both real a…
Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis
Stephan Wojtowytsch
The representation of functions by artificial neural networks depends on a large number of parameters in a non-linear fashion. Suitable parameters of these are found by minimizing…
Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis
Stephan Wojtowytsch
Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine learning. The noise encountered in these applications is different from that in many theor…
On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers
Weinan E, Stephan Wojtowytsch
A recent numerical study observed that neural network classifiers enjoy a large degree of symmetry in the penultimate layer. Namely, if where is a linear map…
Some observations on high-dimensional partial differential equations with Barron data
Weinan E, Stephan Wojtowytsch
We use explicit representation formulas to show that solutions to certain partial differential equations lie in Barron spaces or multilayer spaces if the PDE data lie in such funct…
A priori estimates for classification problems using neural networks
Weinan E, Stephan Wojtowytsch
We consider binary and multi-class classification problems using hypothesis classes of neural networks. For a given hypothesis class, we use Rademacher complexity estimates and dir…