Stephan Wojtowytsch | DeepAI

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Featured Co-authors

Chao Ma
82 publications
Lei Wu
64 publications
Weinan E
62 publications
Shuiwang Ji
56 publications
Xuan Zhang
56 publications
Cong Fu
7 publications
Josiah Park
4 publications
Jonathan Siegel
3 publications
Jacob Helwig
2 publications
Jerry Kurtin
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Kanan Gupta
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∙ 06/09/2023

Group Equivariant Fourier Neural Operators for Partial Differential Equations

We consider solving partial differential equations (PDEs) with Fourier n...

7 Jacob Helwig, et al. ∙

∙ 02/10/2023

Achieving acceleration despite very noisy gradients

We present a novel momentum-based first order optimization method (AGNES...

0 Kanan Gupta, et al. ∙

∙ 09/02/2022

Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality

In this note, we study how neural networks with a single hidden layer an...

0 Stephan Wojtowytsch, et al. ∙

∙ 03/25/2022

Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation

In this article, we prove approximation theorems in classes of deep and ...

0 Josiah Park, et al. ∙

∙ 06/04/2021

Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis

The representation of functions by artificial neural networks depends on...

0 Stephan Wojtowytsch, et al. ∙

∙ 05/04/2021

Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis

Stochastic gradient descent (SGD) is one of the most popular algorithms ...

0 Stephan Wojtowytsch, et al. ∙

∙ 12/10/2020

On the emergence of tetrahedral symmetry in the final and penultimate layers of neural network classifiers

A recent numerical study observed that neural network classifiers enjoy ...

5 Weinan E, et al. ∙

∙ 12/02/2020

Some observations on partial differential equations in Barron and multi-layer spaces

We use explicit representation formulas to show that solutions to certai...

0 Weinan E, et al. ∙

∙ 09/28/2020

A priori estimates for classification problems using neural networks

We consider binary and multi-class classification problems using hypothe...

0 Weinan E, et al. ∙

∙ 09/22/2020

Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

The purpose of this article is to review the achievements made in the la...

270 Weinan E, et al. ∙

∙ 07/30/2020

On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics

We develop Banach spaces for ReLU neural networks of finite depth L and ...

11 Weinan E, et al. ∙

∙ 06/10/2020

Representation formulas and pointwise properties for Barron functions

We study the natural function space for infinitely wide two-layer neural...

0 Weinan E, et al. ∙

∙ 05/27/2020

On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime

We describe a necessary and sufficient condition for the convergence to ...

0 Stephan Wojtowytsch, et al. ∙

∙ 05/21/2020

Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective

We prove that the gradient descent training of a two-layer neural networ...

51 Stephan Wojtowytsch, et al. ∙

∙ 05/21/2020

Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels

We establish a scale separation of Kolmogorov width type between subspac...

22 Weinan E, et al. ∙

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