
Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis
The representation of functions by artificial neural networks depends on...
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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 ...
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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 ...
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Some observations on partial differential equations in Barron and multilayer spaces
We use explicit representation formulas to show that solutions to certai...
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A priori estimates for classification problems using neural networks
We consider binary and multiclass classification problems using hypothe...
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Towards a Mathematical Understanding of Neural NetworkBased Machine Learning: what we know and what we don't
The purpose of this article is to review the achievements made in the la...
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On the Banach spaces associated with multilayer ReLU networks: Function representation, approximation theory and gradient descent dynamics
We develop Banach spaces for ReLU neural networks of finite depth L and ...
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Representation formulas and pointwise properties for Barron functions
We study the natural function space for infinitely wide twolayer neural...
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On the Convergence of Gradient Descent Training for Twolayer ReLUnetworks in the Mean Field Regime
We describe a necessary and sufficient condition for the convergence to ...
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Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective
We prove that the gradient descent training of a twolayer neural networ...
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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...
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Stephan Wojtowytsch
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