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pro vyhledávání: '"Riekert, Adrian"'
It is known that the standard stochastic gradient descent (SGD) optimization method, as well as accelerated and adaptive SGD optimization methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (as, for examp
Externí odkaz:
http://arxiv.org/abs/2406.14340
Autor:
Jentzen, Arnulf, Riekert, Adrian
Stochastic gradient descent (SGD) optimization methods such as the plain vanilla SGD method and the popular Adam optimizer are nowadays the method of choice in the training of artificial neural networks (ANNs). Despite the remarkable success of SGD m
Externí odkaz:
http://arxiv.org/abs/2402.05155
The largest coefficient (in absolute value) of a cyclotomic polynomial $\Phi_n$ is called its height $A(n)$. In case $p$ is a fixed prime it turns out that as $q$ and $r$ range over all primes satisfying $p
Externí odkaz:
http://arxiv.org/abs/2304.09250
Autor:
Riekert, Adrian
In this article we identify a general class of high-dimensional continuous functions that can be approximated by deep neural networks (DNNs) with the rectified linear unit (ReLU) activation without the curse of dimensionality. In other words, the num
Externí odkaz:
http://arxiv.org/abs/2304.05790
In this article we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new strategy to design specific artificial neural network (ANN) architectures
Externí odkaz:
http://arxiv.org/abs/2302.03286
Gradient descent (GD) methods for the training of artificial neural networks (ANNs) belong nowadays to the most heavily employed computational schemes in the digital world. Despite the compelling success of such methods, it remains an open problem to
Externí odkaz:
http://arxiv.org/abs/2212.13111
The training of artificial neural networks (ANNs) is nowadays a highly relevant algorithmic procedure with many applications in science and industry. Roughly speaking, ANNs can be regarded as iterated compositions between affine linear functions and
Externí odkaz:
http://arxiv.org/abs/2207.06246
Gradient descent (GD) type optimization schemes are the standard instruments to train fully connected feedforward artificial neural networks (ANNs) with rectified linear unit (ReLU) activation and can be considered as temporal discretizations of solu
Externí odkaz:
http://arxiv.org/abs/2202.11481
Autor:
Jentzen, Arnulf, Riekert, Adrian
Publikováno v:
Journal of Machine Learning, 1 (2022), pp. 141-246
In this article we study fully-connected feedforward deep ReLU ANNs with an arbitrarily large number of hidden layers and we prove convergence of the risk of the GD optimization method with random initializations in the training of such ANNs under th
Externí odkaz:
http://arxiv.org/abs/2112.09684
In many numerical simulations stochastic gradient descent (SGD) type optimization methods perform very effectively in the training of deep neural networks (DNNs) but till this day it remains an open problem of research to provide a mathematical conve
Externí odkaz:
http://arxiv.org/abs/2112.07369