3 papers
math.NA2025
Error analysis for the deep Kolmogorov method
Iulian Cîmpean, Thang Do, Lukas Gonon +2
The deep Kolmogorov method is a simple and popular deep learning based method for approximating solutions of partial differential equations (PDEs) of the Kolmogorov type. In this w…
cs.LG2025
Non-convergence to the optimal risk for Adam and stochastic gradient descent optimization in the training of deep neural networks
Thang Do, Arnulf Jentzen, Adrian Riekert
Despite the omnipresent use of stochastic gradient descent (SGD) optimization methods in the training of deep neural networks (DNNs), it remains, in basically all practically relev…
cs.LG2025
Mathematical analysis of the gradients in deep learning
Steffen Dereich, Thang Do, Arnulf Jentzen +1
Deep learning algorithms -- typically consisting of a class of deep artificial neural networks (ANNs) trained by a stochastic gradient descent (SGD) optimization method -- are nowa…