2 papers
math.NA2025
Computational Math with Neural Networks is Hard
Michael Feischl, Fabian Zehetgruber
We show that under some widely believed assumptions, there are no higher-order algorithms for basic tasks in computational mathematics such as: Computing integrals with neural netw…
math.NA2024
Towards optimal hierarchical training of neural networks
Michael Feischl, Alexander Rieder, Fabian Zehetgruber
We propose a hierarchical training algorithm for standard feed-forward neural networks that adaptively extends the network architecture as soon as the optimization reaches a statio…