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math.NA2025
Computational Math with Neural Networks is Hard
Michael Feischl, Fabian Zehetgruber, Benedikt Grässle
We establish asymptotic complexity barriers for three basic numerical tasks with neural-network data: integration of a network realization, solution of a Poisson problem with a neu…
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…