@Article{JML-3-1,
author = {Steffen, Dereich and Sebastian, Kassing},
title = {On the Existence of Optimal Shallow Feedforward Networks with ReLU Activation},
journal = {Journal of Machine Learning},
year = {2024},
volume = {3},
number = {1},
pages = {1--22},
abstract = {<p style="text-align: justify;">We prove existence of global minima in the loss landscape for the approximation of continuous
target functions using shallow feedforward artificial neural networks with ReLU activation. This property is
one of the fundamental artifacts separating ReLU from other commonly used activation functions. We propose
a kind of closure of the search space so that in the extended space minimizers exist. In a second step, we show
under mild assumptions that the newly added functions in the extension perform worse than appropriate
representable ReLU networks. This then implies that the optimal response in the extended target space is
indeed the response of a ReLU network.</p>},
issn = {2790-2048},
doi = {https://doi.org/10.4208/jml.230903},
url = {https://global-sci.com/article/91117/on-the-existence-of-optimal-shallow-feedforward-networks-with-relu-activation}
}