Universality of Gradient Descent Neural Network Training

View PDF HTML (experimental) Abstract:It has been observed that design choices of neural networks are often crucial for their successful optimization. In this article, we therefore discuss the question if it is always possible to redesign a neural network so that it trains well with gradient descent. This yields the following universality result: If, for a given network, there is any algorithm that can find good network weights for a classification task, then there exists an extension of this network that reproduces these weights and the corresponding forward output by mere gradient descent training. The construction is not intended for practical computations, but it provides some orientation on the possibilities of meta-learning and related approaches. Subjects: Machine Learning (cs.LG); Machine Learning (stat.ML) MSC classes: 68T07, 68Q04, 90C26 Cite as: arXiv:2007.13664 [cs.LG] (or arXiv:2007.13664v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2007.13664 arXiv-issued DOI via DataCite Submission history From: Gerrit Welper [view email] [v1] Mon, 27 Jul 2020 16:17:19 UTC (31 KB)