Year: 2024
Author: Zheng-An Chen, Yuqing Li, Tao Luo, Zhangchen Zhou, Zhi-Qin John Xu
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 3 : pp. 448–514
Abstract
The phenomenon of distinct behaviors exhibited by neural networks under varying scales of initialization remains an enigma in deep learning research. In this paper, based on the earlier work [Luo et al., J. Mach. Learn. Res., 22:1–47, 2021], we present a phase diagram of initial condensation for two-layer neural networks. Condensation is a phenomenon wherein the weight vectors of neural networks concentrate on isolated orientations during the training process, and it is a feature in non-linear learning process that enables neural networks to possess better generalization abilities. Our phase diagram serves to provide a comprehensive understanding of the dynamical regimes of neural networks and their dependence on the choice of hyperparameters related to initialization. Furthermore, we demonstrate in detail the underlying mechanisms by which small initialization leads to condensation at the initial training stage.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2023-0016
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 3 : pp. 448–514
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 67
Keywords: Two-layer neural network phase diagram dynamical regime condensation.