@Article{CSIAM-AM-5-448,
author = {Chen , Zheng-AnLi , YuqingLuo , TaoZhou , Zhangchen and Xu , Zhi-Qin John},
title = {Phase Diagram of Initial Condensation for Two-Layer Neural Networks},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2024},
volume = {5},
number = {3},
pages = {448--514},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2023-0016},
url = {http://global-sci.org/intro/article_detail/csiam-am/23306.html}
}