Phase Diagram of Initial Condensation for Two-Layer Neural Networks

Phase Diagram of Initial Condensation for Two-Layer Neural Networks

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.

Author Details

Zheng-An Chen

Yuqing Li

Tao Luo

Zhangchen Zhou

Zhi-Qin John Xu