Layer-Wise Conditioning Analysis in Exploring the Learning Dynamics of DNNs

Document Type

Conference Proceeding

Source of Publication

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Publication Date

1-1-2020

Abstract

© 2020, Springer Nature Switzerland AG. Conditioning analysis uncovers the landscape of an optimization objective by exploring the spectrum of its curvature matrix. This has been well explored theoretically for linear models. We extend this analysis to deep neural networks (DNNs) in order to investigate their learning dynamics. To this end, we propose layer-wise conditioning analysis, which explores the optimization landscape with respect to each layer independently. Such an analysis is theoretically supported under mild assumptions that approximately hold in practice. Based on our analysis, we show that batch normalization (BN) can stabilize the training, but sometimes result in the false impression of a local minimum, which has detrimental effects on the learning. Besides, we experimentally observe that BN can improve the layer-wise conditioning of the optimization problem. Finally, we find that the last linear layer of a very deep residual network displays ill-conditioned behavior. We solve this problem by only adding one BN layer before the last linear layer, which achieves improved performance over the original and pre-activation residual networks.

ISBN

9783030585358

ISSN

0302-9743

Publisher

Springer International Publishing

Volume

12347 LNCS

First Page

384

Last Page

401

Disciplines

Computer Sciences

Keywords

Conditioning analysis, Normalization, Residual network

Indexed in Scopus

yes

Open Access

yes

Open Access Type

Green: A manuscript of this publication is openly available in a repository

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