search for


A study on complexity of deep learning model
Journal of the Korean Data & Information Science Society 2017;28:1217-27
Published online November 30, 2017
© 2017 Korean Data & Information Science Society.

Dongha Kim1 · Gyuseung Baek2 · Yongdai Kim3

123Department of Statistics, Seoul National University
Correspondence to: Yongdai Kim
Professor, Department of Statistics, Seoul National University, 56-1 Mountain, Sillim-dong, Gwanak-gu, Seoul metropolis, 151-742, Korea. E-mail:
Received October 31, 2017; Revised November 22, 2017; Accepted November 23, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Deep learning has been studied explosively and has achieved excellent performance in areas like image and speech recognition, the application areas in which computations have been challenges with ordinary machine learning techniques. The theoretical study of deep learning has also been researched toward improving the performance. In this paper, we try to find a key of the success of the deep learning in rich and efficient expressiveness of the deep learning function, and analyze the theoretical studies related to it.
Keywords : Complexity, deep learning, deep neural network, linear regions, trajectory of a function, transition of a function