-

 

 

 




Optimization Online





 

Spurious Local Minima Exist for Almost All Over-parameterized Neural Networks

Tian Ding(dt016***at***ie.cuhk.edu.hk)
Dawei Li(dawei2***at***illinois.edu)
Ruoyu Sun(ruoyus***at***illinois.edu)

Abstract: A popular belief for explaining the efficiency in training deep neural networks is that over-paramenterized neural networks have nice landscape. However, it still remains unclear whether over-parameterized neural networks contain spurious local minima in general, since all current positive results cannot prove non-existence of bad local minima, and all current negative results have strong restrictions to the activation functions, data samples or network architecture. In this paper we answer this question with a surprisingly negative result. In particular, we prove that for almost all deep over-parameterized non-linear neural networks, spurious local minima exist for generic input data samples. Our result helps give a more exact characterization of the landscape of deep neural networks and corrects a long-believed misunderstanding in the past decades.

Keywords: Over-parameterized neural networks; local minima; landscape; deep learning

Category 1: Global Optimization (Theory )

Category 2: Nonlinear Optimization (Other )

Citation:

Download: [PDF]

Entry Submitted: 10/04/2019
Entry Accepted: 10/04/2019
Entry Last Modified: 10/04/2019

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society