---
_id: '9198'
abstract:
- lang: eng
text: "The optimization of multilayer neural networks typically leads to a solution\r\nwith
zero training error, yet the landscape can exhibit spurious local minima\r\nand
the minima can be disconnected. In this paper, we shed light on this\r\nphenomenon:
we show that the combination of stochastic gradient descent (SGD)\r\nand over-parameterization
makes the landscape of multilayer neural networks\r\napproximately connected and
thus more favorable to optimization. More\r\nspecifically, we prove that SGD solutions
are connected via a piecewise linear\r\npath, and the increase in loss along this
path vanishes as the number of\r\nneurons grows large. This result is a consequence
of the fact that the\r\nparameters found by SGD are increasingly dropout stable
as the network becomes\r\nwider. We show that, if we remove part of the neurons
(and suitably rescale the\r\nremaining ones), the change in loss is independent
of the total number of\r\nneurons, and it depends only on how many neurons are
left. Our results exhibit\r\na mild dependence on the input dimension: they are
dimension-free for two-layer\r\nnetworks and depend linearly on the dimension
for multilayer networks. We\r\nvalidate our theoretical findings with numerical
experiments for different\r\narchitectures and classification tasks."
acknowledgement: M. Mondelli was partially supported by the 2019 LopezLoreta Prize.
The authors thank Phan-Minh Nguyen for helpful discussions and the IST Distributed
Algorithms and Systems Lab for providing computational resources.
article_processing_charge: No
author:
- first_name: Alexander
full_name: Shevchenko, Alexander
last_name: Shevchenko
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
citation:
ama: 'Shevchenko A, Mondelli M. Landscape connectivity and dropout stability of
SGD solutions for over-parameterized neural networks. In: Proceedings of the
37th International Conference on Machine Learning. Vol 119. ML Research Press;
2020:8773-8784.'
apa: Shevchenko, A., & Mondelli, M. (2020). Landscape connectivity and dropout
stability of SGD solutions for over-parameterized neural networks. In Proceedings
of the 37th International Conference on Machine Learning (Vol. 119, pp. 8773–8784).
ML Research Press.
chicago: Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and
Dropout Stability of SGD Solutions for Over-Parameterized Neural Networks.” In
Proceedings of the 37th International Conference on Machine Learning, 119:8773–84.
ML Research Press, 2020.
ieee: A. Shevchenko and M. Mondelli, “Landscape connectivity and dropout stability
of SGD solutions for over-parameterized neural networks,” in Proceedings of
the 37th International Conference on Machine Learning, 2020, vol. 119, pp.
8773–8784.
ista: Shevchenko A, Mondelli M. 2020. Landscape connectivity and dropout stability
of SGD solutions for over-parameterized neural networks. Proceedings of the 37th
International Conference on Machine Learning. vol. 119, 8773–8784.
mla: Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and Dropout
Stability of SGD Solutions for Over-Parameterized Neural Networks.” Proceedings
of the 37th International Conference on Machine Learning, vol. 119, ML Research
Press, 2020, pp. 8773–84.
short: A. Shevchenko, M. Mondelli, in:, Proceedings of the 37th International Conference
on Machine Learning, ML Research Press, 2020, pp. 8773–8784.
date_created: 2021-02-25T09:36:22Z
date_published: 2020-07-13T00:00:00Z
date_updated: 2023-10-17T12:43:19Z
day: '13'
ddc:
- '000'
department:
- _id: MaMo
external_id:
arxiv:
- '1912.10095'
file:
- access_level: open_access
checksum: f042c8d4316bd87c6361aa76f1fbdbbe
content_type: application/pdf
creator: dernst
date_created: 2021-03-02T15:38:14Z
date_updated: 2021-03-02T15:38:14Z
file_id: '9217'
file_name: 2020_PMLR_Shevchenko.pdf
file_size: 5336380
relation: main_file
success: 1
file_date_updated: 2021-03-02T15:38:14Z
has_accepted_license: '1'
intvolume: ' 119'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 8773-8784
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of the 37th International Conference on Machine Learning
publication_status: published
publisher: ML Research Press
quality_controlled: '1'
status: public
title: Landscape connectivity and dropout stability of SGD solutions for over-parameterized
neural networks
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 119
year: '2020'
...