Spurious Valleys and Clustering Behavior of Neural Networks

Samuele Pollaci

Spurious Valleys and Clustering Behavior of Neural Networks

Research output: Chapter in Book/Report/Conference proceeding › Conference paper

Abstract

Neural networks constitute a class of functions that are typically non-surjective, with high-dimensional fibers and complicated image. We prove two main results concerning the geometry of the loss landscape of a neural network. First, we provide an explicit effective bound on the sizes of the hidden layers so that the loss landscape has no spurious valleys, which guarantees the success of gradient descent methods. Second, we present a novel method for analyzing whether a given neural network architecture with monomial activation function can represent a target function of interest. The core of our analysis method is the study of a specific set of error values, and its behavior depending on different training datasets.

Original language	English
Title of host publication	Proceedings of the 40th International Conference on Machine Learning
Editors	Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, Jonathan Scarlett
Publisher	Proceedings of Machine Learning Research (PMLR)
Pages	28079-28099
Number of pages	21
Volume	202
Publication status	Published - Jul 2023
Event	Fortieth International Conference on Machine Learning - Hawaiʻi Convention Center, 1801 Kalākaua Avenue , Honolulu, United States Duration: 23 Jul 2023 → 29 Jul 2023 Conference number: 40 https://icml.cc/Conferences/2023

Publication series

Name	Proceedings of Machine Learning Research
ISSN (Electronic)	2640-3498

Conference

Conference	Fortieth International Conference on Machine Learning
Abbreviated title	ICML 2023
Country/Territory	United States
City	Honolulu
Period	23/07/23 → 29/07/23
Internet address	https://icml.cc/Conferences/2023

Bibliographical note

Funding Information:
The results contained in this paper are part of the author's Master's thesis project, carried out at Bonn University with advisors Daniel Huybrechts and Emre Setöz. The paper was completed during the first year of the author's doctoral studies at Vrije Universiteit Brussel with supervisor Bart Bogaerts. This work was partially supported by Fonds Wetenschappelijk Onderzoek - Vlaanderen (project G0B2221N) and the Flemish Government (Onderzoeksprogramma Artificiële Intelligentie (AI) Vlaanderen).

Funding Information:
The results contained in this paper are part of the author’s Master’s thesis project, carried out at Bonn University with advisors Daniel Huybrechts and Emre Setöz. The paper was completed during the first year of the author’s doctoral studies at Vrije Universiteit Brussel with supervisor Bart Bo-gaerts. This work was partially supported by Fonds Weten-schappelijk Onderzoek – Vlaanderen (project G0B2221N) and the Flemish Government (Onderzoeksprogramma Arti-ficiële Intelligentie (AI) Vlaanderen).

Publisher Copyright:
© 2023 Proceedings of Machine Learning Research. All rights reserved.

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Cite this

Pollaci, S. (2023). Spurious Valleys and Clustering Behavior of Neural Networks. In A. Krause, E. Brunskill, K. Cho, B. Engelhardt, S. Sabato, & J. Scarlett (Eds.), Proceedings of the 40th International Conference on Machine Learning (Vol. 202, pp. 28079-28099). (Proceedings of Machine Learning Research). Proceedings of Machine Learning Research (PMLR). https://openreview.net/forum?id=TuHgrnPHZq

Pollaci, Samuele. / Spurious Valleys and Clustering Behavior of Neural Networks. Proceedings of the 40th International Conference on Machine Learning. editor / Andreas Krause ; Emma Brunskill ; Kyunghyun Cho ; Barbara Engelhardt ; Sivan Sabato ; Jonathan Scarlett. Vol. 202 Proceedings of Machine Learning Research (PMLR), 2023. pp. 28079-28099 (Proceedings of Machine Learning Research).

@inproceedings{2085f69e234a4731b04ea3219a3f48d5,

title = "Spurious Valleys and Clustering Behavior of Neural Networks",

abstract = "Neural networks constitute a class of functions that are typically non-surjective, with high-dimensional fibers and complicated image. We prove two main results concerning the geometry of the loss landscape of a neural network. First, we provide an explicit effective bound on the sizes of the hidden layers so that the loss landscape has no spurious valleys, which guarantees the success of gradient descent methods. Second, we present a novel method for analyzing whether a given neural network architecture with monomial activation function can represent a target function of interest. The core of our analysis method is the study of a specific set of error values, and its behavior depending on different training datasets.",

author = "Samuele Pollaci",

note = "Funding Information: The results contained in this paper are part of the author's Master's thesis project, carried out at Bonn University with advisors Daniel Huybrechts and Emre Set{\"o}z. The paper was completed during the first year of the author's doctoral studies at Vrije Universiteit Brussel with supervisor Bart Bogaerts. This work was partially supported by Fonds Wetenschappelijk Onderzoek - Vlaanderen (project G0B2221N) and the Flemish Government (Onderzoeksprogramma Artifici{\"e}le Intelligentie (AI) Vlaanderen). Funding Information: The results contained in this paper are part of the author{\textquoteright}s Master{\textquoteright}s thesis project, carried out at Bonn University with advisors Daniel Huybrechts and Emre Set{\"o}z. The paper was completed during the first year of the author{\textquoteright}s doctoral studies at Vrije Universiteit Brussel with supervisor Bart Bo-gaerts. This work was partially supported by Fonds Weten-schappelijk Onderzoek – Vlaanderen (project G0B2221N) and the Flemish Government (Onderzoeksprogramma Arti-fici{\"e}le Intelligentie (AI) Vlaanderen). Publisher Copyright: {\textcopyright} 2023 Proceedings of Machine Learning Research. All rights reserved.; Fortieth International Conference on Machine Learning, ICML 2023 ; Conference date: 23-07-2023 Through 29-07-2023",

year = "2023",

month = jul,

language = "English",

volume = "202",

series = "Proceedings of Machine Learning Research",

publisher = "Proceedings of Machine Learning Research (PMLR)",

pages = "28079--28099",

editor = "{ Krause}, Andreas and Brunskill, {Emma } and Cho, {Kyunghyun } and Engelhardt, {Barbara } and Sivan Sabato and { Scarlett}, Jonathan",

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Pollaci, S 2023, Spurious Valleys and Clustering Behavior of Neural Networks. in A Krause, E Brunskill, K Cho, B Engelhardt, S Sabato & J Scarlett (eds), Proceedings of the 40th International Conference on Machine Learning. vol. 202, Proceedings of Machine Learning Research, Proceedings of Machine Learning Research (PMLR), pp. 28079-28099, Fortieth International Conference on Machine Learning, Honolulu, Hawaii, United States, 23/07/23. <https://openreview.net/forum?id=TuHgrnPHZq>

Spurious Valleys and Clustering Behavior of Neural Networks. / Pollaci, Samuele.
Proceedings of the 40th International Conference on Machine Learning. ed. / Andreas Krause; Emma Brunskill; Kyunghyun Cho; Barbara Engelhardt; Sivan Sabato; Jonathan Scarlett. Vol. 202 Proceedings of Machine Learning Research (PMLR), 2023. p. 28079-28099 (Proceedings of Machine Learning Research).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper

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Spurious Valleys and Clustering Behavior of Neural Networks

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