Path homologies of deep feedforward networks

Samir Chowdhury; Thomas Gebhart; Steve Huntsman; Matvey Yutin

doi:10.1109/ICMLA.2019.00181

Path homologies of deep feedforward networks

Samir Chowdhury, Thomas Gebhart, Steve Huntsman, Matvey Yutin

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

11 Scopus citations

Abstract

We provide a characterization of two types of directed homology for fully-connected, feedforward neural network architectures. These exact characterizations of the directed homology structure of a neural network architecture are the first of their kind. We show that the directed flag homology of deep networks reduces to computing the simplicial homology of the underlying undirected graph, which is explicitly given by Euler characteristic computations. We also show that the path homology of these networks is non-trivial in higher dimensions and depends on the number and size of the layers within the network. These results provide a foundation for investigating homological differences between neural network architectures and their realized structure as implied by their parameters.

Original language	English (US)
Title of host publication	Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019
Editors	M. Arif Wani, Taghi M. Khoshgoftaar, Dingding Wang, Huanjing Wang, Naeem Seliya
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1077-1082
Number of pages	6
ISBN (Electronic)	9781728145495
DOIs	https://doi.org/10.1109/ICMLA.2019.00181
State	Published - Dec 2019
Event	18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019 - Boca Raton, United States Duration: Dec 16 2019 → Dec 19 2019

Publication series

Name	Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019

Conference

Conference	18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019
Country/Territory	United States
City	Boca Raton
Period	12/16/19 → 12/19/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Keywords

Deep Learning
Homology
Neural Networks
Path Homology
Topology

Publisher link

10.1109/ICMLA.2019.00181

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Chowdhury, S., Gebhart, T., Huntsman, S., & Yutin, M. (2019). Path homologies of deep feedforward networks. In M. A. Wani, T. M. Khoshgoftaar, D. Wang, H. Wang, & N. Seliya (Eds.), Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019 (pp. 1077-1082). Article 8999174 (Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICMLA.2019.00181

Path homologies of deep feedforward networks. / Chowdhury, Samir; Gebhart, Thomas; Huntsman, Steve et al.
Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019. ed. / M. Arif Wani; Taghi M. Khoshgoftaar; Dingding Wang; Huanjing Wang; Naeem Seliya. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1077-1082 8999174 (Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019).

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

Chowdhury, S, Gebhart, T, Huntsman, S & Yutin, M 2019, Path homologies of deep feedforward networks. in MA Wani, TM Khoshgoftaar, D Wang, H Wang & N Seliya (eds), Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019., 8999174, Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019, Institute of Electrical and Electronics Engineers Inc., pp. 1077-1082, 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019, Boca Raton, United States, 12/16/19. https://doi.org/10.1109/ICMLA.2019.00181

Chowdhury S, Gebhart T, Huntsman S, Yutin M. Path homologies of deep feedforward networks. In Wani MA, Khoshgoftaar TM, Wang D, Wang H, Seliya N, editors, Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019. Institute of Electrical and Electronics Engineers Inc. 2019. p. 1077-1082. 8999174. (Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019). doi: 10.1109/ICMLA.2019.00181

Chowdhury, Samir ; Gebhart, Thomas ; Huntsman, Steve et al. / Path homologies of deep feedforward networks. Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019. editor / M. Arif Wani ; Taghi M. Khoshgoftaar ; Dingding Wang ; Huanjing Wang ; Naeem Seliya. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 1077-1082 (Proceedings - 18th IEEE International Conference on Machine Learning and Applications, ICMLA 2019).

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Path homologies of deep feedforward networks

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