research-article

Public Access

Identifying Core Functional Networks and Functional Modules within Artificial Neural Networks via Subsets Regression

Authors:

Jeff CluneAuthors Info & Claims

GECCO '16: Proceedings of the Genetic and Evolutionary Computation Conference 2016

Pages 181 - 188

https://doi.org/10.1145/2908812.2908839

Published: 20 July 2016 Publication History

Abstract

As the power and capabilities of Artificial Neural Networks (ANNs) grow, so do their size and complexity. To both decipher and improve ANNs, we need to build better tools that help us understand their inner workings. To that end, we introduce an algorithm called Subsets Regression on network Connectivity (SRC). SRC allows us to prune away unimportant nodes and connections in ANNs, revealing a core functional network (CFN) that is simpler and thus easier to analyze. SRC can also identify functional modules within an ANN. We demonstrate SRC's capabilities on both directly and indirectly encoded ANNs evolved to solve a modular problem. In many of the cases when evolution produces a highly entangled, non-modular ANN, SRC reveals that a CFN is hidden within these networks that is actually sparse and modular. That finding will substantially impact the sizable and ongoing research into the evolution of modularity and will encourage researchers to revisit previous results on that topic. We also show that the SRC algorithm can more accurately estimate the modularity Q-Score of a network than state-of-the-art approaches. Overall, SRC enables us to greatly simplify ANNs in order to better understand and improve them, and reveals that they often contain hidden modular structures within.

References

[1]

M Gethsiyal Augasta and T Kathirvalavakumar. Pruning algorithms of neural networks--a comparative study. Central European Journal of Computer Science, 3(3):105--115, 2013.

[2]

Y. Bengio, I. J. Goodfellow, and A. Courville. Deep learning. Book in preparation for MIT Press, 2015.

[3]

Dmitri B Chklovskii. Exact solution for the optimal neuronal layout problem. Neural computation, 16(10):2067--2078, October 2004.

Digital Library

[4]

J. Clune, B.E. Beckmann, P.K. McKinley, and C. Ofria. Investigating whether HyperNEAT produces modular neural networks. In Proc. Genetic & Evolutionary Comput. Conf., pages 635--642. ACM, 2010.

Digital Library

[5]

J. Clune, B.E. Beckmann, C. Ofria, and R.T. Pennock. Evolving coordinated quadruped gaits with the HyperNEAT generative encoding. In Proc. IEEE Cong. Evolutionary Comput, pages 2764--2771, 2009.

Digital Library

[6]

J. Clune, J-B. Mouret, and H. Lipson. The evolutionary origins of modularity. Proc. Royal Society B, 280(20122863), 2013.

[7]

J. Clune, K.O. Stanley, R.T. Pennock, and C. Ofria. On the performance of indirect encoding across the continuum of regularity. IEEE Trans. Evolutionary Comput, 15(4):346--367, 2011.

Digital Library

[8]

K. O. Ellefsen, J-B. Mouret, J. Clune, and J. C. Bongard. Neural modularity helps organisms evolve to learn new skills without forgetting old skills. PLoS Comput Biol, 11(4):e1004128, 2015.

[9]

T. F. Fuller, A. Ghazalpour, J. E. Aten, T. A. Drake, A. J. Lusis, and S. Horvath. Weighted gene coexpression network analysis strategies applied to mouse weight. Mammalian Genome, 18(6--7):463--472, 2007.

[10]

Masafumi Hagiwara. A simple and effective method for removal of hidden units and weights. Neurocomputing, 6(2):207--218, 1994.

[11]

J. Huizinga, J. Clune, and J-B Mouret. Evolving neural networks that are both modular and regular: Hyperneat plus the connection cost technique. In Proc. Genetic & Evolutionary Comput. Conf, pages 697--704. ACM, 2014.

Digital Library

[12]

N. Kashtan and U. Alon. Spontaneous evolution of modularity and network motifs. Proc. Nat'l Acad. Sciences, 102(39):13773--13778, September 2005.

[13]

Y. LeCun, J. S. Denker, S. A. Solla, R. E. Howard, and L. D. Jackel. Optimal brain damage. In NIPs, volume 89, 1989.

Digital Library

[14]

Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278--2324, 1998.

[15]

J. Lehman and K.O. Stanley. Abandoning objectives: Evolution through the search for novelty alone. Evolutionary Computation, 19(2):189--223, 2011.

Digital Library

[16]

E. A. Leicht and M. E. J. Newman. Community structure in directed networks. Physical review letters, pages 118703--118707, 2008.

[17]

H. Lipson. Principles of modularity, regularity, and hierarchy for scalable systems. Journal of Biological Physics and Chemistry, 7(4):125, 2007.

[18]

H. Mengistu and J. Clune. The evolutionary origins of hierarchy. In preparation.

[19]

A. Miller. Subset selection in regression. CRC Press, 2002.

[20]

J-B Mouret and S. Doncieux. Sferes v2: Evolvin' in the multi-core world. In Evolutionary Computation (CEC), 2010 IEEE Congress on, pages 1--8. IEEE, 2010.

[21]

M. E. J. Newman. Modularity and community structure in networks. Proc. Nat'l Acad. Sciences, 103(23):8577--8582, 2006.

[22]

M. E. J. Newman and M. Girvan. Finding and evaluating community structure in networks. Physical review E, 69(2):026113, 2004.

[23]

S. M. Smith, K. L. Miller, and et. al. Network modelling methods for fmri. Neuroimage, 54(2):875--891, 2011.

[24]

O. Sporns and R. F. Betzel. Modular brain networks. Annual review of psychology, 67(1), 2015.

[25]

K.O. Stanley and R. Miikkulainen. A taxonomy for artificial embryogeny. Artificial Life, 9(2):93--130, 2003.

Digital Library

[26]

G.F. Striedter. Principles of brain evolution. Sinauer Associates Sunderland, MA, 2005.

[27]

R Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), pages 267--288, 1996.

[28]

P. Verbancsics and K. O. Stanley. Constraining connectivity to encourage modularity in hyperneat. In Proc. Genetic & Evolutionary Comput. Conf, pages 1483--1490. ACM, 2011.

Digital Library

[29]

G. Wagner, M. Pavlicev, and J. M. Cheverud. The road to modularity. Nature Reviews Genetics, 8(12):921--31, December 2007.

[30]

Hong-Jie Xing and Bao-Gang Hu. Two-phase construction of multilayer perceptrons using information theory. Neural Networks, IEEE Transactions on, 20(4):715--721, 2009.

Digital Library

[31]

J. Yosinski, J.and Clune, A. Nguyen, T. Fuchs, and H. Lipson. Understanding neural networks through deep visualization. ICML Deep Learning workshop., 2015.

Cited By

van der Merwe AVandenheever D(2024)Evolving interpretable neural modularity in free-form multilayer perceptrons through connection costsNeural Computing and Applications10.1007/s00521-023-09117-436:3(1459-1476)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s00521-023-09117-4
Mayer SSotto LGarcke J(2023)The Elements of Flexibility for Task-Performing SystemsIEEE Access10.1109/ACCESS.2023.323887211(8029-8056)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3238872
Velez RClune J(2017)Diffusion-based neuromodulation can eliminate catastrophic forgetting in simple neural networksPLOS ONE10.1371/journal.pone.018773612:11(e0187736)Online publication date: 16-Nov-2017
https://doi.org/10.1371/journal.pone.0187736

Index Terms

Identifying Core Functional Networks and Functional Modules within Artificial Neural Networks via Subsets Regression
1. Computing methodologies
  1. Machine learning
    1. Machine learning approaches
      1. Neural networks

Recommendations

Noise Suppression by Artificial Neural Networks
AWICT 2017: Proceedings of the Second International Conference on Advanced Wireless Information, Data, and Communication Technologies

In this research paper, noise suppression ability of associative memories (e.g. Hopfield neural network) is briefly summarized. Motivated by this fact, noise suppression abilities of trained convolutional network are discussed. Introducing the concept ...
Implementation of feedforward artificial neural networks with learning using standard CMOS technology
Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks

A computationally efficient artificial neural network (ANN) for the purpose of dynamic nonlinear system identification is proposed. The major drawback of feedforward neural networks, such as multilayer perceptrons (MLPs) trained with the backpropagation ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Conferences

GECCO '16: Proceedings of the Genetic and Evolutionary Computation Conference 2016

July 2016

1196 pages

ISBN:9781450342063

DOI:10.1145/2908812

Editor:
Tobias Friedrich
Hasso Plattner Institute
,
General Chair:
Frank Neumann
University of Adelaide
,
Program Chair:
Andrew M. Sutton
Hasso Plattner Institute

Copyright © 2016 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Sponsors

SIGEVO: ACM Special Interest Group on Genetic and Evolutionary Computation

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 July 2016

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

Conference

GECCO '16

Sponsor:

SIGEVO

GECCO '16: Genetic and Evolutionary Computation Conference

July 20 - 24, 2016

Colorado, Denver, USA

Acceptance Rates

GECCO '16 Paper Acceptance Rate 137 of 381 submissions, 36%;

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
324
Total Downloads

Downloads (Last 12 months)39
Downloads (Last 6 weeks)7

Reflects downloads up to 25 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

van der Merwe AVandenheever D(2024)Evolving interpretable neural modularity in free-form multilayer perceptrons through connection costsNeural Computing and Applications10.1007/s00521-023-09117-436:3(1459-1476)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s00521-023-09117-4
Mayer SSotto LGarcke J(2023)The Elements of Flexibility for Task-Performing SystemsIEEE Access10.1109/ACCESS.2023.323887211(8029-8056)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3238872
Velez RClune J(2017)Diffusion-based neuromodulation can eliminate catastrophic forgetting in simple neural networksPLOS ONE10.1371/journal.pone.018773612:11(e0187736)Online publication date: 16-Nov-2017
https://doi.org/10.1371/journal.pone.0187736

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Table of Contents